Empirical Main Sequence Research Articles

Superhumps in Cataclysmic Binaries. XXV. qcrit, \U0001d6dc(q), and Mass‐Radius

ABSTRACTWe report on successes and failures in searching for positive superhumps in cataclysmic variables, and show the superhumping fraction as a function of orbital period. Basically, all short‐period system do, all long‐period systems do not, and a 50% success rate is found at Porb = 3.1 ± 0.2 hr. We can use this to measure the critical mass ratio for the creation of superhumps. With a mass‐radius relation appropriate for cataclysmic variables, and an assumed mean white‐dwarf mass of 0.75 M⊙, we find a mass ratio qcrit = 0.35 ± 0.02. We also report superhump studies of several stars of independently known mass ratio: OU Vir, XZ Eri, UU Aqr, and KV UMa (=XTE J1118+480). The latter two are of special interest, because they represent the most extreme mass ratios for which accurate superhump measurements have been made. We use these to improve the ε(q) calibration, by which we can infer the elusive q from the easy‐to‐measure ε (the fractional period excess of Psuperhump over Porb). This relation allows mass and radius estimates for the secondary star in any cataclysmic variable (CV) showing superhumps. The consequent mass‐radius law shows an apparent discontinuity in radius near 0.2 M⊙, as predicted by the disrupted magnetic braking model for the 2.1–2.7 hr period gap. This is effectively the “empirical main sequence” for CV secondaries.

An empirical test of the theoretical population corrections to the red clump absolute magnitude

The mean absolute magnitude of the local red clump (RC), MRCλ, is a very well-determined quantity owing to the availability of accurate Hipparcos parallaxes for several hundred RC stars, potentially allowing it to be used as an accurate extragalactic distance indicator. Theoretical models predict that the RC mean magnitude is dependent on both age and metallicity and, furthermore, that these dependences are non-linear. This suggests that a population correction, ΔMRCλ, based on the star formation rate (SFR) and age–metallicity relation (AMR) of the system in question, should be applied to the local RC magnitude before it can be compared to the RC in any other system in order to make a meaningful distance determination. Using a sample of eight Galactic open clusters and the Galactic globular cluster 47 Tuc, we determine the cluster distances, and hence the RC absolute magnitude in V, I and K, by applying our empirical main-sequence (MS) fitting method, which utilizes a large sample of local field dwarfs with accurate Hipparcos parallaxes. The nine clusters have metallicities in the range −0.7 ≤[Fe/H]≤+0.02 and ages from 1 to 11 Gyr, enabling us to make a quantitative assessment of the age and metallicity dependences of ΔMRCλ predicted by the recent theoretical models of Girardi & Salaris and Salaris & Girardi. We find excellent agreement between the empirical data and the models in all three passbands, with no statistically significant trends or offsets, thus fully confirming the applicability of the models to single-age, single-metallicity stellar populations. Since, from the models, ΔMRCλ is a complicated function of both metallicity and age, if this method is used to derive distances to composite populations, it is essential to have an accurate assessment of the SFR and AMR of the system in question, if errors of several tenths of a magnitude are to be avoided. Using recent determinations of the SFR and AMR for four systems — the Large and Small Magellanic Clouds, Carina and the solar neighbourhood — we examine the quantity IRCobs−KRCobs, which is the difference between the mean magnitude of the RC in the I band and the K band. Comparing the theoretical predictions with the most recent observational data, we find complete agreement between the observations and the models, thus confirming even further the applicability of the population corrections predicted from theory.

Hydrogen Deficiency in Algol Secondaries

AbstractA study was carried out for 309 Algol systems to show that most of the secondary components of low mass-ratio systems are hydrogen deficient stars. This hydrogen deficiency is evident from their positions on a Δ log L - Δ log T plot, where Δ is the difference between the observed quantity, log L or log Te, and the value of the same quantity for a star of the same mass on the empirical Main Sequence. The secondary components are shown to occupy the region of mass losing helium dwarfs on this plot. A correlation has also been obtained between the excess of effective temperature and the mass ratio of the system.

Mass Loss in Semi-Detached Binaries

AbstractPre-Main-Sequence contracting objects, post-Main-Sequence expanding stars and mass-losing components of semi-detached systems all occupy more or less the same region in the conventional H-R-diagram. We make a transformation to variables Δ (logL) and Δ (log Te), where Δ is the difference between the observed quantity, log L or log Te, and the value of that quantity which a star of the same mass would have on the empirical Main Sequence. It is demonstrated that a plot between the new variables clearly separates the mass-losing stars from other objects which is essentially an effect of the increasing abundance of helium relative to hydrogen.