[Paper Review] Photometric Variability in Kepler Target Stars. III. Comparison with the Sun on Different Timescales

Gibor Basri, Lucianne M. Walkowicz+1 more|arXiv (Cornell University)|Mar 30, 2013

Stellar, planetary, and galactic studies18 references60 citations

TL;DR

This study compares photometric variability of Kepler's solar-type stars with the Sun across timescales from 30 minutes to 3 months using refined Kepler light curves and a noise model. It confirms the Sun is representative of typical stellar variability on timescales longer than half a day, with 25–33% of solar-type stars more active than the Sun, and finds increasing activity with cooler temperatures, especially among M dwarfs.

ABSTRACT

We utilize Kepler data to study the precision differential photometric variability of solar-type and cooler stars at different timescales, ranging from half an hour to 3 months. We define a diagnostic that characterizes the median differential intensity change between data bins of a given timescale. We apply the same diagnostics to SOHO data that has been rendered comparable to Kepler. The Sun exhibits similar photometric variability on all timescales as comparable solar-type stars in the Kepler field (it is not unusually quiet). The previously-defined photometric "range" serves as our activity proxy (driven by starspot coverage). We revisit the fraction of comparable stars in the Kepler field that are more active than the Sun. The exact active fraction depends on what is meant by "more active than the Sun", and on the magnitude limit of the sample of stars considered. This active fraction is between a quarter and a third (depending on the timescale). We argue that a reliable result requires timescales of half a day or longer and stars brighter than Kepler magnitude of 14, otherwise non-stellar noise distorts it. We also analyze main sequence stars grouped by temperature from 6500-3500K. As one moves to cooler stars, the active fraction of stars becomes steadily larger (greater than 90% for early M dwarfs). The Sun is a good photometric model at all timescales for those cooler stars that have long-term variability within the span of solar variability.

Motivation & Objective

• To determine whether the Sun is representative of typical photometric variability in solar-type stars observed by Kepler.
• To quantify the fraction of Kepler stars more active than the Sun across different timescales and stellar temperatures.
• To develop a robust noise model to isolate intrinsic stellar variability from instrumental and observational noise.
• To assess the reliability of activity diagnostics in fainter stars, where non-stellar noise dominates.
• To examine how variability trends change across the main sequence, particularly for cooler stars.

Proposed method

• Utilizes Kepler Quarter 9 light curves processed with the PDC-MAP pipeline to minimize instrumental systematics.
• Applies a three-parameter noise model to define the lower envelope of variability, separating intrinsic stellar signal from noise.
• Defines two diagnostics: R_var (range of differential intensity over long timescales) and MDV(t_bin) (median differential intensity change over bin timescales).
• Compares these diagnostics between Kepler stars and SOHO solar data, rendered comparable to Kepler's photometric precision.
• Uses random phase sampling of solar cycles to assess when Kepler stars exceed solar variability levels.
• Applies magnitude and temperature binning (500K intervals) to analyze variability trends across stellar types.

Experimental results

Research questions

• RQ1 Is the Sun photometrically typical among solar-type stars in the Kepler field across different timescales?
• RQ2 What fraction of Kepler's solar-type stars exhibit greater photometric variability than the Sun, and how does this fraction depend on timescale and stellar magnitude?
• RQ3 How does the photometric variability of stars change with effective temperature, particularly for cooler stars?
• RQ4 To what extent is the observed variability in Kepler stars due to intrinsic stellar activity versus instrumental or observational noise?
• RQ5 Can the Sun serve as a reliable photometric model for stellar variability in stars with convective envelopes?

Key findings

• The Sun exhibits photometric variability levels consistent with the majority of solar-type stars in the Kepler field on timescales longer than half a day.
• Approximately 25–33% of brighter solar-type stars (M_Kep < 14) are more active than the Sun, depending on the timescale and definition of 'more active'.
• For timescales shorter than 12 hours, the active fraction is dominated by noise, making reliable comparisons impossible for fainter stars.
• The active fraction increases steadily with cooler stellar temperatures, exceeding 90% for M dwarfs.
• The Sun is a good photometric model for stars with convective envelopes across all timescales longer than 30 minutes, especially when normalized by R_var.
• Intrinsically variable stars in cooler samples (T_eff < 4500K) show a concentration at high MDV values, indicating a distinct population of highly variable stars.