Modeling of the Solar Spectral Irradiance and its
variability
The Sun can also smile :))
Outline
• rotation cycle
• secular time-scale
Calculations of the solar spectrum
COde for Solar Irradiance (COSI)
Millions of atomic and molecular transitions
Non-local thermodynamic equilibrium
5
4
3
2
1
0
125
0.08
135
140
145
0.06
ATLAS 3
0.04
COSI
0.02
Irradiance [W m-2nm-1] Irradiance [W m-2nm-1] Irradiance [W m-2nm-1]
130
0.00
160
1.0
0.8
180
200
150
220
155
160
240
0.6
0.4
0.2
0.0
240
2.0
260
280
300
320
1.5
1.0
0.5
0.0
320
2.5
2.0
340
360
380
400
420
440
Wavelength [nm]
460
480
1.5
1.0
0.5
0.0
400
Irradiance [W m-2nm-1] Irradiance [W m-2nm-1] Irradiance [W m-2nm-1] Irradiance [W m-2nm-1] Irradiance [W m-2nm-1]
Irradiance [W m-2nm-1]
Irradiance ·10-4 [W m-2nm-1]
Comparison with ATLAS 3
2.5
2.0
1.5
1.0
0.5
0.0
480
2.0
500
520
540
560
580
600
620
640
660
680
700
720
740
760
780
800
820
840
Wavelength [nm]
860
880
1.5
1.0
0.5
0.0
560
2.0
1.5
1.0
0.5
0.0
640
1.5
1.0
0.5
0.0
720
1.2
1.0
0.8
0.6
0.4
0.2
0.0
800
Irradiance from active components
0.5
0.4
Quiet Sun
plage
LTE
NLTE
Sunspot
0.3Bright network
0.2
1.5
300
400
500
600
bright
network
700
1.0
200
1.6
LTE
1.5
NLTE
1.4
F/C
F - C [W m-2nm-1]
0.10
2.5
2.0
0.1
less contrast
0.0
200
0.15
3.5
3.0
P/C
P - C [W m-2nm-1]
Plage
4.0
0.05
250
1.3
1.2
1.1
0.00
200
300
400
500
Wavelength [nm]
600
700
1.0
200
250
Wa
A data. Both of them are presented in Fig. 9. LYRA version 1 dataset
produced taking all data into account, while LYRA version 2 dataset was
Modeling of the solar variability
uced excluding two aforementioned intervals from the analysis and assuming
Mainirradiance
assumption.
Variations
the solar
irradiance
areThe
directly
the solar
did not
changeinduring
these
intervals.
difference
related
to the indicates
evolutionthe
of surface
magnetic
flux
een these
datasets
accuracy
of our analysis.
Sunspot Model S
Modeling with COSI
Model
P irradiance
is section we calculate the synthetic profile of Plage
the spectral
solar
bility for the period analyzed in Sect. 2. We follow a well-developed aph (see e.g. Foukal and Lean, 1988, Fligge, Solanki, and Unruh, 2000, Krivova
Bright
network
Solanki, 2008, Domingo et al., 2009) and calculate
the time-dependent
solar
F
rum as a sum of the spectra from the quiet Sun Model
and different
active features.
mploy a 4-component model which treats separately contributions from the
Sun, sunspots, active network and plage areas. According to this model
Quiet Sun Model C
olar spectrum I(λ, t) can be written as
I(λ, t) =
�
(αQS (µk , t)IQS (λ, µk ) + αS (µk , t)IS (λ, µk )+
k
+ αAN (µk , t)IAN (λ, µk ) + αP (µk , t)IP (λ, µk )) ,
(1)
Rotational cycle. PREMOS/PICARD measurements
Herzberg channel (215 nm)
quiet Sun, plage, active network, sunspot (umbra and penumbra) spectra calculated with COSI
HMI filling factors provided by MPS group
The Sun among its stellar cohort
The Sun
30 years of observations
25 Sun-like stars × 20 years of observations = 500 years
Variability vs. Activity
No. 1, 2007
PATTERNS OF VARIATION AMONG SUN
Fig. 7.— Long-term (cycle timescale) photometric
variation vs.etaverage
Lockwood
al. (2007)
chromospheric activity level.
Fig. 9.— Slo
emission variati
variability (y
tively well-d
Where to put the present Sun?
Stellar photometry - Stromgren (b+y)/2
Imax - Imin, mW m-2 nm-1
20
There is 15
no long-term records of the solar
irradiance in the visible spectrum
10
“Stellar” papers overestimate present solar
Radick et 5al. (1998) - 0.00044 mag
variability
They
assumed that TSI and photometric variabilities are connected as if they
are caused by change of the solar effective temperature
0
-5
Lean et al.200
2005 - 0.00027 400
mag
600
Wavelength, nm
Krivova et al. 2010 - 0.00017 mag
800
SIM (extrapolated) - 0.0004 mag
Shapiro et al. 2011 - 0.00017 mag
TSI, W/m2
3
0
2
Shapiro et 500
al. (2011)
1000
1500
2000
1
temporal mean1 of the solar variability is approximately 2 times
800
smaller than presently measured
800
600
600
1700
1800
1900
Φ, MeV
400
200
0
-500
0
-1
1600
5
RMS20, 10-4 mag
Φ, MeV
-500
6 (b+y) / 2, 10-3 mag
TSI, W/m2
1368
1368
Can
we use present solar location for comparison?
1366
1366
1364
1364
1362
1362
5 solar location is rather peculiar
1360 Present
1360
Lean et al. (2005)
4
satellite epoch 1358
1358
Krivova et al. (2010)
2000
4
3
2
0
1
500
Year
1000
1500
2000
400
200
0
1
0
Fig. 2. Modulation potential
(lower
panel)
and1900
TSI reconstructions
(upper panel)
1600
1700
1800
2000
the modulation potential derived from 10
Be records from the Greenland Ice core Pro
Year
composites shown in Fig. 1 (red and cyan curves). The gray-shaded area indicates th
Activity vs. Variability
Lockwood
inclinationmean
temporal
et
effect
al. position
(2007)
from Knaack
+ stars et
with
al. unconfirmed
(2001)
variability
Variability, log(rms(b+y)/2)
log(rms(b+y)/2)
Variability,
-1.5
-1.5
-2.0
-2.0
If-2.5
the 11-year cycle is the only harmonic in the solar irradiance
-2.5
then the Sun is a clear outlier
-3.0
-3.0
-3.5
-3.5
-4.0
-4.0
-5.2
-5.2
-5.0
-4.8
-4.6
-4.4
Chromospheric Activity, logR’HK
-4.2
-4.0
-4.0
– 10 –
5
4
4
2
3
02
Lean et al. (2005)
Krivova et al. (2010)
Shapiro et al. (2011)
-21
0
-4
-1
1600
5
10
4
8
RMS20, 10-4-4 mag
RMS20, 10 mag
! (b+y)
(b+y) // 2,
2, 10
10-3-3 mag
mag
6
Long-term trend in the solar irradiance
1700
1800
1900
2000
2000
1700
1800
Year
1900
2000
2000
3
6
42
21
0
1600
Fig. 2.— Upper panel: Annual (b+y)/2 values versus time according to the Krivova et al.
Solar variability back in time
two free parameters
RMS20, 10-4 mag
amplitude of the 11-year cycle, V11
25
20
15
10
5
0
V11 =0.0002 mag
VLT=0.005
0
RMS20, 10-4 mag
amplitude of the long-term trend, VLT
500
1000
Year AC
V11 =0.0002 mag
VLT=0.001
1500
25
20
15
10
5
0
-2500
-2000
-1500
Year BC
-1000
-500
Different scenarios for the solar trajectory
Different scenarios for the solar trajectory
16
Different scenarios for the solar trajectory
17
Different scenarios for the solar trajectory
18
Possible constrains on the historical solar variability
straightforward interpretation: 0.55% change in Stromgren (b+y)
between the Maunder
minimum and present 10
10
10-3 VLT
8
8
BUT...
6
6
4
4
0.17% change is within the error range
2
2
corresponds to 1.9-2.7 W/m2 TSI change
6 8 10 12
-4
,
10
mag
0
0
0
2 THANK
4 6 8 YOU!
10 12
RMS20, 10-4 mag
0
0
2 4 6 8
RMS20, 10-4 m
Left panel:
The
dependency
the VLT parameter on the solar variabili
dependency of theFig.
VLT5.—
parameter
on the
solar
variability,ofretrieved
No. 1, 2009
ACTIVITY AND VARIABILITY OF SUN-LIKE ST
Figure 11. Activity vs. photometric variability of our sample. The Sun does not
appear as an outlier among the variability envelope of inactive solar analogs.
Drop lines from each plot symbol show where the point would move with
perfectly stable comparison stars. The dotted line is the regression on the same
scale as L07, while the dashed line is the regression obtained for the present
sample.
Hall et al. (2009)
Figure 12. Relative chro
mean activity level for o
and 18 Sco (the filled
variable of the inactive s