The Astrophysical Journal Letters, 739:L45 (6pp), 2011 October 1doi:10.1088/2041-8205/739/2/L45
C ?2011. The American Astronomical Society. All rights reserved. Printed in the U.S.A.
ACTIVITY–BRIGHTNESS CORRELATIONS FOR THE SUN AND SUN-LIKE STARS
D. G. Preminger, G. A. Chapman, and A. M. Cookson
San Fernando Observatory, Department of Physics and Astronomy, California State University Northridge, Northridge, CA, USA
Received 2010 December 15; accepted 2011 July 27; published 2011 September 7
We analyze the effect of solar features on the variability of the solar irradiance in three different spectral ranges.
Our study is based on two solar-cycles’ worth of full-disk photometric images from the San Fernando Observatory,
obtained with red, blue, and Caii K-line filters. For each image we measure the photometric sum, Σ, which is
the relative contribution of solar features to the disk-integrated intensity of the image. The photometric sums in
the red and blue continuum, Σrand Σb, exhibit similar temporal patterns: they are negatively correlated with solar
activity, with strong short-term variability, and weak solar-cycle variability. However, the Caii K-line photometric
sum, ΣK, is positively correlated with solar activity and has strong variations on solar-cycle timescales. We show
that we can model the variability of the Sun’s bolometric flux as a linear combination of Σrand ΣK. We infer that,
over solar-cycle timescales, the variability of the Sun’s bolometric irradiance is directly correlated with spectral
line variability, but inversely correlated with continuum variability. Our blue and red continuum filters are quite
similar to the Str¨ omgren b and y filters used to measure stellar photometric variability. We conclude that active stars
whose visible continuum brightness varies inversely with activity, as measured by the Ca HK index, are displaying
a pattern that is similar to that of the Sun, i.e., radiative variability in the visible continuum that is spot-dominated.
Key words: stars: activity – stars: solar-type – Sun: activity – Sun: chromosphere – Sun: photosphere – Sun:
Total solar irradiance (TSI) is the bolometric solar energy
flux received at the Earth at its average distance of 1 AU,
measured since 1978 by a succession of spacecraft instru-
ments. Figure 1 shows the composite TSI record, compiled by
Fr¨ ohlich (2000, 2006) at the World Radiation Center at
Sunspot cycles 21, 22, and 23 are clearly visible. Sunspots are
manifestations of magnetic active regions, and their properties
can be measured directly on solar images and magnetograms.
Solar activity modulates TSI in a complex way: at solar max-
imum, when there are a large number of active regions, TSI
is high on average, but TSI drops sharply every time a large
sunspot group transits the solar disk.
Several Sun-like stars also show evidence of magnetic ac-
tivity, and their variability has been studied extensively with
photometry and spectroscopy (Radick et al. 1998; Lockwood
et al. 2007; Hall et al. 2009). For stars, magnetic activity cannot
be observed directly; instead, Ca HK emission index is taken
as a proxy for magnetic activity, and Str¨ omgren b+y bright-
ness is taken as a measure of bolometric brightness. One of
the fundamental questions asked regarding these solar analogs
is: do brightness and activity for these stars vary in a Sun-like
way? Observations by Lockwood et al. (2007) and Hall et al.
(2009) have shown that Sun-like stars seem to fall into two
groups, according to the correlation between their b+y bright-
ness and Ca HK emission: highly active stars display an inverse
correlation, while less active stars a direct one. They concluded
that there is some critical stellar activity level at which the
activity–brightness relation reverses. The Sun was put into the
less active group because we observe a direct correlation be-
tween time-averaged TSI and solar activity level.
In this work, we examine the relationship between TSI and
photometric solar data from the San Fernando Observatory
(SFO) and discuss what it reveals about the activity–brightness
correlations for the Sun-as-a-star. We then compare our results
with the activity–brightness relations that have been measured
for Sun-like stars.
2. SOLAR PHOTOMETRY AT THE SAN
2.1. Observing Program
At the SFO, full-disk photometric solar images are recorded
daily with two purpose-built telescopes, CFDT1 (5??pixels) and
CFDT2 (2.??5 pixels), described in Chapman et al. (1997). The
SFO observational record now includes about two solar-cycles’
worth of solar images at different wavelengths. The images
pertinent to this study are those at 672.3 nm with a 10 nm
bandpass (red), 472.3 nm with a 10 nm bandpass (blue), and
393.4 nm with a 1 nm bandpass (Caii K). Using the Kurucz
solar flux atlas (Kurucz 2005), we determined that photospheric
spectral lines block ∼2% and ∼11% of the continuum flux in
the passbands of the red and blue filters, respectively. Thus, our
red and blue images show primarily continuum emission, from
of the Caii K line, hence our Ca K images show emission in this
strong spectral line, which is formed in the chromosphere and
upper photosphere. Sample images appear in Preminger et al.
(2001). All images exhibit bright and dark features on a “quiet”
background. These features are manifestations of magnetic
active regions at different heights in the solar atmosphere. Dark
sunspots are the most prominent features on the red and blue
continuum images, while both sunspots and bright plages are
distinct in the Caii K-line images.
2.2. Data Analysis
SFO data reduction and analysis procedures are described
in detail in Walton et al. (1998) and Preminger et al. (2002).
Presented here is a brief overview. SFO images are suited to
The Astrophysical Journal Letters, 739:L45 (6pp), 2011 October 1Preminger, Chapman, & Cookson
The results of this study may help unite observations of
activity versus brightness for the Sun and Sun-like stars. In
doing so, they may help answer a persistent question regarding
the source of the Sun’s bolometric irradiance variations: is the
enhancement at solar maximum really caused by the magnetic
features discernable on Caii K-line (chromospheric) images?
Models such as that described by Equation (3), which assume
that known magnetic features are responsible for all irradiance
does not prove causation. Could the real source of long-term
variability be small-scale, low-contrast photospheric features
that we cannot resolve on our continuum images, or could the
solar cycle change in TSI be driven by co-temporal changes
in the effective temperature or radius of the photosphere? We
propose that if the mechanism of irradiance variability is the
same for the Sun and Sun-like stars, we can rule out these
possibilities: for, if Sun-like stars are indeed like the Sun, their
bolometric brightness should increase with activity, on stellar-
cycle timescales. This increase cannot have its origin in the
photosphere, since total visible continuum brightness (disk-
integrated, from all sources) is observed to decrease at the
same time. Therefore long-term bolometric variability must be
caused by the effects of magnetic active regions on spectral line
emission from the higher layers of the stellar atmosphere. In
order to confirm this hypothesis, it will be necessary to measure
the bolometric variability of Sun-like stars.
This research has been partially supported by NASA Living
with a Star grant NNX07AT19G, NASA grant NNX11AB51G,
and by NSF grant ATM-0848518.
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