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Register a new userObservational Constraints on the Degenerate Mass-Radius Relation
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The white dwarf mass-radius relationship is fundamental to modern astrophysics. It is central to routine estimation of DA white dwarf masses derived from spectroscopic temperatures and gravities. It is also the basis for observational determinations of the white dwarf initial-final mass relation. Nevertheless, definitive and detailed observational confirmations of the mass-radius relation (MRR) remain elusive due to a lack of sufficiently accurate white dwarf masses and radii. Current best estimates of masses and radii allow only broad conclusions about the expected inverse relation between masses and radii in degenerate stars. In this paper we examine a restricted set of 12 DA white dwarf binary systems for which accurate (1) trigonometric parallaxes, (2) spectroscopic effective temperatures and gravities, and (3) gravitational redshifts are available. We consider these three independent constraints on mass and radius in comparison with an appropriate evolved MRR for each star. For the best-determined systems it is found that the DA white dwarfs conform to evolved theoretical MRRs at the 1-{sigma} to 2-{sigma} level. For the white dwarf 40 Eri B (WD0413-077) we find strong evidence for the existence of a thin hydrogen envelope. For other stars improved parallaxes will be necessary before meaningful comparisons are possible. For several systems current parallaxes approach the precision required for the state-of-the-art mass and radius determinations that will be obtained routinely from the Gaia mission. It is demonstrated here how these anticipated results can be used to firmly constrain details of theoretical mass-radius determinations.
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The fundamental properties of low-mass stars are not as well understood as those of their more massive counterparts. The best method for constraining these properties, especially masses and radii, is to study eclipsing binary systems, but only a small number of late-type (M0 or later) systems have been identified and well-characterized to date. We present the discovery and characterization of six new M dwarf eclipsing binary systems. The twelve stars in these eclipsing systems have masses spanning 0.38-0.59 Msun and orbital periods of 0.6--1.7 days, with typical uncertainties of ~0.3% in mass and 0.5--2.0% in radius. Combined with six known systems with high-precision measurements, our results reveal an intriguing trend in the low-mass regime. For stars with M=0.35-0.80 Msun, components in short-period binary systems (P<1 day; 12 stars) have radii which are inflated by up to 10% (mean=4.8+/-1.0%) with respect to evolutionary models for low-mass main-sequence stars, whereas components in longer-period systems (>1.5 days; 12 stars) tend to have smaller radii (mean=1.7+/-0.7%). This trend supports the hypothesis that short-period systems are inflated by the influence of the close companion, most likely because they are tidally locked into very high rotation speeds that enhance activity and inhibit convection. In summary, very close binary systems are not representative of typical M dwarfs, but our results for longer-period systems indicate that the evolutionary models are broadly valid in the M~0.35-0.80 Msun regime.
The Gaia Data Release 1 (DR1) sample of white dwarf parallaxes is presented, including 6 directly observed degenerates and 46 white dwarfs in wide binaries. This data set is combined with spectroscopic atmospheric parameters to study the white dwarf mass-radius relationship (MRR). Gaia parallaxes and G magnitudes are used to derive model atmosphere dependent white dwarf radii, which can then be compared to the predictions of a theoretical MRR. We find a good agreement between Gaia DR1 parallaxes, published effective temperatures (Teff) and surface gravities (log g), and theoretical MRRs. As it was the case for Hipparcos, the precision of the data does not allow for the characterisation of hydrogen envelope masses. The uncertainties on the spectroscopic atmospheric parameters are found to dominate the error budget and current error estimates for well-known and bright white dwarfs may be slightly optimistic. With the much larger Gaia DR2 white dwarf sample it will be possible to explore the MRR over a much wider range of mass, Teff, and spectral types.
Most globular clusters have half-mass radii of a few pc with no apparent correlation with their masses. This is different from elliptical galaxies, for which the Faber-Jackson relation suggests a strong positive correlation between mass and radius. Objects that are somewhat in between globular clusters and low-mass galaxies, such as ultra-compact dwarf galaxies, have a mass-radius relation consistent with the extension of the relation for bright ellipticals. Here we show that at an age of 10 Gyr a break in the mass-radius relation at ~10^6 Msun is established because objects below this mass, i.e. globular clusters, have undergone expansion driven by stellar evolution and hard binaries. From numerical simulations we find that the combined energy production of these two effects in the core comes into balance with the flux of energy that is conducted across the half-mass radius by relaxation. An important property of this `balanced evolution is that the cluster half-mass radius is independent of its initial value and is a function of the number of bound stars and the age only. It is therefore not possible to infer the initial mass-radius relation of globular clusters and we can only conclude that the present day properties are consistent with the hypothesis that all hot stellar systems formed with the same mass-radius relation and that globular clusters have moved away from this relation because of a Hubble time of stellar and dynamical evolution.
Young stellar clusters across nearly five orders of magnitude in mass appear to follow a power-law mass-radius relationship (MRR), $R_{star} propto M_{star}^{alpha}$, with $alpha approx 0.2 - 0.33$. We develop a simple analytic model for the cluster mass-radius relation. We consider a galaxy disc in hydrostatic equilibrium, which hosts a population of molecular clouds that fragment into clumps undergoing cluster formation and feedback-driven expansion. The model predicts a mass-radius relation of $R_{star} propto M_{star}^{1/2}$ and a dependence on the kpc-scale gas surface density $R_{star} propto Sigma_{rm g}^{-1/2}$, which results from the formation of more compact clouds (and cluster-forming clumps within) at higher gas surface densities. This environmental dependence implies that the high-pressure environments in which the most massive clusters can form also induce the formation of clusters with the smallest radii, thereby shallowing the observed MRR at high-masses towards the observed $R_{star} propto M_{star}^{1/3}$. At low cluster masses, relaxation-driven expansion induces a similar shallowing of the MRR. We combine our predicted MRR with a simple population synthesis model and apply it to a variety of star-forming environments, finding good agreement. Our model predicts that the high-pressure formation environments of globular clusters at high redshift naturally led to the formation of clusters that are considerably more compact than those in the local Universe, thereby increasing their resilience to tidal shock-driven disruption and contributing to their survival until the present day.
The mass-radius relation of white dwarfs is largely determined by the equation of state of degenerate electrons, which causes the stellar radius to decrease as mass increases. Here we observationally measure this relation using the gravitational redshift effect, a prediction of general relativity that depends on the ratio between stellar mass and radius. Using observations of over three thousand white dwarfs from the Sloan Digital Sky Survey and the Gaia space observatory, we derive apparent radial velocities from absorption lines, stellar radii from photometry and parallaxes, and surface gravities by fitting atmospheric models to spectra. By averaging the apparent radial velocities of white dwarfs with similar radii and, independently, surface gravities, we cancel out random Doppler shifts and measure the underlying gravitational redshift. Using these results, we empirically measure the white dwarf mass-radius relation across a wide range of stellar masses. Our results are consistent with leading theoretical models, and our methods could be used with future observations to empirically constrain white dwarf core composition and evolution.
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