CALIFORNIA STATE UNIVERSITY, NORTHRIDGE
CHROMOSPHERIC PROPERTIES OF THE SUN-AS-A-STAR
A thesis submitted in partial fulfillment of the requirements
For the degree of Master of Science
in Physics
By
Luis David Contreras
May 2014
The thesis of Luis David Contreras is approved:
Ana Cadavid, Ph.D
Date
Christian Damian, Ph.D
Date
Debi Choudhary, Ph.D, Chair
Date
California State University, Northridge
ii
Acknowledgements
This thesis and my tenure at CSUN were supported by the LSAMP Bridge to the Doctorate program, NSF Award number HRD-1139803. I would like to thank Dr. Cristina
Cadavid, Dr. Karla Pelliter, and Dr. Kathy Marsaglia for their support and mentorship during my three years in the Master Program. I would also like to thank my advisor Dr. Debi
Choudhary, I am very grateful to him for taking me as his student and guiding me through
my project.
Lastly, I would like to thank my parents and my family for all their support, encouragement and for believing in me. You have helped and encourage me to follow my dreams
which is how I got to where I am today.
This work utilizes SOLIS data obtained by the NSO Integrated Synoptic Program
(NISP), managed by the National Solar Observatory, which is operated by the Association
of Universities for Research in Astronomy (AURA), Inc. under a cooperative agreement
with the National Science Foundation.
iii
Table of Contents
Signature page
ii
Acknowledgements
iii
Abstract
vii
1
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
1
1
1
2
3
5
Data and Analysis
2.1 SOLIS Spectrograph . . . . . . . . . . . . . . . .
2.1.1 ISS . . . . . . . . . . . . . . . . . . . . .
2.1.2 VSM . . . . . . . . . . . . . . . . . . . .
2.2 Mount Wilson Observatory . . . . . . . . . . . . .
2.3 Analysis . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Equivalent Width . . . . . . . . . . . . . .
2.3.2 H-α . . . . . . . . . . . . . . . . . . . . .
2.3.3 He . . . . . . . . . . . . . . . . . . . . . .
2.3.4 Na D I . . . . . . . . . . . . . . . . . . . .
2.3.5 Ca II . . . . . . . . . . . . . . . . . . . .
2.3.6 Ca II H . . . . . . . . . . . . . . . . . . .
2.3.7 Ca II K . . . . . . . . . . . . . . . . . . .
2.3.8 Helium EW, MPSI and MWSI . . . . . . .
2.3.9 Ca II K Full DIsk Index, MPSI and MWSI
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
6
6
6
9
11
12
12
14
16
18
19
21
22
24
25
3
Results and Discussion
3.1 Magnetic Field Effect on the Equivalent Width . . . . . . . . . . . . . . .
3.2 Magnetic Field Effect on Chromospheric Heating . . . . . . . . . . . . . .
3.3 Mount Wilson Strength Indices Effect on Livingston Data . . . . . . . . . .
26
27
28
29
4
Conclusion and Future Work
31
4.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2
Introduction
1.1 The solar Chromosphere . . .
1.2 Chromosphere of the Sun . . .
1.3 Chromospheres on other Stars
1.4 Magnetic Fields . . . . . . . .
1.5 Purpose . . . . . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
References
33
Appendix: Matlab Codes
36
iv
List of Figures
1.1
Basic schematic of the Sun . . . . . . . . . . . . . . . . . . . . . . . . . .
1
2.1
2.2
2.3
2.4
2.5
2.6
2.7
Absorption spectrum of Na D I . . . . . . . . . . . . . . . . . . . . . . . .
Fe I 6301.5-6302.5 nm spectra and its corresponding Stokes parameters . .
Full-disk Mean Total Flux profile . . . . . . . . . . . . . . . . . . . . . . .
MPSI data since the 1970s . . . . . . . . . . . . . . . . . . . . . . . . . .
MWSI data since the 1970s . . . . . . . . . . . . . . . . . . . . . . . . . .
Description of Equivalent Width . . . . . . . . . . . . . . . . . . . . . . .
Spectrum of H-α, the vertical lines show the region where the equivalent
width is calculated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
H-α spectra corrected for red and blue shifts. . . . . . . . . . . . . . . . .
Equivalent width of H-α against the Full-DIsk Mean Total Magnetic Flux .
One example of an absorption spectrum of the Helium. . . . . . . . . . . .
Helium spectra corrected for red and blue shifts. . . . . . . . . . . . . . . .
The equivalent width of Helium against the Full-Disk Mean Total Magnetic
Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Example of a Na D I absorption spectrum . . . . . . . . . . . . . . . . . .
All Na D I spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The equivalent width of Na D I against the Full-Disk Total Magnetic Flux .
One example of an absorption spectrum of the Ca II H line. . . . . . . . . .
Ca II spectra corrected for red and blue shifts. . . . . . . . . . . . . . . . .
Equivalent width of Ca II against the Full-Disk Mean Total Magnetic Flux .
One example of an absorption spectrum of the Ca II H line . . . . . . . . .
All Ca II H spectra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The equivalent width of Ca II H against the Full-Disk Mean Total Magnetic
Flux. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
One example of an absorption spectrum of the Ca II K line . . . . . . . . .
All Ca II K spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The equivalent width of Ca II K against the Full-Disk Mean Total Magnetic
Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The equivalent width of Helium against the Magnetic Plage Strength Index
The equivalent width of Helium against the Mount Wilson Sunspot Index .
The Ca II K Full-Disk Index against the Magnetic Plage Strength Index . .
The Ca II K Full-Disk Index against the Mount Wilson Sunspot Index Index
9
10
11
12
12
13
2.8
2.9
2.10
2.11
2.12
2.13
2.14
2.15
2.16
2.17
2.18
2.19
2.20
2.21
2.22
2.23
2.24
2.25
2.26
2.27
2.28
3.1
3.2
3.3
14
14
15
16
16
17
18
18
19
19
20
20
21
21
22
22
23
24
24
25
25
25
This figure shows the formation of spectral lines at different height in the
solar atmosphere [21]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
This figure shows the equivalent width vs the full disk mean total magnetic
flux of all the lines used in this study . . . . . . . . . . . . . . . . . . . . . 27
The EW of He I, and Ca II K Full Disk Index plotted against the MPSI and
MWSI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
v
List of Tables
3.1
3.2
The height of formation for each spectral line and the slope of the equivalent width vs the full disk total magnetic flux. . . . . . . . . . . . . . . . . 28
Results for Livingston Data . . . . . . . . . . . . . . . . . . . . . . . . . . 29
vi
ABSTRACT
CHROMOSPHERIC PROPERTIES OF THE SUN-AS-A-STAR
By
Luis David Contreras
Master of Science in Physics
The chromospheric activity of the Sun is governed by the surface magnetic field often measured at the photosphere. We study the dependence of chromospheric activity on
magnetic field of the Sun as a star by using observations by Integrated Sunlight Spectrometer (ISS) and Vector Spectromagnetograph (VSM) of Synoptic Optical Long-term
Investigations of the Sun (SOLIS) instrument. The chromospheric activity is measured as
the equivalent width (EW) of spectral lines in H-α, He I 10830 nm, Ca II 854.2 nm, Ca II H
and K, and Na D I 589.6 nm obtained with the ISS. The full disk mean total magnetic flux
(FDMTMF) observed with the VSM is used as the measure of magnetic activity of the Sun.
The equivalent width of Ca II K and He I 10830 nm measured by Livingston along with the
Magnetic Plage Strength Index (MPSI) value and a Mount Wilson Sunspot Index (MWSI)
obtained with 150-Foot SOlar Tower in Mt. Wilson Observatory are used to further study
the relationship between the magnetic field and chromospheric activity.
vii
Chapter 1
Introduction
1.1
The solar Chromosphere
The chromosphere lies between the photosphere and the corona and it was first observed in solar eclipses. During a solar eclipse the Sun’s glaring disk is covered by the
moon, revealing the chromosphere and the corona [2]. Above the photosphere the kinetic
temperature of the matter decreases until it passes through a temperature minimum of 3500
K to 4000 K at a height of a few hundred kilometers [3]. It then rises gradually through the
chromosphere and then much more rapidly in the transition region until the coronal temperature is reached. It was in the spectrum of the chromosphere that Helium was observed
before it was discovered on earth [4]. Chromospheric activity, which encompasses diverse
phenomena that produce emission in excess of that expected from a radiative equilibrium
atmosphere, it tightly linked to the stellar magnetic field, whether periodic or irregular, and
is therefore tied to the structure of the subsurface convection zone, the star’s rotation and
the regeneration of the magnetic field via a self-sustaining dynamo [5].
Figure 1.1: Basic schematic of the Sun [1].
1.2
Chromosphere of the Sun
It has been known for a very long time that chromosphere is very inhomogeneous. The
main structures of the quiet chromosphere are called spicules. Spicules come in two types,
type 1 spicules are ubiquitous throughout the solar atmosphere and live approximately 10
1
minutes longer than the more dynamic jet-like type 2 [6]. Studies of spicules are based on
H-α movies obtained from an artificial eclipse. Very few data on spicules are available in
the weaker lines and in the continuum gathered from a real solar eclipse. It is also very
difficult to study the variation of these inhomogeneities across the solar surface. These
difficulties can be overcome by observing the chromosphere on the solar disk. Since the invention of the spectroheliograph, such studies have been possible by using monochromatic
images taken in the core and wings of strong Fraunhofer lines [7].
Knowledge of the chromosphere is based mainly on observations made outside the solar
limb using a real or artificial eclipse of the Sun. Real eclipse observations have given a vast
amount of data of the lower height of the chromosphere [7]. Observers of solar eclipses
first defined the chromosphere by the appearance of hydrogen emission lines near the solar
limb, as the moon progressively eclipsed the photosphere and chromosphere. After initial
confusion, the top of the chromosphere was set at about 5000 km above the limb, with an
extension of 4000 to 10,000 km in the form of spicules. During the same period, coronal
observers brought the lower limit of the million degree corona down to 5000 km. In the
case of the Sun, it is abundantly clear that the chromosphere and the transition region
are manifestations of mechanical energy and momentum input. The outward increase of
temperature requires an input of heat, the basic source which are the convection zone and
possibly rotation [3].
The only immediately clear signature of the chromosphere in regions of the spectrum
accessible from the ground are the H-α line at 6563 Å, the helium lines at 10830 and 5876
Å, and the emission peaks in the H and K lines. A more careful examination of the spectrum
reveals many more chromospheric components. All lines with r0 < 10−4 ,where r0 is the
ratio of continuum opacity, that are preferentially excited at higher temperatures are formed
partially within the chromosphere. The latter group includes helium and Balmer lines, and
the former group includes all of the strong lines with well-developed wings. This group
includes the lines of Ca II H and K , the Na D and Mg b, the resonance line of Ca I, and
several of the strongest lines of Fe I and Fe II.
If the chromosphere were not present, the helium line would disappear, Balmer lines
would decrease in equivalent width, emission peaks in the H and K lines would probably
disappear and central intensities of the Na D and Mg b, and strong Fe lines would decrease.
Such changes would be obvious in the case of He and Ca II lines and possibly in Hydrogenα [3]. Spectral lines that are prominent in the chromosphere are the H and K lines of singly
ionize calcium. The strength of the H and K lines vary with the Sunspot cycle, the lines
being stronger at Sunspot maximum. H and K emission, which is measured with the Mount
Wilson S index, can be observed in other stars and is used as evidence of the existence of
chromospheres and stellar magnetic activity [4, 8].
1.3
Chromospheres on other Stars
Under some considerations, one can argue that a chromosphere exist for almost any
star. One expects to find thick chromospheres in cool stars. Dissipation of excess mechanical heating can happen in cool stars via ionization of hydrogen as the plasma warms at
2
increasingly large heights above the photosphere. Hot stars with partially or highly ionized
photospheres have already used up this electron pool at their visible surfaces, and thus cannot support the extended chromospheres we see in the cool half of the Hertzsprung-Russell
(HR) diagram [5]. Magnetic and non-magnetic sources of activity imply the presence of
surface convection, this roughly happens in late A and cooler dwarfs, and in more massive
stars as they leave the main sequence and develop convection zones [5].
Evidence has been found for chromospheric emission in dwarfs as hot as Altair, A7
IV-V. Observations from Far Ultraviolet Spectroscopic Explorer (FUSE) have concluded
from a sample of A dwarfs that high temperature of emissions indicative of coronae and
by inference chromospheres, appears at about 8250 K. The chromospheres near this limit
are quite weak, with emissions being at most a few percent of solar values. Recent semiempirical models of M star atmospheres indicate the presence of a chromosphere even
for low activity M stars [5]. Age also plays an important role in the incidence of stellar
chromospheres. Older stars exhibit less chromospheric activity and lower rotation speeds,
which are coupled together. Since the magnetic fields that are generated by rotations are
transferred outward by the ionized gas, the outflowing gas cannot rotate with the same
period as the star. This means that the connecting lines exert a small force that slows the
star down over time, causing the chromosphere to diminish [9].
In late type stars such as G, K and M, chromospheres can be detected by detailed high
resolution spectroscopy of the strongest lines, such as Ca II K and H. In stars such as this,
the chromosphere is of low density, hot gas, and generates emission lines. With enough
detail one can see a narrow bright K line, K2, centered on the very broad absorption. Even
the gases of the chromosphere can become fairly opaque as it absorbs some of its own
radiation. This results in the an even narrower absorption, K3, in the center of the of the
emission line [9]. As one approaches the main sequence of G type stars, energy radiated
in the Ca II K and H lines increase, implying that the prominence of the chromosphere
relative to the photosphere does was well.
Stars of type F also show evidence of a chromosphere, although the strength of the Ca
II H and K lines seems to fade slowly. Further evidence is supported by the increase of
ration speed on F type stars while apposed to the slow rotating G, K and M stars. As one
progresses toward the A type stars, the Ca II H and K lines diminish rapidly to the point of
being undetectable. This means that one cannot use them as an indicator of a chromosphere.
It is thought that B and O type stars, or any late-type star, have no chromosphere, since the
Ca II H and K are not even present [9].
1.4
Magnetic Fields
The Sun’s magnetic field is generated by the Sun’s slow rotation coupled with the circulating ionized gases in its deep convection zone that makes it behave as a vast dynamo
[9]. Stellar activity cycles have long been considered to be the results of a self sustaining
dynamo [5]. The magnetic field can be measured and analyzed via the Zeeman effect in
the center of Sunspots, where the fields are thousands of gauss [4, 9, 10]. In the presence
of magnetic fields, the the energies of the states of atoms can be split. This means that the
3
spectral lines can be split into several spectral lines with slightly different frequencies [4].
In oder for the Zeeman effect to take effect the magnetic field has to be strong. In each
of these spectrum the light is polarized in a characteristic way. In perfectly polarized light
the waves all oscillate in the same direction. In partial polarization there is a preferential
direction which is common in nature and easily detected. Because of a variety of broadening effects, the actual splitting in stellar spectra cannot usually be seen, but the changes in
polarization across a line can be detected [9, 10].
With the use of the Babcock magnetograph, the surface distribution of the magnetic
fields of the Sun was revealed for the first time. Irregular weak magnetic fields are distributed all over the solar surface. Magnetic fields are also virtually coextensive with plage
regions observed in H-α or in the calcium K line. The same was also observed in between
weak emissions in the chromospheric network and weak magnetic fields. Emission in the
K line always corresponds to the presence of magnetic fields. This also holds true for the
enhanced He 10830 absorption [10].
The magnetograph further revealed that the general dipole field is not permanent but
rather it varies with the Sunspot cycle [10]. The average period of the Sunspot cycle is
approximately 11 years, although it is irregular and and period can vary between 9 and
12.5 years. Sunspots are confined to the activity belts with extend to about 45◦ latitude on
either side of the solar equator. The first Sunspots tend to appear at high latitudes. During
the course of the solar cycle, Sunspots tend to appear at progressively lower latitudes. The
last Sunspots in a cycle appear close to the equator [11]. This is caused by the magnetic
field being sheared and twisted by differential solar rotation. Like most gaseous bodies, the
Sun does not spin uniformly. The basic rotation period is 25 days near the equator while it
is 30 days close to the pole. Since the magnetic field is locked into the electrically charged
ionized matter in the photosphere, the rotation distorts the field, slowly wrapping it around
the Sun [9].
Heating of the solar chromosphere and the corona is influenced by the Sun’s strong
magnetic field. The magnetic field emerges from the photosphere, carrying energy from
the solar surface into the chromosphere and corona which is deposited as heat [1, 12].
With the discovery of magnetic fields in Sunspots, polarity laws were soon established.
During a given cycle the majority of Sunspots on the northern hemisphere are of the same
polarity, whereas the majority of the Sunspots in the southern hemisphere are of opposite
polarity. In the following solar cycle, the polarities are reversed. Thus the period of magnetic activity cycle is twice the Sunspot cycle or approximately 22 years. A stated before,
the solar cycle is irregular sometimes lasting a little as 8 years or as long as 15 years [11].
Solar activity cycles have also been found in other stars. The level of activity in a
star strongly affects the chromosphere, and consequently the strengths of the H and K line
emission cores. Using the data of the 40 year HK Project at Mount Wilson Observatory
(MWO), Baliunas et al. found that 60% of stars in the MWO survey exhibited periodic,
cyclic variations, 25% showed irregular variability, and 15% had flat activity records [5].
Cycles can also vary depending on the star, for example HD 81809 has a well determined
4
cycle of 8.2 years, 18 Sco has a 7.1 year cycle and 15 Sge has a small cycle of 2.4 ± 0.3
years []. The MWO time series also shows that young , high activity stars exhibit irregular
cycles, while older stars such as the Sun exhibit well-defined cycles [5].
1.5
Purpose
So far, here is no satisfactory theory on solar chromospheric heating. Theories that
do exists are based on short period acoustic waves, which are applicable to most of the
chromosphere. A satisfactory theory would require models of different regions of the chromosphere such as cell boundary and interiors, plages, Sunspots and quiescent prominences.
In the chromosphere, the magnetic field energy density exceeds the kinetic energy density.
In fact, the magnetic field plays a dominant role in heating the chromosphere whenever it
is present [12].
The purpose of this thesis is to study the dependence of chromospheric structure on
the magnetic field. We select chromospheric lines for which the contribution function is
at different heights, such that when they are combined together, they span over the entire
chromosphere. The relationship between equivalent width and the magnetic field will then
show the amount of chromospheric heating at a given height. The Ca II K and He I equivalent widths will be used to further study the relationship between the magnetic field and
chromospheric activity. An overview of the observations taken from the Kitt Peak Observatory and the 150 ft. tower in Mount WIlson, is given in the fist part of Chapter 2. The
methods and analysis are given in the second part of Chapter 2. Results and discussions of
the influence of magnetic fields on the equivalent width is given chapter 3. The conclusion
is given in Chapter 4 and finally, a look into future work is given in Chapter 5.
5
Chapter 2
Data and Analysis
2.1
SOLIS Spectrograph
The spectral lines and the mean total magnetic flux used in this study were obtained
with the Synoptic Optical Long-term Investigations of the Sun (SOLIS), a synoptic facility for solar observations over a long time frame designed and built by the National Solar
Observatory (NSO). SOLIS provides unique observations of the Sun on a continuing basis
for several decades to understand solar activity cycles, sudden energy releases in the solar
atmosphere and solar irradiance changes and their relationships to global change. SOLIS is
composed of a single equatorial mount carrying three telescopes: the 50 cm Vector Spectromagnetograph (VSM), the 14 cm Full-Disk Patrol (FDP) and the 8 mm Integrated Sunlight
Spectrometer (ISS). For the purpose of this thesis, I used only data taken from the ISS and
the VSM telescopes.
2.1.1
ISS
The ISS instrument is designed to obtain high spectral resolution (R ∼
= 300,000) observations of the Sun as a star in the range of wavelengths 350nm through 1100 nm [13]. The
ISS observations of the integrated Sunlight spectra are accomplished through the use of an
optical fiber system composed of six major sections. These are:
• Fiber-optic feed
• Fiber-optic, six position spectrograph input selector
• Prism type predispenser
• Czerny-Turner two meter focal length, f 1/4 grating spectrograph operating in a double pass configuration
• Two axis, XY CCD camera scanning stage at spectrograph operating in a double pass
congifuration
• 1024 × 256 SITe CCD
The fiber optic feed consists of a Polymicro FV series, UV enhanced stepped index
fiber of 710 µm diameter. The 660 µm cladding is protected with a Polyimide buffer. The
inner core OD is 600 µm. The entire length of the fiber is further protected by a PVC and
Stainless Strip wound jacket. Four fibers are available as inputs to the ISS. Fibers 1 and 2
are primarily solar light feeds. The solar fibers are fed by means of an 8 mm aperture lens
with a focal length of 40 mm and produce a f/5 beam. The first of these fibers projects a
400 µm image of the Sun directly on the end of the fiber. The second fiber feed is identical
to the first except that the imaging lens looks through an iodine vapor cell to provide a well
6
known absorption spectra superimposed on the solar spectra, this is used for calibration.
The third and fourth fibers are used as calibration sources for the ISS. Fiber 3 is a quartz
lamp illuminator used for flat fielding of the CCD. FIber 4 is reversed for use with an
Uranium hollow cathode emission lamp but is currently not in use. The positional accuracy
and repeatability of the fiber translations is better than 10 µm [14]. The fiber assembly
transmits light to a McPherson 2-m Czerny-Turner double pass spectrograph located in a
temperature controlled room below the telescope [13].
A prism pre dispenser mounted between the fiber positioned and the main spectrograph
slit, is used for the isolation of the desired wavelength. This predispenser employs a 316
g/mm grating blazed at 63.5 degrees which allows for the passage of of non-dispersed light,
for use in zero order spectrograph alignment [14].
The spectrograph has an entrance slit with an adjustable 5-500 µm spectral, 20 mm
spatial, 30 µm × 1 mm nominal A30 µm slit using a 600 µm fiber, the image will smear
to a width of 50 µm at the blaze angle. The shutter is an Intermediate shutter in double
path. It has sn optical collimator and camera mirror Al-MgF2 with grating of 316 G/mm
Blaze 7500 at 6.8◦ in the wavelength range 3800 to 10840Å. The CCD camera head is
mounted on a precision XY translation stage that moves the CCD along the dispersion
and spatial direction in a precisely controlled and repeatable way. The camera used at the
spectrograph ext is a modified Model 500 produced by Spectral Instruments. The detector
is a SITe 1024 times 128 format with pixel size of 24µm and a readout rate of 10 Hz. The
CCD is Thermoelctric cooled to −10◦ [14].
A single CCD frame is recorded for each spectral line observed. More calibration
frames are obtained in order to meet scientific specifications for a photometric precision
of 0.1%. Processed data is stored and accessed at high speed for the length of the solar
cycle since the variation of line parameters with the cycle is the most interesting scientific
question for the ISS. Current core ISS program included 10 spectral ranges observed twice
a day with a storage requirement of 524 kB per frame [14].
The ISS records spectra of calibration sources for flatfielding and for wavelength calibration. The calibration source for flatfielding is the solar image itself, but is can include
the quartz lamp is it is necessary. Wavelength calibration is based o either a gas absorption
cell or a comparison lamp, depending on the application of the given spectrum. Spectra
can be obtained in a low resolution mode (R = 30,000) whose main purpose is to provide
sufficient spectral range in a single spectrum so that the entire bandpass which is used in
stellar flux calibrations included in a single observation [14].
For each spectral band, observation are taken from four four different positions by
moving the CCD in respect to the spectra in the spectrograph focal plane. The first image
(1,512 × 1014 pixels) is taken with the CCD centered at the corresponding wavelength for
a given spectral band. The second image is shifted by 1 pixel in the direction of dispersion
, the third image is shifted by 11 pixels and the fourth image is shifted by 129 pixels. It
takes about 5 minutes to complete the full cycle of observation for most spectral bands. Ca
II K and He I take the longest, with about 12 to 15 minutes respectively. The four images
7
are used for the purpose of flatfielding and to create the final spectrum for a given spectral
band. Because in the four images the CCD is shifted in respect to fixed spectral features,
the same pixels are exposed to a different level of light. Assuming that the solar source
remains constant during the observing cycle of 3-15 minutes, the images can be used to
derive flatfield. A dark field is taken for each observed spectral range at the beginning of
the four image cycle by closing the intermediate shutter of the double pass system. The
same dark field is used for all four images taken in each spectral band [13, 14].
After applying dark and flat fields, spectral features on four spectral images are aligned
and the astigmatic images are averaged in the spatial direction to create the final spectra
line profile for a given spectral band. In this averaging, each spatial spectrum of the four
512 × 1024 pixel images is weighted by the square root of its total intensity. The final
products are intensity as a function of pixel number and its error for each pixel. In the
next step of data reduction, the pixel position of selected spectral lines is determined. Pixel
positions are converted to nanometers using known wavelengths of selected spectral lines
from high resolution spectra taken with the NSO Fourier Transform Spectrometer. Reduced
spectra are saved in FITS format as double array with three axes: wavelength in Ångstroms,
continuum normalized intensity, and error in intensity for each pixel. This level 1 FITS files
constitute the basic ISS data product [13].
The wavelength calibration sources include an iodine absorption cell. Sunlight passing
through the cell produces an iodine absorption spectrum superimposed on the solar spectrum. By recording both the integrated solar spectrum and the iodine absorption spectrum
simultaneously as they traverse the same optical path, ultra-high precision measurements
of Doppler shifts in the solar spectrum seen as a star can be performed [14].
A solar extinction monitor is included in the ISS head mounted on the Full Disk Patrol
(FDP) instrument. it is important to motor extinction gradients across the solar disk, since
unexpected gradients can lead to artificial weighting that can influence the interpretation of
spectral features. This can occur in both observed shape and line strength. In addition, the
relative signal levels of each solar image are used as a guide to integration times during ISS
observations [14].
8
Na D I 589.6 nm
1
0.9
0.8
Scaled Intensity
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
589.1
589.2
589.3
589.4
589.5
589.6
589.7
Wavelength (nm)
589.8
589.9
590
590.1
Figure 2.1: Example of absorption spectrum of Na D I from the ISS
2.1.2
VSM
The VSM is responsible for taking high quality magnetic field observations in the photosphere and the chromosphere by recording the Zeeman-induced polarization of spectral
lines. It is 50 cm aperture telescope with a 10% obstruction which is sufficient to achieve
the required polarization sensitivity. To match the CCD pixel size of 16 µm per pixel, an
f/6.6 is required [15].
The VSM operates in four different observing modes at three different wavelengths.
These four modes are:
• photosphereic full-disk vector magneto grams using the FeI 630.15 and 630.25 nm
lines (Stokes I, Q, U, V)
• chromospheric full-disk magneto grams using the CaII 854.2 nm (Stokes I and V)
• full disk HeI 1083.0 nm line characteristics (Stokes I) and the near SiI line
• photospheric full-disk longitudinal magneto grams using the FeI 630.15 and 630.25
nm lines (Stokes I and V)
9
Figure 2.2: Spectra for Fe I 6301.5-6302.5 corresponding to Stokes parameters (top to
bottom) V, Q, U, and I. Image credit: http://solis.nso.edu/VSMOverview.html.
The CaII 854.2 nm and the HeI 1083.0 nm where chosen to provide a continuum record
of the current data set from the Kitt Peak Vacuum Telescope (KPVT). To measure vector
magnetic fields outside Sunspots in the visible part of the spectrum, it is required to observe
at least two spectral lines with different Landé factors. The FeI 630.15 and the 630.25 nm
lines were chosen because they are the most appropriate lines to measure magnetic fields
in quiet as well as active regions [15].
The telescope is a 50 cm quasi Ritchey-Chetien with two lens field corrector to provide
adequate image quality over the field of view, minimal geometric distortion, equal image
size for all wavelengths and a tele centric beam to minimize the field of view effects in the
polarization modulators. The entrance window minimizes contamination of the optics and
is completely filled with helium. The windows thickness is 6 mm to minimize its influence
on the polarization instruments. A fan system circulates the helium in such as way as to
minimize the temperature gradients inside the telescope and cool the secondary mirror.
The image of the Sun is built on the entrance slit of the Littrow spectrograph the length of
the slit covers 2048 arc seconds. To compensate for the curvature of spectral lines in the
spectrograph’s focal plane, the spectrograph is slit is slightly curved with radius of 258.77
mm. Scanning image by a curved slit results in a geometric distortion of the solar disk
figure [16, 15].
The two polarization packages, one for 630.2 and the other for 854.2 nm, are located in
front of the spectrograph slit. Three separate LCD polarization modulators are placed on
a mechanical slide behind the spectrograph entrance slit. Separate modulators are used for
observing and deriving vector spectropolarimetry in FeI 630.15-630.25 nm wavelengths
range and line-of-sight polarimetry in FeI 630.15-630.25 nm and Ca II 854.2 nm wavelength ranges [16].
The image of spectra is formed near the spectrograph slit, where the focal beam-splitter
splits the image of the spectrograph slit into two equal parts each of 1024 arc seconds
10
long.Light from each part is reimaged slit into a separate CCD camera of 1024 × 512
pixels in size. The polarizing beam-splitters are located in front of each camera. With
these optical arrangements, one camera is taking data from one solar hemisphere and the
other camera records spectra from the other hemisphere. Both cameras take data in two
orthogonal polarization states [16].
A full-disk magnetogram is contructed by scanning the solar image, which is done by
moving the telescope in declination. It takes about .6 seconds to record one scan line in FeI
region and about 1.2 seconds for the Ca II line. In addition to full-disk, VSM can take a
series of area scans by scanning a portion of the solar disk by declination[16].
The mean field values used in this work are determined from the daily measurements
of the line of sight magnetic flux density observed with 1 arcsecond pixel before January 1,
2010 and 1.1 arcsecond pixel after January 1, 2010. The measurements are averaged over
the full disk and their values are measured in Gauss per pixel. The mean total magnetic flux
is the average of the absolute values of the measurements. Pixels within .99 solar radii from
the disk center and with absolute values bigger then 0.2 Gauss are the only ones included in
the computations. The solar line of sight mean magnetic fields signals are calculated with
integrated VSM full disk Fe I 630.15 nm longitudinal photospheric magnetograms [27].
Figure 2.3: Full-disk Mean Total Flux obtained from the Vector Spectromagnetogram using
full-disk Fe I 630.15 nm. Image credit: http://solis.nso.edu/0/vsm_mnfield.html.
2.2
Mount Wilson Observatory
The Magnetic Plage Strength Index (MPSI) and the Mount Wilson Sunspot Index
(MWSI) were calculated at the 150-foot solar tower at the Mount WIlson Observatory
since the 1070s using Fe I 5250 Å magnetograms. The MPSI is calculated by adding the
absolute values of the magnetic field strength for all pixels where the absolute values of
the magnetic field strength is between 10 and 100 gauss. The number is then divided by
the total number of pixels regardless of field strength [17]. The MWSI is calculated in a
similar manner, in which the summation is done over all pixels whose absolute value of the
magnetic files strength is greater than 100. That number is then also divided by the total
11
number of pixels regardless of field strength [18].
Figure 2.4: MPSI data since the 1970s. Image credit:http://obs.astro.ucla.edu/150_
data.html.
Figure 2.5: MWSI data since the 1970s. Image credit: http://obs.astro.ucla.edu/
150_data.html.
2.3
2.3.1
Analysis
Equivalent Width
Activity in this study means measuring the line strength of each absorption spectrum.
The strength of the line is the total absorption of the spectra, the amount of light that has
been removed from the continuos spectrum [19]. The way this is done is by calculating the
equivalent width.
12
The equivalent width is the width of a section of the continuum with has the same area
(total absorption) as the observed line.
Figure 2.6: The area, a, of an absorption line measured below the continuum has the same
area as the rectangular line profile, b. Image credit: http://ircamera.as.arizona.edu/
astr_250/Lectures/Lecture_15.htm.
The advantage of using the equivalent width is that it is independent of exposure, while
some instruments broaden the lines, the total absorption of the line does not change much.
This means that the total absorption does not depend on the line’s shape [19, 20].
If one is to select only a fraction of the spectrum instead of the whole, then the equation
used is
Z λ2 Fc − Fλ
dλ
(2.1)
Wλ =
Fc
λ1
Whre Fλ the Scaled Intensity has been normalized, Fc = 1. Then reduces to:
Z λ2
Wλ =
(1 − Fλ ) dλ
(2.2)
λ1
In an absorption spectrum, the the darkest absorption lines are those whose equivalent
widths are greatest while the faintest spectra have smaller equivalent widths. The equivalent
width is dependent on the number of atoms that are in the correct state in which they can
absorb the specific wavelength [19].
13
2.3.2
H-α
H−alpha 656.3 nm
1
0.9
0.8
Scaled Intensity
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
655.6
655.8
656
656.2
656.4
Wavelength (nm)
656.6
656.8
657
Figure 2.7: Example of an absorption spectrum of the H-α line. The vertical lines are the
limits of integration used in calculating the equivalent width.
To calculate the equivalent width of H-α, I wrote a Matlab program to import and read
all of the .fts files which contain solar spectra data of H-α derived from the ISS. The .fts
files have three rows, row 1 has the wavelength λ measured in nanometers (nm), row 2 has
the scaled intensity, and row 3 has the estimated signal error. The name of the file also
contain the date it was created. From the name of the file I extract the date. From the data,
I extract rows 1 and 2, I then plot row2 vs row 1to make spectral graphs.
When plotting the data points, I plot the graphs of all the files into a single window, the
reason I do this is to see if the spectral lines are either red shifted or blue shifted from the
core value 656.3 nm. In the case of of H-α, some of the spectral lines are shifted. The way
I correct this is by finding the minimum value of the scaled intensity of each spectral line,
then I calculate the difference between the minimum and the core value of 656.3 nm. Once
I know this difference I shift the entire spectral line to the core value of 656.3 nm.
656.3 nm (H−alpha)
1
1
0.9
0.9
0.8
0.8
0.7
0.6
0.5
0.7
0.6
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
655.6
655.8
656
656.2
656.4
wavelength (nm)
656.3 nm (H−alpha)
1.1
Scaled Intensity
Scaled Intensity
1.1
656.6
656.8
0.1
655.6
657
(a) All H-α spectrum
655.8
656
656.2
656.4
wavelength (nm)
656.6
656.8
657
(b) H-α spectrum shifted to 656.3 nm
Figure 2.8: All H-α spectrum in their original position and shifted to 656.3 nm.
14
Student Version of MATLAB
Student Version of MATLAB
I calculate the equivalent width of each .fts file using the formula in equation 2.2 with
the limits of integration 656.2 nm and 565.4. After I calculate the equivalent width, I store
its value and its date into an a × 2 matrix, where a is the number of files. Column 1 stores
the date of the .fts file and column 2 stores the value of equivalent width.
Using the data from the Full-Disk Mean Magnetic Flux also obtained from the data of
SOLIS, I extract the mean total magnetic flux and the date it was created. This information
is stores in a b × 2 matrix. Column 1 stores the date and column 2 stores the value of the
FDMTMF.
I now have two matrices, one containing the date the spectral lines are taken and the
equivalent width and another matrix that has the mean total magnetic flux and the date the
data was taken. In order to plot the equivalent width versus mean total magnetic flux, I
match the dates in which both values were taken. I do this using the intersection function
in Matlab. This function matches the dates that are in both data sets. Now, I combine all
three values, into a n × 3 matrix. Column 1 contains the dates the data was taken, column 2
contains the FDMTMF values and column 3 contains the values for the equivalent width.
Plotting the values in column 3 against the values of column 2, results in Figure 2.9
0.118
0.1175
Ha 656.3 nm Equivalent Width (nm)
0.117
0.1165
0.116
0.1155
0.115
0.1145
0.114
2
4
6
8
10
12
Full Disk Mean Total Magnetic Flux (gauss)
14
16
Figure 2.9: The Equivalent Width decreases as the mean total magnetic flux increases.
The best fit line is found using the polyfit command in Matlab, in Figure 2.9 the line has
a slope m= −0.1850±0.1107×10−4 . The coefficient of determination, R2 which describes
describes the statistical model is 0.0028.
15
2.3.3
He
He 1083.0 nm
1.4
1.2
Scaled Intensity
1
0.8
0.6
0.4
0.2
0
1082.2
1082.4
1082.6
1082.8
1083
1083.2
Wavelength (nm)
1083.4
1083.6
1083.8
1084
Figure 2.10: One example of an absorption spectrum of the Helium.
In order to calculate the equivalent width of He, I use a similar Matlab program to
import and read all of the .fts files which contain solar spectra data of He derived from the
ISS telescope. I extract the date and from the data, I extract rows 1 and 2. I the plot row2
vs row 1to make spectral graphs.
When plotting the data points, I plot the all the absorption line into a single window, to
see if the spectral lies either red shifted or blue shifted from the core value of 1083.0 nm.
For He I, the spectral lines will be shifted not to the 1083.0 nm point, but instead to the
silicon Si I 10827.16 line.
1083.0 nm (He I)
1.6
1.4
1.4
1.2
1.2
Scaled Intensity
Scaled Intensity
1083.0 nm (He I)
1.6
1
0.8
1
0.8
0.6
0.6
0.4
0.4
0.2
1082 1082.2 1082.4 1082.6 1082.8 1083 1083.2 1083.4 1083.6 1083.8 1084
wavelength (nm)
0.2
1082 1082.2 1082.4 1082.6 1082.8 1083 1083.2 1083.4 1083.6 1083.8 1084
Wavelength (nm)
(a) All He I spectrum
(b) He I spectrum shifted to 1082.7 nm
Figure 2.11: All Helium spectra before and after being shifted to the Si I 10827.16 line.
I then calculate the equivalent width of each .fts file using equation 2.2 with the limits
of integration 1082.9 and 1083.1. After I calculate the equivalent width, I store its value
and its date into an a × 2 matrix, where a is the number of files. Column 1 stores the date
Student Version of MATLAB
16
Student Version of MATLAB
of the .fts file and column 2 stores the value of equivalent width. Using the data from the
Full-Disk Mean Magnetic Flux also obtained from the data of SOLIS, I extract the mean
total magnetic flux and the date it was created.
I now have two matrices, one containing the date the spectral lines are taken and the
equivalent width and another matrix that has the mean total magnetic flux and the date the
data was taken. In order to plot the equivalent width versus mean total magnetic flux, I
match the dates in which both values were taken. I do this using the intersection function
in Matlab. This function matches the dates that are in both data sets. Now, I combine all
three values, into a n × 3 matrix. Column 1 contains the date the data was taken, column 2
contains the value for the mean total magnetic flux and column 3 contains the value for the
equivalent width. I then plot column 3 versus column 2 and get Figure 2.12
He I 1083.0 nm Equivalent Width (nm)
0.015
0.01
0.005
0
2
4
6
8
10
12
Full Disk Mean Total Magnetic Flux (gauss)
14
16
Figure 2.12: The equivalent width of He I increases as the mean total magnetic flux increases.
The line of best fit has slope m= 1.6813 ± 0.3035 × 10−4 , and an R2 of 0.0296.
17
2.3.4
Na D I
Na D I 589.6 nm
1
0.9
0.8
Scaled Intensity
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
589.1
589.2
589.3
589.4
589.5
589.6
589.7
Wavelength (nm)
589.8
589.9
590
590.1
Figure 2.13: One example of an absorption spectrum of the Na D I line.
To calculate the equivalent width of Na D I, I plot all the spectra into a single window,
the reason I do this is to see if the spectral lies either red shifted or blue shifted from the
core value of 589.6 nm.
589.6 nm (Na D I)
1
0.9
0.8
Scaled Intensity
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
589
589.2
589.4
589.6
589.8
wavelength (nm)
590
590.2
590.4
Figure 2.14: All Na D I spectra
Since the plots are not shifted too much, I calculate the equivalent width of each .fts
file using the equation 2.2 where 589.5 and 589.7 are the limits of integration and can be
visualized in Figure 2.13. After I calculate the equivalent width, I store its value and its
date into an a × 2 matrix, where a is the number of files. Column 1 stores the date of the
Student Version of MATLAB
file for which the equivalent width was calculated and column 2 stores the equivalent width
value. The data for the FDMTMF from the VSM is stored into a b × 2 matrix.
In order to plot the equivalent width versus mean total magnetic flux, I match the dates
18
in which both values were taken. I do this using the intersection function in Matlab. This
function matches the dates that are in both data sets. Now, I combine all three values, into
a n × 3 matrix. Column 1 contains the date the data was taken, column 2 contains the value
for the mean total magnetic flux and column 3 contains the value for the equivalent width.
The plot of this is given in Figure 2.15
0.068
Na D 589.6 nm Equivalent Width (nm)
0.066
0.064
0.062
0.06
0.058
0.056
4
6
8
10
12
Full Disk Mean Total Magnetic Flux (gauss)
14
16
Figure 2.15: The equivalent width decreases as the mean total magnetic flux increases.
The slope of the line of best fit is m= −0.8496 ± 0.6639 × 10−4 , and an R2 of 0.0057.
2.3.5
Ca II
Ca II 854.2 nm
1
0.9
0.8
Scaled Intensity
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
853.2
853.4
853.6
853.8
854
854.2
854.4
Wavelength (nm)
854.6
854.8
855
855.2
Figure 2.16: One example of an absorption spectrum of the Ca II H line.
To calculate the equivalent width of Ca II, I plot the spectral lines into a single window,
the reason I do this is to see if the spectral lies either red shifted or blue shifted from them
set wavelength, in the case of Ca II, this value is 854.2 nm. SInce some of the lines are
shifted, move them so that all the dips line up at the 854.2 nm wavelength.
19
854.2.0 nm (Ca II)
1
1
0.9
0.9
0.8
0.8
0.7
0.6
0.5
0.7
0.6
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
853
853.5
396.8 nm (Ca II H)
1.1
Scaled Intensity
Scaled Intensity
1.1
854
854.5
wavelength (nm)
855
(a) All Ca II spectrum
0.1
853
855.5
853.5
854
854.5
wavelength (nm)
855
855.5
(b) Ca II spectrum shifted to 854.2 nm
Figure 2.17: All Ca II spectrum in their original position and shifted to 854.2 nm.
I calculate the equivalent width of each .fts file using the equation 2.2 where 854.1
and 854.3 are the limits of integration. In figure 2.16, one can see the bounds used in the
integration. After I calculate the equivalent width, I store its value and its date into an
a × 2 matrix, where a is the number of files. Using the data from the VSM, I extract the
FDMTMF and the date it was created.I stored this values into an b × 2 matrix.
Student Version of MATLAB
Student Version of MATLAB
In order to plot the equivalent width versus mean total magnetic flux, I match the dates
in which both values were taken. I do this using the intersection function in Matlab. This
function matches the dates that are in both data sets. Now, I combine all three values, into
a n × 3 matrix. Column 1 contains the date the data was taken, column 2 contains the value
for the mean total magnetic flux and column 3 contains the value for the equivalent width.
The plot Column 3 against column 2 is given in Figure 2.18
0.1088
Ca II 854.2 nm Equivalent Width (nm)
0.1086
0.1084
0.1082
0.108
0.1078
0.1076
0.1074
0.1072
0.107
2
4
6
8
10
12
Full Disk Mean Total Magnetic Flux (gauss)
14
16
Figure 2.18: The equivalent width decreases as the mean total magnetic flux increases.
Where the line represents the best fit line between all points with slope m = −1.3232 ±
0.0944 × 10−4 , and an R2 of 0.1630.
20
2.3.6
Ca II H
Ca II H 396.8 nm
0.45
0.4
0.35
Scaled Intensity
0.3
0.25
0.2
0.15
0.1
0.05
0
396.4
396.5
396.6
396.7
396.8
Wavelength (nm)
396.9
397
397.1
Figure 2.19: One example of an absorption spectrum of the Ca II H line
In order to calculate the equivalent width of Ca II H, I first plot the data of all the spectra
into a single window to see if the spectral lies either red shifted or blue shifted from the
core value of 396.8 nm. Looking at Figure 2.20, we can see that none of the spectra are
shifted.
396.8 nm (Ca II H)
0.45
0.4
0.35
Scaled Intensity
0.3
0.25
0.2
0.15
0.1
0.05
0
396.4
396.5
396.6
396.7
396.8 396.9
wavelength (nm)
397
397.1
397.2
397.3
Figure 2.20: All Ca II H spectra.
I calculate the Equivalent width of each .fts file using equation 2.2 where the limits of
integration are 396.8 and 396.9 and are represented as the black lines in Figure 2.19, . After
I calculate the equivalent width, I store its value and its date into an a × 2 matrix, where a is
the number of files. Column 1 stores the date of the file for which the equivalent width was
Student Version of MATLAB
calculated and column 2 stores the equivalent width value. Using the data from the VSM I
grab the FDMTMF and store it a b × 2 matrix.
21
In order to plot the equivalent width versus mean total magnetic flux, I match the dates
in which both values were taken. I do this using the intersection function in Matlab. This
function matches the dates that are in both data sets. Now, I combine all three values, into
a n × 3 matrix. Column 1 contains the date the data was taken, column 2 contains the value
for the mean total magnetic flux and column 3 contains the value for the equivalent width.
0.0913
Ca II H 396.8 nm Equivalent Width (nm)
0.0912
0.0911
0.091
0.0909
0.0908
0.0907
0.0906
0.0905
0.0904
2
3
4
5
6
7
8
Full Disk Mean Total Magnetic Flux (gauss)
9
10
11
Figure 2.21: The equivalent width decreases as the mean total magnetic flux increases.
Where the line represents the line of best fit between all points with slope m =−0.8657±
0.0269 × 10−4 and an R2 = 0.5589.
2.3.7
Ca II K
Ca II K 393.4 nm
0.35
0.3
Scaled Intensity
0.25
0.2
0.15
0.1
0.05
0
393
393.1
393.2
393.3
393.4
Wavelength (nm)
393.5
393.6
393.7
Figure 2.22: One example of an absorption spectrum of the Ca II K line
To calculate the equivalent width of Ca II K, I use Matlab program to import and read
all of the .fts files which contain solar spectra data of Ca II K. I plot the data of all the files
into a single window, the reason I do this is to see if the spectral lies either red shifted or
22
blue shifted from the core value of 393.4 nm. Looking at Figure 2.23, the spectra are not
shifted from 393.4 nm.
393.4 nm (Ca II K)
0.4
0.35
Scaled Intensity
0.3
0.25
0.2
0.15
0.1
0.05
393
393.1
393.2
393.3
393.4
wavelength (nm)
393.5
393.6
393.7
Figure 2.23: All Ca II K spectra
I calculate the equivalent width of each .fts file using equation 2.2, where 393.32 and
393.42 are the limits of integration and are represented by the black lines in Figure 2.22.
After I calculate the equivalent width, I store its value and its date into an a × 2 matrix,
where a is the number of files. Column 1 stores the date of the file for which the equivalent
Student Version of MATLAB
width was calculated and column 2 stores the equivalent width value. Using the data from
the Full-Disk Mean Magnetic Flux also obtained from the VSM, I extract the mean total
magnetic flux and the date it was created. I store this values as a b × 2 matrix where column
1 stores the date and the column 2 stores the FDMTMF value.
In order to plot the equivalent width versus mean total magnetic flux, I match the dates
in which both values were taken. I do this using the intersection function in Matlab. This
function matches the dates that are in both data sets. Now, I combine all three values, into
a n × 3 matrix. Column 1 contains the date the data was taken, column 2 contains the value
for the mean total magnetic flux and column 3 contains the value for the equivalent width.
Plotting the values in column 2 against the values of column 1 gives Figure 2.24
23
Ca II K 393.4 nm Equivalent Width (nm)
0.0822
0.082
0.0818
0.0816
0.0814
0.0812
2
3
4
5
6
7
8
Full Disk Mean Total Magnetic Flux (gauss)
9
10
11
Figure 2.24: The equivalent width decreases as the mean total magnetic flux increases.
Where the slope of the best fit line is m= −1.0581±0.0351×10−4 and the R2 = 0.4765.
2.3.8
Helium EW, MPSI and MWSI
The Equivalent width of Helium obtained from Livingston is plotted against the MPSI
and the MWSI obtained from the Mount WIlson 150 ft. solar tower. In order to plot the
equivalent width against both the MPSI and the MWSI data, I have to match the dates the
data was created from both sets. The problem I ran into is that the dates from both data
sets (MPSI and MWSI) where in julian dates. I changed from julian to gregorian using a
function already in Matlab. Once I transform the dates, I intersect the dates of both data
sets in order to match the date the equivalent width was created with the date in which
both the MPSI and MWSI were created. Once I find where the data sets intersect, I plot
the equivalent width against the MPSI, Figure 2.25 and the equivalent width against the
MWSI, Figure 2.26
Equivalenth Width He 10830 (mA)
100
90
80
70
60
50
40
30
0
1
2
3
Magnetic Plage Strength Index
4
5
6
Figure 2.25: The equivalent width of Helium increases as the Magnetic Plage Strength
Index increases.
Where the line of best fit has slope, m = 7.9117 ± 0.2463.
24
Equivalenth Width He 10830 (mA)
100
90
80
70
60
50
40
30
0
0.5
1
1.5
2
2.5
Mount Wilson Sun Spot Index
3
3.5
4
Figure 2.26: The equivalent width of Helium increases as the Mount Wilson Sun Spot
Index increases.
The line of best fit has slope, m= 13.1196 ± 0.9192.
2.3.9
Ca II K Full DIsk Index, MPSI and MWSI
The Ca II K Full-Disk Index also obtained from Livingston is plotted against the MPSI
and the MWSI. In order to plot the Ca II K Full-Disk Index against both the MPSI and the
MWSI data, I have again, matched the dates the data was created for both sets. Like before,
I change the dates from julian to gregorian. Once I transform the dates, I intersect the dates
of both data sets in order to match the date the equivalent width was created with the date
in which both the MPSI and MWSI were created. Once I find where the data sets intersect,
I plot the equivalent width against the MPSI in one plot and the equivalent width against
the MWSI in another plot.
0.09
Ca II K Full Disk Index
0.085
0.08
0.075
0.07
0.065
0.06
0.055
0
1
2
3
Magnetic Plage Strength Index
4
5
6
Figure 2.27: TheCa II K Full-Disk Index increases as the Magnetic Plage Strength Index
increases.
The line of best fit has slope, m = 0.47528 ± 0.0080 × 10−2 .
0.1
Ca II K Full Disk Index
0.09
0.08
0.07
0.06
0.05
0
0.5
1
1.5
Mount Wilson Sun Spot Index
2
2.5
3
Figure 2.28: The Ca II K Full-Disk Index increases as the Mount Wilson Sun Spot Index
increases.
The line of best fit has slope, m =11.206 ± 0.509 × 103 .
25
Chapter 3
Results and Discussion
The magnetic field in the Sun is generated in the convection zone and emerges onto the
surface through the photosphere. This means that the photospheric magnetic field represents the total net magnetism of the Sun. As a result, the solar chromosphere is sustained
by the magnetic field. The goal of this study is to find the dependence of chromospheric
structure on the magnetic field. We used three sources of magnetic fields, from the VSM,
we used the full-disk mean total magnetic flux, and from Mount Wilson, we used mean
plage magnetic fields, and mean Sunspot magnetic fields. The chromospheric lines used
in this study are selected such that the contribution function is at different heights. The
relationship between the equivalent width and the magnetic field will show the amount of
chromospheric heating at a given height. This is the first time a study like this have been
performed, therefore the results in this section cannot be compared to other studies.
Transition region
106K
Photosphere
Chromosphere
Corona
CIV
Ly
Temperature
He I 10830A
105K
Mg II h/k
HINODE/BFI
UV/EUV spectrograph
Ca II H/K
Ca II 8542Å
H
Mg I b
Na I D1/D2
104K
Fe I
HINODE/NFI
SOLAR-C
UV-Vis-NIR telescope
HINODE/SP
100
10000
Height (km)
Figure 3.1: This figure shows the formation of spectral lines at different height in the solar
atmosphere [21].
As we can see from Figure 3.1, the lines used in this study are those whose formation
span over the entire chromosphere. The lines of Ca II, Ca II H and K form in the lower
chromosphere, but they span over almost all the chromosphere. The formation of the Na D
I line spans over most of the photosphere all the way to the chromosphere. The formation
of Helium and H-α lines is spans the upper chromosphere almost all the way to the corona
region.
26
3.1
Magnetic Field Effect on the Equivalent Width
0.015
0.118
0.1175
He I 1083.0 nm Equivalent Width (nm)
Ha 656.3 nm Equivalent Width (nm)
0.117
0.1165
0.116
0.1155
0.01
0.005
0.115
0.1145
0.114
2
4
6
8
10
12
Full Disk Mean Total Magnetic Flux (gauss)
14
0
16
2
4
(a) H-α EW vs FDMTMF
6
8
10
12
Full Disk Mean Total Magnetic Flux (gauss)
14
16
(b) He I EW vs FDMTMF
0.068
0.1088
0.066
Ca II 854.2 nm Equivalent Width (nm)
Na D 589.6 nm Equivalent Width (nm)
0.1086
0.064
0.062
0.06
0.1084
0.1082
0.108
0.1078
0.1076
0.1074
0.058
0.1072
0.056
4
6
8
10
12
Full Disk Mean Total Magnetic Flux (gauss)
14
0.107
16
2
(c) Na D I EW vs FDMTMF
4
6
8
10
12
Full Disk Mean Total Magnetic Flux (gauss)
14
16
(d) Ca II EW vs FDMTMF
0.0913
0.0822
Ca II K 393.4 nm Equivalent Width (nm)
Ca II H 396.8 nm Equivalent Width (nm)
0.0912
0.0911
0.091
0.0909
0.0908
0.0907
0.082
0.0818
0.0816
0.0906
0.0814
0.0905
0.0904
2
3
4
5
6
7
8
Full Disk Mean Total Magnetic Flux (gauss)
9
10
11
(e) Ca II H EW vs FDMTMF
0.0812
2
3
4
5
6
7
8
Full Disk Mean Total Magnetic Flux (gauss)
9
10
11
(f) Ca II K vs FDMTMF
Figure 3.2: This figure shows the equivalent width vs the full disk mean total magnetic flux
of all the lines used in this study
From Figures 3.2a, 3.2b, and 3.2d, the equivalent width of H-α, He I, and Ca II have
more scattering and takes on a wider range of values for magnetic field strength of 4-6
gauss. It is not until above 6 gauss that the equivalent width begins to form a linear relationship. For Na D I, as shown in Figure 3.2c, the equivalent width is scattered throughout
the plot, with most of the equivalent width values settling in the lower part of the plot. Ca
27
II H and K show a stronger linear relation as shown in Figures 3.2e, and 3.2f, with Ca II
K showing the best linear relationship. In both cases, most of the greater equivalent widths
are grouped in the lower magnetic field.
We can see that in all lines except for He I, there is an inverse relationship between the
equivalent width and the magnetic field. Since the equivalent width measures the strength
of the lines, it is clear that the magnetic field makes the lines in the lower to mid chromosphere brighter. Helium on the other hand is produced high above the chromosphere, its
equivalent width increases with the magnetic field. This means that chromospheric lines
created high above the chromosphere become darker in the presence of magnetic fields.
3.2
Magnetic Field Effect on Chromospheric Heating
Results: EW vs FDTMF
Line
Response Height (km)
Slope (nm/gauss)
H-α (656.3 nm)
1000-2000
−0.1850 ± 0.1107 × 10−4
He I (1083.0 nm)
2000
1.6813 ± 0.3035 × 10−4
Ca II (854.2 nm)
780
−1.3232 ± 0.0944 × 10−4
Ca II H (396.8 nm)
980
−0.8657 ± 0.0269 × 10−4
Ca II K (393.4 nm)
940
−1.0581 ± 0.0351 × 10−4
Na D I (589.6 nm)
350
−0.8496 ± 0.6639 × 10−4
Uncertainty in slope
59.85%
18.05%
7.13%
3.10%
3.32%
78.14%
R2
0.0028
0.0296
0.1630
0.5589
0.4765
0.0057
Table 3.1: The height of formation for each spectral line and the slope of the equivalent
width vs the full disk total magnetic flux.
By looking at the slopes of the plots, we can also derive information about chromospheric heating. A steeper slope means that there is more magnetic field contribution to
the heating of the chromosphere. Looking at Table 3.1, we find that the slope of the Ca II
(854.2 nm) line is steeper than that of the lines Ca II H (396.8 nm) and K (393.4 nm) and
H-α. This is due to the the fact that Ca II is produced at a lower height compared to H-α
and the Ca II H and K lines. This shows that the magnetic field contribution is higher for
lines produced at a lower height. For Na D I, we can see that the slope of the line is less
steep than that of Ca II, even though it is also formed at the lowest height. This can be due
to the fact that Na D I is mostly a photospheric line, and in the photosphere, the temperature
is colder. The line of He I (1083.0 nm) has the steepest slope of all lines. The steeper slope
for this line is due to the influence of the heating mechanisms in of the transition region and
coronal radiation more so than the magnetic field. Thus one can conclude that while the
lower chromosphere is mostly heated by the magnetic field. In the higher chromosphere,
heating is mostly influenced by the coronal back radiation.
28
3.3
Mount Wilson Strength Indices Effect on Livingston Data
0.09
0.1
0.085
Ca II K Full Disk Index
Ca II K Full Disk Index
0.09
0.08
0.075
0.07
0.065
0.08
0.07
0.06
0.06
0.055
0
1
2
3
Magnetic Plage Strength Index
4
5
0.05
6
0
0.5
(a) Ca II K vs MPSI
2
2.5
3
100
Equivalenth Width He 10830 (mA)
Equivalenth Width He 10830 (mA)
1.5
Mount Wilson Sun Spot Index
(b) Ca II K vs MWSI
100
90
80
70
60
50
40
30
1
0
1
2
3
Magnetic Plage Strength Index
4
5
90
80
70
60
50
40
30
6
(c) He I vs MPSI
0
0.5
1
1.5
2
2.5
Mount Wilson Sun Spot Index
3
3.5
4
(d) He I K vs MWSI
Figure 3.3: The EW of He I, and Ca II K Full Disk Index plotted against the MPSI and
MWSI
Results: EW vs Mount WIlson Index Data
Line EW
Index
Slope (milli-Å/gauss)
Uncertainty in slope
He I (1083.0 nm) EW MPSI
7.9117 ± 0.2463
3.11%
Ca II K (393.4 nm)
MPSI 0.47528 ± 0.0080 × 10−2
1.69%
He I (1083.0 nm) EW MWSI
13.1196 ± 0.9192
7.00%
Ca II K (393.4 nm)
MWSI
11.206 ± 0.509 × 103
4.54%
R2
0.4627
0.8619
0.1453
0.4638
Table 3.2: The equivalent width measured by Livingston, the Mount Wilson Index Data
and the slope of EW plotted against each Index.
Figures 3.3a,3.3b, show direct relationships between the Ca II K Full Disk Index, and
the Mount Wilson Magnetic Flux Indices. The relationship between Ca II K Full Disk
Index and the MPSI having the most linear relationship than any other plot. The values
being linear up to a MPSI value of 2. The relationship between the Call K Full Disk Index,
stays relatively liner up to a MWSI value of 1.
The fact that the Ca II K Full Disk Index increases for both the MPSI and MWSI means
that Ca II K gets brighter with both plage and Sunspot magnetic fields. Comparing the
slopes from Tables 3.1 and 3.2, we ca see that the MWSI has the steeper slope, followed by
the MPSI and FDMTMF respectively. This shows that heat is influenced more by Sunspots
than any other type of magnetic field.
Figures 3.3c, and 3.3d, show that the MPSI looks linear up until a MPSI value of 1, it
then continues to increase up to a value of 3.5, after which it starts decreasing slowly. The
relationship between the He I equivalent width and the MWSI is very nonlinear form the
start, and most of the equivalent width values increase between MWSI values of 0 and 1
after which that start to slowly decrease.
Both plots, show that the line of best fit increases in both indices. This means that the
29
equivalent width of He I becomes darker as the plage and Sunspot magnetic field increase.
Looking at Tables 3.1, and 3.2, the slope of the MWSI is steeper than both the MPSI and
FDMTMF respectively. This shows that the Sunspot magnetic field contributes more to
heating.
30
Chapter 4
Conclusion and Future Work
4.1
Conclusion
This study focused on the dependence of chromospheric structure on the magnetic field.
Chromospheric structure was measured by calculating the equivalent width of 6 types of
absorption spectra. We used chromospheric absorption lines that form at different heights in
the chromosphere. The reason for this is that the relationship between the equivalent width
and the magnetic field shows the amount of chromospheric heating at any given height. We
also used the Ca II K and the He equivalent widths measured by Livingston and the MPSI
and MWSI from Mount WIlson to further study the relationship between chromospheric
heating due by plage and sunspot magnetic field. As stead before, this is the first time a
study of this kind has been conducted, and the results have not been published.
We find that for lines that form in the lower to mid chromosphere, such as H-α, Na D I,
Ca II, and Ca II H and K, the magnetic field makes the lines brighter. In this region, we also
find chromospheric heating is mostly influenced by the magnetic field. From Table 3.1, we
can see that the uncertainty of slope and R2 for the equivalent width of Ca II, and Ca II H
and K, are better correlated with the magnetic field.Their uncertainty if slope is smaller and
the R2 values are bigger. The equivalent width of H-α and Na D I show no correlation with
the magnetic field, their uncertainty in slope are the biggest and their R2 are the smallest.
For He I, which is formed in the upper chromosphere the lines gets darker with the
magnetic field. In this regime, although the slope of the best fit line was strongest, the
uncertainty in slope is big and the R2 is small, showing a weak relationship between the
equivalent width of He I and the magnetic field. This means that heating in the upper
chromosphere is due to processes in the transition region and coronal back radiation.
The measurement of the Livingston data and that of the MPSI and MWSI, showed
that the Ca II K Full Disk Index gets brighter with both plage and sunspot magnetic field.
Table 3.2 shows that the Ca II K Full Disk Index is strongly correlated with the MPSI, its
slope uncertainty is the lowest at 1.69% and its R2 of 0.8619 indicates that it is a strong
fit. Correlation between the Ca II K Full Disk Index and the MWSI is okay although the
uncertainty in slope is small, its R2 value of 0.4638 shows that both quantities have a weak
relationship. The relationship between He I, with the MPSI and MWSI showed that plage
and sunspot magnetic field make the lines darker. A weak correlation between He I and the
MPSI is also found, although the slope uncertainty is small, its R2 is 0.4627. We can also
say that there is no correlation between He I and the MWSI, in this case the uncertainty
slope is big and the R2 value is small, at 0.1453. For both cases, the steeper slope occurred
when the Livingston data was plotted against the MWSI, showing that although the sunspot
magnetic field is localized, it contributes more to chromospheric heating whenever it is
present.
31
Although most linear relationships between the equivalent width and magnetic field
are weak (low R2 ), we can conclude that the relationship between these quantities is more
complicated and possibly nonlinear. One reason for having low R2 values is the fact than
most data points tend to be located in the low magnetic field. Over time, as the solar
cycle moves from solar minimum to maximum, the data will be better distributed for high
magnetic field values, making R2 bigger.
4.2
Future Work
The data used in this study was obtained for the Kitt Peak Observatory over a 6 year period starting from 2006. In order to fully study the dependence of chromospheric structure
on the magnetic field, the data should encompass the full 22 year cycle of the sun. This
would allow us to have more measurements for the stronger magnetic fields with values
above 4 gauss and thus a greater spread of data.
Ultimately, we would like to apply the method used in this study in order to study how
the magnetic field influences heating of other stars. A first attempt would be to study stars
whose activity cycles are similar to that of the Sun since the magnetic field variations would
be similar. Acquiring spectra for H-α, Na D I, He I, and Ca II could prove troublesome,
however Ca II H and K spectra have been recorded as part of the 40 year HK Project at
Mount Wilson [5].
32
References
[1] Bennet, J. Donahue, D. Schneider, N. Voit, M. The Essential Cosmic Perspective
(San Francisco, Pearson Addiso-Wesley, 2008). Pp. 278-296.
[2] Foukal, P. Solar Astrophysics(New York, Wiley, 1990). Pp 277-315.
[3] Athay, R. G. The Chromosphere and the Transition Region. In The Sun as a Star,
ed. S. Jordan, NASA SP-450. Pp. 85-133 (1981).
[4] Tayler, R.J. The Sun as a Star(Cambridge, New York, NY,USA, 1997). Pp 1-242.
[5] Hall, J. C. Stellar Chromospheric Activity. Living Rev. Solar Phys. 5, 1-53 (2008).
[6] De Pontieu, B., McIntosh, S. W., Hansteen, V. H., et al. A Tale of Two Spicules: The
Impact of Spicules on the Magnetic Chromosphere. PASJ 59, 1-8 (2007).
[7] Beckers, J. M. A Study of the Fine Structures in the Solar Chromosphere(AFCRL
Environmental Research paper No. 49: Ph. D thesis Utrech University) 1964.
[8] Duncan et al. CA II H and K measurements made at Mount Wilson Observatory,
1966-1983. ApJS 76, 383-430 (1991).
[9] Kaler, J. B. Stars and their Spectra: An Introduction to the Spectral Sequence(Cambridge, New York, NY, USA, 1997). Pp.1-300.
[10] Zirin, H. The Solar Atmosphere (Waltah, Blaisdell Pub. Co. 1966). Pp. 212-270.
[11] Zwaan, C. The Chromosphere and the Transition Region. In The Sun as a Star, ed.
S. Jordan, NASA SP-450. Pp. 163-177 (1981).
[12] Jordan, S. D. Chromospheric Heating. In The Sun as a Star, ed. S. Jordan, NASA
SP-450. Pp. 301-317 (1981).
[13] Bertello, L., Pevtsov, A.A., Harvey, J.W., and Toussiant, R.M. Improvements in the
determination of ISS Ca II K parameters. Solar Physics 272, 229-242 (2011).
[14] Integrated Sunlight Spectrometer. In National SOlar Observatory. http://solis.
nso.edu/docs/ISS_details.pdf (2012).
[15] Vector SPectromagnetograph. In National SOlar Observatory. http://solis.nso.
edu/docs/VSM_details.pdf (2013).
[16] Balasubramaniam, K. S., Pevtsov, A.A. ” Ground-based synoptic instrumentation
for solar observations” Proc. SPIE 8148, 814809 (2011).
[17] Bertello et al. The Mount Wilson Ca II K plage index time series. Solar Physics 264,
31-44 (2010).
33
[18] Ballester, J. L., Olver, R., Carbonell. The Near 160 Day Periodicity in the Photospheric Magnetic Flux. The Astrophysical Journal 566, 505-511 (2002).
[19] Kaufmann, W. J. Freedman, R. A. Universe (New York, W. H. Freeman, 1999) Pp.
471-472.
[20] Kitchin, C. R. Optical Astronomical Spectroscopy (Bistol, Institute of Physics Pub,
1995) Pp. 214.
[21] Katsukawa, Y. Basic requirements to the instrument for diagnostics
of chromospheric magnetic fields with SOLAR-C[8-9].Retrieved from
http://hinode.nao.ac.jp/SOLAR-C/Meeting/SCSDM2/katsukawa2.pdf
[22] Alexei A. Pevtsov, Luca Bertello, Andrey G. Tlatov, Ali Kilcik, Yury A. Nagovitsyn,
Edward W. Cliver. Cyclic and Long-term Variation of Sunspot Magnetic Field. Solar
Physics 289, 1-13 (2012).
[23] Carroll, B. W., Ostlie, D. A. An introduction to Modern Astrophysics (Pearson
Addison-Wesley, San Francisco 2007) Pp. 267-268.
[24] Demidov, M. L.,Zhigalov, V. V., Peshcherov, V. S., Grigoryev, V. M. An Investigation of the Sun-as-a-Star Magnetic Field Through Spectropolarimetric Measurements. Solar Physics 209, 217-232 (2002).
[25] Donnelly, R.F., White, O. R., Livingston, W. C. The solar Ca II K index and the Mg
II core-to-wing ratio. Solar Physics 152, 69-76 (1994).
[26] Fisher, R.; Seagraves, P.; Sime, D. G.; McCabe, M.; Mickey, D. The Sun as a star 1982 June 14-August 13. Astrophysical Journal 280, 873-878 (1984).
[27] Full-Disk Mean Magnetic Flux (2012). URL http://solis.nso.edu/vsm/vsm_
mnfield.html
[28] Hammond, A. L. Solar Variability: Is the Sun an Inconstant Star?. Science 191,
1159-1160 (1976).
[29] Ioshpa, B. A., Obridko, V. N., Shelting, B. D. Short-Period Oscillations of the Magnetic Field of the Sun as a Star. Solar Physics 29, 385-392 (1973).
[30] Jones, H. P.,Chapman, G. A.; Harvey, K. L., et al. A Comparison of Feature Classfication Matheods for Modeling Solar Irradiance Variation. Solar Physics 248, 323337 (2008).
[31] Kobel, P., Solanki, S. K., Borrero, J. M. The Continuum Intensity as a Function of
Magnetic Field. I. Active Region and Quiet Sun Magnetic Elements. Astronomy and
Astrophysics 531, 1-14 (2011).
[32] Kotov, V. A., Scherrer, P. H., Howard, R. F., Haneychuk, V. I. Magnetic Field of the
Sun as a Star: The Mount Wilson Observatory Catalog 1970-1982. Astrophysical
Journal Supplement 116, 103-117 (1988).
34
[33] LaBonte, B. J. Spectra of Plages on the Sun and Stars. I. Ca II H and K Lines. The
Astronomical Journal Supplement Series 62, 229-239 (1986).
[34] Lanza, A. F., et al. Magnetic Activity in the Photosphere of CoRoT-Exo-2a? . Active
Longitudes and Short-Term Spot Cycle in a Young Sun-Like Star. Astronomy and
Astrophysics 493, 193-200 (2009).
[35] Livingston,W.C., White, O.R., Wallace, L.,Giampa, M. S. Sun-as-a-Star Spectrum
Variations 1974-2006. The Astrophysical Journal 657, 1137-1149 (2007).
[36] Livingston,W.C., White, O.R., Wallace, L., Harvey, J. Sun-as-a-Star, Chromospheric
Lines, 1974-2009. MnSAI 81, 643-645 (2010).
[37] Naqvi, M.F., Marquette, W.H., Tritschler, A. and Denker, C. The Big Bear Solar Observatory Ca II K-line index for Solar Cycle 23. Astron. Nachr 33, 696-703 (2010).
[38] Oranje, B. J. The Ca II K from the Sun as a Star I. Observational Parameters. Astron.
Astrophys. 122, 88-94 (1983).
[39] Oranje, B. J. The Ca II K from the Sun as a Star II. The plage Emission Profile.
Astron. Astrophys. 124, 43-49 (1983).
[40] Pevtsov, A.A., Bertello, L., Tlatov, A.G., Kilcik, A., Nagovitsyn, Y.A., Cliver, E.W.
Cyclic and Long-term Variations of Sunspot Magnetic FIelds. Solar Physics, 1-13
(2013).
[41] Rebolo, R., Garcia Lopez, R., Beckman, J. E., et al. Chromospheres of Late-Type
Active and Quiescent Dwarfs. I - An Atlas of High Resolution CA II H Profiles.
Astronomy and Astrophysics Supplement Series 80, 135-148 (1989).
[42] Rutten R.J. Observing the Solar Chromosphere. Physics of Chromospheric Plasmas,
ASP Conference Series 368, 27-48 (2007).
[43] Rutten, Robert J. Sun-as-a-Star Line Formation. Astronomical Society of the Pacific
9, 91-102 (1990).
[44] Schrijver, C. J. Radiative Fluxes from the Outer Atmosphere of a Star Like the Sun
- A Construction Kit. Astronomy and Astrophysics 189, 163-172 (1988).
[45] Skumanich, A.; Lean, J. L.; Livingston, W. C.; White, O. R. The Sun as a Star Three-Component Analysis of Chromospheric Variability in the Calcium K Line.
Astrophysical Journal 282, 776-783 (1984).
[46] Wu, D.J., Fang, C. Sunspot Chromospheric Heating by Kinetic Alfvén Waves.
Ap.J.659, L181-L184 (2007).
[47] Wilson, O.C. Flux Measurements at the Centers of Stellar H- and K-Lines. Ap.J.
153, 221-34 (1968).
35
Magnetic vs HaLine plot.m
%{
Luis Contreras
This program Takes t h e E q u i v a l e n t
Width o f H−a l p h a and t h e mean t o t a l
m a g n e t i c f l u x o f t h e s u n and p l o t s them
against eachother .
%}
%{
The f i r s t f u n c t i o n i m p o r t s t h e f i l e s
f o r H−a l p h a and e x t r a c t s
t h e w a v e l e n g t h and i n t e n s i t y . The s e c o n d
f u n c t i o n c u m p u t e s t h e E q u i v a l e n t Width .
INT c o n t a i n s t h e d a t e o f t h e f i l e and t h e
E q u i v a l e n t Width .
%}
[ T] = H A S p e c t r u m I n t e n s i t y ( ’HA/ ∗ f t s ’ ) ;
[ INT ] =HAEqualWidth ( T ) ;
%{
l o a d t h e mean t o t a l m a g n e t i c f l u x
d a t a . The m a t r i x h a s t h e d a t e t h e f i l e
was c r e a t e d and t h e mean t o t a l m a g n e t i c
flux .
%}
l o a d ( ’ M a g n e t i c f i e l d d a t a . mat ’ ) ;
%{
F i n d s t h e d a t e s t h a t a r e t h e same i n b o t h
INT and m a g n e t i c f i e l d d a t a and e x t r a c t s
them . HaMag now c o n t a i n s t h e d a t e e a c h f i l e
was c r e a t e d , t h e m a g n e t i c f i e l d d a t a , and t h e
E q u i v a l e n t Width d a t a .
%}
P = Mag ( : , 1 ) ;
Q=INT ( : , 1 ) ;
[C, ia , i b ]= i n t e r s e c t ( P ,Q ) ;
H a l i n e =INT ( i b , : ) ;
M a g n e t i c =Mag ( i a , : ) ;
36
HaMag = [C M a g n e t i c ( : , 2 ) H a l i n e ( : , 2 ) ] ;
%{
F i n d s t h e b e s t f i t l i n e , up t o d e g r e e 1 .
%}
p = p o l y f i t ( HaMag ( : , 2 ) , HaMag ( : , 3 ) , 1 ) ;
r = p ( 1 ) . ∗ HaMag ( : , 2 ) + p ( 2 ) ; %
m=p ( 1 ) %f i n d s t h e s l o p e o f t h e l i n e
h = figure
%{
P l o t s the Magnetic f i e l d d a t a in the
x−a x i s and t h e E q u i v a l e n t Width on t h e
y−a x i s . The L i n e o f b e s t f i t i s a l s o
plotted .
%}
s c a t t e r ( HaMag ( : , 2 ) , HaMag ( : , 3 ) , ’ k ’ ) ;
h o l d on ;
p l o t ( HaMag ( : , 2 ) , r , ’ k ’ ) ;
hold off ;
x l a b e l ( ’ F u l l D i s k Mean T o t a l M a g n e t i c F l u x ( g a u s s ) ’ )
y l a b e l ( ’ Ha 6 5 6 . 3 nm E q u i v a l e n t Width ( nm ) ’ )
ylim ( [ 0 . 1 1 4 0 . 1 1 8 ] )
box on
s a v e a s ( h , ’ Ha EW FDMTMF’ , ’ eps ’ )
HASpectrumIntensity.m
%{
Luis Contreras
This programs p l o t s the spectrums of
a l l t h e . f t s f i l e s i n a f o l d e r and S u p e r
i m p o s s e s them i n t o a s i n g l e f i g u r e
%}
f u n c t i o n [ T , X p o i n t s , Y p o i n t s ] = H A S p e c t r u m I n t e n s i t y ( dirName )
%{
Gets the d a t a f o r the c u r r e n t d i r e c t o r y
Find the index f o r d i r e c t o r i e s
37
Get a l i s t o f t h e f i l e s
find the s i z e of f i l e L i s t
f i n d s t h e number o f c o l u m n s i n f i l e L i s t
%}
d i r D a t a = d i r ( dirName ) ;
dirIndex = [ dirData . i s d i r ] ;
f i l e L i s t = { d i r D a t a ( ˜ d i r I n d e x ) . name } ’ ;
T=[];
A= 6 5 6 . 3 ;
L = size ( fileList );
L1 =L ( 1 ) ;
figure
%{
T h i s B e g i n s t h e l o o p by g e t t i n g t h e
j t h f i l e name , makes an e n t r y i n t h e
c e l l c h a r a c t e r , and t a k e s t h e w a v e l e n g t h ,W,
and t h e i n t e n i s t y , S I . I t t h e n s t o r e s them i n
T.
%}
f o r j = 1 : L1
L = fileList ( j );
S = char (L ) ;
I = fitsread (S );
W = I (1 ,:);
SI = I ( 2 , : ) ;
%{
F i n d s t h e minimum v a l u e and s h i f t s t h e
e n t i r e s p e c t r u m s o t h a t t h e min i s
always a t 8 5 4 . 2 . I t a l s o s e t t h e bounds of
integration .
%}
[X, Y] = min ( S I ) ;
Wmin = W(Y ) ;
dx = Wmin−A;
newW = W−dx ;
in =656.2;
fn =656.4;
%{
38
T h i s f i n d s and e x t r a c t s t h e w a v e l e n g t h and t h e
i n t e n s i t y i n between t h e l i m i t s i f i n t e g r a t i o n .
T s t o r e s t h e f i l e name , and t h e minimum p o i n t s .
%}
Y = f i n d (newW<=f n & newW>=i n ) ;
Y p o i n t s = S I (Y ) ;
X p o i n t s = newW(Y ) ;
[ X1 , Y1 ] = min ( Y p o i n t s ) ;
MinheY= Y p o i n t s ( Y1 ) ;
MinheX= X p o i n t s ( Y1 ) ;
T= [T ; L MinheX MinheY dx ] ;
%{
Plots the shited I n t e n s i t i e s
%}
p l o t (newW , S I )
hold a l l
end
%{
p l o t s t h e minimum p o i n t s
%}
T1= c e l l 2 m a t ( T ( : , 2 ) ) ;
T2 = c e l l 2 m a t ( T ( : , 3 ) ) ;
figure
s c a t t e r ( T1 , T2 ) ;
end
HAEqualWidth.m
%{
Luis Contreras
T h i s p r o g r a m c a l c u l a t e s t h e E q u i v a l e n t Width
o f HA s p e c t r a l l i n e when t h e
minima a r e n o t i n t h e same p l a n e .
%}
f u n c t i o n [ INT ] =HAEqualWidth ( T )
%{
S e t s a l l c o n s t a n t s and empty
matrices
%}
T=T ;
Wl = 0 ;
39
INT = [ ] ;
A= 6 5 6 . 3 ;
L = s i z e (T ) ;
L1 =L ( 1 ) ;
%{
T h i s b e g i n s t h e l o o p by g e t t i n g t h e
j t h f i l e name , makes an e n t r y i n t h e
c e l l c h a r a c t e r , and t a k e s t h e w a v e l e n g t h ,W,
and t h e i n t e n i s t y , S I . I t a l s o s h i f t s t h e
i n t e n s i t i t i e s s o t h a t t h e mins a r i n 6 5 6 . 3 .
%}
f o r i = 1 : L1
L = T( i , 1 ) ;
S= c h a r ( L ) ;
N=S ( 1 5 : 2 2 ) ;
y e a r = s t r 2 n u m (N ) ;
I = fitsread (S );
W = I (1 ,:);
SI = I ( 2 , : ) ;
[X, Y] = min ( S I ) ;
Wmin = W(Y ) ;
dx = Wmin−A;
newW = W−dx ;
%{
S e t s up t h e i n t e g r a l , i t d e n o t e s t h e l i m t s
of i n t e g r a t i o n f i n d s e x t r a c t s the e n t i r e
I n t e n s i t y v a l u e s in between t h o s e l i m i t s .
I t a l s o f i n d s dx .
%}
in =656.2;
fn =656.4;
Y = f i n d (newW<=f n & newW>=i n ) ;
Y p o i n t s = S I (Y ) ;
X p o i n t s = newW(Y ) ;
S = s i z e ( Ypoints ) ;
S1 = S ( 1 , 2 ) ;
Dl = ( fn−i n ) / S1 ;
j =1;
%{
Computes t h e E q u i v a l e n t Width o f e a c h
f i l e by i n t e g r a t i n g o v e r t h e I n t e n s i t y
u s i n g t h e f o r m u l a 1−F / F0 , where F0 i s
set to 1.
40
%}
w h i l e ( j <= S1 )
Wl = (1− Y p o i n t s ( j ) ) ∗ Dl+ Wl ;
j = j +1;
end
INT = [ INT ; y e a r Wl ] ;
Wl = 0 ;
end
41
Magnetic vs HeLine plot.m
%{
Luis Contreras
This program Takes t h e E q u i v a l e n t
Width o f H−a l p h a and t h e mean t o t a l
m a g n e t i c f l u x o f t h e s u n and p l o t s them
against eachother
%}
%{
The f u n c t i o n i m p o r t s t h e f i l e s
f o r He I and e x t r a c t s
t h e w a v e l e n g t h and i n t e n s i t y , c u m p u t e s
t h e E q u i v a l e n t Width .
INT c o n t a i n s t h e d a t e o f t h e f i l e and t h e
E q u i v a l e n t Width
%}
[ INT ] = HeEqualWidth ( ’HE / ∗ . f t s ’ ) ;
%{
l o a d t h e mean t o t a l m a g n e t i c f l u x
d a t a . The m a t r i x h a s t h e d a t e t h e f i l e
was c r e a t e d and t h e mean t o t a l m a g n e t i c
flux .
%}
l o a d ( ’ M a g n e t i c f i e l d d a t a . mat ’ ) ;
%{
F i n d s t h e d a t e s t h a t a r e t h e same i n b o t h
INT and m a g n e t i c f i e l d d a t a and e x t r a c t s
them . HEMag now c o n t a i n s t h e d a t e e a c h f i l e
was c r e a t e d , t h e m a g n e t i c f i e l d d a t a , and t h e
E q u i v a l e n t Width d a t a .
%}
P = Mag ( : , 1 ) ;
Q=INT ( : , 1 ) ;
[C, ia , i b ]= i n t e r s e c t ( P ,Q ) ;
H E l i n e =INT ( i b , : ) ;
M a g n e t i c =Mag ( i a , : ) ;
HEMag = [C M a g n e t i c ( : , 2 ) H E l i n e ( : , 2 ) ] ;
42
%{
F i n d s t h e b e s t f i t l i n e , up t o d e g r e e 1 .
%}
p = p o l y f i t ( HEMag ( : , 2 ) , HEMag ( : , 3 ) , 1 ) ;
r = p ( 1 ) . ∗ HEMag ( : , 2 ) + p ( 2 ) ; %
m=p ( 1 ) %f i n d s t h e s l o p e o f t h e l i n e
h= f i g u r e
%{
P l o t s the Magnetic f i e l d d a t a in the
x−a x i s and t h e E q u i v a l e n t Width on t h e
y−a x i s . The L i n e o f b e s t f i t i s a l s o
plotted .
%}
s c a t t e r ( HEMag ( : , 2 ) , HEMag ( : , 3 ) , ’ k ’ ) ;
h o l d on ;
p l o t ( HEMag ( : , 2 ) , r , ’ k ’ ) ;
hold off ;
x l a b e l ( ’ F u l l D i s k Mean T o t a l M a g n e t i c F l u x ( g a u s s ) ’ )
y l a b e l ( ’ He I 1 0 8 3 . 0 nm E q u i v a l e n t Width ( nm ) ’ )
ylim ( [ 0 0 . 0 1 5 ] )
box on
s a v e a s ( h , ’ HE EW FDMTMF’ , ’ eps ’ )
HeEqualWidth.m
%{
Luis Contreras
T h i s p r o g r a m c a l c u l a t e s t h e E q u i v a l e n t Width
o f HA s p e c t r a l l i n e when t h e
minima a r e n o t i n t h e same p l a n e .
%}
f u n c t i o n [ INT ] =HAEqualWidth ( T )
%{
S e t s a l l c o n s t a n t s and empty
matrices
43
%}
T=T ;
Wl = 0 ;
INT = [ ] ;
A= 6 5 6 . 3 ;
L = s i z e (T ) ;
L1 =L ( 1 ) ;
%{
T h i s b e g i n s t h e l o o p by g e t t i n g t h e
j t h f i l e name , makes an e n t r y i n t h e
c e l l c h a r a c t e r , and t a k e s t h e w a v e l e n g t h ,W,
and t h e i n t e n i s t y , S I . I t a l s o s h i f t s t h e
i n t e n s i t i t i e s s o t h a t t h e mins a r i n 6 5 6 . 3 .
%}
f o r i = 1 : L1
L = T( i , 1 ) ;
S= c h a r ( L ) ;
N=S ( 1 5 : 2 2 ) ;
y e a r = s t r 2 n u m (N ) ;
I = fitsread (S );
W = I (1 ,:);
SI = I ( 2 , : ) ;
[X, Y] = min ( S I ) ;
Wmin = W(Y ) ;
dx = Wmin−A;
newW = W−dx ;
%{
S e t s up t h e i n t e g r a l , i t d e n o t e s t h e l i m t s
of i n t e g r a t i o n f i n d s e x t r a c t s the e n t i r e
I n t e n s i t y v a l u e s in between t h o s e l i m i t s .
I t a l s o f i n d s dx .
%}
in =656.2;
fn =656.4;
Y = f i n d (newW<=f n & newW>=i n ) ;
Y p o i n t s = S I (Y ) ;
X p o i n t s = newW(Y ) ;
S = s i z e ( Ypoints ) ;
S1 = S ( 1 , 2 ) ;
Dl = ( fn−i n ) / S1 ;
j =1;
%{
44
Computes t h e E q u i v a l e n t Width o f e a c h
f i l e by i n t e g r a t i n g o v e r t h e I n t e n s i t y
u s i n g t h e f o r m u l a 1−F / F0 , where F0 i s
set to 1.
%}
w h i l e ( j <= S1 )
Wl = (1− Y p o i n t s ( j ) ) ∗ Dl+ Wl ;
j = j +1;
end
INT = [ INT ; y e a r Wl ] ;
Wl = 0 ;
end
45
Magnetic vs NaDILine plot.m
%{
Luis Contreras
This program Takes t h e E q u i v a l e n t
Width o f H−a l p h a and t h e mean t o t a l
m a g n e t i c f l u x o f t h e s u n and p l o t s them
against eachother .
%}
%{
The f i r s t f u n c t i o n i m p o r t s t h e f i l e s
f o r Na D I and e x t r a c t s
t h e w a v e l e n g t h and i n t e n s i t y . The s e c o n d
f u n c t i o n c u m p u t e s t h e E q u i v a l e n t Width .
INT c o n t a i n s t h e d a t e o f t h e f i l e and t h e
E q u i v a l e n t Width .
%}
[ T] = S p e c t r u m I n t e n s i t y ( ’ NaD / ∗ . f t s ’ ) ;
[ INT ] = NaDEqualWidth ( T ) ;
%{
l o a d t h e mean t o t a l m a g n e t i c f l u x
d a t a . The m a t r i x h a s t h e d a t e t h e f i l e
was c r e a t e d and t h e mean t o t a l m a g n e t i c
flux .
%}
l o a d ( ’ M a g n e t i c f i e l d d a t a . mat ’ ) ;
%{
F i n d s t h e d a t e s t h a t a r e t h e same i n b o t h
INT and m a g n e t i c f i e l d d a t a and e x t r a c t s
them . NaDMag now c o n t a i n s t h e d a t e e a c h f i l e
was c r e a t e d , t h e m a g n e t i c f i e l d d a t a , and t h e
E q u i v a l e n t Width d a t a .
%}
P = Mag ( : , 1 ) ;
Q=INT ( : , 1 ) ;
[C, ia , i b ]= i n t e r s e c t ( P ,Q ) ;
N a D l i n e =INT ( i b , : ) ;
M a g n e t i c =Mag ( i a , : ) ;
NaDMag = [C M a g n e t i c ( : , 2 ) N a D l i n e ( : , 2 ) ] ;
46
%{
F i n d s t h e b e s t f i t l i n e , up t o d e g r e e 1 .
%}
p = p o l y f i t ( NaDMag ( : , 2 ) , NaDMag ( : , 3 ) , 1 ) ;
r = p ( 1 ) . ∗ NaDMag ( : , 2 ) + p ( 2 ) ;
m = p (1)% f i n d s t h e s l o p e o f t h e l i n e
h = figure
%{
P l o t s the Magnetic f i e l d d a t a in the
x−a x i s and t h e E q u i v a l e n t Width on t h e
y−a x i s . The L i n e o f b e s t f i t i s a l s o
plotted .
%}
s c a t t e r ( NaDMag ( : , 2 ) , NaDMag ( : , 3 ) , ’ k ’ ) ;
h o l d on ;
p l o t ( NaDMag ( : , 2 ) , r , ’ k ’ ) ;
hold off ;
x l a b e l ( ’ F u l l D i s k Mean T o t a l M a g n e t i c F l u x ( g a u s s ) ’ )
y l a b e l ( ’ Na D 5 8 9 . 6 nm E q u i v a l e n t Width ( nm ) ’ )
box on
s a v e a s ( h , ’ NaD EW FDMTMF’ , ’ eps ’ )
SpectrumIntensity.m
%{
Luis Contreras
This programs p l o t s the spectrums of
a l l t h e . f t s f i l e s i n a f o l d e r and S u p e r
i m p o s s e s them i n t o a s i n g l e f i g u r e
%}
f u n c t i o n [ T] = S p e c t r u m I n t e n s i t y ( dirName )
%{
Gets the d a t a f o r the c u r r e n t d i r e c t o r y
Find the index f o r d i r e c t o r i e s
47
Get a l i s t o f t h e f i l e s
find the s i z e of f i l e L i s t
f i n d s t h e number o f c o l u m n s i n f i l e L i s t
%}
d i r D a t a = d i r ( dirName ) ;
dirIndex = [ dirData . i s d i r ] ;
f i l e L i s t = { d i r D a t a ( ˜ d i r I n d e x ) . name } ’
L = size ( fileList );
L1 =L ( 1 ) ;
T=[];
figure
%{
T h i s B e g i n s t h e l o o p by g e t t i n g t h e
j t h f i l e name , makes an e n t r y i n t h e
c e l l c h a r a c t e r , and t a k e s t h e w a v e l e n g t h ,W,
and t h e i n t e n i s t y , S I . I t t h e n s t o r e s them i n
T
%}
f o r j = 1 : L1
L = fileList ( j );
S = char (L ) ;
I = fitsread (S );
W = I (1 ,:);
SI = I ( 2 , : ) ;
T= [T ; L ] ;
%p l o t s W a v e l e n g t h v s S c a l e d I n t e n s i t y
p l o t (W, S I )
hold a l l
end
%{
r e p e a t s t h e p r o c e s s f o r a l l f i l e s on
the folder
%}
end
NADEqualWidth.m
%{
Luis Contreras
T h i s p r o g r a m c a l c u l a t e s t h e E q u i v a l e n t Width
48
o f Na D I s p e c t r a l l i n e when t h e
minima a r e n o t i n t h e same p l a n e .
%}
f u n c t i o n [ INT ] = NaDEqualWidth ( T )
%{
S e t s a l l c o n s t a n t s and empty
matrices
%}
T=T ;
Wl = 0 ;
INT = [ ] ;
L = s i z e (T ) ;
L1 =L ( 1 ) ;
%{
T h i s b e g i n s t h e l o o p by g e t t i n g t h e
j t h f i l e name , makes an e n t r y i n t h e
c e l l c h a r a c t e r , and t a k e s t h e w a v e l e n g t h ,W,
and t h e i n t e n i s t y , S I .
%}
f o r i = 1 : L1
L = T( i ) ;
S = char (L ) ;
N=S ( 1 5 : 2 2 ) ;
y e a r = s t r 2 n u m (N ) ;
I = fitsread (S );
W = I (1 ,:);
SI = I ( 2 , : ) ;
%{
S e t s up t h e i n t e g r a l , i t d e n o t e s t h e l i m t s
of i n t e g r a t i o n f i n d s e x t r a c t s the e n t i r e
I n t e n s i t y v a l u e s in between t h o s e l i m i t s .
I t a l s o f i n d s dx .
%}
in =589.5;
fn =589.7;
Y = f i n d (W<=f n & W>=i n ) ;
Y p o i n t s = S I (Y ) ;
X p o i n t s = W(Y ) ;
S = s i z e ( Ypoints ) ;
S1 = S ( 1 , 2 ) ;
49
Dl = ( fn−i n ) / S1 ;
j =1;
%{
Computes t h e E q u i v a l e n t Width o f e a c h
f i l e by i n t e g r a t i n g o v e r t h e I n t e n s i t y
u s i n g t h e f o r m u l a 1−F / F0 , where F0 i s
set to 1.
%}
w h i l e ( j <= S1 )
Wl = (1− Y p o i n t s ( j ) ) ∗ Dl+ Wl ;
j = j +1;
end
INT = [ INT ; y e a r Wl ] ;
Wl = 0 ;
end
end
50
Magnetic vs CaII Line plot.m
%{
Luis Contreras
This program Takes t h e E q u i v a l e n t
Width o f Ca I I K and t h e mean t o t a l
m a g n e t i c f l u x o f t h e s u n and p l o t s them
against eachother .
%}
%{
The f i r s t f u n c t i o n i m p o r t s t h e f i l e s
f o r Ca I I H and e x t r a c t s
t h e w a v e l e n g t h and i n t e n s i t y . The s e c o n d
f u n c t i o n c u m p u t e s t h e E q u i v a l e n t Width .
INT c o n t a i n s t h e d a t e o f t h e f i l e and t h e
E q u i v a l e n t Width .
%}
[ T] = S p e c t r u m I n t e n s i t y ( ’ C a I I H / ∗ . f t s ’ ) ;
[ INT ] = C a I I H E q u a l W i d t h ( T ) ;
%{
l o a d t h e mean t o t a l m a g n e t i c f l u x
d a t a . The m a t r i x h a s t h e d a t e t h e f i l e
was c r e a t e d and t h e mean t o t a l m a g n e t i c
flux .
%}
l o a d ( ’ M a g n e t i c f i e l d d a t a . mat ’ ) ;
%{
F i n d s t h e d a t e s t h a t a r e t h e same i n b o t h
INT and m a g n e t i c f i e l d d a t a and e x t r a c t s
them . CaIIHMag now c o n t a i n s t h e d a t e e a c h f i l e
was c r e a t e d , t h e m a g n e t i c f i e l d d a t a , and t h e
E q u i v a l e n t Width d a t a .
%}
P = Mag ( : , 1 ) ;
Q=INT ( : , 1 ) ;
[C, ia , i b ]= i n t e r s e c t ( P ,Q ) ;
C a I I H l i n e =INT ( i b , : ) ;
M a g n e t i c =Mag ( i a , : ) ;
51
CaIIHMag = [C M a g n e t i c ( : , 2 ) C a I I H l i n e ( : , 2 ) ] ;
%{
F i n d s t h e b e s t f i t l i n e , up t o d e g r e e 1 .
%}
p = p o l y f i t ( CaIIHMag ( : , 2 ) , CaIIHMag ( : , 3 ) , 1 ) ;
r = p ( 1 ) . ∗ CaIIHMag ( : , 2 ) + p ( 2 ) ;
m = p ( 1 ) %f i n d s t h e s l o p e o f t h e l i n e
h = figure
%{
P l o t s the Magnetic f i e l d d a t a in the
x−a x i s and t h e E q u i v a l e n t Width on t h e
y−a x i s . The L i n e o f b e s t f i t i s a l s o
plotted .
%}
s c a t t e r ( CaIIHMag ( : , 2 ) , CaIIHMag ( : , 3 ) , ’ k ’ ) ;
h o l d on ;
p l o t ( CaIIHMag ( : , 2 ) , r , ’ k ’ ) ;
hold off ;
x l a b e l ( ’ F u l l D i s k Mean T o t a l M a g n e t i c F l u x ( g a u s s ) ’ )
y l a b e l ( ’ Ca I I H 3 9 6 . 8 nm E q u i v a l e n t Width ( nm ) ’ )
ylim ( [ 0 . 0 9 0 4 0 . 0 9 1 4 ] )
box on
s a v e a s ( h , ’ CaIIH EW FDMTMF ’ , ’ eps ’ )
CaIISpectrumIntensity.m
%{
Luis Contreras
This programs p l o t s the spectrums of
a l l t h e . f t s f i l e s i n a f o l d e r and S u p e r
i m p o s s e s them i n t o a s i n g l e f i g u r e
%}
f u n c t i o n [ T , X p o i n t s , Y p o i n t s ] = C a I I S p e c t r u m I n t e n s i t y ( dirName )
%{
Gets the d a t a f o r the c u r r e n t d i r e c t o r y
52
Find the index f o r d i r e c t o r i e s
Get a l i s t o f t h e f i l e s
find the s i z e of f i l e L i s t
f i n d s t h e number o f c o l u m n s i n f i l e L i s t
%}
d i r D a t a = d i r ( dirName ) ;
dirIndex = [ dirData . i s d i r ] ;
f i l e L i s t = { d i r D a t a ( ˜ d i r I n d e x ) . name } ’ ;
T=[];
A= 8 5 4 . 2 ;
L = size ( fileList );
L1 =L ( 1 ) ;
figure
%{
T h i s b e g i n s t h e l o o p by g e t t i n g t h e
j t h f i l e name , makes an e n t r y i n t h e
c e l l c h a r a c t e r , and t a k e s t h e w a v e l e n g t h ,W,
and t h e i n t e n i s t y , S I . I t t h e n s t o r e s them i n
T.
%}
f o r j = 1 : L1
L = fileList ( j );
S = char (L ) ;
I = fitsread (S );
W = I (1 ,:);
SI = I ( 2 , : ) ;
%{
F i n d s t h e minimum v a l u e and s h i f t s t h e
e n t i r e s p e c t r u m s o t h a t t h e min i s
always a t 8 5 4 . 2 . I t a l s o s e t t h e bounds of
integration .
%}
[X, Y] = min ( S I ) ;
Wmin = W(Y ) ;
dx = Wmin−A;
newW = W−dx ;
in =854.1;
fn =854.3;
%{
53
T h i s f i n d s and e x t r a c t s t h e w a v e l e n g t h and t h e
i n t e n s i t y i n between t h e l i m i t s i f i n t e g r a t i o n .
T s t o r e s t h e f i l e name , and t h e minimum p o i n t s .
%}
Y = f i n d (newW<=f n & newW>=i n ) ;
Y p o i n t s = S I (Y ) ;
X p o i n t s = newW(Y ) ;
[ X1 , Y1 ] = min ( Y p o i n t s ) ;
MinheY= Y p o i n t s ( Y1 ) ;
MinheX= X p o i n t s ( Y1 ) ;
T= [T ; L MinheX MinheY dx ] ;
%{
Plots the shited I n t e n s i t i e s
%}
p l o t (newW , S I )
hold a l l
end
%{
p l o t s t h e minimum p o i n t s
%}
T1= c e l l 2 m a t ( T ( : , 2 ) ) ;
T2 = c e l l 2 m a t ( T ( : , 3 ) ) ;
figure
s c a t t e r ( T1 , T2 ) ;
end
CaIIEqualWidth.m
%{
Luis Contreras
%T h i s p r o g r a m c a l c u l a t e s t h e E q u i v a l e n t
Width o f Ca I I s p e c t r a l l i n e when t h e
minima a r e n o t i n t h e same p l a n e .
%}
f u n c t i o n [ INT ] = C a I I E q u a l W i d t h ( T )
%{
S e t s a l l c o n s t a n t s and empty
matrices
%}
T=T ;
Wl = 0 ;
INT = [ ] ;
54
A= 8 5 4 . 2 ;
L = s i z e (T ) ;
L1 =L ( 1 ) ;
%{
T h i s b e g i n s t h e l o o p by g e t t i n g t h e
j t h f i l e name , makes an e n t r y i n t h e
c e l l c h a r a c t e r , and t a k e s t h e w a v e l e n g t h ,W,
and t h e i n t e n i s t y , S I . I t a l s o s h i f t s t h e
i n t e n s i t i t i e s s o t h a t t h e mins a r i n 8 5 4 . 2 .
%}
f o r i = 1 : L1
L = T( i , 1 ) ;
S= c h a r ( L ) ;
N=S ( 1 5 : 2 2 ) ;
y e a r = s t r 2 n u m (N ) ;
I = fitsread (S );
W = I (1 ,:);
SI = I ( 2 , : ) ;
[X, Y] = min ( S I ) ;
Wmin = W(Y ) ;
dx = Wmin−A;
newW = W−dx ;
%{
S e t s up t h e i n t e g r a l , i t d e n o t e s t h e l i m t s
of i n t e g r a t i o n f i n d s e x t r a c t s the e n t i r e
I n t e n s i t y v a l u e s in between t h o s e l i m i t s .
I t a l s o f i n d s dx .
%}
in =854.1;
fn =854.3;
Y = f i n d (newW<=f n & newW>=i n ) ;
Y p o i n t s = S I (Y ) ;
X p o i n t s = newW(Y ) ;
S = s i z e ( Ypoints ) ;
S1 = S ( 1 , 2 ) ;
Dl = ( fn−i n ) / S1 ;
j =1;
%{
Computes t h e E q u i v a l e n t Width o f e a c h
f i l e by i n t e g r a t i n g o v e r t h e I n t e n s i t y
u s i n g t h e f o r m u l a 1−F / F0 , where F0 i s
set to 1.
%}
w h i l e ( j <= S1 )
55
Wl = (1− Y p o i n t s ( j ) ) ∗ Dl+ Wl ;
j = j +1;
end
INT = [ INT ; y e a r Wl ] ;
Wl = 0 ;
end
end
56
Magnetic vs CaIIH Line plot.m
%{
Luis Contreras
This program Takes t h e E q u i v a l e n t
Width o f Ca I I K and t h e mean t o t a l
m a g n e t i c f l u x o f t h e s u n and p l o t s them
against eachother .
%}
%{
The f i r s t f u n c t i o n i m p o r t s t h e f i l e s
f o r Ca I I H and e x t r a c t s
t h e w a v e l e n g t h and i n t e n s i t y . The s e c o n d
f u n c t i o n c u m p u t e s t h e E q u i v a l e n t Width .
INT c o n t a i n s t h e d a t e o f t h e f i l e and t h e
E q u i v a l e n t Width .
%}
[ T] = S p e c t r u m I n t e n s i t y ( ’ C a I I H / ∗ . f t s ’ ) ;
[ INT ] = C a I I H E q u a l W i d t h ( T ) ;
%{
l o a d t h e mean t o t a l m a g n e t i c f l u x
d a t a . The m a t r i x h a s t h e d a t e t h e f i l e
was c r e a t e d and t h e mean t o t a l m a g n e t i c
flux .
%}
l o a d ( ’ M a g n e t i c f i e l d d a t a . mat ’ ) ;
%{
F i n d s t h e d a t e s t h a t a r e t h e same i n b o t h
INT and m a g n e t i c f i e l d d a t a and e x t r a c t s
them . CaIIHMag now c o n t a i n s t h e d a t e e a c h f i l e
was c r e a t e d , t h e m a g n e t i c f i e l d d a t a , and t h e
E q u i v a l e n t Width d a t a .
%}
P = Mag ( : , 1 ) ;
Q=INT ( : , 1 ) ;
[C, ia , i b ]= i n t e r s e c t ( P ,Q ) ;
C a I I H l i n e =INT ( i b , : ) ;
M a g n e t i c =Mag ( i a , : ) ;
57
CaIIHMag = [C M a g n e t i c ( : , 2 ) C a I I H l i n e ( : , 2 ) ] ;
%{
F i n d s t h e b e s t f i t l i n e , up t o d e g r e e 1 .
%}
p = p o l y f i t ( CaIIHMag ( : , 2 ) , CaIIHMag ( : , 3 ) , 1 ) ;
r = p ( 1 ) . ∗ CaIIHMag ( : , 2 ) + p ( 2 ) ;
m = p ( 1 ) %f i n d s t h e s l o p e o f t h e l i n e
h = figure
%{
P l o t s the Magnetic f i e l d d a t a in the
x−a x i s and t h e E q u i v a l e n t Width on t h e
y−a x i s . The L i n e o f b e s t f i t i s a l s o
plotted .
%}
s c a t t e r ( CaIIHMag ( : , 2 ) , CaIIHMag ( : , 3 ) , ’ k ’ ) ;
h o l d on ;
p l o t ( CaIIHMag ( : , 2 ) , r , ’ k ’ ) ;
hold off ;
x l a b e l ( ’ F u l l D i s k Mean T o t a l M a g n e t i c F l u x ( g a u s s ) ’ )
y l a b e l ( ’ Ca I I H 3 9 6 . 8 nm E q u i v a l e n t Width ( nm ) ’ )
ylim ( [ 0 . 0 9 0 4 0 . 0 9 1 4 ] )
box on
s a v e a s ( h , ’ CaIIH EW FDMTMF ’ , ’ eps ’ )
SpectrumIntensity.m
%{
Luis Contreras
This programs p l o t s the spectrums of
a l l t h e . f t s f i l e s i n a f o l d e r and S u p e r
i m p o s s e s them i n t o a s i n g l e f i g u r e
%}
f u n c t i o n [ T] = S p e c t r u m I n t e n s i t y ( dirName )
58
%{
Gets the d a t a f o r the c u r r e n t d i r e c t o r y
Find the index f o r d i r e c t o r i e s
Get a l i s t o f t h e f i l e s
find the s i z e of f i l e L i s t
f i n d s t h e number o f c o l u m n s i n f i l e L i s t
%}
d i r D a t a = d i r ( dirName ) ;
dirIndex = [ dirData . i s d i r ] ;
f i l e L i s t = { d i r D a t a ( ˜ d i r I n d e x ) . name } ’
L = size ( fileList );
L1 =L ( 1 ) ;
T=[];
figure
%{
T h i s B e g i n s t h e l o o p by g e t t i n g t h e
j t h f i l e name , makes an e n t r y i n t h e
c e l l c h a r a c t e r , and t a k e s t h e w a v e l e n g t h ,W,
and t h e i n t e n i s t y , S I . I t t h e n s t o r e s them i n
T
%}
f o r j = 1 : L1
L = fileList ( j );
S = char (L ) ;
I = fitsread (S );
W = I (1 ,:);
SI = I ( 2 , : ) ;
T= [T ; L ] ;
%p l o t s W a v e l e n g t h v s S c a l e d I n t e n s i t y
p l o t (W, S I )
hold a l l
end
%{
r e p e a t s t h e p r o c e s s f o r a l l f i l e s on
the folder
%}
end
59
CaII HEqualWidth
%{
Luis Contreras
T h i s p r o g r a m c a l c u l a t e s t h e E q u i v a l e n t Width
o f Ca I I H s p e c t r a l l i n e when t h e
minima a r e n o t i n t h e same p l a n e .
%}
f u n c t i o n [ INT ] = C a I I H E q u a l W i d t h ( T )
%{
S e t s a l l c o n s t a n t s and empty
matrices
%}
T=T ;
Wl = 0 ;
INT = [ ] ;
L = s i z e (T ) ;
L1 =L ( 1 ) ;
%{
T h i s b e g i n s t h e l o o p by g e t t i n g t h e
j t h f i l e name , makes an e n t r y i n t h e
c e l l c h a r a c t e r , and t a k e s t h e w a v e l e n g t h ,W,
and t h e i n t e n i s t y , S I .
%}
f o r i = 1 : L1
L = T( i ) ;
S = char (L ) ;
N=S ( 1 5 : 2 2 ) ;
y e a r = s t r 2 n u m (N ) ;
I = fitsread (S );
W = I (1 ,:);
SI = I ( 2 , : ) ;
%{
S e t s up t h e i n t e g r a l , i t d e n o t e s t h e l i m t s
of i n t e g r a t i o n f i n d s e x t r a c t s the e n t i r e
I n t e n s i t y v a l u e s in between t h o s e l i m i t s .
I t a l s o f i n d s dx .
%}
in =396.8;
fn =396.9;
Y = f i n d (W<=f n & W>=i n ) ;
Y p o i n t s = S I (Y ) ;
X p o i n t s = W(Y ) ;
60
S = s i z e ( Ypoints ) ;
S1 = S ( 1 , 2 ) ;
Dl = ( fn−i n ) / S1 ;
j =1;
%{
Computes t h e E q u i v a l e n t Width o f e a c h
f i l e by i n t e g r a t i n g o v e r t h e I n t e n s i t y
u s i n g t h e f o r m u l a 1−F / F0 , where F0 i s
set to 1.
%}
w h i l e ( j <= S1 )
Wl = (1− Y p o i n t s ( j ) ) ∗ Dl+ Wl ;
j = j +1;
end
INT = [ INT ; y e a r Wl ] ;
Wl = 0 ;
end
end
61
Magnetic vs CaII Kline plot.m
%{
Luis Contreras
This program Takes t h e E q u i v a l e n t
Width o f H−a l p h a and t h e mean t o t a l
m a g n e t i c f l u x o f t h e s u n and p l o t s them
against eachother .
%}
%{
The f i r s t f u n c t i o n i m p o r t s t h e f i l e s
f o r Ca I I K and e x t r a c t s
t h e w a v e l e n g t h and i n t e n s i t y . The s e c o n d
f u n c t i o n c u m p u t e s t h e E q u i v a l e n t Width .
INT c o n t a i n s t h e d a t e o f t h e f i l e and t h e
E q u i v a l e n t Width .
%}
[ T] = S p e c t r u m I n t e n s i t y ( ’ C a I I K / ∗ . f t s ’ ) ;
[ INT ] = C a I I K E q u a l W i d t h ( T ) ;
%{
l o a d t h e mean t o t a l m a g n e t i c f l u x
d a t a . The m a t r i x h a s t h e d a t e t h e f i l e
was c r e a t e d and t h e mean t o t a l m a g n e t i c
flux .
%}
l o a d ( ’ M a g n e t i c f i e l d d a t a . mat ’ ) ;
%{
F i n d s t h e d a t e s t h a t a r e t h e same i n b o t h
INT and m a g n e t i c f i e l d d a t a and e x t r a c t s
them . CaII KMag now c o n t a i n s t h e d a t e e a c h f i l e
was c r e a t e d , t h e m a g n e t i c f i e l d d a t a , and t h e
E q u i v a l e n t Width d a t a .
%}
P = Mag ( : , 1 ) ;
Q=INT ( : , 1 ) ;
[C, ia , i b ]= i n t e r s e c t ( P ,Q ) ;
C a I I K l i n e =INT ( i b , : ) ;
M a g n e t i c =Mag ( i a , : ) ;
CaII KMag = [C M a g n e t i c ( : , 2 ) C a I I K l i n e ( : , 2 ) ] ;
62
%{
F i n d s t h e b e s t f i t l i n e , up t o d e g r e e 1 .
%}
p = p o l y f i t ( CaII KMag ( : , 2 ) , CaII KMag ( : , 3 ) , 1 ) ;
r = p ( 1 ) . ∗ CaII KMag ( : , 2 ) + p ( 2 ) ;
m=p ( 1 ) %f i n d s t h e s l o p e o f t h e l i n e
h= f i g u r e
%{
P l o t s the Magnetic f i e l d d a t a in the
x−a x i s and t h e E q u i v a l e n t Width on t h e
y−a x i s . The L i n e o f b e s t f i t i s a l s o
plotted .
%}
s c a t t e r ( CaII KMag ( : , 2 ) , CaII KMag ( : , 3 ) , ’ k ’ ) ;
h o l d on ;
p l o t ( CaII KMag ( : , 2 ) , r , ’ k ’ ) ;
hold off ;
x l a b e l ( ’ F u l l D i s k Mean T o t a l M a g n e t i c F l u x ( g a u s s ) ’ )
y l a b e l ( ’ Ca I I K 3 9 3 . 4 nm E q u i v a l e n t Width ( nm ) ’ )
ylim ( [ 0 . 0 8 1 2 0 . 0 8 2 4 ] )
box on
s a v e a s ( h , ’ CaIIK EW FDMTMF ’ , ’ eps ’ )
SpectrumIntensity.m
%{
Luis Contreras
This programs p l o t s the spectrums of
a l l t h e . f t s f i l e s i n a f o l d e r and S u p e r
i m p o s s e s them i n t o a s i n g l e f i g u r e
%}
f u n c t i o n [ T] = S p e c t r u m I n t e n s i t y ( dirName )
63
%{
Gets the d a t a f o r the c u r r e n t d i r e c t o r y
Find the index f o r d i r e c t o r i e s
Get a l i s t o f t h e f i l e s
find the s i z e of f i l e L i s t
f i n d s t h e number o f c o l u m n s i n f i l e L i s t
%}
d i r D a t a = d i r ( dirName ) ;
dirIndex = [ dirData . i s d i r ] ;
f i l e L i s t = { d i r D a t a ( ˜ d i r I n d e x ) . name } ’
L = size ( fileList );
L1 =L ( 1 ) ;
T=[];
figure
%{
T h i s B e g i n s t h e l o o p by g e t t i n g t h e
j t h f i l e name , makes an e n t r y i n t h e
c e l l c h a r a c t e r , and t a k e s t h e w a v e l e n g t h ,W,
and t h e i n t e n i s t y , S I . I t t h e n s t o r e s them i n
T
%}
f o r j = 1 : L1
L = fileList ( j );
S = char (L ) ;
I = fitsread (S );
W = I (1 ,:);
SI = I ( 2 , : ) ;
T= [T ; L ] ;
%p l o t s W a v e l e n g t h v s S c a l e d I n t e n s i t y
p l o t (W, S I )
hold a l l
end
%{
r e p e a t s t h e p r o c e s s f o r a l l f i l e s on
the folder
%}
end
64
CaII KEqualWidth.m
%{
Luis Contreras
This program c a l c u l a t e s t h e
E q u i v a l e n t Width o f Ca I I K
spectral line .
%}
f u n c t i o n [ INT ] = C a I I K E q u a l W i d t h ( T )
%{
S e t s a l l c o n s t a n t s and empty
matrices
%}
T=T ;
Wl = 0 ;
INT = [ ] ;
L = s i z e (T ) ;
L1 =L ( 1 ) ;
%{
T h i s b e g i n s t h e l o o p by g e t t i n g t h e
j t h f i l e name , makes an e n t r y i n t h e
c e l l c h a r a c t e r , and t a k e s t h e w a v e l e n g t h ,W,
and t h e i n t e n i s t y , S I .
%}
f o r i = 1 : L1
L = T( i ) ;
S = char (L ) ;
N=S ( 1 5 : 2 2 ) ;
y e a r = s t r 2 n u m (N ) ;
I = fitsread (S );
W = I (1 ,:);
SI = I ( 2 , : ) ;
%{
S e t s up t h e i n t e g r a l , i t d e n o t e s t h e l i m t s
of i n t e g r a t i o n f i n d s e x t r a c t s the e n t i r e
I n t e n s i t y v a l u e s in between t h o s e l i m i t s .
I t a l s o f i n d s dx .
%}
in =393.32;
fn =393.41;
65
Y = f i n d (W<=f n & W>=i n ) ;
Y p o i n t s = S I (Y ) ;
X p o i n t s = W(Y ) ;
S = s i z e ( Ypoints ) ;
S1 = S ( 1 , 2 ) ;
Dl = ( fn−i n ) / S1 ;
j =1;
%{
Computes t h e E q u i v a l e n t Width o f e a c h
f i l e by i n t e g r a t i n g o v e r t h e I n t e n s i t y
u s i n g t h e f o r m u l a 1−F / F0 , where F0 i s
set to 1.
%}
w h i l e ( j <= S1 )
Wl = (1− Y p o i n t s ( j ) ) ∗ Dl+ Wl ;
j = j +1;
end
INT = [ INT ; y e a r Wl ] ;
Wl = 0 ;
end
end
66
wc10830vsMPSI.m
%{
T h i s c o d e p l o t s t h e E q u i v a l e n t Width (EW) o f
Helium computed by l i v i n g s t o n
a g a i n s t the Magnetic Plage S t r e n g t h
I n d e x ( MPSI ) and t h e Mount W i l s o n
S u n s p o t I n d e x (MWSI) o b t a i n e d from
Mount WIlson .
%}
%{
l o a d s t h e d a t a o f t h e E q u i v a l e n t Width
computed by l i v i n g s t o n and t h e MPSI
and MWSI d a t a c o r r e c t e d from j u l i a n
date to gregorian date .
%}
l o a d ( ’ f d 1 0 8 3 0 . mat ’ )
l o a d ( ’ M P S I Y e a r s h o r t . mat ’ )
h = f i g u r e ( ’ P o s i t i o n ’ , [100 , 100 , 900 , 3 0 0 ] ) ;
%{
C r e a t e s t h e b e s t f i t l i n e f o r t h e EW and MPSI
%}
p = p o l y f i t ( MPSIYear ( : , 2 ) , f d 1 0 8 3 0 ( : , 2 ) , 1 ) ;
r = p ( 1 ) . ∗ MPSIYear ( : , 2 ) + p ( 2 ) ;
p (1)
%{
P l o t s t h e E u i v a l e n t Width o f Helium
p l o t t e d a g a i n s t t h e MPSI
%}
s c a t t e r ( MPSIYear ( : , 2 ) , f d 1 0 8 3 0 ( : , 2 ) , ’ k ’ )
h o l d on
p l o t ( MPSIYear ( : , 2 ) , r , ’ k ’ ) ;
ylim ([ 3 0 100])
x l a b e l ( ’ Magnetic Plage S t r e n g t h Index ’ )
y l a b e l ( ’ E q u i v a l e n t h Width He 10830 (mA) ’ )
box on
s a v e a s ( h , ’ He MPSI ’ , ’ eps ’ )
67
g = f i g u r e ( ’ P o s i t i o n ’ , [100 , 100 , 900 , 3 0 0 ] ) ;
%{
Creates the best f i t
%}
l i n e f o r t h e EW and MWSI
p = p o l y f i t ( MPSIYear ( : , 3 ) , f d 1 0 8 3 0 ( : , 2 ) , 1 ) ;
r = p ( 1 ) . ∗ MPSIYear ( : , 3 ) + p ( 2 ) ;
p (1) % finds the slope
%{
P l o t s t h e E u i v a l e n t Width o f Helium p l o t t e d
a g a i n s t t h e MWSI
%}
s c a t t e r ( MPSIYear ( : , 3 ) , f d 1 0 8 3 0 ( : , 2 ) , ’ k ’ )
h o l d on
p l o t ( MPSIYear ( : , 3 ) , r , ’ k ’ ) ;
x l a b e l ( ’ Mount W i l s o n Sun S p o t I n d e x ’ )
y l a b e l ( ’ E q u i v a l e n t h Width He 10830 (mA) ’ )
ylim ([ 3 0 100])
box on
s a v e a s ( g , ’ He MWSI ’ , ’ eps ’ )
68
fd1vsMPSI.m
%{
T h i s c o d e p l o t s t h e E q u i v a l e n t Width (EW)
o f Ca I I K computed by l i v i n g s t o n
a g a i n s t the Magnetic Plage S t r e n g t h
I n d e x ( MPSI ) and t h e Mount W i l s o n
S u n s p o t I n d e x (MWSI) o b t a i n e d from
Mount WIlson .
%}
%{
l o a d s t h e d a t a o f t h e E q u i v a l e n t Width
computed by l i v i n g s t o n and t h e MPSI
and MWSI d a t a c o r r e c t e d from j u l i a n
date to gregorian date .
%}
l o a d ( ’ f d 1 k i n d e x . mat ’ )
l o a d ( ’ MPSI19701912 . mat ’ )
%{
F i n d t h e d a t e s t h a t a r e t h e same i n
both matrices . I t then find the values
t h a t c o i n c i d e s i n b o t h t h e EW i n Ca I I K
m a t r i x and t h e Moount WIlson I n d e x
Data Matrix . F I n a l l y t h o s e v a l u e s
a r e s t o r e d i n t h e kindexKMag M a t r i x .
%}
P = MPSI19701912 ( : , 1 ) ;
Q= f d 1 k i n d e x ( : , 1 ) ;
[C, ia , i b ]= i n t e r s e c t ( P ,Q ) ;
k i n d e x l i n e = fd1kindex ( ib , : ) ;
M a g n e t i c =MPSI19701912 ( i a , : ) ;
kindexKMag = [C M a g n e t i c ( : , 2 ) M a g n e t i c ( : , 3 )
kindexline ( : , 2 ) ] ;
%{
C r e a t e s t h e b e s t f i t l i n e f o r t h e EW and MPSI
%}
p = p o l y f i t ( kindexKMag ( : , 2 ) , kindexKMag ( : , 4 ) , 1 ) ;
r = p ( 1 ) . ∗ kindexKMag ( : , 2 ) + p ( 2 ) ;
69
p ( 1 ) %f i n d s t h e s l o p e
h = f i g u r e ( ’ P o s i t i o n ’ , [100 , 100 , 900 , 3 0 0 ] ) ;
%{
P l o t s t h e E u i v a l e n t Width o f Ca I I K p l o t t e d
a g a i n s t t h e MPSI
%}
s c a t t e r ( kindexKMag ( : , 2 ) , kindexKMag ( : , 4 ) , ’ k ’ ) ;
h o l d on
p l o t ( kindexKMag ( : , 2 ) , r , ’ k ’ ) ;
x l a b e l ( ’ Magnetic Plage S t r e n g t h Index ’ ) ;
y l a b e l ( ’ Ca I I K F u l l D i s k I n d e x ’ ) ;
box on ;
hold off
s a v e a s ( h , ’ CaII K MPSI ’ , ’ eps ’ )
%{
C r e a t e s t h e b e s t f i t l i n e f o r t h e EW and MWSI
%}
p = p o l y f i t ( kindexKMag ( : , 3 ) , kindexKMag ( : , 4 ) , 1 ) ;
r = p ( 1 ) . ∗ kindexKMag ( : , 3 ) + p ( 2 ) ;
p (1)
g = f i g u r e ( ’ P o s i t i o n ’ , [100 , 100 , 900 , 3 0 0 ] ) ;
%{
P l o t s t h e E u i v a l e n t Width o f Helium p l o t t e d
a g a i n s t t h e MWSI
%}
s c a t t e r ( kindexKMag ( : , 3 ) , kindexKMag ( : , 4 ) , ’ k ’ )
h o l d on
p l o t ( kindexKMag ( : , 3 ) , r , ’ k ’ ) ;
x l a b e l ( ’ Mount W i l s o n Sun S p o t I n d e x ’ )
y l a b e l ( ’ Ca I I K F u l l D i s k I n d e x ’ )
box on ;
s a v e a s ( g , ’ CaII K MWSI ’ , ’ eps ’ )
70