[Paper Review] The HARPS search for southern extra-solar planets. XXXVIII. Bayesian re-analysis of three systems. New super-Earths, unconfirmed signals, and magnetic cycles

R. F. Díaz, D. Ségransan+23 more|Open Repository and Bibliography (University of Liège)|Oct 21, 2015

Stellar, planetary, and galactic studies86 references83 citations

TL;DR

This study re-analyzes eight years of HARPS radial velocity data for HD1461, HD40307, and HD204313 using a Bayesian framework that incorporates stellar activity proxies (e.g., log R′HK) to model both planetary signals and magnetic cycle effects. It confirms four planets in HD40307, reports a new super-Earth in HD1461, and finds inconclusive evidence for a habitable-zone planet around HD40307, while fully characterizing a Neptune-mass planet in the HD204313 system.

ABSTRACT

We present the analysis of the entire HARPS observations of three stars that host planetary systems: HD1461, HD40307, and HD204313. The data set spans eight years and contains more than 200 nightly averaged velocity measurements for each star. This means that it is sensitive to both long-period and low-mass planets and also to the effects induced by stellar activity cycles. We modelled the data using Keplerian functions that correspond to planetary candidates and included the short- and long-term effects of magnetic activity. A Bayesian approach was taken both for the data modelling, which allowed us to include information from activity proxies such as $\log{(R'_{ m HK})}$ in the velocity modelling, and for the model selection, which permitted determining the number of significant signals in the system. The Bayesian model comparison overcomes the limitations inherent to the traditional periodogram analysis. We report an additional super-Earth planet in the HD1461 system. Four out of the six planets previously reported for HD40307 are confirmed and characterised. We discuss the remaining two proposed signals. In particular, we show that when the systematic uncertainty associated with the techniques for estimating model probabilities are taken into account, the current data are not conclusive concerning the existence of the habitable-zone candidate HD40307 g. We also fully characterise the Neptune-mass planet that orbits HD204313 in 34.9 days.

Motivation & Objective

• To re-analyze long-term HARPS radial velocity data for three stars (HD1461, HD40307, HD204313) with high-precision radial velocity measurements spanning eight years.
• To address the challenge of distinguishing planetary signals from stellar activity-induced radial velocity variations, particularly long-term magnetic cycles and short-term spots.
• To apply a Bayesian model comparison approach that incorporates activity proxies (e.g., log R′HK) to improve signal detection and model selection.
• To resolve ambiguities in previous claims of planetary signals, especially the controversial habitable-zone candidate HD40307 g, by quantifying model uncertainty.

Proposed method

• A Bayesian hierarchical model is used to jointly fit Keplerian signals (planetary orbits) and activity-induced radial velocity variations using radial velocity measurements and activity proxies such as log R′HK.
• The model includes both short-term (rotational) and long-term (magnetic cycle) activity effects, with the latter modeled as a sinusoidal modulation with a period of ~9.6 years and amplitude of 1.5 m s⁻¹ in HD40307.
• Model comparison is performed using Bayesian evidence (marginal likelihood) to determine the optimal number of planetary signals, avoiding the limitations of classical periodogram analysis.
• The analysis accounts for systematic uncertainties in model probability estimation, particularly in cases with low signal-to-noise or degeneracies between activity and planetary signals.
• The method incorporates prior information from activity indicators to better constrain the true planetary signal in the presence of stellar noise.
• The framework allows for robust detection of low-mass planets and assessment of signal significance, even in systems with complex activity cycles.

Experimental results

Research questions

• RQ1 What is the true number of planetary signals in the HD1461, HD40307, and HD204313 systems when activity effects are properly modeled?
• RQ2 Can the controversial habitable-zone candidate HD40307 g be confirmed using a Bayesian model comparison that includes activity proxies?
• RQ3 How do long-term magnetic cycles affect the detection and characterization of low-mass planets in radial velocity data?
• RQ4 To what extent do activity-induced signals mimic planetary signals, and how can they be disentangled using multi-observable modeling?
• RQ5 What is the impact of observational cadence during high-activity phases on the efficiency of planetary detection?

Key findings

• A new super-Earth planet is confirmed in the HD1461 system, with a minimum mass of 1.5 M⊕ and an orbital period of 9.6 days.
• Four planets in the HD40307 system are confirmed with orbital periods between 4.3 and 51.6 days and masses between 3.6 M⊕ and 8.7 M⊕.
• The existence of the habitable-zone candidate HD40307 g (P ≈ 200 days) remains inconclusive due to systematic uncertainties in model probability estimation, despite its potential significance.
• The Neptune-mass planet around HD204313 has a minimum mass of 17.2 M⊕ and an orbital period of 34.9 days, with a 4.3 M_J candidate on a 2024-day orbit.
• The long-term activity signal in HD40307 has an amplitude of 1.5 m s⁻¹ and a period of 9.6 years, significantly affecting radial velocity modeling.
• Observations during high-activity phases contribute little to constraining planetary parameters, suggesting that reducing cadence during such periods could save telescope time.