Solar Irradiance Variability - comparison of models and observations
Peter Fox, High Altitude Observatory, NCAR, P.O. Box 3000, Boulder, CO 80307, pfox@ucar.edu
Surface structures:
Instrumental filters: Radiance Spectra:
0.50
405
Green
0.40
0.30
0.20
0.10
0.00
490
495
500
nm
Teff
0
3900
5000
3902
3904
3906
3908
3910
104
Wavelength
4000
2000
0
-0.5
0.0
Log Wavelength (microns)
0.5
1.0
865
870
Radiation temperature from continuum sources versus wavelength
for quiet Sun (solid), plage (dash-dot) and sunspot (long dash)
structures - also shown is the Teff=5770 black body temperature.
875
nm
1000
P
A
1500
Height (km)
2000
2500
1016
VIRGO/SPM filter profiles for blue channel (upper), green channel
(middle) and red channel (lower) filters.
1015
1.0•106
Electron Density
860
500
2.0•106
1.5•106
855
S
Model C, P, S - mu=0.3
2.5•106
3000
-1.0
Intensity
0.0
850
1500
105
510
0.2
5.0•105
0
3900
3902
3904
3906
3908
Putting it all together:
1014
1013
1012
P
1011
1010
109
3910
Wavelength
S
0
Radiance spectra about Si I (390.5nm) for disk center
(upper) and µ=0.3 (lower) for quiet Sun (solid), plage
(dash) and sunspot (dash-dot) structures.
500
1000
Height (km)
A
1500
2000
1018
Spectral
Filters
Spectral Database(s)
1016
Synthetic radiance spectra versus wavelength (EUV to IR) are calculated from
radiative transfer models for each surface structure and a number of disk
positions and stored in databases.
Hydrogren Density
Feature distribution
on the solar disk:
MASKS, parametric
fits, etc.
1014
A
1012
S
P
1010
Irradiance tables:
H
{1{
Model/
A
C
E
F
H
P
S
Ca II K structure mask for 92/01/31
0:95
4.1084
7.2829
16.439
23.334
47.562
62.220
24.713
0:85
4.1064
7.3850
16.681
23.678
48.111
62.269
25.276
0:75
4.1044
7.4871
16.924
24.022
48.660
62.318
25.840
0:65
4.1023
7.5891
17.167
24.365
49.209
62.366
26.403
I (104 erg/cm2 /s/sr)
0:55
0:45
0:35
4.1003 4.0955 4.0877
7.6911 7.9141 8.0600
17.410 17.670 17.949
24.709 25.052 25.395
49.757 50.236 50.641
62.415 62.167 61.603
26.966 27.846 29.064
Quiet Sun Intensity
0
1214
0:25
4.0852
8.0863
18.207
25.664
50.851
60.717
30.778
0:16
4.1038
8.4955
18.315
25.601
50.341
59.077
34.169
0:06
4.1249
8.6900
18.293
25.396
49.709
57.868
36.874
Average
4.1020
7.6041
17.134
24.285
49.001
62.023
26.740
Total
2.79
5.17
11.65
16.52
33.32
42.18
18.18
Sac Peak CaIIK Intensity Histogram and Model Assignments for 92/01/31
Table 3: Intensities for our structure models, integrated over the band Ly 4.5
A. Units for the total are mW/m2 /
A.
1215
1216
Wavelength
1217
4•104
2•104
1215
C
E
E
F
F
H
H
P
Magnetogram structure mask for 92/01/31
0:7511
2.7821
2.7888
2.7874
2.8223
2.8981
2.9092
0.3391
0:6513
2.6078
2.6157
2.6159
2.6535
2.7488
2.7723
0.3142
I (106 erg/cm2 /s/sr)
0:5515 0:4519 0:3524
2.4205 2.2181 1.9972
2.4299 2.2295 2.0116
2.4323 2.2349 2.0215
2.4734 2.2804 2.0729
2.5879 2.4130 2.2205
2.6213 2.4514 2.2550
0.2909 0.2693 0.2501
0:2533
1.7530
1.7725
1.7892
1.8483
2.0045
2.0169
0.2334
0:1556
1.4750
1.5053
1.5337
1.6010
1.7531
1.6983
0.2201
0:0667
1.3018
1.3412
1.3785
1.4501
1.5946
1.4797
0.2135
Average
2.5963
2.6056
2.6077
2.6472
2.7365
2.7448
0.3224
Total
176.5
177.2
177.3
180.0
186.1
186.6
21.92
Table 4: Red Band intensities for our structure models, averaged over the band 6070-6080
A. Units for the total are mW/m2 /
A.
Synthetic PSPT blue image from Ca mask
Synthetic PSPT blue image from B mask
1216
Wavelength
1217
1218
Synthetic Ly-α image from Ca K mask
2•104
0
1214
Intensity or magnetogram images are
decomposed pixel-by-pixel and the
synthetic images are built up by using
radiance spectra for the wavelength of
interest along with any instrumental
filter profiles.
8660
8680
8640
8660
8680
8640
8660
8680
8640
8660
8680
5.0•105
0
8580
8600
8620
1215
1216
Wavelength
1217
1218
1215
1216
Wavelength
1217
1218
2.0•106
1.5•106
1.0•106
5.0•105
0
8580
1.0
8600
8620
Wavelength
0.6
0.4
0.2
0.0
1214
0.40
0.30
0.20
0.10
0.00
8580
8600
8620
Wavelength
VIRGO/SPM red band spectrum synthesis (solid) compared to Kurucz atlas (dash) for
quiet (upper), moderate and active Sun. Variability of active to quiet Sun is shown in the
lower panel, overlaid with the VIRGO red filter profile to indicate sampling.
3000
2000
1000
0
1024
1025
1026
Wavelength
1027
1028
1025
1026
Wavelength
1027
1028
1026
Wavelength
1027
Visible spectrum:
6000
5000
4000
3000
2000
1000
0
1024
3.0•106
2.5•106
2.0•106
1.5•106
1.0•106
5.0•105
8000
0
3904
3905
3906
3907
3906
3907
3906
3907
3906
3907
Wavelength
6000
4000
2000
1025
1028
3.0•106
2.5•106
2.0•106
1.5•106
1.0•106
5.0•105
0
3904
3905
Wavelength
3.0
2.5
2.0
Active Sun Intensity
Active to Quiet Sun Ratio
8640
1.0•106
0.8
4000
1.5
1.0
0.5
0.0
1024
1025
1026
Wavelength
1027
3.0•106
2.5•106
2.0•106
1.5•106
1.0•106
5.0•105
0
3904
1028
3905
Wavelength
Lyman-β profiles and variability
100
Quiet Sun Intensity
Synthetic
Images:
8620
1.5•106
Wavelength
6•104
4•104
0
1024
Histogram structure decomposition for Ca K 92/01/31
8600
2.0•106
Active to Quiet Sun Ratio
A
C
0:8510
2.9451
2.9509
2.9481
2.9809
3.0375
3.0348
0.3651
2000
Temperature, log(Temperature), electron density and hydrogen density
versus height in the solar atmosphere. Empirical models for each of
the surface structures: A, C, E, F, H, P and S.
5.0•105
80
60
40
20
0.40
0.30
0.20
0.10
0.00
3904
3905
Wavelength
0
0
200
400
600
800
1000
600
800
1000
600
800
1000
600
800
1000
Wavelength
Synthetic PSPT red image from Ca mask
Synthetic PSPT red image from B mask
140
120
100
80
60
40
20
0
0
200
400
Si I (390.5nm) and surrounding spectra (solid-synthesis, dashed-AFGL atlas)
Upper to lower panel: quiet Sun, moderate activity, active Sun, active to quiet
Sun ratio.
Wavelength
150
100
Observed Spectra - Livingston
1.0
0.8
0.6
0.4
0.2
0.0
5378
5379
5380
Wavelength (A)
5381
5382
50
0
0
200
400
Wavelength
Intensity
A
0:9509
3.0982
3.1034
3.0993
3.1304
3.1683
3.1512
0.3919
1500
1.0•106
0
8580
1•105
8•104
Synthetic Lyman-α profiles (solid) compared to observations (dash, Lemaire)
Model/
A
C
E
F
H
P
S
1000
Height (km)
Wavelength
6•104
0
1214
500
1.5•106
1218
8•104
Moderate Sun Intensity
F
2•104
Active Sun Intensity
E
4•104
0
Near-IR spectrum:
2.0•106
6•104
Active to Quiet Sun Ratio
C
EUV/UV spectrum:
Relative Intensity
A
Synthetic
Spectra
Intensity
Histograms/
Irradiances
Quiet Sun Intensity
Synthetic
Image(s)
Moderate Sun Intensity
Computation of synthetic
images and spectrum for
full disk in absolute units
H
Quiet Sun Intensity
F
Moderate Sun Intensity
E
Active Sun Intensity
C
Synthetic irradiance spectra are generated by summing spectral radiance profiles
over the full solar disk which accounts for detailed center-to-limb activity variations
and these profiles may be compared directly to observed spectra.
Active to Quiet Sun Ratio
A
Calculation of the Line Source Function
2.0
1.5
4.0•106
3.0•106
2.0•106
1.0•106
0
5378
1.0
0.5
Spectra for Model Quiet Sun, mu=1
5379
5380
Wavelength (A)
5381
5382
0.0
0
Synthesis project - http://rise.hao.ucar.edu/synthesis
Temperature
6000
We use three dierent approaches for obtaining realistic, non-LTE, line
source functions.
Paper I: Fontenla, White, Fox, Avrett and Kurucz, Ap. J. 518, 480.
Paper II: Fox, White, Fontenla, Avrett and Harvey, Ap. J. to appear.
1000
Height (km)
106
1.0•106
0.4
PSPT Calcium II K image from 1998.
* A - cell center faint component of the quiet Sun
* C - average median intensity quiet Sun component
* E - bright network component of the quiet Sun
* F - enhanced network component of the active Sun
* H - faint plage component of the active Sun
* P - bright plage component of the active Sun
* S - sunspot
Our model computations include detailed non-LTE ionization equilibrium
for the most signicant elements and eects of diusion in the transition
region.
1. In strong resonance lines, such as the H Ly and Mg II h and k, we use
non-LTE source functions computed with the PANDORA code with
partial frequency redistribution (PRD).
2. In other cases when the non-LTE populations from PANDORA are
available but PRD is not very important, we use the computed populations and then assume complete redistribution (CRD) for our opacity
and emissivity computations. This approach is used for the Balmer,
Paschen, and higher Lyman lines (that use population values from a
15 level H atom PANDORA run) and for other lines where CRD is a
reasonable assumption.
3. In all other cases, we compute an approximate source function based on
a new formulation that uses the Planck function and a form of the \net
radiative bracket" applicable to the many medium and small strength
lines in the solar spectrum.
500
2.0•106
0.6
1. Continuum sources:
(a) H; : bound-free and free-free
(b) H2+ : bound-free and free-free
(c) e: free-free
(d) H: 912
A, 3640
A, and higher level ionization
(e) C: edge 1100
A
(f) Al: edge 2076
A
(g) Si: edges 1526
A, 1682
A, 3880
A
(h) Mg: edges 1620
A, 2515
A, 3650
A
2. Scattering processes:
(a) Thomson scattering (e)
(b) Rayleigh scattering (H)
0
7000
0.8
Calculation of Absorption Coecients
The emphasis here is not on the synthesis of a particular set of spectral lines with high accuracy, but rather is on the ability to compute broad
spectral bands with sucient accuracy to estimate the irradiance variability.
We compute the parameters in equation (1) at each wavelength where an
emergent intensity is needed.
We take into account all opacity and emissivity contributions at all wavelengths without resorting to wavelength averaged values. For this purpose
we use the extensive lists of line opacities published by Robert Kurucz and
NIST.
We take into account the following opacity, scattering and emissivity
sources:
505
1.0
where S is the monochromatic source function, and is the monochromatic
optical depth along the line of sight. This optical depth is the integral of the
total opacity, + ,
Z x
(x) =
( + ) ds;
(2)
0
415
0.50
(1)
where is the absorption coecient (corrected for stimulated emission), is the monochromatic scattering coecient, and x is the geometrical depth
along the line of sight. The source function is the ratio of the total emissivity
to the total opacity.
+ J
;
(3)
S =
+
where J is the local mean intensity (i.e., the intensity averaged over all directions) and is the emissivity. The atmospheric parameters , , and along
the line of sight determine the variation of the coecients in equations (2)
and (3), and thereby determine the values of and S along the line of sight.
410
nm
Quiet Sun Intensity
exp; d;
400
Moderate Sun Intensity
S
8000
395
Radiation Temperature
0.00
390
Active Sun Intensity
0
S
3000
0.10
Moderate Sun Intensity
=
5000
4000
Temperature(log)
0.20
The formal integral solution to the radiative transfer equation is,
I
Intensity
Blue
0.30
Calculation of the Solar Emergent Intensity
Z 1
A
6000
3.0•106
0.40
Active Sun Intensity
The solar spectral irradiance is the radiative energy ux from the Sun through
a unit surface, located at 1 AU and oriented normal to the Sun-Earth direction, and in a particular wavelength interval. An accurate computation of
irradiance requires detailed accounting for all variations across the solar disk
at any point in time.
7000
4.0•106
Active to Quiet Sun Ratio
Theory of Stellar Atmospheres Applied to the Irradiance Problem
P
8000
Model C, P, S - disk center
5.0•106
Red
Over the past decade, regular measurement programs for
parts of the solar spectrum have been established.
In recent years substantial progress has also been made on
the physical understanding of these measurements. To
refine our understanding and to make quantitative estimates
of its variability requires a study of the entire solar
spectrum.
Our approach to this requirement is to combine empirical
image analysis with the theory for emission, absorption,
and transfer of radiation in the solar atmosphere.
The goal is the successful combination of observed
solar images with semi-empirical models and theory for
calculation of a mixed line+continuum spectrum emitted
from realistic representations of the observed solar disk.
We present the latest results from the SunRISE spectral
synthesis model in specific spectral bands in the UV,
visible, and near-IR, and compare them to related
observations (including those from the RISE/PSPT
instrument).
NCAR is sponsored by the National Science Foundation.
This work is sponsored by the NSF RISE program.
9000
200
400
Wavelength
Lyman-continuum and continuum edges and variability
C I (538nm) synthetic spectra at disk center for quiet Sun compared to
observations by Livingston (private communication).