EMPEROR

I. Exoplanet MCMC parallel tempering for RV orbit retrieval

¹ Instituto de Estudios Astrofísicos, Facultad de Ingeniería y Ciencias, Universidad Diego Portales, Av. Ejército 441, Santiago, Chile
² Centro de Astrofísica y Tecnologías Afines (CATA), Casilla 36-D, Santiago, Chile

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 28 February 2025
Accepted: 19 October 2025

Abstract

Aims. This paper presents EMPEROR, an open-source Python-based framework designed for the efficient detection and characterisation of exoplanets by using radial velocity (RV) methods. Its combination of performance, flexibility, and ease of use makes it a robust tool for any exoplanet detection endeavour. EMPEROR integrates dynamic nested sampling (DNS) and adaptive parallel tempering (APT) Markov chain Monte Carlo (MCMC) techniques, supporting multiple noise models such as Gaussian processes (GPs) and moving averages (MA). The framework facilitates systematic model comparison using statistical metrics, including Bayesian evidence (ln 𝒵) and Bayesian information criterion (BIC), while providing automated, publish-ready visualisations.

Methods. EMPEROR was evaluated across three distinct systems to assess its capabilities in different detection scenarios. The sampling performance, model selection, and search for Earth-mass planets were investigated in data for 51 Pegasi, HD 55693, and Barnard’s star (GJ 699).

Results. For 51 Pegasi, we find APT achieves an effective sampling increase by a factor of 3.76 over DNS, while retrieving tighter parameter estimates. For HD 55693, the stellar rotation, P_rot = 29.72_−0.02+^0.01, and magnetic cycle, P_mag = 2557.0^−36.7+^70.1, were recovered, while demonstrating the sensitivity of ln 𝒵 to prior selection. For Barnard’s star, several noise models were compared and the confirmed planet parameters were successfully retrieved with all of them. The best model shows a period of 3.1536±0.0003 d, minimum mass of 0.38±0.03 M_⊕, and semi-major axis of 0.02315±0.00039 AU.

Conclusions. Purely statistical inference might be insufficient on its own for robust exoplanet detection. Effective methodologies must integrate domain knowledge, heuristic criteria, and multi-faceted model comparisons. The versatility of EMPEROR in handling diverse noise structures, its systematic model selection, and its improved performance make it a valuable tool for RV exoplanetary studies.