The Astrophysical Journal, 694:1085–1098, 2009 April 1 doi:10.1088/0004-637X/694/2/1085 C 2009. The American Astronomical Society. All rights reserved. Printed in the U.S.A. DIRECTLY DETERMINED LINEAR RADII AND EFFECTIVE TEMPERATURES OF EXOPLANET HOST STARS Gerard T. van Belle1 and Kaspar von Braun2 1 European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748 Garching, Germany; [email protected] 2 NASA Exoplanet Science Institute, California Institute of Technology, MC 100-22, Pasadena, CA 91125, USA; [email protected] Received 2008 October 15; accepted 2008 December 31; published 2009 March 23 ABSTRACT We present interferometric angular sizes for 12 stars with known planetary companions, for comparison with 28 additional main-sequence stars not known to host planets. For all objects we estimate bolometric fluxes and red- denings through spectral-energy distribution (SED) fits, and in conjunction with the angular sizes, measurements of effective temperature. The angular sizes of these stars are sufficiently small that the fundamental resolution limits of our primary instrument, the Palomar Testbed Interferometer, are investigated at the sub-milliarcsecond level and empirically established based upon known performance limits. We demonstrate that the effective tem- perature scale as a function of dereddened (V − K)0 color is statistically identical for stars with and without planets. A useful byproduct of this investigation is a direct calibration of the TEFF scale for solarlike stars, as − ∆ − = a function of both spectral type and (V K)0 color, with an precision of T (V K)0 138 K over the range (V − K)0 = 0.0–4.0 and ∆T SpType = 105 K for the range F6V–G5V. Additionally, in an Appendix we provide SED fits for the 166 stars with known planets which have sufficient photometry available in the literature for such fits; this derived “XO-Rad” database includes homogeneous estimates of bolometric flux, reddening, and angular size. Key words: infrared: stars – stars: fundamental parameters – techniques: interferometric Online-only material: color figures 1. INTRODUCTION determination of their distances (Perryman et al. 1997; Perryman &ESA1997); in combination with angular size measurements, 3 The formation, evolution, and environment of extrasolar their linear radii can be determined. planets are heavily influenced by their respective parent stars, The aim of this publication is to provide directly determined including the location and extent of the habitable zone. To R and TEFF astrophysical parameters of these 12 EHSs along provide constraints on the characterization of these planets, it is with equivalently derived parameters for a control group of therefore of significant scientific value to directly determine 28 main-sequence stars not currently known to host extrasolar the astrophysical parameters of the host stars. Of particular planets. In addition, we present estimates of astrophysical pa- interest are stellar radius (R) and effective surface temperature rameters for all currently known EHSs with sufficient literature photometry (166 of the 230 known).4 The literature photom- (TEFF) since these two parameters help uniquely characterize our knowledge of extrasolar planet environments. In the case of etry and aforementioned SED fitting provides, for the sample radius, planetary radii are frequently not directly measured but of 166 EHS stars, estimates of FBOL and θEST, done in the established through observations of transit events as a ratio of same way as done by van Belle et al. (2008), if a TEFF is as- planet to stellar radius. Measurements of planetary temperature sumed to be associated with the particular SED template being are directly linked to the spectral characteristics of the star used to fit the stellar photometry. These estimates of FBOL and irradiating the planet. θEST are presented in the “XO-Rad” database at the end of this For extrasolar planet hosting stars (EHSs) that can be re- paper. solved with interferometers, their angular sizes (θ) are directly We describe the observations and data reduction of these measured. Since the Stefan–Boltzman Law (Stefan 1879; Boltz- stars in Section 4; supporting data and SED fits are described 2 1/4 in Section 3; derived effective temperatures and radii are mann 1884) can be rewritten as TEFF ∼ (FBOL/θ ) , where F is the reddening-corrected bolometric flux, the effective presented in Section 5, along with comparisons of our values BOL to previous investigations (where available); finally, a detailed temperature TEFF can be directly measured for these stars. We obtained data with the Palomar Testbed Interferometer (PTI) for statical comparison of the EHS stars versus our control group is nine nearby EHSs with the aim of directly measuring their an- seen in Section 5.3. gular diameters, and computed estimates of their FBOL through spectral energy distribution (SED) fitting to their available lit- erature photometry. Additional EHS angular diameters from 3 It is misleading, however, to indicate that interferometric angular size measurements independently lead to characterizations of stellar luminosity. A the Center for High Angular Resolution Astronomy (CHARA) common mistake is to assume that radius and temperature measurements Array are also folded into this investigation (Baines et al. derived from a single interferometric angular size can be combined through use ∼ 2 4 2007, 2008a). Further interferometric work relevant to the di- of the Stefan–Boltzman law (L R TEFF) to “measure” luminosity. A cursory ameters of EHSs can be found in Mozurkewich et al. (1991, examination of the relationship between angular size and radius (R ∼ θ)and ∼ −1/2 2003). temperature (TEFF θ ) will demonstrate the new information contained in an angular size measurement is discarded when calculating L:only Observational biases cause a large fraction of known EHSs to bolometric flux and distance information affect measures of L. be nearby, enabling the use of Hipparcos parallaxes for a direct 4 As of 2008 February 1. 1085 1086 VAN BELLE & VON BRAUN Vol. 694 2. DESCRIPTION OF THE DATA SETS the 0.3 µmto30µm are used as available, including Johnson UBV (see, for example, Eggen 1963; Moreno 1971) Stromgren We present interferometric results on two different data sets: ubvyβ (Piirola 1976), 2MASS JHKs (Cutri et al. 2003), Geneva 1. Known EHSs for which we were able to obtain PTI data (Rufener 1976), and Vilnius UPXYZS (Zdanavicius et al. (Section 4) and calculate angular radii (Section 5). Knowl- 1972); flux calibrations are based upon the values given in edge of angular radii imposes an independent constraint Fukugita et al. (1995) and Cox (2000). The results of the fitting on the SED fitting (Section 3) and allows TEFF to be a de- for the calibrator stars is given in Table 1; for the EHSA and termined directly. We were also able to augment our PTI control sample stars, Table 2, and for the “XO-Rad” database, data with seven stars published from the CHARA Array by Table 3. Baines et al. (2008a). This data set comprises 12 stars, four of which have data from both CHARA and PTI. Together 4. OBSERVATIONS AND DATA REDUCTION this sample of EHSs with angular sizes is our “EHSA” 4.1. Visibility and Angular Sizes sample. 2. A number of main-sequence stars for which it was deemed The calibration of the target star visibility (V 2) data is per- 2 possible to resolve angular radii using PTI. This data set formed by estimating the interferometer system visibility (VSYS) comprises 28 stars and will be referred to as our “control using the calibration sources with model angular diameters and 2 sample.” These stars are not currently known to host then normalizing the raw target star visibility by VSYS to esti- extrasolar planets and thus serve as a comparison group mate the V2 measured by an ideal interferometer at that epoch for the EHSs with respect to astrophysical parameters. (Mozurkewich et al. 1991; Boden et al. 1998; van Belle & van Belle 2005). Uncertainties in the system visibility and the cali- Additionally, SED fits are provided for all the well- brated target visibility are inferred from internal scatter among characterized EHSs (status 2008 February 1, according to the the data in an observation using standard error-propagation cal- Exoplanet Encyclopedia5). The source data set comprises ap- culations (Boden et al. 1999). Calibrating our pointlike cal- proximately 230 stars (including those for which we obtained ibration objects against each other produced no evidence of PTI data), although most of the fainter (V>10) stars are ex- systematics, with all objects delivering reduced V 2 = 1. cluded due to a lack of available photometry; they are presented Visibility and uniform disk (UD) angular size (θUD) are related in the “XO-Rad” database in the Appendix. SED fitting for these 2 2 using the first Bessel function (J1): V = [2J1(x)/x] , where the stars is performed based on literature photometry and spectral − spatial frequency x = πBθ λ 1. We may establish UD angu- templates with associated estimates of effective temperatures. UD lar sizes for the target stars observed by the interferometer since the accompanying parameters (projected telescope-to-telescope 3. SUPPORTING DATA AND SPECTRAL ENERGY separation, or baseline, B and wavelength of observation λ)are DISTRIBUTION FITTING well characterized during the observation. The UD angular size For all of the sources considered in this investigation, SED can (and should) be connected to a more physical limb darkened fits were performed. Each fit, accomplished using available (LD) angular size (θLD); however, this is a minor effect since photometry and an appropriate template spectrum, produces θLD/θUD is small in the near-infrared (< 1.5%; see, for example, estimates for the bolometric flux (FBOL), the angular diameter Scholz & Takeda 1987; Tuthill 1994; Dyck et al. 1996, 1998; (θEST) and the reddening (AV); effective temperature during Davis et al. 2000). the SED fit is fixed for each of the template spectra.