[Paper Review] Empirical Limits on Radial Velocity Planet Detection for Young Stars

Lynne A. Hillenbrand, Howard Isaacson+4 more|arXiv (Cornell University)|Aug 15, 2014

Stellar, planetary, and galactic studies3 citations

TL;DR

This study establishes empirical limits on radial velocity (RV) planet detection around young, active stars by linking stellar chromospheric activity ($R'_{HK}$) to RV jitter. Using a sample of 150+ young solar-mass stars, it shows that jitter increases with activity, setting minimum detectable planet masses at >0.3, >0.2, and >0.1 $M_{\text{Jupiter}}$ for stars younger than 100, 300, and 1,000 Myr, respectively, under typical observation conditions.

ABSTRACT

We report initial results from our long term search using precision radial velocities for planetary-mass companions located within a few AU of stars younger than the Sun. Based on a sample of >150 stars, we define a floor in the radial velocity scatter, sigma_RV, as a function of the chromospheric activity level R'_{HK}. This lower bound to the jitter, which increases with increasing stellar activity, sets the minimum planet mass that could be detected. Adopting a median activity-age relationship reveals the astrophysical limits to planet masses discernable via radial velocity monitoring, as a function of stellar age. Considering solar-mass primaries having the mean jitter-activity level, when they are younger than 100 / 300 / 1000 Myr, the stochastic jitter component in radial velocity measurements restricts detectable companion masses to > 0.3 / 0.2 / 0.1 M_Jupiter. These numbers require a large number -- several tens -- of radial velocity observations taken over a time frame longer than the orbital period. Lower companion mass limits can be achieved for stars with less than the mean jitter and/or with an increased number of observations.

Motivation & Objective

• To determine the astrophysical limits on detecting low-mass planets via radial velocity (RV) monitoring around young, active stars.
• To quantify how stellar activity, measured by $R'_{HK}$, increases RV jitter and degrades planet detection sensitivity.
• To establish empirical relationships between $R'_{HK}$, RV scatter ($\sigma_{RV}$), and minimum detectable companion mass.
• To assess the impact of observation cadence and number of measurements on detecting sub-Jupiter mass planets around young stars.
• To compare empirical jitter-activity relations with prior theoretical models, showing significant discrepancies at high activity levels.

Proposed method

• Measured radial velocity scatter ($\sigma_{RV}$) across a sample of 150+ young, solar-mass stars with ages <1 Gyr.
• Correlated $\sigma_{RV}$ with chromospheric activity levels ($R'_{HK}$) derived from Ca II H and K line core fluxes.
• Fitted a linear relationship between $R'_{HK}$ and $\sigma_{RV}$ after iteratively removing 3$\sigma$ outliers to define empirical jitter limits.
• Used the Narayan et al. (2005) formalism to convert $\sigma_{RV}$ into minimum detectable planet mass for circular orbits.
• Simulated detection probabilities based on number of observations (Nobs) and orbital periods to derive 50% detection thresholds.
• Compared the empirical jitter-activity relation with prior models (e.g., Isaacson & Fischer 2010, Santos et al. 2010, Saar & Donahue 1997), revealing steeper slopes in the active regime.

Experimental results

Research questions

• RQ1 What is the empirical relationship between stellar chromospheric activity ($R'_{HK}$) and radial velocity jitter ($\sigma_{RV}$) in young, active stars?
• RQ2 What is the minimum planet mass that can be detected via radial velocity monitoring as a function of stellar age and activity level?
• RQ3 How does the number of radial velocity observations affect the detectability of low-mass planets around young stars?
• RQ4 How do existing theoretical jitter-activity relations compare to empirical measurements in the high-activity regime of young stars?
• RQ5 To what extent does stellar activity limit the detection of planetary companions within a few AU of young solar-mass stars?

Key findings

• The empirical jitter-activity relation shows that $\sigma_{RV}$ increases from ~3 m/s at low activity (log $R'_{HK} \approx -5$) to over 195 m/s at high activity (log $R'_{HK} \approx -4$).
• For young stars with mean jitter-activity levels, the minimum detectable planet mass is >0.3 $M_{\text{Jupiter}}$ for stars younger than 100 Myr, >0.2 $M_{\text{Jupiter}}$ at 300 Myr, and >0.1 $M_{\text{Jupiter}}$ at 1,000 Myr.
• The empirical jitter-activity relation is significantly steeper than prior models, especially at high activity levels, indicating that previous models underestimate jitter in very active young stars.
• Stars with lower-than-average jitter can achieve lower minimum detectable masses, and increasing the number of observations improves sensitivity to lower-mass planets.
• The study demonstrates that for a 1 $M_{\odot}$ star, a 50% detection probability for a planet is achievable only for masses above 0.3 $M_{\text{Jupiter}}$ in stars younger than 100 Myr, assuming more than 20 observations.
• The empirical relation shows that radial velocity monitoring of young stars is limited by stellar activity, not instrumental noise, especially for orbital periods shorter than the observation baseline.