Radial velocities in very-low mass stars

Detecting Planets Around Very Low Mass Stars with the Radial Velocity Method


The detection of planets around very low-mass stars with the radial velocity method is hampered by the fact that these stars are very faint at optical wavelengths where the most high-precision spectrometers operate. We investigate the precision that can be achieved in radial velocity measurements of low mass stars in the near infrared (nIR) -, -, and -bands, and we compare it to the precision achievable in the optical assuming comparable telescope and instrument efficiencies. For early-M stars, radial velocity measurements in the nIR offer no or only marginal advantage in comparison to optical measurements. Although they emit more flux in the nIR, the richness of spectral features in the optical outweighs the flux difference. We find that nIR measurement can be as precise than optical measurements in stars of spectral type M4, and from there the nIR gains in precision towards cooler objects. We studied potential calibration strategies in the nIR finding that a stable spectrograph with a ThAr calibration can offer enough wavelength stability for m s precision. Furthermore, we simulate the wavelength-dependent influence of activity (cool spots) on radial velocity measurements from optical to nIR wavelengths. Our spot simulations reveal that the radial velocity jitter does not decrease as dramatically towards longer wavelengths as often thought. The jitter strongly depends on the details of the spots, i.e., on spot temperature and the spectral appearance of the spot. At low temperature contrast ( K), the jitter shows a decrease towards the nIR up to a factor of ten, but it decreases substantially less for larger temperature contrasts. Forthcoming nIR spectrographs will allow the search for planets with a particular advantage in mid- and late-M stars. Activity will remain an issue, but simultaneous observations at optical and nIR wavelengths can provide strong constraints on spot properties in active stars.

Subject headings:
stars: activity — stars: low-mass, brown dwarfs — stars: spots — techniques: radial velocities

1. Introduction

The search for extrasolar planets with the radial velocity technique has led to close to 400 discoveries of planets around cool stars of spectral type F–M9. Fourteen years after the seminal discovery of 51 Peg b by Mayor & Queloz (1995), the radial velocity technique is still the most important technique to discover planetary systems, and radial velocity measurements are required to confirm planetary candidates found by photometric surveys including the satellite missions CoRoT and Kepler.

The largest number of planets found around solar-type stars are approximately as massive as Jupiter, and are orbiting their parent star at around 1 AU or below. In order to find Earth-mass planets in orbit around a star, the radial velocity technique either has to achieve a precision on the order of 0.1 m s, or one has to search around less massive stars, which would show a larger effect due to the gravitational influence of a companion. Therefore, low-mass M dwarfs are a natural target for the search for low-mass planets with the radial velocity technique. In addition, there seems to be no general argument against the possibility of life on planets that are in close orbit around an M dwarf (inside the habitable zone; Tarter et al., 2007). So these stars are becoming primary targets for the search for habitable planets.

So far, only a dozen M dwarfs are known to harbor one or more planets (e.g., Marcy et al., 1998; Udry et al., 2007). The problem with the detection of radial velocity variations in M dwarfs is that although they make up more than 70 % of the Galaxy including our nearest neighbors, they are also intrinsically so faint that the required data quality can not usually be obtained in a reasonable amount time, at least not in the spectral range most high resolution spectrographs operate at. M dwarfs have effective temperatures of 4000 K or less, and they emit the bulk of their spectral energy at wavelengths redward of 1 m. The flux emitted by an M5 dwarf at a wavelength of 600 nm is about a factor of 3.5 lower than the flux emitted at 1000 nm. Thus, infrared spectroscopy can be expected to be much more efficient in measuring radial velocities of low-mass stars.

A second limit on the achievable precision of radial velocity measurements is the presence of apparent radial velocity variations by corotating features and temporal variations of the stellar surface. Such features may influence the line profiles, and that can introduce a high noise level or be misinterpreted as radial velocity variations due to the presence of a planet. Flares on active M dwarfs might not pose a substantial problem to radial velocity measurements (Reiners, 2009), but corotating spots probably do. Desort et al. (2007) modeled the effect of a cool spot for observations of sun-like stars at optical wavelengths. Their results hint at a decrease of spot-induced radial velocity signals towards longer wavelengths. Martín et al. (2006) report the decrease of a radial velocity signal induced by a starspot on the very active M9 dwarf LP 944-20 ( km s); the amplitude they find is 3.5 km s at optical wavelengths but only an rms dispersion of 0.36 km s at 1.2 m. Thus, observations at infrared wavelength regions may substantially reduce the effect of stellar activity on radial velocity measurements, which would allow the detection of low-mass planets around active stars.

In this paper, we investigate the precision that can be reached in radial velocity measurements at infrared wavelength regions. The first goal of our work is to study the detectability of planets around low-mass stars using infrared spectrographs. We focus on the wavelength bands , and because these are the regions where spectrographs can be built at relatively low cost. Extending the wavelength coverage to the -band imposes much larger costs because of severe cooling requirements and large gaps in the spectral format. We chose to exclude this case from the current paper. Our second motivation is to see to what extent the radial velocity signal of active regions can be expected to vanish at infrared wavelength regions. So far, only rough estimates based on contrast arguments are available, and no detailed simulation has been performed.

The paper is organized as follows. In §2, we introduce the spectral characteristics of M dwarfs and compare model spectra used for our simulations to observations. In §3, we calculate radial velocity precisions that can be achieved at different wavelengths, and we investigate the influence of calibration methods. In §4, we simulate the effect of starspots on radial velocities in the infrared, and §5 summarizes our results.

2. Near infrared spectra of M dwarfs

M dwarfs emit the bulk of their flux at near-infrared (nIR) wavelengths between 1 and 2 m. However, high-resolution spectrographs operating in the nIR are not as ubiquitous as their counterparts in the optical. Therefore, our knowledge about M dwarf spectra past 1 m is far behind what is known about the visual wavelength range. Another complication is that strong absorption bands of water from the Earth’s atmosphere cover large fractions of the nIR wavelength range. Only some discrete portions of the region 1 – 2 m can be used for detailed spectroscopic work. For our investigation of radial velocity precision in M dwarfs, we concentrate on the t