Dean M. Townsley

Three-Dimensional Simulations of the Deflagration Phase of the Gravitationally Confined Detonation Model of Type Ia Supernovae

We report the results of a series of three-dimensional (3D) simulations of the deflagration phase of the gravitationally confined detonation mechanism for Type Ia supernovae. In this mechanism, ignition occurs at one or several off-center points, resulting in a burning bubble of hot ash that rises rapidly, breaks through the surface of the star, and collides at a point opposite the breakout on the stellar surface. We find that detonation conditions are robustly reached in our 3D simulations for a range of initial conditions and resolutions. Detonation conditions are achieved as the result of an inwardly directed jet that is produced by the compression of unburnt surface material when the surface flow collides with itself. A high-velocity outwardly directed jet is also produced. The initial conditions explored in this paper lead to conditions at detonation that can be expected to produce large amounts of 56Ni and small amounts of intermediate-mass elements. These particular simulations are therefore relevant only to high-luminosity Type Ia supernovae. Recent observations of Type Ia supernovae imply a compositional structure that is qualitatively consistent with that expected from these simulations.

CATACLYSMIC VARIABLE PRIMARY EFFECTIVE TEMPERATURES: CONSTRAINTS ON BINARY ANGULAR MOMENTUM LOSS

We review the most decisive currently available measurements of the surface effective temperatures, T eff, of white dwarf (WD) primaries in cataclysmic variables (CVs) during accretion quiescence, and use these as a diagnostic for their time-averaged accretion rate, . Using time-dependent calculations of the WD envelope, we investigate the sensitivity of the quiescent T eff to long-term variations in the accretion rate. We find that the quiescent T eff provides one of the best available tests of predictions for the angular momentum loss and resultant mass-transfer rates which govern the evolution of CVs. While gravitational radiation is completely sufficient to explain the of strongly magnetic CVs at all P orb, faster angular momentum loss is required to explain the temperatures of dwarf nova primaries (nonmagnetic systems). This provides evidence that a normal stellar magnetic field structure near the secondary, providing for wind launching and attachment, is essential for the enhanced braking mechanism to work, directly supporting the well-known stellar wind braking hypothesis. The contrast in is most prominent for orbital periods P orb > 3 h, above the so-called period gap, where differs by orders of magnitude, but a modest enhancement is also present at shorter P orb. The averaging time which reflects depends on itself, being as much as 105 years for low- systems and as little as 103 years for high- systems. We discuss in some detail the security of conclusions drawn about the CV population in light of these time scales and our necessarily incomplete sample of systems, finding that, due to the time necessary for the quiescent T eff to adjust, the consistency of measurements between different systems places significant constraints on possible long-timescale variation in . Measurements for nonmagnetic systems above the period gap fall below predictions from traditional stellar wind braking prescriptions, but above more recent predictions with somewhat weaker angular momentum loss. We also discuss the apparently high T effs found in the VY Scl stars, showing that these most likely indicate in this subclass even larger than predicted by stellar wind braking.

Theoretical Modeling of the Thermal State of Accreting White Dwarfs Undergoing Classical Nova Cycles

White dwarfs experience a thermal renaissance when they rec ive mass from a stellar companion in a binary. For accretion rates< 10M⊙ yr−1, the freshly accumulated hydrogen/helium envelope ignite s in a thermally unstable manner that results in a classical novae (CN) outbu rst and ejection of material. We have undertaken a theoretical study of the impact of the accumulating envelop n the thermal state of the underlying white dwarf (WD). This has allowed us to find the equilibrium WD core tempe ratures, the classical nova ignition masses and the thermal luminosities for WDs accreting at rates of 10 −11 − 10M⊙ yr−1. These accretion rates are most appropriate to WDs in cataclysmic variables (CVs) of Porb . 7 hr, many of which accrete sporadically as dwarf novae. We have included 3He in the accreted material at levels appropriate for CVs and find that it significantly modifies the CN ignition mass. Initial comparisons of our CN i gnition masses with measured ejected masses find reasonable agreement and point to ejection of material comp arable to that accreted. Subject headings: binaries: close—novae, cataclysmic variables– nuclear re actions, nucleosynthesis, abundances — stars: dwarf novae —white dwarfsWhite dwarfs (WDs) experience a thermal renaissance when they receive mass from a stellar companion in a binary. For accretion rates of less than 10-8 M☉ yr-1, the freshly accumulated hydrogen/helium envelope ignites in a thermally unstable manner that results in a classical nova (CN) outburst and ejection of material. We have undertaken a theoretical study of the impact of the accumulating envelope on the thermal state of the underlying WD. This has allowed us to find the equilibrium WD core temperatures (Tc), the CN ignition masses (Mign), and the thermal luminosities for WDs accreting at rates of 10-11 to 10-8 M☉ yr-1. These accretion rates are most appropriate for WDs in cataclysmic variables (CVs) of Porb 7 hr, many of which accrete sporadically as dwarf novae. We have included 3He in the accreted material at levels appropriate for CVs and find that it significantly modifies the CN ignition mass. We compare our results with several others from the CN literature and find that the inclusion of 3He leads to lower values of Mign for 10-10 M☉ yr-1 and that for values below this the particular authors assumption concerning Tc, which we calculate consistently, is a determining factor. Initial comparisons of our CN ignition masses with measured ejected masses find reasonable agreement and point to ejection of material comparable to that accreted.

SPONTANEOUS INITIATION OF DETONATIONS IN WHITE DWARF ENVIRONMENTS: DETERMINATION OF CRITICAL SIZES

Some explosion models for Type Ia supernovae (SNe Ia), such as the gravitationally confined detonation (GCD) or the double detonation sub-Chandrasekhar (DDSC) models, rely on the spontaneous initiation of a detonation in the degenerate / material of a white dwarf (WD). The length scales pertinent to the initiation of the detonation are notoriously unresolved in multidimensional stellar simulations, prompting the use of results of one-dimensional simulations at higher resolution, such as those performed for this work, as guidelines for deciding whether or not conditions reached in the higher dimensional full star simulations successfully would lead to the onset of a detonation. Spontaneous initiation relies on the existence of a suitable gradient in self-ignition (induction) times of the fuel, which we set up with a spatially localized nonuniformity of temperature?a hot spot. We determine the critical (smallest) sizes of such hot spots that still marginally result in a detonation in WD matter by integrating the reactive Euler equations with the hydrodynamics code FLASH. We quantify the dependences of the critical sizes of such hot spots on composition, background temperature, peak temperature, geometry, and functional form of the temperature disturbance, many of which were hitherto largely unexplored in the literature. We discuss the implications of our results in the context of modeling of SNe Ia.

Measuring White Dwarf Accretion Rates via Their Effective Temperatures

Our previous theoretical study of the impact of an accreting envelope on the thermal state of an underlying white dwarf (WD) has yielded equilibrium core temperatures, classical nova ignition masses, and thermal luminosities for WDs accreting at time-averaged rates of = 10-11 to 10-8 M☉ yr-1. These values are appropriate to WDs in cataclysmic variables (CVs) of Porb 7 hr, many of which accrete sporadically as dwarf novae. Approximately 30 nonmagnetic dwarf novae have been observed in quiescence, when the accretion rate is low enough for spectral detection of the WD photosphere and a measurement of Teff. We use our theoretical work to translate the measured Teff values into local time-averaged accretion rates, confirming the factor of 10 drop in predicted for CVs as they transit the period gap. For dwarf novae below the period gap, we show that if is that given by gravitational radiation losses alone, then the WD masses are greater than 0.8 M☉. An alternative conclusion is that the masses are closer to 0.6 M☉ and is 3-4 times larger than that expected from gravitational radiation losses. In either case, it is very plausible that a subset of CVs with Porb < 2 hr will have Teff values low enough for them to become nonradial pulsators, as discovered by van Zyl and collaborators for GW Lib.

Study of the Detonation Phase in the Gravitationally Confined Detonation Model of Type Ia Supernovae

We study the gravitationally confined detonation (GCD) model of Type Ia supernovae (SNe Ia) through the detonation phase and into homologous expansion. In the GCD model, a detonation is triggered by the surface flow due to single-point, off-center flame ignition in carbon-oxygen white dwarfs (WDs). The simulations are unique in terms of the degree to which nonidealized physics is used to treat the reactive flow, including weak reaction rates and a time-dependent treatment of material in nuclear statistical equilibrium (NSE). Careful attention is paid to accurately calculating the final composition of material which is burned to NSE and frozen out in the rapid expansion following the passage of a detonation wave over the high-density core of the WD; and an efficient method for nucleosynthesis postprocessing is developed which obviates the need for costly network calculations along tracer particle thermodynamic trajectories. Observational diagnostics are presented for the explosion models, including abundance stratifications and integrated yields. We find that for all of the ignition conditions studied here a self-regulating process comprised of neutronization and stellar expansion results in final 56Ni masses of ~1.1?M ?. But, more energetic models result in larger total NSE and stable Fe-peak yields. The total yield of intermediate mass elements is ~0.1?M ? and the explosion energies are all around 1.5 ? 1051 erg. The explosion models are briefly compared to the inferred properties of recent SN Ia observations. The potential for surface detonation models to produce lower-luminosity (lower 56Ni mass) SNe is discussed.

Flame Evolution During Type Ia Supernovae and the Deflagration Phase in the Gravitationally Confined Detonation Scenario

We develop an improved method for tracking the nuclear flame during the deflagration phase of a Type Ia supernova and apply it in a study of the variation in outcomes expected from the gravitationally confined detonation (GCD) paradigm. A simplified three-stage burning model and a nonstatic ash state are integrated with an artificially thickened advection-diffusion-reaction (ADR) flame front in order to provide an accurate but highly efficient representation of the energy release and electron capture in and after the unresolvable flame. We demonstrate that neither our ADR nor our energy release methods generate significant acoustic noise, as has been a problem with previous ADR-based schemes. We proceed to model aspects of the deflagration, particularly the role of buoyancy of the hot ash, and find that our methods are reasonably well behaved with respect to numerical resolution. We show that if a detonation occurs in material swept up by the material ejected by the first rising bubble but gravitationally confined to the white dwarf (WD) surface (the GCD paradigm), the density structure of the WD at detonation is systematically correlated with the distance of the deflagration ignition point from the center of the star. Coupled to a suitably stochastic ignition process, this correlation may provide a plausible explanation for the variety of nickel masses seen in Type Ia supernovae.

Capturing the Fire: Flame Energetics and Neutronization for Type Ia Supernova Simulations

We develop and calibrate a realistic model flame for hydrodynamic simulations of deflagrations in white dwarf (Type Ia) supernovae. Our flame model builds on the advection-diffusion-reaction model of Khokhlov and includes electron screening and Coulomb corrections to the equation of state in a self-consistent way. We calibrate this model flame—its energetics and timescales for energy release and neutronization—with self-heating reaction network calculations that include both these Coulomb effects and up-to-date weak interactions. The burned material evolves postflame due to both weak interactions and hydrodynamic changes in density and temperature. We develop a scheme to follow the evolution, including neutronization, of the NSE state subsequent to the passage of the flame front. As a result, our model flame is suitable for deflagration simulations over a wide range of initial central densities and can track the temperature and electron fraction of the burned material through the explosion and into the expansion of the ejecta.

The Thermal State of the Accreting White Dwarf in AM Canum Venaticorum Binaries

We calculate the heating and cooling of the accreting white dwarf (WD) in the ultracompact AM Canum Venaticorum (AM CVn) binaries and show that the WD can contribute significantly to their optical and ultraviolet emission. We estimate the WDs effective temperature, Teff, using the optical continuum for a number of observed binaries, and we show that it agrees well with our theoretical calculations. Driven by gravitational radiation losses, the time-averaged accretion rate, , decreases monotonically with increasing Porb, covering 6 orders of magnitude. If the short-period (Porb 50,000 K accreting WD. At longer Porb we calculate the Teff and absolute visual magnitude, MV, that the accreting WD will have during low accretion states, and we find that the WD naturally crosses the pulsational instability strip. Discovery and study of pulsations could allow for the measurement of the accumulated helium mass on the accreting WD, as well as its rotation rate. Accretion heats the WD core, but for Porb > 40 minutes, the WDs Teff is set by its cooling as plummets. For the two long-period AM CVn binaries with measured parallaxes, GP Com and CE 315, we show that the optical broadband colors and intensity are those expected from a pure helium atmosphere WD. This confirms that the WD brightness sets the minimum light in wide AM CVn binaries, allowing for meaningful constraints on their population density from deep optical searches, both in the field and in globular clusters.

Classical Novae as a Probe of the Cataclysmic Variable Population

Classical novae (CNe) are the brightest manifestation of mass transfer onto a white dwarf (WD) in a cataclysmic variable (CV). As such, they are probes of the mass transfer rate, , and WD mass, MWD, in these interacting binaries. Our calculations of the dependence of the CN ignition mass, Mign, on and MWD yields the recurrence times of these explosions. We show that the observed CNe orbital period distribution is consistent with the interrupted magnetic braking evolutionary scenario, in which at orbital periods Porb > 3 hr mass transfer is driven by angular momentum loss via a wind from the companion star, and at Porb < 3 hr by gravitational radiation. About 50% of CNe occur in binaries accreting at 10-9 M☉ yr-1 with Porb = 3 - 4 hr, with the remaining 50% split evenly between Porb longer (higher ) and shorter (lower ) than this. This resolution of the relative contribution to the CN rate from different CVs tells us that 3(9) × 105 CVs with WD mass 1.0(0.6) M☉ are needed to produce one CN per year. In addition, one CN per year requires a CV birthrate of 1(2) × 10-4 yr-1 and likely ejects mass into the interstellar medium at a rate of = 3(9) × 10-5 M☉ yr-1. Using the K-band-specific CN rate measured in external galaxies, we find a CV birthrate of 2(4) × 10-4 yr-1 per 1010 L☉,K, very similar to the luminosity specific Type Ia supernova rate in elliptical galaxies. Likewise, we predict that there should be 60-180 CVs for every 106 L☉,K in an old stellar population. The population of X-ray-identified CVs in the globular cluster 47 Tuc is similar to this number, showing no overabundance relative to the field. The observed CN Porb distribution also contains evidence for a CV population that has no period gap. These are likely systems with a strongly magnetic WD (polars) in which it has been suggested that the field interferes with the wind of the companion, limiting angular momentum losses to those of gravitational radiation and eliminating the period gap. With this reduced , polars evolve more slowly than systems that undergo magnetic braking. Using a two-component steady state model of CV evolution, we show that the fraction of CVs that are magnetic (22%) implies a birthrate of 8% relative to nonmagnetic CVs, similar to the fraction of strongly magnetic field WDs.