The Thermal Evolution of the Donors in AM CVn Binaries

(Abridged) We calculate the full stellar-structural evolution of donors in AM CVn systems formed through the WD channel coupled to the binary's evolution. Contrary to assumptions made in prior modelling, these donors are not fully convective over much of the AM CVn phase and do not evolve adiabatically under mass loss indefinitely. Instead, we identify three distinct phases of evolution: a mass transfer turn-on phase (during which the orbital period continues to decrease even after contact, the donor contracts, and the mass transfer rate accelerates to its maximum), a phase in which the donor expands adiabatically in response to mass loss, and a cooling phase beginning at orbital periods of approximately 45--55 minutes during which the donor contracts. The physics that determines the behaviour in the first and third phases, both of which are new outcomes of this study, are discussed in some detail. We find the overall duration of the turn-on phase to be between $\sim 10^4$-$10^6$ yrs, significantly longer than prior estimates. We predict the donor's luminosity and effective temperature. During the adiabatic expansion phase (ignoring irradiation effects), the luminosity is approximately $10^{-6}$--$10^{-4} L_\odot$ and the effective temperature is approximately 1000--1800 K. However, the flux generated in the accretion flow dominates the donor's intrinsic light at all times. The impact of irradiation on the donor extends the phase of adiabatic expansion to longer orbital periods and alters the donor's observational characteristics. Irradiated donors during the adiabatic phase can attain a surface luminosity of up to $\approx10^{-2} L_\odot$. We argue that the turn-on and cooling phases both will leave significant imprints on the AM CVn population's orbital period distribution.Comment: (20 pages, 20 figures, accepted to the Monthly Notices of the Royal Astronomical Society

The Connection Between Low-Mass X-ray Binaries and (Millisecond) Pulsars: A Binary Evolution Perspective

I review the evolutionary connection between low-mass X-ray binaries (LMXBs) and pulsars with binary companions (bPSRs) from a stellar binary evolution perspective. I focus on the evolution of stellar binaries with end-states consisting of a pulsar with a low-mass (<1.0 solar mass) companion, starting at the point the companion's progenitor first initiates mass transfer onto the neutron star. Whether this mass transfer is stable and the physics driving ongoing mass transfer partitions the phase space of the companions's initial mass and initial orbital period into five regions. The qualitative nature of the mass-transfer process and the binary's final end-state differ between systems in each region; four of these regions each produce a particular class of LMXBs. I compare the theoretical expectations to the populations of galactic field LMXBs with companion-mass constraints and field bPSRs. I show that the population of accreting millisecond pulsars are all identified with only two of the four LMXB classes and that these systems do not have readily identifiable progeny in the bPSR population. I discuss which sub-populations of bPSRs can be explained by binary evolution theory and those that currently are not. Finally I discuss some outstanding questions in this field.Comment: 9 pages, 5 figures, to appear in the proceedings of the 40 Years of Pulsars conference held at McGill University in August 200

Ultracompact Binaries as Bright X-Ray Sources in Elliptical Galaxies

Chandra observations of distant elliptical galaxies have revealed large numbers of Low Mass X-ray Binaries (LMXBs) accreting at rates in excess of 10^{-8} solar masses per year. The majority of these LMXBs reside in globular clusters (GCs) and it has been suggested that many of the field LMXBs also originated in GCs. We show here that ultracompact binaries with orbital periods of 8-10 minutes and He or C/O donors of 0.06-0.08 solar masses naturally provide the observed accretion rates from gravitational radiation losses alone. Such systems are predicted to be formed in the dense GC environment, a hypothesis supported by the 11.4 minute binary 4U 1820-30, the brightest persistent LMXB in a Galactic GC. These binaries have short enough lifetimes (less then 3 Myr) while bright that we calculate their luminosity function under a steady-state approximation. This yields a luminosity function slope in agreement with that observed for luminosities in the range of 6E37 ergs/sec to 5E38 ergs/sec, encouraging us to use the observed numbers of LMXBs per GC mass to calculate the accumulated number of ultracompact binaries. For a constant birthrate over 8 Gyrs, the number of ultracompact binaries which have evolved through this bright phase is nearly 4000 in a 10 million solar mass GC, consistent with dynamical interaction calculations. Perhaps most importantly, if all ultracompacts become millisecond radio pulsars, then the observed normalization agrees with the inferred number of millisecond radio pulsars in 47 Tuc and Galactic GCs in general.Comment: to Appear in Astrophysical Journal Letter

Gravitational Settling of ^{22}Ne in Liquid White Dwarf Interiors--Cooling and Seismological Effects

We assess the impact of the trace element ^{22}Ne on the cooling and seismology of a liquid C/O white dwarf (WD). Due to this elements' neutron excess, it sinks towards the interior as the liquid WD cools. The subsequent gravitational energy released slows the cooling of the WD by 0.25--1.6 Gyrs by the time it has completely crystallized, depending on the WD mass and the adopted sedimentation rate. The effects will make massive WDs or those in metal rich clusters (such as NGC 6791) appear younger than their true age. Our diffusion calculations show that the ^{22}Ne mass fraction in the crystallized core actually increases outwards. The stability of this configuration has not yet been determined. In the liquid state, the settled ^{22}Ne enhances the internal buoyancy of the interior and changes the periods of the high radial order g-modes by approximately 1%. Though a small adjustment, this level of change far exceeds the accuracy of the period measurements. A full assessment and comparison of mode frequencies for specific WDs should help constrain the still uncertain ^{22}Ne diffusion coefficient for the liquid interior.Comment: 26 pages (11 text pages with 15 figures); to appear in The Astrophysical Journa

White Dwarf Donors in Ultracompact Binaries: The Stellar Structure of Finite Entropy Objects

We discuss the mass-radius (M-R) relations for low-mass (M<0.1 Msun) white dwarfs (WDs) of arbitrary degeneracy and evolved (He, C, O) composition. We do so with both a simple analytical model and models calculated by integration of hydrostatic balance using a modern equation of state valid for fully ionized plasmas. The M-R plane is divided into three regions where either Coulomb physics, degenerate electrons or a classical gas dominate the WD structure. For a given M and central temperature, T_c, the M-R relation has two branches differentiated by the model's entropy content. We present the M-R relations for a sequence of constant entropy WDs of arbitrary degeneracy parameterized by M and T_c for pure He, C, and O. We discuss the applications of these models to the recently discovered accreting millisecond pulsars. We show the relationship between the orbital inclination for these binaries and the donor's composition and T_c. In particular we find from orbital inclination constraints that the probability XTE J1807-294 can accommodate a He donor is approximately 15% while for XTE J0929-304, it is approximately 35%. We argue that if the donors in ultracompact systems evolve adiabatically, there should be 60-160 more systems at orbital periods of 40 min than at orbital periods of 10 min, depending on the donor's composition.Comment: emulateapj style, 11 pages, 12 figures. Accepted to the Astrophysical Journal. Tables with interpolation routines of the M-R relations are available at http://www.physics.ucsb.edu/~cjdeloye/research.htm

The Turn-On of Mass Transfer in AM CVn Binaries: Implications for RX J0806+1527 and RX J1914+2456

We report on evolutionary calculations of the onset of mass transfer in AM CVn binaries, treating the donor's evolution in detail. We show that during the early contact phase, while the mass transfer rate, \Mdot, is increasing, gravity wave (GW) emission continues to drive the binary to shorter orbital period, \Porb. We argue that the phase where \Mdot > 0 and \nudot > 0 (\nu = 1/\Porb) can last between $10^3$ and $10^6$ yrs, significantly longer than previously estimated. These results are applied to RX J0806+1527 (\Porb = 321 s) and RX J914+2456 (\Porb=569 s), both of which have measured \nudot > 0. \emph{Thus, a \nudot > 0 does not select between the unipolar inductor and accretion driven models proposed as the source of X-rays in these systems}. For the accretion model, we predict for RX J0806 that \ddot{\nu} \approx \ee{1.0-1.5}{-28} Hz s$^{-2}$ and argue that timing observations can probe $\ddot{\nu}$ at this level with a total $\approx 20$ yr baseline. We also place constraints on each system's initial parameters given current observational data.Comment: 5 pages, 3 figures, accepted to ApJ

Arbitrarily Degenerate Helium White Dwarfs as Donors in AM CVn Binaries

We apply the Deloye & Bildsten (2003) isentropic models for donors in ultracompact low-mass X-ray binaries to the AM CVn population of ultracompact, interacting binaries. The mass-radius relations of these systems' donors in the mass range of interest (M_2<0.1 \msun) are not single-valued, but parameterized by the donor's specific entropy. This produces a range in the relationships between system observables, such as orbital period, \Porb, and mass transfer rate, \Mdot. For a reasonable range in donor specific entropy, \Mdot can range over several orders of magnitude at fixed \Porb. We determine the unique relation between \Mdot and $M_2$ in the AM CVn systems with known donor to accretor mass ratios, $q=M_2/M_1$. We use structural arguments, as well as each system's photometric behavior, to place limits on \Mdot and $M_2$ in each. Most systems allow a factor of about 3 variation in \Mdot, although V803 Cen, if the current estimates of its $q$ are accurate, is an exception and must have M_2 \approx 0.02 \msun and \Mdot \approx 10^{-10} \msun yr$^{-1}$. Our donor models also constrain each donor's core temperature, $T_c$, range and correlate $T_c$ with $M_2$. We examine how variations in donor specific entropy across the white dwarf family \citep{nele01a} of AM CVn systems affects this population's current galactic distribution. Allowing for donors that are not fully degenerate produces a shift in systems towards longer \Porb and higher \Mdot increasing the parameter space in which these systems can be found. This shift increases the fraction of systems whose \Porb is long enough that their gravity wave (GW) signal is obscured by the background of detached double white dwarf binaries that dominate the GW spectrum below a frequency $\approx 2$ mHz.Comment: 13 pages, 10 figures, uses emulateapj.cls. Accepted to Astrophysical Journa