[Paper Review] A quantitative analysis of stellar activity based on CoRoT photometric data

J. C. Hulot, F. Baudin+2 more|arXiv (Cornell University)|Apr 12, 2011

Astronomical Observations and Instrumentation1 references3 citations

TL;DR

This study introduces a Fourier-based activity index derived from CoRoT photometric light curves to quantify stellar microvariability across 430 main-sequence stars. Using a generalized semi-Lorentzian fit to low-frequency power spectra, it correlates the index with Rossby number and finds higher activity in cooler stars, with characteristic timescales increasing with rotation period.

ABSTRACT

The CoRoT satellite has made available high precision photometric observations of a large number of stars of different spectral types. Continuous photometric time series allow the characterization of stellar microvariability in a systematic way. We determine an index indicating the level of activity, derived from photometric data, for a large sample of stars with different color temperatures. We also assess to what extent this index can be related to an estimated Rossby number for stars whose rotation period can be estimated. We also estimate a characteristic lifetime of the surface heterogeneities. Our work is based on the Fourier analysis of stellar light curves. We analyzed the Fourier power spectra of 430 selected light curves obtained by CoRoT during three observation runs. The low-frequency contribution of the stellar variability is modelled by a "generalized semi-lorentzian" profile. An activity index is derived from the fitted amplitude and width of the semi-lorentzian model. Some of the Fourier spectra exhibit a rotational modulation which enables the determination of the rotation period. In addition, a convective turnover time is derived from a grid of stellar models, so that a Rossby number can be estimated. A characteristic lifetime of the phenomena causing the observed power at low frequency is assessed from the fitted model of the power spectrum and is compared to the rotation period. Higher values of the microvariability index are observed among the coolest stars from our sample. 28 light curves show a clear rotational modulation. The estimated Rossby number of most of the observed stars with a rotational modulation is less than 1. The activity index decreases with increasing Rossby number. The quality of the CoRoT data enables the determination of the characteristic lifetime of active structures. It is shown to increase with the rotation period.

Motivation & Objective

• To develop a quantitative, Fourier-based activity index from high-precision CoRoT photometric light curves for a large sample of main-sequence stars.
• To assess the relationship between the derived activity index and the Rossby number, using rotation periods estimated from light curve modulations.
• To estimate the characteristic lifetime of surface heterogeneities causing low-frequency photometric variability.
• To investigate the influence of stellar color temperature, rotation, and convective turnover on activity levels.
• To evaluate the limitations of single-parameter activity proxies like the Rossby number in the presence of observational biases and activity cycles.

Proposed method

• Fourier analysis of 430 CoRoT light curves to model low-frequency power excess using a generalized semi-Lorentzian profile.
• Fitting the amplitude and width of the semi-Lorentzian to derive a quantitative activity index from the power spectrum.
• Identifying rotational modulation in light curves via low-frequency peaks to estimate rotation periods.
• Using stellar model grids to compute convective turnover times and derive the Rossby number (Ro = P_rot / τ_conv).
• Estimating the characteristic lifetime of active structures from the fitted Lorentzian model parameters.
• Comparing the derived activity index with color temperature, Rossby number, and rotation period across spectral types.

Experimental results

Research questions

• RQ1 How does the Fourier-based activity index correlate with stellar color temperature across the main sequence?
• RQ2 To what extent can the derived activity index be linked to the Rossby number for stars with measurable rotation periods?
• RQ3 What is the relationship between the characteristic lifetime of surface heterogeneities and the stellar rotation period?
• RQ4 How do observational biases (e.g., short timescales, viewing geometry) affect the detection of rotational modulation and activity indices?
• RQ5 Can the activity index reliably quantify microvariability in stars without clear rotational modulation?

Key findings

• The activity index is highest for the coolest stars in the sample, showing a clear anti-correlation with color temperature.
• 28 light curves exhibit clear rotational modulation, with rotation periods decreasing with increasing color temperature.
• Most stars with rotational modulation have a Rossby number less than 1, indicating high magnetic activity, consistent with expectations.
• The activity index decreases with increasing Rossby number, confirming the inverse relationship between activity and dynamo efficiency.
• The characteristic lifetime of active structures increases with rotation period, though scatter is observed due to differing surface features (e.g., spots vs. faculae).
• The method successfully quantifies activity even in non-modulated stars, but unresolved low-frequency peaks may overestimate activity in slowly rotating M dwarfs.