[Paper Review] Maximum entropy detection of planets around active stars

P. Petit, J. Morin+6 more|arXiv (Cornell University)|Feb 28, 2015

Scientific Research and Discoveries1 references1 citations

TL;DR

This paper proposes a maximum entropy-based tomographic inversion method to detect close-in planets around active stars by simultaneously retrieving Doppler maps and orbital parameters. It successfully recovers radial velocity amplitudes down to ~50 m s⁻¹—near the photon noise limit—except when planetary orbits approach co-rotation, where biases emerge in amplitude estimates while period and phase remain robust.

ABSTRACT

Context. The high spot coverage of young active stars is responsible for distortions of spectral lines that hamper the detection of close-in planets through radial velocity methods. Aims. We aim to progress towards more e cient exoplanet detection around active stars by optimizing the use of Doppler Imaging in radial velocity measurements. Methods. We propose a simple method to simultaneously extract a brightness map and a set of orbital parameters through a tomographic inversion technique derived from classical Doppler mapping. Based on the maximum entropy principle, the underlying idea is to determine the set of orbital parameters that minimizes the information content of the resulting Doppler map. We carry out a set of numerical simulations to perform a preliminary assessment of the robustness of our method, using an actual Doppler map of the very active star HR 1099 to produce a realistic synthetic data set for various sets of orbital parameters of a single planet in a circular orbit. Results. Using a simulated time-series of 50 line profiles a ected by a peak-to-peak activity jitter of 2.5 km s 1 , we are able in most cases to recover the radial velocity amplitude, orbital phase and orbital period of an artificial planet down to a radial velocity semi-amplitude of the order of the radial velocity scatter due to the photon noise alone (about 50 m s 1 in our case). One noticeable exception occurs when the planetary orbit is close to co-rotation, in which case significant biases are observed in the reconstructed radial velocity amplitude, while the orbital period and phase remain robustly recovered. Conclusions. The present method constitutes a very simple way to extract orbital parameters from heavily distorted line profiles of active stars, when more classical radial velocity detection methods generally fail. It is easily adaptable to most existing Doppler Imaging codes, paving the way towards a systematic search for close-in planets orbiting young, rapidly-rotating stars.

Motivation & Objective

• To improve exoplanet detection around active stars where high spot coverage distorts spectral lines.
• To overcome limitations of classical radial velocity methods in the presence of strong stellar activity.
• To develop a robust, simple method that simultaneously inverts Doppler maps and orbital parameters.
• To assess the method’s performance under realistic conditions using synthetic data from an active star (HR 1099).
• To enable systematic detection of close-in planets around young, rapidly rotating stars.

Proposed method

• The method applies the maximum entropy principle to minimize the information content of Doppler maps during orbital parameter retrieval.
• It performs a tomographic inversion of time-series line profiles to jointly estimate brightness maps and orbital parameters.
• Orbital parameters (period, phase, semi-amplitude) are optimized to yield the smoothest possible Doppler map under the maximum entropy criterion.
• The approach is implemented via a numerical inversion framework compatible with existing Doppler imaging codes.
• Simulations use a realistic Doppler map of HR 1099 to generate synthetic line profiles with activity jitter of 2.5 km s⁻¹.
• The method is tested across various planetary orbital parameters in circular orbits to evaluate robustness.

Experimental results

Research questions

• RQ1 Can the maximum entropy principle improve the detection of close-in planets in the presence of strong stellar activity?
• RQ2 How accurately can orbital parameters be recovered when line profiles are severely distorted by spots?
• RQ3 What is the sensitivity limit of the method in terms of radial velocity amplitude detection?
• RQ4 How does orbital configuration—particularly co-rotation—impact the reliability of the retrieved parameters?
• RQ5 Can this method be integrated into existing Doppler imaging pipelines with minimal modification?

Key findings

• The method successfully recovers radial velocity semi-amplitudes down to approximately 50 m s⁻¹, matching the photon noise limit in the simulation.
• Orbital period and phase are robustly recovered across all tested configurations, even in the presence of strong activity jitter.
• Significant biases occur in the recovered radial velocity amplitude when the planetary orbit approaches co-rotation with the star’s rotation.
• The method remains effective even with a peak-to-peak activity jitter of 2.5 km s⁻¹, a realistic level for active stars.
• The approach is computationally simple and easily adaptable to existing Doppler imaging software.
• The technique enables detection of close-in planets in stars where classical radial velocity methods typically fail.