### 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) |
---|---|

Pages (from-to) | 573-582 |

Number of pages | 10 |

Journal | Astrophysical Journal |

Volume | 663 |

Issue number | 1 I |

DOIs | |

State | Published - Jul 1 2007 |

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### All Science Journal Classification (ASJC) codes

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*Astrophysical Journal*,

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

}

*Astrophysical Journal*, vol. 663, no. 1 I, pp. 573-582. https://doi.org/10.1086/518413

**The mass and radius of the unseen M dwarf companion in the single-lined eclipsing binary hat-tr-205-013.** / Beatty, Thomas G.; Fernández, José M.; Latham, David W.; Bakos, Gáspár Á; Kovács, Géza; Noyes, Robert W.; Stefanik, Robert P.; Torres, Guillermo; Everett, Mark E.; Hergenrother, Carl W.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The mass and radius of the unseen M dwarf companion in the single-lined eclipsing binary hat-tr-205-013

AU - Beatty, Thomas G.

AU - Fernández, José M.

AU - Latham, David W.

AU - Bakos, Gáspár Á

AU - Kovács, Géza

AU - Noyes, Robert W.

AU - Stefanik, Robert P.

AU - Torres, Guillermo

AU - Everett, Mark E.

AU - Hergenrother, Carl W.

PY - 2007/7/1

Y1 - 2007/7/1

N2 - 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/R2 = 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, Vrot sin irot = 28.9 ± 1.0 km s-1, gives a primary radius of RA = 1.28 ± 0.04 R⊙. Our light-curve analysis leads to the radius of the secondary, RB = 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 MB = 0.124 ± 0.010 M⊙ and MA = 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.

AB - 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/R2 = 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, Vrot sin irot = 28.9 ± 1.0 km s-1, gives a primary radius of RA = 1.28 ± 0.04 R⊙. Our light-curve analysis leads to the radius of the secondary, RB = 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 MB = 0.124 ± 0.010 M⊙ and MA = 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.

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U2 - 10.1086/518413

DO - 10.1086/518413

M3 - Article

AN - SCOPUS:34547222380

VL - 663

SP - 573

EP - 582

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 1 I

ER -