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Issue
A&A
Volume 604, August 2017
Article Number L6
Number of page(s) 6
Section Letters
DOI https://doi.org/10.1051/0004-6361/201731107
Published online 01 August 2017

© ESO, 2017

Eclipsing binary stars enable empirical measurements of the stellar mass-radius relation. The low-mass regime, down to the hydrogen-burning mass limit, is poorly constrained by measurements of mass and radius, but is of particular relevance to the study of exoplanets. Stars with masses below 0.25 M⊙ are the most common stellar objects (Kroupa 2001; Chabrier 2003; Henry et al. 2006) and prove to be excellent candidates for the detection of Earth-sized planets (Berta-Thompson et al. 2015; Gillon et al. 2016, 2017; Luger et al. 2017) and their atmospheric characterization (de Wit et al. 2016). Determining the properties of exoplanets requires an accurate knowledge of their host star parameters, in particular the stellar mass. This motivates the study of low-mass eclipsing binaries (henceforth EBLMs; Triaud et al. 2013; Gómez Maqueo Chew et al. 2014), to empirically measure the mass-radius relation. In this context, we report our results on the eclipsing binary EBLM J0555-57. The system was detected by the Wide Angle Search for Planets (WASP1; Pollacco et al. 2006), and was identified as a non-planetary false-positive through follow-up measurements with the CORALIE spectrograph. We use radial velocities and two eclipse observations by the TRAPPIST and Euler telescopes, to determine the mass and radius of EBLM J0555-57Ab, to 85.2+4.0-3.0\hbox{$^{+4.0}_{-3.0}$}MJup (0.081 M⊙) and 0.84+0.14-0.04\hbox{$^{+0.14}_{-0.04}$}RJup (0.084 R⊙). This places EBLM J0555-57Ab at the minimum of the stellar mass-radius relation.

1. Observations

The source 1SWASPJ055532.69-571726.0 (EBLM J0555-57, J0555-57 for brevity) was observed by WASP-South between 2008-09-29 and 2012-03-22. The Hunter algorithm (Collier Cameron et al. 2007) detected 17 transit-like signals from 34 091 observations over four seasons, at a period of 7.7576 days. We obtained 30 spectra of EBLM J0555-57A, using the high-resolution fibre-fed CORALIE échelle-spectrograph (Queloz et al. 2001), mounted on the Euler telescope, between 2013-11-14 and 2017-01-21.

Two eclipse observations in the near-infrared z′-band were obtained with the Euler (Lendl et al. 2013) and TRAPPIST (Gillon et al. 2011; Jehin et al. 2011) telescopes, on the nights of 2014-02-24 and 2015-12-23 respectively. The observations reveal that our target was blended by a star that we label as J0555-57B. To confirm the source of the transit signal we compared observations with a large 38-pixel (px) aperture encompassing both stars, and a small 16 px aperture centred on the brighter star. A deeper transit signal was observed with the small aperture, identifying J0555-57A as the source of the eclipse signal. One spectrum of EBLM J0555-57B was obtained. The systemic radial velocities of the A and B components, γA = 19.537 ± 0.015 km s-1 and γB = 19.968 ± 0.021 km s-1, are nearly identical. A very similar position angle of the B component is observed on (blended) 2MASS images from 1999 and the Euler image, which shows that A and B also share the same proper motion. This confirms that EBLM J0555-57A, B, and the transiting EBLM J0555-57Ab constitute a hierarchical triple system.

Focused images in the B, V, R, and z′-bands were obtained with Euler on 2014-02-23 and 2016-01-10. We measured the separation between the primary and blend star to be 2.48 ± 0.01′′, with a position angle, PA = −105.57 ± 0.23°. The magnitude difference, Δz′ = 0.753 ± 0.035 mag, translates into a flux-dilution of the eclipse depth by a factor 1.500 ± 0.016. The eclipse observations were reduced to obtain a photometric light-curve, as described in Lendl et al. (2012) and Delrez et al. (2014) for Euler and TRAPPIST, respectively. A significant out-of-transit observation before ingress was obtained, but few out-of-transit measurements after egress could be made. Using literature broadband optical photometry and 2MASS J, H, and K magnitudes for the A and B components combined, together with the multi-colour magnitude differences (Δb = 0.95 ± 0.01 mag, Δr = 0.786 ± 0.017 mag, Δv = 0.832 ± 0.014 mag), we estimated IRFM temperatures (Blackwell & Shallis 1977) of 6450 ± 200 K and 5950 ± 200 K for the A and B components, respectively. A comparison to stellar model fluxes (Castelli & Kurucz 2004) was used, assuming a solar composition. The multi-colour observations and a Gaia DR1 parallax measurement (Gaia Collaboration 2016) were used to derive individual radii, RA = 1.17 ± 0.10 R⊙, and RB = 0.94 ± 0.08 R⊙. The parallax and angular separation of the A and B components determine a projected outer semi-major axis aAB,p = 479 ± 38 au.

thumbnail Fig. 1

Focused image (z′-band) of EBLM J0555-57 by Euler, resolving the eclipsed (A) and tertiary (B) components.

thumbnail Fig. 2

FWHM of the CCF of the spectra of EBLM J0555-57A. Blue: clean sample, red: contaminated sample. Grey: random draws from the posterior of the clean sample.

2. Data analysis

2.1. Radial velocities

Radial velocities of EBLM J0555-57A were extracted by cross-correlating individual spectra with a numerical G2 mask (Pepe et al. 2002). Varying seeing conditions resulted in fluctuations in the amount of flux from J0555-57B that enters the CORALIE fibre. This contamination can be identified by the full-width at half-maximum (FWHM) of the cross-correlation function (CCF). To select the non-contaminated spectra, we assumed two populations of points, a contaminated sample and a clean sample, with distinct means and variances. Following Hogg et al. (2010), a Markov chain Monte Carlo (MCMC) sampler was used to marginalise over the clean sample mean and variance, the contaminated sample mean and variance, and the prior probability that any point comes from the contaminated sample. We rejected a radial-velocity measurement and its associated spectrum when the FWHM had a posterior probability <1% to originate from the clean distribution, as indicated in Fig. 2. We excluded one point with a discrepant value in the span of the bisector inverse slope.

2.2. Spectral analysis

Atmospheric parameters were obtained via a wavelet-based Monte Carlo method (Gill et al., in prep.). The 18 spectra identified as uncontaminated were median-combined onto an identically sampled wavelength grid. After continuum regions were determined and normalised with spline functions, the spectrum was decomposed using a discrete Daubechies (k = 4) wavelet transform. We filtered out wavelet coefficients that corresponded to high-order noise and low-order systematics, associated with poor continuum placement. A grid of models was generated with the radiative transfer code spectrum (Gray & Corbally 1994), using marcs model atmospheres (Gustafsson et al. 2008), and version 5 of the GES atomic line list using iSpec (Blanco-Cuaresma et al. 2016), with solar abundances from Asplund et al. (2009). Filtered coefficients were compared to those from the grid of models using an MCMC sampler implemented in emcee (Foreman-Mackey et al. 2013). We used four free parameters, Teff, [Fe/H], log g, and vsini⋆, in the range 4000−8000 K (250 K steps), l3.5−5 dex (log g, 0.25 dex steps) and –1−1 dex (Fe/H, 0.5 dex steps).

The median value of the cumulative posterior probability distribution was used to estimate the atmospheric parameters for J0555-57A (Table 1). The precision associated with the wavelet method underestimates the uncertainty, so we adopt uncertainties by Blanco-Cuaresma et al. (2014) for the synthetic spectral fitting technique of Gaia FGK benchmark stars (124 K, 0.21 dex, and 0.14 dex for Teff, log g, and [Fe/H], respectively). The spectroscopic temperature measurements, TeffA = 6461 ± 124 K (18 spectra) and TeffB = 5717 ± 124 K (1 pectrum) are consistent with the initial IRFM estimates.

thumbnail Fig. 3

Transits of EBLM J0555-57Ab, observed by Euler (top), and TRAPPIST (bottom), with the best-fit model and residuals shown in the lower panels.

thumbnail Fig. 4

CORALIE radial velocities and Keplerian model for EBLM J0555-57A. Uncertainties are smaller than the symbols. Lower panels: residuals and span of bisector inverse slope (BIS).

3. Model of the data

The radial velocity and light curves were modeled using the ellc binary star model (Maxted 2016)2. An MCMC sampler (emcee; Foreman-Mackey et al. 2013), was used to fit the transit light-curves and radial velocities in a framework similar to that described in Triaud et al. (2013). We used the Bayesian information criterion (BIC; Schwarz 1978) to compare detrending baselines of varying complexity in time-, position-, FWHM-, and background-dependence. A flat baseline with a linear background subtraction is preferred for both light curves. Indeed both observations show a large fluctuation in the background flux.

Table 1

Parameters of EBLM J0555-57A and Ab.

The parameters used in the MCMC sampling are the period P, the mid-transit time t0, the observed transit depth Dobs, the transit duration W, the impact parameter b, the semi-amplitude K, the parameters esinω\hbox{$\sqrt{e} \sin \omega$}, ecosω\hbox{$\sqrt{e} \cos \omega$}, and the systemic velocity γ. The RV sample was separated into two parts, with distinct systemic velocities, to account for a change in the zero-point of CORALIE after a recent upgrade (Triaud et al. 2017). The geometric parameters of the system, R1/a, R2/a, and i were derived from the MCMC parameters using the formalism from Winn (2010), and were then passed to ellc. The TRAPPIST sequence was interrupted by a meridian flip; to account for a possible systematic offset in the flux measurement, an offset-factor was included for measurements before the flip.

We used a quadratic limb-darkening law in the MCMC analysis, with a Gaussian prior on coefficients that were interpolated from Claret (2004), using the spectroscopic parameters Teff, [Fe/H] and log g. We included nuisance parameters in the MCMC sampler, that scale uncertainties in the photometry and radial velocity to account for white noise. The baseline parameters for a linear background subtraction, meridian flip, and normalization are fitted by a least-squares algorithm. Where not explicitly stated otherwise, we used unbounded, or sensibly bounded uniform priors to constrain parameters to physical intervals, for instance (0 <e< 1). The B-component dilutes the transit depth by a factor fd = fA/ (fA + fB), where fA and fB denote the flux from the A and B components respectively. We sampled a Gaussian prior on this depth dilution factor, fd = 1.500 ± 0.016, to compute the true transit depth Dcalc at every step in the Markov chains. This calculated transit depth was used in the derivation of the physical parameters.

We analyzed this first global fit for correlated noise in the photometry (Gillon et al. 2012; Winn et al. 2008). The light curve was binned in the range of 10 to 30 min and the maximum root-mean square (rms) deviation of the residuals in this bin range was determined. The flux uncertainties were then rescaled by the ratio of the maximum binned rms deviation to the rms deviation of the un-binned residuals. This increased the uncertainties by factors of 2.02 and 1.37 for TRAPPIST and Euler respectively. We then performed a global MCMC fit using 100 chains of 10 000 steps each.

The modes of the marginalised posterior distributions for each jump parameter are reported with upper and lower 68% confidence intervals. The physical parameters of the system were derived from the MCMC parameters, in particular the parameter log g2, which is independent of the primary star mass (Southworth et al. 2004). We used the primary star density to iteratively refine the primary mass estimate M1. An initial primary density was estimated from the transit and was used to determine a primary mass using bagemass (Maxted et al. 2014). bagemass uses stellar evolution models by Weiss & Schlattl (2007). The primary star mass was then used with the transit and radial velocity model, to compute an updated density, and we proceeded iteratively. The calculated density was found to be consistent from the first iteration step.

thumbnail Fig. 5

Mass-radius posterior distribution for EBLM J0555-57Ab with an 68% confidence region (dashed). Isochrones for solar metalicity (Baraffe et al. 2015), and sub-solar metalicity [M/H = −0.5] (Baraffe et al. 1998) are plotted. Objects from Triaud et al. (2013), Ségransan et al. (2003), Demory et al. (2009), Bayliss et al. (2017), Díaz et al. (2014), Johnson et al. (2011), Siverd et al. (2012) and Chen et al. (2014) are also shown.

4. Results

Independently of any assumptions for the primary star, we obtain a surface gravity logg2=5.50-0.13+0.03\hbox{$\log g_2 = 5.50^{+0.03}_{-0.13}$} for EBLM J0555-57Ab, comparable to that of the recently announced brown dwarf EPIC 201702477b (Bayliss et al. 2017). We determine a mass function f(m)=0.0003686 -0.0000049+0.0000037\hbox{$f(m) = 0.0003686\,^{+0.0000037}_{-0.0000049}$}M⊙. Using the primary star mass determined with bagemass, we find a stellar companion with mass 85.2-3.9+4.0\hbox{$85.2^{+4.0}_{-3.9}$}MJup (0.0813-0.0037+0.0038\hbox{$0.0813^{+0.0038}_{-0.0037}$}M⊙) and radius 0.84-0.04+0.14\hbox{$0.84^{+0.14}_{-0.04}$}RJup (0.084-0.004+0.014\hbox{$0.084^{+0.014}_{-0.004}$}R⊙). This implies a mass ratio q=0.0721-0.0017+0.0019\hbox{$q = 0.0721 ^{+0.0019}_{-0.0017}$}. A lower uncertainty in the radius measurement may be achievable by high-precision photometry (e.g. TESS; Sullivan et al. 2015). The fit of the radial velocity results in an RMS deviation of 65 m s-1, and our analysis reveals a low but significant orbital eccentricity, e=0.0894-0.0036+0.0035\hbox{$e = 0.0894^{+0.0035}_{-0.0036}$}. The BIC of a forced circular fit, and the Lucy-Sweeney test (Lucy & Sweeney 1971) validate this orbital eccentricity, since its measurement is significant at ~25σ. The non-zero eccentricity of EBLM J0555-57Ab could indicate a previous orbital decay, for instance by Kozai-Lidov oscillations (Lidov 1961; Kozai 1962) induced by J0555-57B, or an undetected body, followed by tidal friction (Fabrycky & Tremaine 2007). At the current semi-major axis, a = 0.0817 au, such Kozai-Lidov oscillations are likely suppressed by general-relativistic precession (Fabrycky & Tremaine 2007; Petrovich 2015). It is unlikely that a contamination of the spectra causes the measured non-zero eccentricity, but further spectroscopic observations with a fibre of smaller diameter can clarify this. We note a discrepancy between the spectroscopic log g1spec = 4.18 ± 0.21 and that derived from the calculated radius and prior mass, logg1=4.5-0.13+0.03\hbox{$\log g_1 = 4.5^{+0.03}_{-0.13}$}. Spectroscopic measurements of log  g are known to be poorly constrained (Torres et al. 2012; Bruntt et al. 2012; Doyle 2015). We verify that adopting a prior on log g1 for the spectroscopic analysis, using the derived value, leads to a primary and companion mass and radius that are consistent with the previous result.

We conclude that EBLM J0555-57Ab is located just above the hydrogen-burning mass limit that separates stellar and sub-stellar objects (~ 83MJup for objects with [M/H] = –0.5; Baraffe et al. 1998). In Fig. 5 we show the posterior distribution of J0555-57Ab on the mass-radius diagram for brown dwarfs and low-mass stars. Our results using bagemass indicate an age of 1.9 ± 1.2 Gy for J0555-57A. The mass and radius of J0555-57Ab are consistent with models of a metal-poor, low-mass star. J0555-57Ab does not show evidence of a radius that is inflated, for instance by magnetic fields, as hypothesized by Lopez-Morales (2007) for low-mass stars. With its location on the lower bound of the mass-radius relation for stellar objects, J0555-57Ab is a critical object in the empirical calibration of the mass-radius relation in this regime. J0555-57Ab has a mass similar to that of TRAPPIST-1A. (Gillon et al. 2016, 2017). The low radius of EBLM J0555-57Ab, comparable to that of the low-mass star 2MASS J0523-1403 (Dieterich et al. 2014), demonstrates the size dispersion for low-mass stars. It is essential that such variations are understood as we prepare for the detection of multi-planetary systems orbiting ultra-cool dwarfs by experiments such as SPECULOOS (Gillon et al. 2013).

2

We validated ellc on two EBLM systems published in Triaud et al. (2013), reaching a 1σ-agreement on the derived parameters.

Acknowledgments

We thank the anonymous referee for valuable comments that improved the manuscript. The Swiss Euler Telescope is funded by the Swiss National Science Foundation. TRAPPIST-South is a project funded by the Belgian Fonds (National) de la Recherche Scientifique (F.R.S.-FNRS) under grant FRFC 2.5.594.09.F, with the participation of the Swiss National Science Foundation (FNS/SNSF). WASP-South is hosted by the South African Astronomical Observatory and we are grateful for their ongoing support and assistance. L. Delrez acknowledges support from the Gruber Foundation Fellowship. M. Gillon and E. Jehin are Belgian F.R.S.-FNRS Research Associates. This work was partially supported by a grant from the Simons Foundation (PI Queloz, grant number 327127).

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Appendix A: Radial-velocity data

Table A.1

CORALIE radial velocities of EBLM J0555-57A, and the probability that a point is not contaminated by the blend star.

All Tables

Table 1

Parameters of EBLM J0555-57A and Ab.

In the text
Table A.1

CORALIE radial velocities of EBLM J0555-57A, and the probability that a point is not contaminated by the blend star.

In the text

All Figures

thumbnail Fig. 1

Focused image (z′-band) of EBLM J0555-57 by Euler, resolving the eclipsed (A) and tertiary (B) components.
In the text
thumbnail Fig. 2

FWHM of the CCF of the spectra of EBLM J0555-57A. Blue: clean sample, red: contaminated sample. Grey: random draws from the posterior of the clean sample.
In the text
thumbnail Fig. 3

Transits of EBLM J0555-57Ab, observed by Euler (top), and TRAPPIST (bottom), with the best-fit model and residuals shown in the lower panels.
In the text
thumbnail Fig. 4

CORALIE radial velocities and Keplerian model for EBLM J0555-57A. Uncertainties are smaller than the symbols. Lower panels: residuals and span of bisector inverse slope (BIS).
In the text
thumbnail Fig. 5

Mass-radius posterior distribution for EBLM J0555-57Ab with an 68% confidence region (dashed). Isochrones for solar metalicity (Baraffe et al. 2015), and sub-solar metalicity [M/H = −0.5] (Baraffe et al. 1998) are plotted. Objects from Triaud et al. (2013), Ségransan et al. (2003), Demory et al. (2009), Bayliss et al. (2017), Díaz et al. (2014), Johnson et al. (2011), Siverd et al. (2012) and Chen et al. (2014) are also shown.
In the text

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