Whither Sol?
Doug Rabin
NASA Goddard Space Flight Center
19 September 2012
SORCE Science Meeting
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Acknowledgment
I thank all the researchers credited below—particularly
Jeff Hall, who shared three slides from recent
presentations by him and Wes Lockwood. None of the
work is mine.
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SORCE Science Meeting
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Relationship to Meeting Objectives
Meeting asks:
• Do small scale processes on the Sun give a
reasonable explanation of solar spectral irradiance
(SSI) variability?
We ask a related question:
• Can large scale processes on the Sun cause TSI
and SSI variations over centuries or millennia ?
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SORCE Science Meeting
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Q&A
Question: How might the Sun change on timescales of 100-1000 years?
Answer: We don’t know.
Question: Why not?
First answer: No one asked.*
Second answer: The Sun is no RR Lyrae variable: its internal
changes and variability on these timescales are likely small.
The good news: We can now detect internal changes in the Sun
and in stars very like the Sun. Multidecadal photometric
observations are accumulating. Theory is catching up.
* Not quite true ….
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Stellar Variability: The Big Picture
 hydro  exp  ff 1/ G 
~ 1 hr for the Sun
GM 2 / R
 KH  / L 
L
~ 107 yr for the Sun
 nuc
f  Mc 2 / L
~ 1010 yr for the Sun
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Stellar Evolution: The Big Picture
L  R2 T4eff
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Solar Evolution: The Big Picture
Log L/L
Log L/L
HR Diagram
+ 9x10-11 L /yr
Age (Gy)
Teff (KK)
+ 5x10-11 R /yr
R/R
4
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Age (Gy)
Teff (KK)
5
− 3x10-8 K/yr
Age (Gy)
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How the solar irradiance has varied
Figure 1. (a) Space-borne total solar irradiance
(TSI) measurements are shown on “native” scales
with offsets attributable to calibration errors.
Instrument overlap allows corrections for offsets
and the creation of a composite TSI record. (b)
The average of three different reported
composites [ACRIM, PMOD, and RMIB] adjusted
to match the SORCE/TIM absolute scale. The grey
shading indicates the standard deviation of the
three composites. (c) Irradiance variations
estimated from an empirical model that
combines the two primary influences of facular
brightening and sunspot darkening with their
relative proportions determined via regression
from direct observations made by SORCE/TIM. (d)
The daily sunspot numbers indicate fluctuating
levels of solar activity for the duration of the
database.
Kopp & Lean 2011
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How the solar irradiance may have varied
0.1%
This historical reconstruction of TSI is based on that of Wang, Lean, and Sheeley
(ApJ, 625, 2005) using a flux transport model to simulate the Sun's magnetic flux,
with those annual values provided courtesy of J. Lean.
Kopp 2012
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How the solar irradiance may have varied
0.1%
Vieira, Solanki, Krivova & Usoskin 2011
19 September 2012
Reconstruction based on SATIRE models
with open magnetic flux inferred from 14C
in tree rings and various paleomagnetic
models.
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How the solar irradiance might vary
Two black time series, based on
various historical reconstructions
(discussed by Lean et al. [2005]),
bracket the estimated TSI
variations as the Sun exited
Maunder Minimum.
Kopp & Lean 2011
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How the solar radius may have varied
Perhaps …
Perhaps not …
“… any variations of the size
of the solar envelope must
be within 2.5 km [3.4 mas]
of amplitude over a solar
cycle, a value in perfect
agreement with those
deduced from inversion of
the f–modes in helioseismology, or from space
observations through the
MDI data analysis.” (Rozelot
et al. 2006)
Solar Disk Sextant (Sofia et al. 2012)
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Large-scale Zonal Flows During the Solar Minimum -- Where Is Cycle 25?
Frank Hill1, R. Howe2, R. Komm1, J. Christensen-Dalsgaard3, T. P. Larson4, J. Schou4, M. J.
Thompson5 (1National Solar Obs., 2University of Birmingham, United Kingdom, 3Aarhus University,
Denmark, 4Stanford University, 5High Altitude Observatory)
Combined rotation-rate residuals at 0.99RSUN. Overlaid is the 5G contour of the unsigned magnetic field strength.
Vertical lines indicate (1) the beginning of GONG observations, (2) the onset of widespread magnetic activity
when the flows reach 20 degrees latitude, (3) the most recent observations, and the corresponding epochs one
cycle later/earlier, as judged by the position of the flow belts below 40 degrees. Note the absence of the
poleward branch for cycle 25, which should have appeared in approximately 2009.
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Whither goes Cycle 24? A View from the Fe XIV Corona
Richard C. Altrock (Air Force Research Laboratory)
The previous three cycles had a strong, rapid "Rush to the Poles" in Fe XIV. Cycle 24 displays a
delayed, weak, intermittent, and slow "Rush" that is mainly apparent in the northern
hemisphere. If this Rush persists at its current rate, evidence from previous cycles indicates
that solar maximum will occur in approximately early 2013.
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The Solar-Stellar Connection in the Precision Stellar Astrophysics Era
Marc Pinsonneault (Ohio State University)
Parker Lecture (2011 AAS/SPD)
• Kepler has so far detected Sun-like oscillations in ~1000 stars (Chaplin et
al. 2011).
• We can use helioseismic techniques to measure absolute abundances.
• We can measure the depth of the convection zone (Van Saders &
Pinsonneault 2011).
• We can detect Sun-like differential rotation (Silva-Valio & Lanza 2011;
Huber et al asto-ph/1002.4113)
• But: the solar differential rotation pattern is not universal; the magnitude
of latitudinal and radial DR depends on the balance of rotation and
convection.
• We can study the latitude distribution of starspots and even construct
butterfly diagrams.
• We can use precision age-rotation relationships to determine ages of field
stars to <20% (Epstein & Pinsonneault 2011).
My takeaway: We can now find “all but a DNA match” solar twins and study
them to understand the range of behavior the Sun can potentially exhibit.
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Ensemble Asteroseismology of Solar-Type Stars with the NASA Kepler Mission
W. J. Chaplin, et al., Science 332, 213 (2011)
Black lines show histograms of the observed
distribution of masses (top) and radii (bottom) of
the Kepler ensemble. In red, the predicted
distributions from population synthesis modeling,
after correction for the effects of detection bias.
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Estimates of the luminosities of the stars (in
units of the solar luminosity) of the ensemble
of Kepler stars showing detected solarlike
oscillations, plotted as a function of effective
temperature.
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The radius and mass of the close solar twin 18 Scorpii derived from
asteroseismology and interferometry
M. Bazot et al., A&A 526, L4 (2011)
The brightest solar twin is 18 Sco (HD 146233, HIP 79672; V = 5.5), whose
mean atmospheric parameters are Teff = 5813 ± 21 K, log g = 4.45 ± 0.02
and [Fe/H] = 0.04 ± 0.01 (Takeda & Tajitsu 2009; Ramírez et al. 2009;
Sousa et al. 2008; Meléndez & Ramírez 2007; Takeda et al. 2007;
Meléndez et al. 2006; Valenti & Fischer 2005). Its rotation rate and
magnetic field are also similar to solar ones (Petit et al. 2008). Its position
in the H-R diagram indicates that the star should be slightly younger and
more massive than the Sun (see Nascimento et al. 2009, and references
therein).
An average large frequency separation 134.4±0.3 μHz and angular and linear
radiuses of 0.6759 ± 0.0062 mas and 1.010 ± 0.009 R were estimated. We
used these values to derive the mass of the star, 1.02 ± 0.03 M.
Precision stellar astrophysics!
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S-index and R’HK
b mag
y mag
S index
S  (F
H
 FK ) ( FR  FV )
RHK  FHK
4

T
 eff 
'  R R
RHK
HK
phot
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Vaughan, Preston & Wilson 1978
Noyes et al. 1984
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Spectral Irradiance Variation:
18 Sco vs. SORCE/SIM
b
b mag
y
y mag
S
S index
2000
Strömgren
b y
2010
b, y, and S are positively correlated in 18
Sco, as we find for most solar age stars...
Lockwood, Henry, Hall & Radick 2012
…but SIM suggests b and y
should vary differently
Haigh, Winning, Toumi & Harder 2010
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A star emerging from a Maunder minimum?
HD 140538 = ψSer
?
Activity-Brightness variation.
Filled: direct. Open: inverse.
Radick et al., ApJS 118, 239 (1998)
19 September 2012
• Weak evidence of a transition from
inverse to direct variation
• No secular change in brightness
detected at the 0.1% level
J. Hall, Solar Twins & Stellar Maunder
Minima (AAS 2012)
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Could Fairborn photometric measurements
detect the Sun’s variability?
Yes, but only for about 30% of the comparison star pairs
Cumulative distribution of comparison
star + measurement noise
y
b
ACRIM data degraded to 18 Sco
window and precision
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Lockwood, Henry, Hall & Radick 2012
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Global Solar Structure on Short Timescales
Comparison of the oblateness of
isobaric surfaces calculated with
YREC 2D using various assumptions
about the internal profile of rotation
(uniform rotation or solar-like
differential rotation) and magnetic
fields (dipole-or quadrupole-like
latitudinal dependence). The
calculated values of the oblateness,
ε, reproduce well the value observed
in the Sun.
YREC 2D includes rotation, magnetic fields of arbitrary
configuration, and turbulence, that can be run on very short
time scales (down to 1 year), and that represents all global
parameters (R, L, Teff) with a relative accuracy of 1 part per
million, or better.
Spada, Li, Sofia & Ventura 2012
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Magnetic cycles in a convective dynamo simulation of a young solar-type star
Brown et al., ApJ, 731, 69 (2011)
3 Ω
5 Ω
• Solve the 3D MHD anelastic equations of
motion in a rotating spherical shell.
• Computational domain extends from 0.72
Rsun to 0.97 Rsun.
• Oscillating dynamo behavior is possible
even when the model does not include a
tachocline.
Field line tracings
showing connections
between equatorial
regions and polar cap
from previous cycle
Magnetic wreaths achieved in (a) case D3 (Paper I) and (b) case D5 (this paper). Shown are time–
latitude plots of mean toroidal (longitudinal) magnetic field Bφ at mid-convection zone, with
scaling values indicated. Case D3 builds persistent, time-independent wreaths but the wreaths
achieved in case D5 undergo quasi-regular reversals of polarity (three shown here, with roughly
a 1500 day period). The dynamic range of the color bars is indicated.
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Convective Babcock-Leighton Dynamo Models
Reminder: Not the Sun!
Miesch & Brown, ApJ, 746, L26 (2012)
• Adds to the 3 Ω model of Brown et al.
2011 a poloidal source term in the
magnetic induction equation
(parameterized mean-field forcing)
P  ( Bs2  Ba2 ) ( Bs2  Ba2 )
(d) Mean toroidal field in the middle of the
convection zone for a model with forcing
parameter α0 = 100 m s-1. The color scale
saturates at ±4 kG. (e) Zoomed-in portion of
panel (d).
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where Bs and Ba are the symmetric and
antisymmetric components of Bφ. The
parity P, persistently negative for the
Sun, varies in sign for this model.
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So, wither Sol?
On the one hand:
• There is no strong evidence , from either
observation or theory, that the Sun will exhibit
secular variations > 0.2% in TSI, SSI, or global
properties over 102−106 yr.
On the other hand:
• There’s no strong reason to believe it won’t.
Place your bets!
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SORCE Science Meeting
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