CALIFORNIA STATE UNIVERSITY, NORTHRIDGE
PHOTOMETRIC ANALYSIS OF THE ENERGY·
BALANCE IN A SOLAR ACTIVE REGION
A thesis submitted in partial satisfaction of the
requirements for the degree of Master of Science in
Physics
by
Carolyn Rankin Mallory
January
1985
The thesis of Carolyn R. Mallory is approved:
(Advisor:
(Cha:ii1Il:
Dr. ~n)
California State University, Northridge
ii
TABLE OF CONTENTS
Page
APPROVAL PAGE . .
ii
TABLE OF CONTENTS .
.
LIST OF TABLES
.
. iii
iv
LIST OF FIGURES •
v
ABSTRACT
vi
CHAPTER
I
II
III
IV
INTRODUCTION
1
INSTRUMENTATION AND METHOD OF
OBSERVATION • . . . . • . . .
11
PROGRAM AND METHOD OF DATA ANALYSIS .
19
RESULTS
34
V CONCLUSIONS .
53
REFERENCES
55
iii
LIST OF TABLES
Table
Page
Computer Runs of Reticon Digital
Images for BBSO 18474 • • •
. 35
2
Irradiance Fluctuations from Pixel
Contrasts Determined from First Order
Pixel Identification Scheme . . . • • . . • 37
3
Irradiance Fluctuations from Statistical
Analysis of Histograms of the Pixel
Intensity Distribution . . • • • • . . • • • 38
4
Comparison of Average Sunspot Deficits
from Histogram Analysis and Pixel
Intensity Sums . • . • • • • . . • • . • • • 40
5
Comparison of Average Facular Excesses
from Histogram Analysis and Pixel
Intensity Sums • • • • • . • • • .
• . • 41
6
Comparison of the Average Total
Irradiance Fluctuations [0-C] from
Histogram Analysis and Pixel Intensity
Sums . .
.
. .
.
. . .
. .
.
. .
. . .
. . . 42
7
Calculated Photometric Sunspot Index
(PSI) and Photometric Facular Index
(PFI)
. • . • . • • • . • • • • • • • . 45
8
Comparison of Irradiance Fluctuations
from Diode Array Photometry to PSI
and PFI
9
. . . . . . . . . . . . . . . . . . 46
Calculated Photometric Total Index (PTI)
and Total Irradiance Fluctuations from
Diode Array Photometry [0-C] • • • • • • • . 47
iv
LIST OF FIGURES
Figure
2
Page
Solar Structure . . . . • .
2
Active Region Lifetime Spot and
Plage Development • . . • .
9
3
SFO Reticon Observing Equipment .
14
4
Backside SFO Observing Equipment
17
5
SFO Computer Room . . . . • .
6
Photograph from TV Monitor of
Active Region on 11 July 1982 .
22
7
SFO Tape Conversion Flow Chart
23
8
Calibrated Pixel Plot of Active
Region on 11 July 1982 . . . . .
25
9
Limb Darkening Curve for Active
Region on 11 July 1982 . . . . .
26
Plot of Active Region on 11 July 1982
After Program Identification of
Spot and Plage Areas . . .
30
Plot of [0-C] vs
Spot Deficit vs
51
10
11
.....
20
and Plot of
v
ABSTRACT
PHOTOMETRIC ANALYSIS OF THE ENERGY
BALANCE IN A SOLAR ACTIVE REGION
by
Carolyn Rankin Mallory
Master of Science in Physics
ABSTRACT
Monochromatic data obtained with photodiodes are
presented for the July 1982 disk transit of a medium-young
solar active region.
Extreme care was taken to accurately
determine both facular and spot areas and intensities.
Through the use of equations
fluctuations
relating
to energy changes,
luminosity
the relation between
facular excesses and sunspot deficits was determined.
average sunspot fluctuation,
as a fraction of the quiet
sun luminosity, is -622 parts per million.
Faculae have
an average luminosity fluctuation of +91
million.
The
parts per
The facular energy excess is approximately 14
percent of the sunspot energy deficit.
These data
combined with data for later solar disk transits of the
same active region show that facular energy excesses
vi
increase during the active region lifetime and may,
through some combination of temporary storage and
reradiation,
completely balance energy loss due to
sunspots.
vii
CHAPTER I
INTRODUCTION
The passage of an active region across the solar disk
has been found to affect the sun's total irradiance.
Following an active region appearance,
space-borne
measurements with the Solar Maximum Mission Active Cavity
Radiation Irradiance Monitor (ACRIM) recorded a maximum
fluctuation in irradiance of 0.14% from mean to peak
(Willson, 1981).
Nimbus-6 satellite observations of
decreased irradiance have been positively correlated with
sunspot activity (Foukal and Vernazza, 1979).
The Earth
Radiation Budget exp.eriment aboard the Nimbus-7 satellite
has revealed fluctuations in the solar constant of more
than 0.1% (Hickey, et al.,
1980).
Hudson et al. (1982)
have positively correlated these fluctuations with the
passage of sunspots across the solar disk.
Various attempts have been made (Oster et al.,
1982;
Sofia et al., 1982) to model sunspots and faculae in order
to predict irradiance changes.
Active region models, based
on knowledge of solar structure, attempt to answer the
questions, "In response to an active region's appearance,
how much will the sun's irradiance change, and for how
long?."
Figure 1 presents a structural diagram of the sun.
Different physical processes affecting energy transport
occur in different layers of the sun (Mitton,
1981).
Active regions arise in the photosphere, at the top of the
2
.2 <INTERMEDIATE
ZONE
7 radius
<.
• 7 <. CONVECTION
ZONE < 1. 0 radius
::=:::==::::::::::::::!flpPJHKOTOSPHERE ( 500 KM)
(SUPERADIABATIC REGION)
CHROMOSPHERE
Figure 1.
Solar Structure
3
convection zone.
convection
Strong vertical magnetic fields
zone may serve as
(Biermann, 1941).
in the
the base of sunspots
Knobloch and Weiss (1984) confirm that
overall magnetic fields are coherent within the flux tube
underneath a sunspot.
Noncoherent magnetic fields that
rise due to magnetic bouyancy are postulated to cause
plage, which is seen in the chromosphere.
Chromospheric
plages are coarser and higher lying than faculae.
They
have greater contrast and are more extensive (Eddy, 1983).
Calcium plage areas can be used as a substitute for facular
areas in modeling (Hirayama et al., 1983; Chapman,
Chapman and Lawrence,
1983).
1981;
Faculae often appear
surrounding sunspots and above the photosphere.
Individual
facular granules are small, and it is difficult to resolve
them adequately for a real determination of the specific
intensity (Hirayama,
Okamoto and Hudson,
1983).
In
addition to the difficulty of detection due to small size,
faculae have lower contrast than spots and larger area
(Chapman, 1983).
Foukal (1983) has recently proposed that
faculae have a lower temperature gradient near solar center
than previously thought.
The extent of luminosity change accompanying the
appearance of faculae and spots may depend on the depth and
extent of magnetic perturbations (Hartmann, Londono and
Phillips, 1979).
Calculations indicate that the presence
of many small-scale magnetic flux tubes will decrease
4
efficiency of convection (Peckover and Weiss, 1978).
The result of magnetic perturbation is decreased
convective heat flow to sunspots.
Magnetic inhibition of
completion of the cycle in convection cells is responsible.
This causes a reduction from the normal photospheric
temperature of approximately 6000 °K to a sunspot umbral
temperature of approximately 4000 °K.
There are several
possible ways to account for the missing sunspot energy.
They include:
1 . Direct extraction of energy
2. Immediate local reradiation of blocked flux
3. Immediate global reradiation of blocked flux
4. Long term storage and reradiation of blocked flux.
These are characterized by time scales ranging from several
5
days to 10 years (Newkirk, 1983).
Luminosity is defined as the integral of the radiant
energy of the sun over all angles and frequencies.
Answering the question, "Where is the missing flux?", will
answer the question,
"What
is
happening
to
sol:ar
irradiance?", and therefore to total solar luminosity.
Based on what is known from gas turbulence theory,
only two mechanisms seem logical for direct extraction of
energy from sunspot areas.
The first, adiabatic cooling of
expanding gases, has been effectively ruled out by the
detection of photospheric granulation.
convection
zone
produces
changes
Convection in the
in the adjacent
5
photosphere which are seen as granulation.
Granulation has
been observed in sunspot umbrae (Rosch, 1956; Knobloch and
Weiss, 1984), thus proving that convection in sunspots is
not prevented,
only severely inhibited.
The second
mechanism for direct extraction of energy is cooling caused
by Alfven waves
(Parker,
1974).
If Alfven waves were
generated at the sunspot, they could radiate out into the
corona or be reflected downward into
layers.
d~eper
subphotospheric
Observations have indicated that the inhibition of
convection by sunspots may vary in depth depending on the
depth of the base of the spot.
In order for direct
extraction of energy by Alfven waves to obtain, it would be
necessary that inhibition of convection be limited to a
thin layer of photosphere.
This is contrary to solar
observations (Knobloch and Weiss, 1984).
Detection of immediate local reradiation of blocked
flux has been diligently pursued.
model in which blocked flux
Spruit (1977) proposed a
is accounted for by the
appearance within five days after spot emergence of a
"bright ring."
The "bright ring" appears because the
insulated cylindrical base of a sunspot,
the isolated top
of a magnetic flux tube, is hotter than the surrounding
material.
The maximum "bright ring" flux found so far is
only 0.1 to 0.3% of the spot loss (Foukal, 1983).
Thus, it
does not provide enough flux to make up for the sunspot
deficit.
However, "bright ring" emission plus one or more
6
other methods of reradiation might account for enough
flux.
In an active region model proposed by Hudson and
Willson (1981), it was found that the inclusion of a global
reradiation factor actually decreased the goodness of fit
between the model and 276 days of ACRIM data.
Investigation is proceeding on the fourth mechanism
postulated
to
account
for
missing flux.
Several
investigators do support this idea (Foukal, Fowler and
Livshits,
1983; Fowler, Foukal and Duvall, 1983; Spruit,
1982; Hudson and Wilson, 1981).
If long term storage and
reradiation does account for blocked sunspot flux,
results would occur.
The Solar Constant,
two
total solar
irradiance received per second on a one square meter area
at the top of the earth's atmosphere when the earth is 1 AU
from the sun, would vary.
Second, solar luminosity, total
radiant energy emitted per second in all directions, would
vary.
The storage hypothesis may be tested by measuring
the solar constant over a full solar cycle.
If the
hypothesis is true, the solar constant should be highest
when the number of sunspots is lowest, and conversely the
solar constant should be minimized when solar activity is
maximized.
Continuing experimental work will verify or
discredit the storage hypothesis based on whether an eleven
year modulation of solar luminosity or only solar
irradiance is found to occur (Eddy, 1983).
7
The possibility exists of missing sunspot flux
remaining in or near the related active region and being
reradiated within the active region lifetime.
In this
situation, solar luminosity would remain unchanged over the
timespan of an active region lifetime,
constant would vary.
but the solar
This hypothesis is experimentally
verifiable and has been investigated by Sofia, Oster and
Schatten,
1982; Lawrence, Chapman, Herzog and Shelton,
1983; Newkirk, 1983; and others.
In this model it is
postulated that facular emission is responsible for
reradiation of blocked sunspot flux.
It is thus vitally
important to be able to detect (low contrast) faculae and
accurately assess the area they cover and their flux.
Faculae have routinely been detected from photographic
records.
Because of their low photospheric contrast, this
is not a very reliable method, and poor area accuracy has
had negative effects on experiment validity (Sofia et al.,
1982; Hoyt and Eddy,
and Lawrence, 1984).
1983; Willson, 1981; Chapman, Herzog
Eddy (1983) comments in a discussion
regarding the Solar Constant that facular areas are
particularly poorly known, with estimates differing by an
order of magnitude.
To accomplish accurate sunspot and facular area and
contrast assessment, a solid state imaging system capable
of performing two-dimensional photometric photometry was
developed at San Fernando Observatory.
This equipment
---·
8
greatly improves the identification of facular active
regions (Hinnrichs, 1981).
Complexes of solar activity form within one month,
typically endure for 3 to 6 solar rotations, and are
maintained by fresh injections of magnetic flux.
The total
magnetic flux within a complex keeps steady within a factor
of two.
At the end of the active lifetime, most of the
magnetic flux in the complex may disappear in less than one
rotation, and principally in situ (Gaizauskas, Harvey,
Harvey and Zwaan,
1983).
This suggests that the energy
balance of an active region will not be evident from one
rotation of the complex, but that the entire lifetime of
the active region must be considered.
This viewpoint is
essential for measuring energy balance between sunspot
deficit and facular excess since there is a delay of some
days between the maximum area of the sunspots and the
maximum area of the faculae (Chapman,
1984).
Hirayama,
Okamoto and Hudson (1983) have presented data showing that
the development of plage lags spot development, but that
plage lingers after spot disappearance.
(See Figure 2).
The object of this thesis is to investigate the energy
balance of BBSO 18474 during its July 1982 solar disk
transit.
Other investigators have determined the energy
balance for
this same region during the August and
September disk transits.
Most of the data were obtained at
San Fernando Observatory using photoelectric photometry.
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Figure 2.
Active Region Lifetime Spot and Plage Development
1..0
10
This work is part of an ongoing project at San Fernando
Observatory to investigate the energy balance in solar
active regions.
CHAPTER II
INSTRUMENTATION AND METHOD OF OBSERVATION
The San Fernando Observatory (SFO) is located in the
northern portion of the San Fernando Valley.
is equipped with a 61
The facility
em vacuum telescope,
a
28
em
auxiliary vacuum telescope attached to the 61 em system, a
two-channel vacuum spectroheliograph equipped with 512
channel Reticon S-series linear diode array detectors,
various solar flare patrol telescopes and assorted computer
hardware.
The observatory was originally constructed by
the Aerospace Corporation of El Segundo in 1969, and was
donated to CSUN in 1976.
SFO has a good national and
international reputation both because of the quality of its
solar
observations
and willingness
to share these
observations with other institutions needing data.
Particularly noteworthy are the full disk photographs,
Extreme
Limb
Photometry
data,
and
active
region
photoelectric data.
SFO observations are of high quality because of the
excellent seeing conditions and lack of thunderstorms
during the summer observing season.
Then the sun is at its
highest elevation and therefore observations are taken
through the least atmosphere possible.
Days are longest
then, and data sets are very complete because of the many
hours available for viewing.
There are several ways to approach the determination
11
12
of solar brightness excesses or deficits associated with
faculae and sunspots.
One obvious approach is white light
photography of the full disk.
For quantitative analysis
photographic film itself limits accuracy because of short
dynamic range of response to different intensities, and
non-linearity
of
film
response
intensities film responds to.
much less
over the range of
The dynamic range of film is
than that of the photodiode array,
and in
addition, photodiodes have a linear response function.
Non-uniformities across film images make it very difficult
to pick out plage areas, particularly since their contrast
with the disk is quite low.
Photographic methods would
have required subjective identification of facular granules
(Klabunde, 1981).
Extreme Limb Photometry is limited to moderate spatial
resolution attainable by the large size of the entrance
slit to the Extreme Limb Photometer (ELP)
(Meyer,
1983).
Resolution is typically about 3" parallel to the limb and
38" perpendicular to the limb (Chapman, 1984).
Faculae are emphasized at the limb (Klabunde, 1981)
and spots near disk center.
This is
a result of limb
darkening, producing higher faculae contrast at the limb
and maximum spot contrast at disk center.
The ELP is best
suited to observe the net emission from sunspots and
faculae near the solar limb.
It is desirable to use a sampling technique with both
13
good radial and azimuthal data gathering ability.
Performing full disk photometry,
the ACRIM experiment
aboard the Solar Maximum Satellite gathers
information.
Irradiance equals solar energy/m
irradiance
2
received at
the top of the earth's atmosphere per second.
photometry has
been used
to
SFO ELP
interpret SMM/ACRIM
observations of solar irradiance variations in terms of
solar luminosity (Chapman, 1984).
Data for this thesis were gathered using a linear
diode array positioned at the exit slit of a vacuum
spectroheliograph and tuned to a spectral bandpass of 1.5A
centered at 6264A.
This is a continuum region clear of
absorption lines
in the photospheric and the sunspot
spectrum.
The spectroheliograph was
telescope.
The telescope
convective turbulence
fed by the 28 em
is evacuated to eliminate
along
the
optical path.
A
spectroheliograph is specifically designed to take solar
photographs
in a narrow wavelength range,
monochromatic data (Mitton,
Diode array was
1981).
placed over one
spectroheliograph.
yielding
The Reticon Series S
exit s l i t of
the
All of this equipment as well as the
A/D converter and Varian 620i's which the Reticon signal is
fed to, plus the equipment set up, is shown in Figure 3.
Photoelectric equipment and diode arrays particularly
have electronic and response characteristics well suited to
this application.
Diode arrays
have high spatial
0 .
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15
resolution and the spectroheliograph has high spectral
resolution.
The spatial resolution of the SFO Reticon
system is slightly better than one arc second, which is
comparable to that achieved by using photographic film
(Hinnrichs, 1981).
Reticon response is nearly linear,
so
if the data analysis program were set up to include data
from different wavelengths, it could be done accurately and
compared between wavelengths.
Diodes have a large dynamic
range:
the Reticon S Series detector used at SFO has a
4
dynamic range up to 1 0 : 1 •
The elements used in the
Reticon S series of photodiodes are silicon, and silicon
has excellent response over the range from 300 nm to 1100
nm.
The linear array is composed of 512 photodiode
elements.
These elements are read out at approximately
five scan lines of 512 pixels per second (Chapman, 1983).
At this speed they possess a dynamic range of about 3000:1
3
with a signal to noise ratio of about 10 .
Scan speed is
one of the major factors which controls resolution.
Electrical frequency response will determine the maximum
rate at which data can be gathered.
The optics and the
size and number of detecting elements determine spatial
frequency response.
The actual method of observation with the 28 em,
evacuated, coude focus-type, optical path is as follows:
the telescope is focused by putting the image of the sun's
limb on the edge of the telescope viewing field.
The
16
telescope is focused onto the spectroheliograph.
then goes
The light
through the entrance slit and down into the
approximately three meter long spectroheliograph.
At the
bottom of the spectroheliograph is a diffraction grating,
which breaks up the incident light by wavelengths.
The
light returns through the spectroheliograph to the two exit
slits.
One exit slit is set to a width of 1.5A to isolate
6264A continuum radiation.
The Reticon detector and
associated electronics are mounted above the exit slit.
The amplified analog signal is fed to an A/D converter with
the digital signal fed directly to a Varian 620i computer
and stored on magnetic tape.
focus,
When the telescope is in
the spectroheliograph is focused visually.
telescope focus
The
is re-adjusted by observing the sharpness
of the observed limb displayed on an oscilloscope.
Figure
4 shows the back side of the observing equipment and the
oscilloscope which is used to focus the solar limb.
To
produce
a
two-dimensional
image,
the
spectroheliograph entrance slit, which is oriented parallel
to solar east-west, is scanned across the active region to
make a square 512 x 512 picture.
The spectroheliograph
entrance slit motion and the diode detector read-out are
synchronized.
The resulting 512 x 512 image has a pixel
spacing of 0.94 arc seconds in both the north-south and the
east-west direction and a practical
approximately 2 arc-sec.
resolution of
The diode scanning procedure
17
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18
takes approximately 104 seconds to perform.
Several scans
of active regions were performed each day, weather and sky
conditions permitting.
followed
during full
Several active regions were
disk transit,
appearance to west limb disappearance.
from east limb
CHAPTER III
PROGRAM AND METHOD OF DATA ANALYSIS
San Fernando Observatory obtained photoelectric data
of solar active regions in the form of photodiode images of
portions of the
solar disk.
The
area covered
is
approximately 480 x 480 arc seconds on the solar disk
observed in the monochromatic continuum at 6264A selected
by the vacuum spectroheliogrpah.
Two-dimensional digital
data are produced by placing a 512 channel diode array at
the exit slit of the spectroheliograph and scanning the
slit
across
the
active
region.
The
approximately 105 seconds to accomplish.
scan
takes
Both a constant
scan speed rate and a stable diode clock are critically
important
during
the
scan.
Also,
the atmospheric
transmission should be fairly steady.
The current from each reticon channel was sent through
a current-to-voltage converter and then amplified.
The
resulting analog voltage was sent to a 12 bit A/D converter
and then to a Varian 620i computer, both located in the
telescope observing room.
The output tape from the Varian
620i was transferred to a computer room located at the
observatory.
The computer room is shown in Figure 5.
It
contains another Varian 620i, a Pertec 9 track magnetic
tape drive, a Pertec 7 track tape drive for creation of
edited copy tapes, a Quantex digital image processor, a
Tektronix computer terminal, disk drives and TV equipment
19
20
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.
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il
21
necessary to view Reticon images of solar active regions.
Figure 6 is a photograph taken from the SFO computer room
TV monitor of AR 18474, 11 July 1982 image.
Figure 7 shows the steps in tape conversion from the
SFO raw diode output tape to the first order calibrated
files stored on hard disk in the Cyber 750.
The steps in
tape conversion have been taken to achieve four ends:
obtain compatability between computers, dark and gain
calibrate files to first order,
reduce the amount of
computer storage space used, and to edit the raw data.
Before they can be used,
the raw data must first be
corrected for differing responses of the individual array
diodes.
This calibration is done by the use of dark and
bright calibration scans performed at SFO at the time of
original recording of data.
A ten record dark scan is
taken by closing the spectroheliograph shutter.
The dark
signal recorded is the result of thermal noise of the
diodes.
All 512 diodes are dark-scanned ten times.
The
other calibration file that must be gathered, also at SFO
at the time data are taken,
calibration.
center,
is
the gain (or bright),
This is performed by scanning the solar disk
if and only if no active region is at disk center
at that time.
This scan is also taken ten times per each
Reticon diode channel.
The telescope is run out of focus
to blur solar granulation.
In addition,
the
image is
mechanically scanned across the reticon to further cancel
.
22
z
uJ
Figure 6.
Photograph from TV Monitor of
Active Region on 11 July 1982
--23
SFO TAPE CONVERSION FLOW CHART
ORIGINAL
RAH DATA BOO BPI
(BINARY)
9 TRACK
SFO
COPY & EDIT
7 TRACK
BINARY
I
I
I
CAMPUS
CSUN
I
"'
RSTS
PDP 11/ 70I
7 TRACK
9 TRACK
PDP 11/ 70I
I
( :-~i::erent
·,·:or-j S1zes)
~
9T/1600 BPI (Extra Zeros)
!
X Tape (Takes out 2 Zero Per Word)
j,
MAGNET Unpacks Data, Sguare
r-------..,
Averages So 51 2 x 512 Becomes
256 x 256. (First Order Calibration
CYBER
has been performed)
170/750
9T/1600 BPI
Ready For Use
CYBER
DISK
DRIVES
Calibrated Files
Data available for use by
Magnet/ Integrator, etc.
To TRS for Library Storage
Figure 7.
SFO Tape Conversion Flow Chart
24
solar structure.
Performing this operation at disk center
provides each Reticon channel with a photon source of the
same intensity and spectral composition as
center, which it is.
the sun's
It also circumvents the effects of
limb darkening insofar as possible.
To take out diode
response variation, diode by diode,
this normalization
formula is applied:
I
(0-D)/(G-D)
I
0
measured intensity
G
Gain, or bright photodiode signal
normalization factor
X
200
= observed photodiode signal
D = dark photodiode signal
200
The factor of 200 is used because the solar center is
arbitrarily normalized to 200.
This gain calibration is
done during the data transfer from SFO to the CSUN Cyber
750.
Figure 8 shows a "Calcomp" plot of AR 18474 on 11
July 1982.
of the
The plot was perfonned by the MAGNET subsection
data
analysis
program after
dark and gain
calibrations were performed on the raw data.
Next,
limb darkening must be removed in order to
search for activity.
darkening curve.
Figure 9 displays a typical limb
This curve is for 11 July 1982 and was
plotted by the data analysis program utilized to calculate
energy balance for active region 18474.
Even on the
flattest part of the curve toward solar disk center,
determination of position is critical to subsequent
accuracy of numeric calculations.
As can be seen from
25
I
~~~ R8 l<GU U ;l
rv, A · · 1-- r·. y
II.
LL_._ r\.
\1;
~O•UC\tl
'.h.l\.1
:!~f·
ll'l~iRY"l
r.;_~~c:~
-
IS
d
r:;J .. t:O ru:. lttc~
•.u.rtr::tt. ,. : •!..t..
. •J
- 10
f'~.·
I
~
i vt
tt£CAI IV(
Figure 8.
Calibrated Pixel Plot of Active
Region on 11 July 1982
26
::......
I
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
I
'
l
'
I
'
'
0
I'
I'
i'
i'
I
I
'
l'
'
0
I'
''
I
'
'
I'
'
... . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
N
I
.......
i:
co
Ol
i
'
' ............................ !''
1--------------!
I
~
Q
0
0
0
0
0
0
0
..
7
- ~
:::
-£
-~
N
•
I
:
i
:
I! -------:---- .. -
I --------------!
!
!'
:
!
--------------~
!
l'
:
!
z
z
•
0
0
4
-
.
c
u
s...
0
4-
QJ
--------------·i
i
--------------!
''
'
------------- ---------------''
::
QJ
>
.,....
~
i
''
''
''
C'l
QJ
<
I
~-~
%
!i.
0:
:
%
0
0
.,....
i
~
s::
·•
'''
!
................................................................l
0
4
0
0
(r------- ---------------:
.
...
...
~
s::
>
s...
:::5
u
r:::n
s::
.,....
s::
QJ
~
s...
<l;l
Cl
..0
.....E
!
______________ !0
0
.....1
m
QJ
s...
:::5
r:::n
.,....
I..L.
27
Figure 9, knowledge of exact position becomes increasingly
critical the closer to the limb the data are taken because
the
intensity gradient is
large.
First order
limb
darkening effects may be removed from solar data by the use
of the Pierce and Slaughter (1977) limb darkening equation,
which is:
ID
where fo
=
A + By- + C)A
= cos
e
2
+ DJ-l
3
+ EjJ-
4
+ F)-l S
the heliocentric angle, A through F are
wavelength dependent coefficients, and ID = unsmeared limb
darkening intensity observed above the earth's atmosphere.
Using an iterative approach, it is possible to compare the
observed and theoretical limb darkening to find the best
solution for the image's exact solar disk location.
When
the best fit center is found, new coefficients, A through
F,
can be computed
to
compensate
for
atmospheric
scattering.
For images containing the limb, centers can be found
by a fit-to-observed limb routine, which by a least squares
process performed up to 50 times fits the observed limb to
a theoretical limb curve and thereby determines the center
exactly.
data,
If no limb is included in a particular set of
the program employs an iterative technique based on
taking five test locations for the solar disk center and
numerically finding the location which minimizes the
residuals ·between the limb darkening law and observed
photospheric pixels.
Both the least squares fit to the
28
observed limb and the iterative fit to the limb darkening
function require a first approximation for the location of
the disk center relative to
the
image.
The
first
approximation to the center is found by the use of the Mt.
Wilson sunspot maps.
Using these an estimate is made of
the location of the solar disk center in pixel coordinates.
The limb finder program subsection tells whether an east or
west limb is included in the data by whether the maximum
data gradient is positive or negative.
It does so by
making a list of pixel addresses with maximum gradients
which are presumed to be on the limb.
It then gives this
information to the subroutine Center, which has a least
squares subroutine in it and has stored the published
Ephemeris solar radius for that day.
The Center subroutine
both calculates residuals and the correct scan rate of the
spectroheliograph.
the data,
In the case when no limb is included in
the accuracy of the estimated sun center is
lessened as is evident from a plot of a photospheric scan
corrected for the assumed limb darkening.
If the center is
off, this calibrated curve will have a positive or negative
slope,
instead
of
zero slope
as
i t _should.
By
automatically minimizing the resultant slopes it is
possible to compute the exact disk center provided the
initial estimate is not too far off.
The second major part of the data analysis program is
active region identification.
Once the effects of limb
29
darkening are removed from the image, a 'flat' photosphere
is available
present.
to compare to active and quiet regions
Pixels
approximately
1.25% above mean
photospheric level and approximately 1.75% below mean
photospheric level are binned as belonging to facular and
spot regions, respectively.
Figure 10 is a plot of spot
and facular areas generated after this technique has been
applied to calibrated, limb-darkening removed data for
active region 18474 on 11 July 1982.
The pixel identification scheme is not able to
identify low contrast facular pixels.
To overcome this
problem a statistical approach is employed.
The brightness
distribution for limb-darkening-corrected data can be
represented by an intensity histogram of all the observed
intensities in an image.
Such a histogram contains both
photospheric data and active region data.
A second
histogram can be produced by selecting only data from the
quiet photosphere.
The first histogram,
containing
photosphere plus active pixels, may be compared to the
second,
completely quiet photosphere histogram.
The
difference between the intensity histogram for the entire
image and the quiet photospheric histogram is directly
proportional to any solar activity present in the image
provided that the two histograms are properly normalized
before subtraction.
Both histograms are modelled by skewed
gaussian curves given by:
30
•:
., .
~ :-·
:~~~r-
. . .lihU'
- -:--- .•
t:--fH-·
~·r. •.
·::f.
-!
:ll. __
a;·.: __ ~ ,.!~:l'lr--- ~
-T-~ ~lU
1 ... 1
ol
·~- _;__,
•;:pf ~~m----~IL
• .. '
---i-~i---ttt:--:
......... _;___.__ _
i •:i
~WI
d'fHiiii~
&
-
I
:-- j
L:J
--=i-l
•
.... "'""
11111111111
!+-j
----'.. 7:
'
-~--~~··
-~__..:::__j-:~--~-t~
------· .
t-~
~
--
I
-"'--...!1"-~~-------~------!-~--
I
' '
-~~
-·: .
: f-i
+-
,.
·,
'
--- ('
! :-· ..
~- !-"""!
--:--:
__
·--~~J-_L j
--- :----~
::--111+-----~~-- _ _ _ _,...L --i-----td!"uw..::::...·--"'--:!i"-::!~..--.ffll!~----.,:._...____
--.-J"'---_j_ ' - - - - -
Figure 10.
-
-~-1
-·t-·--~
Plot of Active Region on 11 July 1982
After Program Identification of Spot
and Plage Areas
.
'i
.
·---
31
2
N (I)= A [1 +~(I-a)] e-(I-a) /b
where N (I)
2
member pixels of intensity I
b = distribution width
~
skewness
I = intensity
a = shift in distribution
The difference between the total image and quiet region
skewed Gaussian distribution, showing number of pixels of
each intensity can be used to calculate how many pixels are
above the quiet photosphere,
i.e., contribute facular
excess, or below the quiet photosphere,
spot deficit.
i.e., contribute
The method to obtain these values relies on
finding the exact shape of both distributions using the
moments of the pixel observed number distribution, given
by:
~
S'
00
where
~
0
J-ln
JJ"o
In N (I) d I
--40
= N = Ab~ = number of pixels in
distribution,
= initial number and moment 1
a + 1/2 ~ b2
m1 = ~~
a 2 +a~b 2 +
m2 = P-:~
fta
~!>
rn3 = .)J.Q
The
a
3
+ 3/2 a
2
b
shift in distribution
1/2 b
2
2
+ 3/2 ab
II
a II
2
+
3/4~
b
4
can be determined by
judicious combination of the moment equations to give:
3
~
- 6m
a~
+ 6m 1
2
a + m - 3m m = 0
1 2
3
1
and the distribution width "b 11 can be computed from:
2a
32
\\
II
and the skewness ~ can be computed from:
~ = 2/b 2 (rn-a)
[Herzog et al., 1983].
Both the entire region histogram and the quiet photospheric
histogram are normalized so that
~
0 , the initial number,
is equal to the total number of pixels in the entire image.
By computing the relative shifts between the active and
quiet peaks, the quiet histogram can be subtracted from the
entire region, and the remaining residual is due to active
region pixels.
The normalized first moment of this
residual distribution is
deficit.
the observed flux excess or
Contribution from spots and faculae can be
computed by normalizing
the
peaks
of
the
active
distribution to the same level as the peak of the active
distribution before subtracting.
In principle, taking the
normalized moment between - oo and Intensity of the
photosphere gives
contribution),
the spot contribution,
(deficit
while the normalized moment between
Intensity of the photosphere and +00 gives the facular
contribution,
1983].
(excess contribution).
[Herzog et al.,
In practice, since the quiet region is a subset of
the entire image, there is a large negative excursion in
the subtracted histogram at the photospheric intensity if
the quiet histogram is normalized to the number of pixels
in the entire image.
For this reason, the normalization is
changed to produce the same maxima in both distributions
Q '
33
when the integrals are over spot and facular contributions
only.
Therefore,
the spot and facular contributions
computed by the histogram method are on a slightly
different normalization than the total observed computed
deficit or excess due to solar activity computed by the
histogram technique.
CHAPTER IV
RESULTS
The active region numbered 18474 by Big Bear Solar
Observatory traversed the solar disk between 8 July and 21
July 1982.
This was its second transit and it appears to
have had a
lifetime of at least four transits
sunspots).
The first transit, commencing 12 June and
disappearing
on 23 June;
second,
as above;
(with
third,
beginning 3 August and disappearing 16 August; and, fourth
transit beginning 30 August and ending 12 September, 1982.
Data in this thesis for the second transit are analyzed to
determine spot and facular energy deficits and excesses.
The results thus reflect the energy balance of a young to
medium-young active region.
Table 1 lists the data during transit and number and
recording time of files
for which data were obtained,
using the Reticon Series S photodiode array in conjunction
with the vacuum spectroheliograph and the 28 em vacuum
telescope.
Useable data were obtained for 11 days of the
14 day transit.
Using the mathematical techniques outlined in Chapter
III of this thesis, photodiode data were calibrated to
remove variations caused by unequal response of individual
diodes, and effects of sky transparency changes.
these
first
order
corrections
were
photospheric intensity was determined.
34
made,
After
a mean
Diode array images
35
TABLE 1:
Date
Computer Runs of Reticon Digital Images
for BBSO 18474
File #
July 8
Universal Time
ELP data used
July 9
2
3
4
5
6
21:04
21:12
21:20
22:02
22:10
July 10
1
2
3
5
21:09
21:21
21:55
22:32
July 11
1
2
3
4
5
18:19
18:49
19:18
19:29
19:39
July 13
2
4
22:19
22:58
July 14
1
2
20:58
21:16
July 16
1
7
21:07
21:44
July 17
1
23:37
July 18
1
2
19:03
19:06
July 19
1
7
21:49
24:12
July 20
1
5
9
19:16
19:47
20:14
July 21
ELP data used
36
were compared pixel by pixel to the calibrated mean
photospheric pixels and a determination was made as to
whether the examined pixel was spot, facular or quiet
photosphere.
Any pixel approximately 1.25% brighter than
the calibrated photosphere was classified a facular pixel;
any pixel approximately 1.75% below the calibrated
photosphere was classified a spot pixel.
The asymmetric
percent limits for facular and spot pixel identification
reflect the fact that faculae,
identify due
being more difficult to
to their lower contrast,
must have an
identification limit closer to quiet photospheric values.
The quantity [0-C], observed minus
'clean' photosphere,
represents the net flux change due to the active region.
The data analysis program computes the theoretical quiet
sun flux at a particular heliocentric angle using a
limb-darkened photosphere.
The difference between the
observed photosphere and the calculated clean photosphere,
corrected for limb darkening, at the same angle results in
a value for net flux change due to the active region at
that angle on the solar disk.
Table 2 presents the spot
deficits, facular excesses and net observed-minus-clean
irradiance data resulting from application of this
technique.
Table 3 also presents spot,
facular and net
irradiance fluctuations, but based on using the histogram
approach.
Histogram analysis is a statistical method that
improves identification of data on the low and high side
37
TABLE 2:
Irradiance Fluctuations From Pixel Contrasts Determined
From First Order Pixel Identification (All region 18474)
Date
File ( UT)
July 8
(ELP data)
July 9
2
3
4
5
6
21:04
21:12
21:20
22:02
22:10
July 10
1
2
3
5
July 11
1
2
3
4
5
0-C
(ppm)
Spot Deficit
(ppm)
Facular Excess
(ppm)
- 62.25
23.55
-222.92
-243.19
-213.69
-253.96
-155.83
-301.09
-314.66
-308.99
-336.51
-309.15
78.17
71.47
95.30
82.55
153.32
21:09
21:21
21:55
22:32
-690.45
-763.30
-670.99
-678.50
-813.89
-865.78
-786.29
-855.54
123.44
102.48
115.30
207.04
18:19
18:49
19:18
19:29
19:39
-1007.68
-868.80
-932.03
-926.27
-774.99
-1098.69
-1043.36
-1076.16
-1048.62
-975.69
91.01
174.56
144.13
122.35
200.70
July 13
2 22:19
4 22:58
-1167.01
-1159.81
-1240.01
-1291.86
73.00
132.05
July 14
1 20:58
2 21:16
-574.39
-1421.20
-721.32
-1426.24
146.93
5.04
July 16
1 21:07
7 21:44
-1122.23
-1315.33
-1176.81
-1455.61
54.58
140.28
July 17
1 23:37
-854.07
-926.16
72.09
July 18
1 19:03
2 19:06
-737.36
-402.63
-784.27
-491.13
46.91
88.50
July 19
1 21:49
7 24:12
-57.81
-44.13
-273.44
-213.57
215.63
169.44
July 20
1 19:16
5 19:47
9 20:14
-99.82
-24.42
-65.38
-218.90
-196.90
-208.32
119.08
172.48
142.94
July 21
( ELP data)
-4.4
102.45
38
TABLE 3:
Date
Irradiance Fluctuations From Statistical Analysis
of Histograms of the Pixel Intensity Distribution
File (UT)
0-C
(ppm)
Spot Deficit
(ppm)
Facular Excess
(ppm)
July 8
July 9
2
3
4
5
6
21:04
21:12
21:20
22:02
22:10
-10.73
-5.65
9.48
-13.18
-2.68
-29.24
-5.86
-36.18
-24.73
-65.49
15.76
-2.24
22.35
7.60
53.85
July 10
1
2
3
5
21:09
21:21
21:55
22:32
-798.79
-824.82
-777.17
-828.47
-818.20
-836.62
-792.87
-856.04
22.23
13.68
20.10
38.84
July 11
1
2
3
4
5
18:19
18:49
19:18
19:29
19:39
-939.12
-885.43
-921.72
-957.36
-741.87
-992.83
-1006.82
-1002.35
-1036.01
-864.73
56.83
79.16
61.44
73.88
105.42
July 13
2 22:19
4 22:58
-914.46
-1076.36
-1128.42
-1144.45
213.24
45.25
July 14
1 20:58
2 21:16
-706.83
-1399.91
-1081.60
-1370.52
358.00
5.25
July 16
1 21:07
7 21:44
-855.38
-1161.15
-874.98
-1190.10
20.13
14.26
July 17
1 23:37
-e14.31
-721.02
-8.40
July 18
1 19:03
2 19:06
-656.06
-395.37
-656.64
-441.89
13.22
53.16
July 19
1 21:49
7 24:12
-63.73
-22.71
-232.94
-128.78
169.15
103.07
July 20
1 19:16
5 19:47
9 20:14
-118.61
-112.02
-107.03
-119.51
-111.41
-126.48
-12.57
.86
19.89
July 21
@ '
39
of a distribution.
By binning together pixels of similar
intensity, histogram analysis offers improved ability to
identify low contrast faculae.
Table 4 compares the
average spot deficit as determined by histogram to the
average spot deficit as determined by pixel, and Table 5
does also for facular excesses.
fluctuation,
The total irradiance
[0-C], as obtained from histogram analysis
and from pixel analysis is compared in Table 6.
All data presented so far,
from histogram analysis
and from pixel analysis, have been fairly consistent
within the limitations of each technique; within each set
of data,
and between the sets of data.
All of these
figures are read directly off the data analysis program
output,
and are not hand calculated,
except for the
standard deviations of the mean.
The primary purpose of this thesis is to determine
the energy balance between facular emission and sunspot
deficit for the passage of a medium-young active region
across the solar disk.
Irradiance fluctuations may be
directly determined by the techniques already described of
comparing 'clean' photosphere with observed photosphere.
These techniques measure small variations
brightness.
in pixel
Small contrast features may be missed by
relying solely on continuum photometry.
Therefore, we
will consider photometric indices based on calcium plage
and sunspot areas.
,,
40
TABLE 4:
Comparison of Average Sunspot Deficits From
Histogram Analysis and Pixel Intensity Sums
Date (a 11 18474)
Histogram
Histogram
Spot Deficit Std. Dev.
(ppm)
of the Mean
July 8
Pixel
Spot
Deficit
(ppm)
Pi xe 1 Std.
Dev. of the
Mean
-62.25
July 9
-32.3
9.64
-314.08
5.97
July 10
-825.93
13.45
-837.87
22.88
July 11
-980.55
29.65
-1048.50
20.62
July 13
-1136.44
8.09
-1265.93
26.18
July 14
-1226.06
145.92
-1073.78
356.03
July 16
-1032.54
159.15
-1316.21
140.81
July 17
-721.02
July 18
-549.27
108.59
-637.7
148.05
July 19
-180.86
52.53
-243.50
30.23
July 20
-119.13
4.35
-208.04
6.35
July 21
-926.16
-4.4
'
41
TABLE 5:
Comparison of Average Facular Excesses From
Histogram Analysis and Pixel Intensity Sums
Date
(region 18474)
Histogram
Facular
Excess
Histogram
Std. Dev. of
the Mean
July 8
Pixel
Facular
Excess
Pixel
Std. Dev. of
the Mean
23.55
July 9
20.36
8.99
July 10
23.71
5.35
137.06
23.72
July 11
75.34
8.48
146.54
19.10
July 13
129.24
84.84
102.52
29.82
July 14
181.62
178.16
75.98
71.66
2.96
97.43
43.28
96.162
14.71
July 16
17.195
July 17
-8.40
July 18
33.19
20.17
67.70
21.00
July 19
136.11
33.37
192.53
23.32
July 20
11.10
5.64
144.83
15.73
July 21
72.09
102.45
-42
TABLE 6:
Date
Comparison of the Average Total Irradiance Fluctuations
0-C From Histogram Analysis and Pixel Intensity Sums
Histogram
0-C
His to gram
Std. Dev.
of the Mean
Pixel
0-C
Pi xe 1 Std.
Dev. of the
Mean
1.8
-217.91
16.97
July 8
July 9
-8.34
July 10
-807.31
12.02
-700.81
21.21
July 11
-889.1
38.43
-901.95
38.42
July 13
-995.41
88.06
-1163.41
3.63
July 14
-1053.37
350.05
-997.79
427.70
July 16
-1008.26
154.43
-1218.78
97.53
July 17
-814.31
July 18
-525.71
131. 66
-569.99
169.06
July 19
-43.22
20.71
-50.97
6.90
July 20
-112.55
3.35
-63.20
22.20
July 21
-854.07
-43
The angle of viewing between active region surface
and the earth-bound observer needs
to be represented in
calculations of irradiance fluctuation.
The 'Hot Wall'
facular model proposes that most of the facular contrast
is due to the deeper, hotter parts of the photosphere
shining through low density magnetic flux tubes.
Faculae
become visible only as the flux tube moves toward the
limb, exposing the
'hot wall' (Klabunde, 1981).
Results
obtained by Chapman, Herzog, Lawrence and Shelton,
1984,
clearly indicate that faculae have their most significant
contribution
to
total
irradiance
heliocentric angles ranging from
fluctuation
goo < 8 <53o.
at
The
photometric sunspot index (PSI) formula (Hudson, 1981) and
the photometric facular index (PFI) formula (Chapman and
Meyer, 1983) both include the heliocentric angle.
PSI and
PFI use the area of sunspots and plage, respectively, and
thus
convert
fluctuations.
active
region
areas
to
irradiance
The Photometric Sunspot Index has the form:
PSI= -CsAs (3Jl-2+2y.),
where Cs
As
~
0.164,
SGD published sunspot area, and
= cosine of heliocentric angle.
The Photometric Facular Index has the form:
PFI
Cp Ap ( 2 +)A - 3JA 2) ,
0. 01 '
SGD published plage area, and
-44
y.-.=
cosine of heliocentric angle.
The coefficients Cs
and Cp were calculated from data
obtained with the Extreme Limb Photometer (Chapman and
Meyer,
1983;
Chapman 1984).
calculated PSI and PFI.
irradiance
photometry,
comparison,
Table 8 presents a comparison of
fluctuations
i.e.
on
Table 7 presents the
a
obtained from diode array
pixel-to-pixel brightness
to PSI and PFI, i.e. irradiance fluctuations
obtained from a knowing the heliocentric angle and the
area of each active region.
The Photometric Total Index,
(PTI = PFI +PSI), sums
facular excesses with spot deficits obtained through
calculation of each index.
irradiance fluctuations
photometry data,
(0-C].
Table 9 compares PTI with
obtained from
diode
A comparison of PTI, based on
modeling of sunspot and facular behavior,
irradiance
array
fluctuations,
to
[0-C]
based on two-dimensional
photometry should lead to verification or improvement of
sunspot and facula models.
Determination of the energy balance between facular
excesses and sunspot deficits for the passage of this
active region in July 1982 is the purpose of this thesis.
The energy balance can be calculated by recognizing what
the irradiance fluctuations correspond to.
The luminosity
of a star is defined as the total radiant energy emitted
per second in all directions.
Radiant energy is defined
-45
TABLE 7:
Calculated Photometric Sunspot Index (PSI) and
Photometric Facular Index (PFI)
cos &
(SFO)
Date
Spot
Area
Plage
Area
PSI
(ppm)
PFI
(ppm)
.42
650
1600
145.96
30.24
cos 9
(SGD)
July 8
July 9
.532
.66
1390
3300
598.81
44.88
July 10
.71
.80
1830
10000
1056.42
88.0
July 11
.81
.87
2210
10000
1453.64
60.0
July 13
.965
.98
2090
9700
1673.08
9.7
July 14
.985
.99
2600
10000
2132.0
5.0
July 16
.91
1530
1061. 39
1260
July 17
July 18
.85
1800
10000
1141. 69
69.0
July 19
.765
.77
1260
10300
685.78
101.97
July 20
.776
.65
650
10000
273.69
138.0
.36
90
July 21
Cp
Cs
Ap
As
PSI
PFI
y..
~
= 0.01
= 0.164
=
area pl age
= area spot
= -Cs As ( 3)-'.2
+ 2p.)
Cp Ap ( 2 +Jl-- 3j)- 2)
= cos fT
= heliocentric angle
=
16.37
(l
46
TABLE 8:
Date
Comparison of Irradiance Fluctuations From Diode
Array Pho tome try to PSI and PF I
,M(SFO)
July 8
(SGD)
Spot
Deficit
(SFO)
Facular
Excess
(SFO)
PSI
(ppm)
PFI
(ppm)
.42
-62.25
23.55
-142.96
30.24
}J-
July 9
.532
.66
-314.08
96.16
-598.81
44.88
July 10
.71
.80
-837.87
137.06
-1056.42
88.0
July 11
.81
.87
-1048.50
146.54
-1453.64
60.0
July 13
.965
.98
-1265.93
102.52
-1673.08
9.7
July 14
.985
.99
-1073.78
75.98
-2132.0
5.0
July 16
.91
-1316.21
97.43
-1061.39
July 17
.66
-926.16
72.09
July 18
.445
.85
-637.7
67.70
-1141.69
69.0
July 19
.765
.77
-243.50
192.53
-685.78
101.97
July 20
.776
.65
-208.04
144.83
-273.69
138.0
.36
-4.4
102.45
-16.37
July 21
•
47
TABLE 9:
Calculated Photometric Total Index (PTI) and Total
Irradiance Fluctuation From Diode Array Photometry
0-C
)1'-
(SFO)
Date
July 8
F-
(SGD)
0-C
(ppm)
PTI
(ppm)
.42
-38.7
-112.72
July 9
.532
.66
-217.91
-553.93
July 10
.71
.80
-700.81
-968.42
July 11
.81
.87
-901.95
-1393.64
July 13
.965
.98
-1163.41
-1663.38
July 14
.985
.99
-997.79
-2127. 0
July 16
.91
-1218.78
July 17
-854.07
July 18
.85
-569.99
-1072.69
July 19
.765
.77
-50.97
-583.81
July 20
.776
. 65
-63.20
-135.69
. 36
+98.05
July 21
PTI
= PFI + PSI
48
as the intensity of emission times the area it passes
through times the solid angle.
For a given wavelength,
flux is defined as the integral, over the surface, of the
intensity emitted therefrom times the integral over the
angle of emission.
Using this definition for flux:
~n
=
F
cos
-e-
sin
-8-
d
-e-
id
a
where F = flux
I
intensity
~
heliocentric angle
~
azimuthal angle
Integration over the surface results in:
F = 2
f?z I
1'T
-e =p and
but cos
F = 2 'lT
s~
cos
-9
sin
d
-e =
sin
e
I jA
df-
-
tt
d
-dy
-9
' so
or, to get a positive integral:
F
= 2 Tt'
where )A
r~
I }-\- dJL
in this application can be treated as a weighting
factor relating intensity, I, to the angle on the sun from
which radiation is
emitted.~
limb to one at solar
varies from zero at the
center when
perpendicular to the solar surface.
I,
with
its
weighting
factor
solar normal
is
Combining intensity,
Jl•
I'
=
I_jA-
and
substituting:
0
flux per pixel in quiet sun
=
F
=
21\
~~
I'
djl-
The flux difference between each pixel over the active
elements is:
49
1
Fsun - Fquiet Sun = A F = 2 i\
where
AI
1
So~
I
1
dJL
= intensity change = irradiance fluctuation
[0-C] = observed sun irradiance - clean sun
.irradiance
The flux difference, normalized by quiet sun flux,
therefore:
is
i
1
AF/Fq.s. = SoAI' djl-= Ia[O-C] dJAIf symmetric limits of integration are introduced from
negative one to positive one, rather than zero to positive
one, a factor of 1/2 is
becomes:
introduced and the equation
1
1 I 2~ [ o-c ] d_p..
1::. F /Fqs
-1.
Formulas identical to, or similar to this appear in the
work of Hirayama, Okamoto and Hudson, 1983; Newkirk, 1983;
and Chapman, 1984.
The data actually generated in the program is for
discrete days, so the integral is evaluated by summation.
The summation must occur over all days of active region
disk transit, and therefore,
dp.
=
t:.y.
in this application,
is determined by finding the differences on successive
days of
Jli + 1 from the previous day )J-i·
:6L/L = AF/Fq.S. = 1/2 ~ [0-C]Ajl.
Accordingly,
Eqn. 1
equals the average luminosity fluctuation caused by this
active
region during its disk transit.
It will be
recalled from an earlier definition that luminosity is
defined as total radiant energy emitted per second in all
directions.
Only one side of the sun is directed toward
50
the earth, and thus earth receives flux from one half the
sun.
A factor of one half is therefore introduced in the
final equation for energy in terms of luminosity and time,
AL
AE=
where
.1:1..
x
Lq.s.
Eqn. 2
L = luminosity fluctuation determined from [0-C]
and
t
1/2
x 112
t
Lq.s.
y._ as above in equation 1
total time in seconds of active region transit
across visible disk.
=half quiet sun luminosity.
The value used in these calculations for 1/2
Lq.s.
was 2 x
1o33ergs/second.
Using the relationship in equation 1:
AL/L = 1/2
~
... [0-C]Ajl
the net luminosity fluctuation for the passage of BBSO
18474 was found
luminosity.
to be -531
x 10-6 of the quiet sun
A plot of the curve for the total irradiance
fluctuation [0-C]
versus~
for the visible disk transit
from 8 July to 21 July 1982 for active region 18474 is
given in Figure 11.
The luminosity fluctuation due to sunspots only was
computed to be -622 x 1o-6 of the quiet sun luminosity.
Therefore, facular emission made up just over 14% of the
loss of total emission due to sunspots.
curve for spot deficit only
versus~
A plot of the
for the visible disk
transit of AR 18474 also appears on Figure 11.
As
discussed
previously,
luminosity times time.
energy
is
equal
to
The total time of transit of AR
Figure 11.
Irradiance Fluctuations as a Function of
cos~
V1
I
52
18474 between its time of appearance on the east limb
early on 8 July 1982
(according to SGD #457) and its
disappearance over the west limb about
approximately
1 o6
1 .2 x
seconds.
1700 UT was
In equation 2 for
energy, the energy deficit due to sunspots in AR 18474 was
found to be:
-14.9 x 1035 ergs,
and the energy deficit due to the entire active region:
-12.7 x 1o35 ergs.
In summary,
for the medium-young active region BBSO
18474 disk transit 8 July through 21 July 1982:
luminosity deficit due to spots alone
= -622 x 10-6
luminosity excess due to faculae alone = 91 x 1o-6
net luminosity fluctuation for entire
active region
sunspot deficit in energy units
-14.9 x 1035 ergs
2.2 x 1o35 ergs
faculae excess in energy units
net active region deficit in
energy units
The
time-averaged
approximately
sunspots.
energy
= -531 x 1o-6
= -12.7 x 1o35 ergs
excess
of
faculae
is
14 percent of the energy deficit of
'
Q .
CHAPTER V
CONCLUSIONS
The time-averaged energy excess of faculae in the
July transit of BBSO 18474 is approximately 14 percent of
the energy deficit of sunspots.
An analysis of the energy
balance during the August transit of this active region
determined that facular excesses account for 57 percent of
the energy deficit of sunspots, and by the time of the
September transit, facular excess accounted for 91 percent
of the energy deficit of sunspots.
Facular excesses increased 43 percent between the
July and August active region transits, and 34 percent
between the August and September transits.
Data analysis
is planned to determine by how much facular excesses
increased in subsequent passages.
The results obtained so
far suggest that energy is being stored when the region is
young, and either less energy is stored later in the
active region's lifetime, or perhaps some of the stored
energy is liberated.
The facular excess,
in ergs, for the three transits
analyzed so far, are:
2.2 x 1Q35 ergs for the July transit
3.3 x 1035 ergs for the August transit
5.8 x 1035 ergs for the September transit
It has long been known that active regions evolve
their
form
during their lifetime.
The preceeding
calculations may help reveal exactly how solar active
53
54
regions change and how, or whether, active region energy
balance is maintained.
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