The Mass of the Black Hole in Cygnus X-1

Cygnus X-1 is a binary star system that is comprised of a black hole and a massive giant companion star in a tight orbit. Building on our accurate distance measurement reported in the preceding paper, we first determine the radius of the companion star, thereby constraining the scale of the binary system. To obtain a full dynamical model of the binary, we use an extensive collection of optical photometric and spectroscopic data taken from the literature. By using all of the available observational constraints, we show that the orbit is slightly eccentric (both the radial velocity and photometric data independently confirm this result) and that the companion star rotates roughly 1.4 times its pseudosynchronous value. We find a black hole mass of M =14.8\pm1.0 M_{\sun}, a companion mass of M_{opt}=19.2\pm1.9 M_{\sun}, and the angle of inclination of the orbital plane to our line of sight of i=27.1\pm0.8 deg.Comment: Paper II of three papers on Cygnus X-1; 27 pages including 5 figures and 3 tables, ApJ in pres

Tests of stellar model atmospheres by optical interferometry III: NPOI and VINCI interferometry of the M0 giant gamma Sge covering 0.5 - 2.2 microns

Aims: We present a comparison of the visual and NIR intensity profile of the M0 giant gamma Sagittae to plane-parallel ATLAS 9 as well as to plane-parallel & spherical PHOENIX model atmospheres. Methods: We use previously described visual interferometric data obtained with the NPOI in July 2000. We apply the recently developed technique of coherent integration, and thereby obtain visibility data of more spectral channels and with higher precision than before. In addition, we employ new measurements of the K-band diameter of gamma Sagittae obtained with the instrument VINCI at the VLTI in 2002. Results: The spherical PHOENIX model leads to a precise definition of the Rosseland angular diameter and a consistent high-precision diameter value for our NPOI and VLTI/VINCI data sets of Theta_Ross=6.06 pm 0.02 mas, with the Hipparcos parallax corresponding to R_Ross=55 pm 4 R_sun, and with the bolometric flux corresponding to an effective temperature T_eff=3805 pm 55 K. Our visual visibility data close to the first minimum and in the second lobe constrain the limb-darkening effect and are generally consistent with the model atmosphere predictions. The visual closure phases exhibit a smooth transition between 0 and pi. Conclusions: The agreement between the NPOI and VINCI diameter values increases the confidence in the model atmosphere predictions from optical to NIR wavelengths as well as in the calibration and accuracy of both interferometric facilities. The consistent night-by-night diameter values of VINCI give additional confidence in the given uncertainties. The closure phases suggest a slight deviation from circular symmetry, which may be due to surface features, an asymmetric extended layer, or a faint unknown companion.Comment: 12 pages, 9 figures, accepted by A&A. Also available from http://www.aanda.org/articles/aa/pdf/forth/aa5853_06.pd

Hubble Space Telescope Observations of SV Cam: II. First Derivative Lightcurve Modelling using PHOENIX and ATLAS Model Atmospheres

The variation of the specific intensity across the stellar disc is essential input parameter in surface brightness reconstruction techniques such as Doppler imaging, where the relative intensity contributions of different surface elements are important in detecting starspots. We use PHOENIX and ATLAS model atmospheres to model lightcurves derived from high precision (S/N ~ 5000) HST data of the eclipsing binary SV Cam (F9V + K4V), where the variation of specific intensity across the stellar disc will determine the contact points of the binary system lightcurve. For the first time we use chi^2 comparison fits to the first derivative profiles to determine the best-fitting model atmosphere. We show the wavelength dependence of the limb darkening and that the first derivative profile is sensitive to the limb-darkening profile very close to the limb of the primary star. It is concluded that there is only a marginal difference (< 1sigma) between the chi^2 comparison fits of the two model atmospheres to the HST lightcurve at all wavelengths. The usefulness of the second derivative of the light-curve for measuring the sharpness of the primary's limb is investigated, but we find that the data are too noisy to permit a quantitative analysis.Comment: 10 pages, 20 figures, accepted by MNRA

Tests of stellar model atmospheres by optical interferometry: VLTI/VINCI limb-darkening measurements of the M4 giant psi phe

We present K-band interferometric measurements of the limb-darkened intensity profile of the M4 giant star psi Phoenicis obtained with VLTI/VINCI. High-precision squared visibility amplitudes in the second lobe of the visibility function were obtained employing two 8.2 m UTs. This succeeded one month after light from UTs was first combined for interferometric fringes. In addition, we sampled the visibility function at small spatial frequencies using the 40cm test siderostats. Our measurement constrains the diameter of the star as well as its CLV. We construct a spherical hydrostatic PHOENIX model atmosphere based on spectrophotometric data from the literature and confront its CLV prediction with our interferometric measurement. We compare as well CLV predictions by plane-parallel hydrostatic PHOENIX, ATLAS9, and ATLAS12 models. We find that the Rosseland angular diameter as predicted by comparison of the spherical PHOENIX model with spectrophotometry is in good agreement with our interferometric diameter measurement. The shape of our measured visibility function in the second lobe is consistent with all considered PHOENIX and ATLAS model predictions, and significantly different from UD and FDD models. We derive high-precision fundamental parameters for psi Phe, namely a Rosseland angular diameter of 8.13 +/- 0.2 mas, with the Hipparcos parallax corresponding to a Rosseland linear radius R of 86 +/- 3 Rsun and an effective temperature of 3550 +/- 50 K, with R corresponding to a luminosity of log (L/Lsun)=3.02 +/- 0.06. Together with evolutionary models, these values are consistent with a mass of 1.3 +/- 0.2 Msun, and a surface gravity of log g = 0.68 +/- 0.11.Comment: 13 pages, 6 figures, accepted for publication in A&

Extended envelopes around Galactic Cepheids III. Y Oph and alpha Per from near-infrared interferometry with CHARA/FLUOR

Unbiased angular diameter measurements are required for accurate distances to Cepheids using the interferometric Baade Wesselink method (IBWM). The precision of this technique is currently limited by interferometric measurements at the 1.5% level. At this level, the center-to-limb darkening (CLD) and the presence of circumstellar envelopes (CSE) seem to be the two main sources of bias. The observations we performed aim at improving our knowledge of the interferometric visibility profile of Cepheids. In particular, we assess the systematic presence of CSE around Cepheids in order determine accurate distances with the IBWM free from CSE biased angular diameters. We observed a Cepheid (Y Oph) for which the pulsation is well resolved and a non-pulsating yellow supergiant (alpha Per) using long-baseline near-infrared interferometry. We interpreted these data using a simple CSE model we previously developed. We found that our observations of alpha Per do not provide evidence for a CSE. The measured CLD is explained by an hydrostatic photospheric model. Our observations of Y Oph, when compared to smaller baseline measurements, suggest that it is surrounded by a CSE with similar characteristics to CSE found previously around other Cepheids. We have determined the distance to Y Oph to be d=491+/-18 pc. Additional evidence points toward the conclusion that most Cepheids are surrounded by faint CSE, detected by near infrared interferometry: after observing four Cepheids, all show evidence for a CSE. Our CSE non-detection around a non-pulsating supergiant in the instability strip, alpha Per, provides confidence in the detection technique and suggests a pulsation driven mass-loss mechanism for the Cepheids.Comment: accepted for publication in Ap

Resolving Vega and the inclination controversy with CHARA/MIRC

Optical and infrared interferometers definitively established that the photometric standard Vega (alpha Lyrae) is a rapidly rotating star viewed nearly pole-on. Recent independent spectroscopic analyses could not reconcile the inferred inclination angle with the observed line profiles, preferring a larger inclination. In order to resolve this controversy, we observed Vega using the six-beam Michigan Infrared Combiner on the Center for High Angular Resolution Astronomy Array. With our greater angular resolution and dense (u,v)-coverage, we find Vega is rotating less rapidly and with a smaller gravity darkening coefficient than previous interferometric results. Our models are compatible with low photospheric macroturbulence and also consistent with the possible rotational period of ~0.71 days recently reported based on magnetic field observations. Our updated evolutionary analysis explicitly incorporates rapid rotation, finding Vega to have a mass of 2.15+0.10_-0.15 Msun and an age 700-75+150 Myrs, substantially older than previous estimates with errors dominated by lingering metallicity uncertainties (Z=0.006+0.003-0.002).Comment: Accepted for publication in ApJ Letter