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A full symmetry classification is given for models of energy transport in radiant plasma when the mass density is spatially variable and the diffusivity is nonlinear. A systematic search for conservation laws also leads to some potential symmetries, and to an integrable nonlinear model. Classical point symmetries, potential symmetries and nonclassical symmetries are used to effect variable reductions and exact solutions. The simplest time-dependent solution is shown to be stable, and relevant to a closed system., Comment: 13 pages. arXiv admin note: text overlap with arXiv:math-ph/0605081, arXiv:1101.4755 by other authors

In the frames of the DLVO theory the root mean square amplitude and correlation length of capillary waves in thin liquid films are calculated. Their dependencies on some important physical parameters are studied. Two models are considered: films with classical interfaces and films between lipid bilayers. The performed numerical analysis demonstrates essential difference in their behavior, which is due to the different elastic properties of the film surfaces in the models.

Ultracompact X-ray binaries (UCXBs) are thought to have relatively simple binary evolution post-contact, leading to clear predictions of their luminosity function. We test these predictions by studying the long-term behavior of known UCXBs in our Galaxy, principally using data from the MAXI All-Sky Survey and the Galactic Bulge Scans with RXTE's PCA instrument. Strong luminosity variations are common (and well-documented) among persistent UCXBs, which requires an explanation other than the disk instability mechanism. We measure the luminosity function of known UCXBs in the Milky Way, which extends to lower luminosities than some proposed theoretical luminosity functions of UCXBs. The difference between field and globular cluster X-ray luminosity functions in other galaxies cannot be explained by an increased fraction of UCXBs in globular clusters. Instead, our measured luminosity function suggests that UCXBs only make up a small fraction of the X-ray binaries above a few times 10^36 ergs/s in both old field populations and globular clusters., Comment: 17 pages, 7 pages of which are 6 multi-part figures. ApJ, in press

We study the mass transfer rates and disk stability conditions of ultracompact X-ray binaries (UCXBs) using empirical time-averaged X-ray luminosities from Paper I (Cartwright et al. 2013) and compiled information from the literature. The majority of UCXBs are consistent with evolutionary tracks for white dwarf donors. Three UCXBs with orbital periods longer than 40 minutes have mass transfer rates above 10^{-10} Msun/year, inconsistent with white dwarf donor tracks. We show that if helium star donors can retain their initial high entropy, they can explain the observed mass transfer rates of these UCXBs. Several UCXBs show persistent luminosities apparently below the disk instability limit for irradiated He accretion disks. We point out that a predominantly C and/or O disk (as observed in the optical spectra of several) lowers the disk instability limit, explaining this disagreement. The orbital period and low time-averaged mass transfer rate of 2S 0918-549 provide evidence that the donor star is a low-entropy C/O white dwarf, consistent with optical spectra. We combine existing information to constrain the masses of the donors in 4U 1916-053 (0.064+-0.010 Msun) and 4U 1626-67 (<0.036 Msun for a 1.4 Msun neutron star). We show that 4U 1626-67 is indeed persistent, and not undergoing a transient outburst, leaving He star models as the best explanation for the donor., Comment: 13 pages, 7 figures, ApJ in press

Common-envelope events (CEEs), during which two stars temporarily orbit within a shared envelope, are believed to be vital for the formation of a wide range of close binaries. For decades, the only evidence that CEEs actually occur has been indirect, based on the existence of systems that could not be otherwise explained. Here we propose a direct observational signature of CEE arising from a physical model where emission from matter ejected in a CEE is controlled by a recombination front as the matter cools. The natural range of timescales and energies from this model, as well the expected colors, light-curve shapes, ejection velocities and event rate, match those of a recently-recognized class of red transient outbursts., Comment: 6 main and 22 supplemental pages, 5 total figures, one table and 2 movies. This is the authors version of the work. It is posted here by permission of the AAAS for personal use, not for redistribution. The definitive version was published in Science, vol 339, 2013, http://www.sciencemag.org/content/339/6118/433.abstract

This work aims to present our current best physical understanding of common-envelope evolution (CEE). We highlight areas of consensus and disagreement, and stress ideas which should point the way forward for progress in this important but long-standing and largely unconquered problem. Unusually for CEE-related work, we mostly try to avoid relying on results from population synthesis or observations, in order to avoid potentially being misled by previous misunderstandings. As far as possible we debate all the relevant issues starting from physics alone, all the way from the evolution of the binary system immediately before CEE begins to the processes which might occur just after the ejection of the envelope. In particular, we include extensive discussion about the energy sources and sinks operating in CEE, and hence examine the foundations of the standard energy formalism. Special attention is also given to comparing the results of hydrodynamic simulations from different groups and to discussing the potential effect of initial conditions on the differences in the outcomes. We compare current numerical techniques for the problem of CEE and also whether more appropriate tools could and should be produced (including new formulations of computational hydrodynamics, and attempts to include 3D processes within 1D codes). Finally we explore new ways to link CEE with observations. We compare previous simulations of CEE to the recent outburst from V1309 Sco, and discuss to what extent post-common-envelope binaries and nebulae can provide information, e.g. from binary eccentricities, which is not currently being fully exploited., Comment: 83 pages (11 chapters, 2 appendixes), 10 figures, Astronomy & Astrophysics Review format. This version contains revisions as a response to community comments

Globular clusters (GCs) effectively produce dynamically-formed low-mass X-ray binaries (LMXBs). Observers detect ~100 times more LMXBs per stellar mass in GCs compared to stars in the fields of galaxies. It has also been observationally established that metal-rich GCs are about 3 times more likely to contain an X-ray source than their metal-poor counterparts. Recent observations have shown that this ratio holds in extragalactic GCs for all bright X-ray sources with Lx between 2X10^{37} and 5X10^{38} erg/s. In this Letter, we propose that the observed metallicity dependence of LMXBs in extragalactic GCs can be explained by the differences in the number densities and average masses of red giants in populations of different metallicities. Red giants serve as seeds for the dynamical production of bright LMXBs via two channels - binary exchanges and physical collisions - and the increase of the number densities and masses of red giants boost LMXB production, leading to the observed difference. We also discuss a possible effect of the age difference in stellar populations of different metallicities., Comment: 5 pages, 2 figures, submitted to ApJL

We present comprehensive observational results of the metallicity effect on the fraction of globular clusters (GC) that contain low-mass X-ray binaries (LMXB), by utilizing all available data obtained with Chandra for LMXBs and HST ACS for GCs. Our primary sample consists of old elliptical galaxies selected from the ACS Virgo and Fornax surveys. To improve statistics at both the lowest and highest X-ray luminosity, we also use previously reported results from other galaxies. It is well known that the LMXB fraction is considerably higher in red, metal-rich, than in blue, metal-poor GCs. In this paper, we test whether this metallicity effect is X-ray luminosity-dependent, and find that the effect holds uniformly in a wide luminosity range. This result is statistically significant (at >= 3 sigma) in LMXBs with luminosities in the range LX = 2 x 10^37 - 5 x 10^38 erg s-1, where the ratio of LMXB fractions in metal-rich to metal-poor GCs is R = 3.4 +- 0.5. A similar ratio is also found at lower (down to 10^36 erg s-1) and higher luminosities (up to the ULX regime), but with less significance (~2 sigma confidence). Because different types of LMXBs dominate in different luminosities, our finding requires a new explanation for the metallicity effect in dynamically formed LMXBs. We confirm that the metallicity effect is not affected by other factors such as stellar age, GC mass, stellar encounter rate, and galacto-centric distance., Comment: 21 pages, 5 figures, accepted in ApJ

In interacting binaries, comparison of a donor star's radial response to mass loss with the response of its Roche radius determines whether mass loss persists and, if so, determines the timescale and stability of the ensuing evolutionary phase. For giants with deep convective envelopes, the canonical description holds that once mass transfer begins it typically proceeds catastrophically on the dynamical timescale, as the star cannot lose sufficient heat in order to avoid expansion. However, we demonstrate that the local thermal timescale of the envelope's superadiabatic outer surface layer remains comparable to that of mass loss in most cases of "dynamical" mass loss. We argue therefore that if mass loss proceeds on a timescale longer than this, then even a deep convective envelope will not dramatically expand, as the surface layer will have time to relax thermally and reconstitute itself. We demonstrate that in general the polytropic approximation gives much too strict a criterion for stability, and discuss the dependence of the donor's response on its radius in addition to its core mass. In general, we find that the effective response of the donor on rapid timescales cannot be determined accurately without detailed evolutionary calculations., Comment: 5 pages, 4 figures, 1 table. ApJL accepted

One class of compact binaries of special interest is that of double white dwarfs (DWDs). For many of these systems, the exact nature of the evolutionary channels by which they form remains uncertain. The canonical explanation calls for the progenitor binary system to undergo two subsequent mass-transfer events, both of which are unstable and lead to a common envelope (CE) phase. However, it has been shown that if both CE events obey the standard alpha prescription, it is not possible to reproduce all of the observed systems. As an alternative prescription, the gamma-formalism was proposed, which parametrizes the fraction of angular momentum carried away with mass loss, in contrast to the alpha prescription, which parametrizes energy loss. We demonstrate that the gamma-prescription is also inadequate in describing the evolution of an arbitrary DWD binary; clearly we require a deeper understanding of the physical mechanisms underlying their formation. We then present a detailed model for the evolution of Red Giant -- Main Sequence binaries during the first episode of mass transfer, and demonstrate that their evolution into DWDs need not arise through two phases of dynamical mass loss. Instead, the first episode of dramatic mass loss may be stable, non-conservative mass transfer. The second phase is then well described by the alpha prescription. We find that the considered progenitors can reproduce the properties of the observed helium DWDs in which the younger component is the more massive., Comment: 6 pages, 2 figures. Proceedings for the ESO Conference, the workshop 'Evolution of Compact Binaries', 6-11 March 2011, Vi\~na del Mar, Chile, edited by L. Schmidtobreick, M. R. Schreiber, C. Tappert, ASP conference series

Although several dozen double white dwarfs (DWDs) have been observed, for many the exact nature of the evolutionary channel(s) by which they form remains uncertain. The canonical explanation calls for the progenitor binary system to undergo two subsequent mass-transfer events, both of which are unstable and lead to a common envelope (CE). However, it has been shown that if both CE events obey the standard alpha-prescription (parametrizing energy loss), it is not possible to reproduce all of the observed systems. The gamma-prescription was proposed as an alternative to this description, instead parametrizing the fraction of angular momentum carried away in dynamical-timescale mass loss. In this paper, we analyze simultaneous energy and angular-momentum conservation, and show that the gamma-prescription cannot adequately describe a CE event for an arbitrary binary, nor can the first phase of mass loss always be understood in general as a dynamical-timescale event. We consider in detail the first episode of mass transfer in binary systems with initially low companion masses, with a primary mass in the range 1.0--1.3 solar masses and an initial mass ratio between the secondary and primary stars of 0.83--0.92. In these systems, the first episode of dramatic mass loss may be stable, non-conservative mass transfer. This strips the donor's envelope and dramatically raises the mass ratio; the considered progenitor binary systems can then evolve into DWDs after passing through a single CE during the second episode of mass loss. We find that such a mechanism reproduces the properties of the observed DWD systems which have an older component with less than approximately 0.46 solar masses and mass ratios between the younger and older WDs greater than 1., Comment: Submitted to ApJ, ApJ format. 15 pages, 17 figures, 2 tables

Although many double white dwarfs (DWDs) have been observed, the evolutionary channel by which they are formed from low-mass/long-period red-giant-main-sequence (RG-MS) binaries remains uncertain. The canonical explanations involve some variant of double common-envelope (CE) evolution, however it has been found that such a mechanism cannot produce the observed distribution. We present a model for the initial episode of mass transfer (MT) in RG-MS binaries, and demonstrate that their evolution into double white dwarfs need not arise through a double-CE process, as long as the initial primary's core mass (Md,c) does not exceed 0.46M$_{\odot}$. Instead, the first episode of dramatic mass loss may be stable, non-conservative MT. We find a lower bound on the fraction of transferred mass that must be lost from the system in order to provide for MT, and demonstrate the feasibility of this channel in producing observed low-mass (with M$_{d,c}$ < 0.46M$_{\odot}$) DWD systems., Comment: 2 pages, 1 figure, Conference Proceedings for the International Conference on Binaries, Mykonos, Greece

Inspired by the recent identification of the first candidate BH-WD X-ray binaries, where the compact accretors may be stellar-mass black hole candidates in extragalactic globular clusters, we explore how such binaries could be formed in a dynamical environment. We provide analyses of the formation rates via well known formation channels like binary exchange and physical collisions and propose that the only possibility to form BH-WD binaries is via coupling these usual formation channels with subsequent hardening and/or triple formation. Indeed, we find that the most important mechanism to make a BH-WD X-ray binary from an initially dynamically formed BH-WD binary is triple induced mass transfer via the Kozai mechanism. Even using the most optimistic estimates for the formation rates, we cannot match the observationally inferred production rates if black holes undergo significant evaporation from the cluster or form a completely detached subcluster of black holes. We estimate that at least 1% of all formed black holes, or presumably 10% of the black holes present in the core now, must be involved in interactions with the rest of the core stellar population., Comment: 10 pages, 2 figures, submitted to ApJ

Using our recently improved Monte Carlo evolution code, we study the evolution of the binary fraction in globular clusters. In agreement with previous N-body simulations, we find generally that the hard binary fraction in the core tends to increase with time over a range of initial cluster central densities for initial binary fractions <~ 90%. The dominant processes driving the evolution of the core binary fraction are mass segregation of binaries into the cluster core and preferential destruction of binaries there. On a global scale, these effects and the preferential tidal stripping of single stars tend to roughly balance, leading to overall cluster binary fractions that are roughly constant with time. Our findings suggest that the current hard binary fraction near the half-mass radius is a good indicator of the hard primordial binary fraction. However, the relationship between the true binary fraction and the fraction of main-sequence stars in binaries (which is typically what observers measure) is non-linear and rather complicated. We also consider the importance of soft binaries, which not only modify the evolution of the binary fraction, but can drastically change the evolution of the cluster as a whole. Finally, we describe in some detail the recent addition of single and binary stellar evolution to our cluster evolution code., Comment: 8 pages, 7 figures in emulateapj format. Submitted to ApJ

In this paper we consider generalization of procedure of construction of potential systems for systems of partial differential equations with multidimensional spaces of conservation laws. More precisely, for construction of potential systems in cases when dimension of the space of local conservation laws is greater than one, instead of using only basis conservation laws we use their arbitrary linear combinations being inequivalent with respect to equivalence group of the class of systems or symmetry group of the fixed system. It appears that the basis conservation laws can be equivalent with respect to groups of symmetry or equivalence transformations, or vice versa, the number of independent in this sense linear combinations of conservation laws can be grater than the dimension of the space of conservation laws. The first possibility leads to an unnecessary, often cumbersome, investigation of equivalent systems, the second one makes possible missing a great number of inequivalent potential systems. Examples of all these possibilities are given., Comment: 5 pages