Inferring hemispheric asymmetries of stellar active regions through the information content of astrometric signals

Abstract

Photometric light curves suffer from fundamental degeneracies that limit surface information recovery. We demonstrate that astrometry enables access to complementary information through photocentre variations induced by rotating surface features. The forthcoming commissioning of microarcsecond-precision astrometric missions presents an opportunity to improve stellar surface mapping. This paper extends a previous theoretical framework for stellar surface mapping, along three primary directions: (1) we derive analytical selection rules showing that astrometry is sensitive to spherical harmonic modes not detectable via photometry, particularly odd-$\ell$ modes that encode north-south asymmetries; (2) we quantify the information content of combined photometric and astrometric observations, showing that the rank of observable modes grows faster for combined observations than for either technique alone, though the fraction of recoverable modes still decreases asymptotically with increasing spatial resolution; and (3) we reframe astrometric jitter-traditionally treated as noise in exoplanet studies-as a signal encoding stellar surface structure. Given the limited proposed target lists of high-precision astrometric missions, this capability is particularly valuable: understanding host star surfaces is crucial for both removing stellar signals from exoplanet detections and characterising star-planet interactions. We show that while Sun-like stars require sub-microarcsecond precision, evolved stars with angular diameter and larger spots present immediate opportunities with current technology, such as the Gaia mission.

Figures (13)

• Figure 1: All spherical harmonic modes up to and including degree five, viewed pole on.
• Figure 2: All spherical harmonic modes up to and including degree five, viewed equatorially.
• Figure 3: A diagram of the shape of the photometric deflection caused by a single starspot rotating at a constant rate across a stellar disk, from $-\pi/2$ (left limb / bluer) to $+\pi/2$ (right limb / redder). The signal includes foreshortening and limb-darkening. The size of both the signal and starspot are not to scale.
• Figure 4: A step plot demonstrating the cumulative number of spherical harmonic modes accessible via different observing methods. The dashed black line represents the total possible number of spherical harmonic modes. The upper x axis is the characteristic scale of each spherical harmonic degree. The coloured lines represent the mean cumulative rank for each observational method across 500 inclinations, randomly sampled in $\cos\theta_\text{obs}$. The number of accessible modes increases approximately linearly with $\ell_{\max}$ for each method individually, while the combined astrometric and photometric observations recover modes at a faster rate, demonstrating that the two techniques provide complementary information.
• Figure 5: This figure shows the posterior shrinkage factors for each spherical harmonic mode, up to degree 9, for different observational methods, viewed from the stellar equator. Each mode in the degree is organised, left to right, as $m = 0, 1, -1, 2, -2, ..., \ell, -\ell$. Note that for odd$-\ell$ modes, only astrometry can constrain any modes. Also note that as the degree increases, the relative number of modes with any constraint decreases.