### Abstract

We derive masses and radii for both components in the single-lined eclipsing binary HAT-TR-205-013, which consists of an F7 V primary and a late M dwarf secondary. The system's period is short, P = 2.230736 ± 0.000010 days, with an orbit indistinguishable from circular, e = 0.012 ± 0.021. We demonstrate generally that the surface gravity of the secondary star in a single-lined binary undergoing total eclipses can be derived from characteristics of the light curve and spectroscopic orbit. This constrains the secondary to a unique line in the mass-radius diagram, with M/R^{2} = constant. For HAT-TR-205-013, we assume the orbit has been tidally circularized and that the primary's rotation has been synchronized and aligned with the orbital axis. Our observed line broadening, V_{rot} sin i_{rot} = 28.9 ± 1.0 km s^{-1}, gives a primary radius of R_{A} = 1.28 ± 0.04 R_{⊙}. Our light-curve analysis leads to the radius of the secondary, R_{B} = 0.167 ± 0.006 R _{⊙}, and the semimajor axis of the orbit, a = 7.54 ± 0.30 M_{⊙} = 0.0351 ± 0.0014 AU. Our single-lined spectroscopic orbit and the semimajor axis then yield the individual masses M_{B} = 0.124 ± 0.010 M_{⊙} and M_{A} = 1.04 ± 0.13 M_{⊙}. Our result for HAT-TR-205-013 B lies above the theoretical mass-radius models from the Lyon group, consistent with results from double-lined eclipsing binaries. The method we describe offers the opportunity to study the very low end of the stellar mass-radius relation.

Original language | English (US) |
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Pages (from-to) | 573-582 |

Number of pages | 10 |

Journal | Astrophysical Journal |

Volume | 663 |

Issue number | 1 I |

DOIs | |

State | Published - Jul 1 2007 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Astronomy and Astrophysics
- Space and Planetary Science

### Keywords

- Binaries: eclipsing
- Binaries: spectroscopic
- Stars: fundamental parameters
- Stars: low-mass, brown dwarfs
- Stars: rotation

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## Cite this

*Astrophysical Journal*,

*663*(1 I), 573-582. https://doi.org/10.1086/518413