Showing papers by "Phil Arras published in 2006"
TL;DR: In this article, the authors present a comprehensive treatment of the linear modes of a hydrodynamic, non-self-gravitating, polytropic slender torus, with arbitrary specific angular momentum distribution, orbiting in an arbitrary axisymmetric space-time with reflection symmetry.
Abstract: Accretion flows with pressure gradients permit the existence of standing waves which may be responsible for observed quasi-periodic oscillations (QPO's) in X-ray binaries. We present a comprehensive treatment of the linear modes of a hydrodynamic, non-self-gravitating, polytropic slender torus, with arbitrary specific angular momentum distribution, orbiting in an arbitrary axisymmetric space-time with reflection symmetry. We discuss the physical nature of the modes, present general analytic expressions and illustrations for those which are low order, and show that they can be excited in numerical simulations of relativistic tori. The mode oscillation spectrum simplifies dramatically for near Keplerian angular momentum distributions, which appear to be generic in global simulations of the magnetorotational instability. We discuss our results in light of observations of high frequency QPO's, and point out the existence of a new pair of modes which can be in an approximate 3:2 ratio for arbitrary black hole spins and angular momentum distributions, provided the torus is radiation pressure dominated. This mode pair consists of the axisymmetric vertical epicyclic mode and the lowest order axisymmetric breathing mode.
92 citations
TL;DR: In this paper, the authors consider the thermal structure and radii of strongly irradiated gas giant planets over a range in mass and irradiating flux and find that the cooling rate of the planet is sensitive to the surface boundary condition, which depends on the detailed manner in which starlight is absorbed and energy redistributed by fluid motion.
Abstract: We consider the thermal structure and radii of strongly irradiated gas giant planets over a range in mass and irradiating flux. The cooling rate of the planet is sensitive to the surface boundary condition, which depends on the detailed manner in which starlight is absorbed and energy redistributed by fluid motion. We parameterize these effects by imposing an isothermal boundary condition T ≡ Tdeep below the photosphere and then constrain Tdeep from the observed masses and radii. We compute the dependence of luminosity and core temperature on mass, Tdeep, and core entropy, finding that simple scalings apply over most of the relevant parameter space. These scalings yield analytic cooling models that exhibit power-law behavior in the observable age range 0.1-10 Gyr and are confirmed by time-dependent cooling calculations. We compare our model to the radii of observed transiting planets and derive constraints on Tdeep. Only HD 209458 has a sufficiently accurate radius measurement that Tdeep is tightly constrained; the lower error bar on the radii for other planets is consistent with no irradiation. More accurate radius and age measurements will allow for a determination of the correlation of Tdeep with the equilibrium temperature, informing us about both the greenhouse effect and day-night asymmetries.
79 citations
TL;DR: In this article, the authors present a comprehensive treatment of the linear modes of a hydrodynamic, non-self-gravitating, polytropic slender torus, with arbitrary specific angular momentum distribution, orbiting in an arbitrary axisymmetric spacetime with reflection symmetry.
Abstract: Accretion flows with pressure gradients permit the existence of standing waves which may be responsible for observed quasi-periodic oscillations (QPO's) in X-ray binaries. We present a comprehensive treatment of the linear modes of a hydrodynamic, non-self-gravitating, polytropic slender torus, with arbitrary specific angular momentum distribution, orbiting in an arbitrary axisymmetric spacetime with reflection symmetry. We discuss the physical nature of the modes, present general analytic expressions and illustrations for those which are low order, and show that they can be excited in numerical simulations of relativistic tori. The mode oscillation spectrum simplifies dramatically for near Keplerian angular momentum distributions, which appear to be generic in global simulations of the magnetorotational instability. We discuss our results in light of observations of high frequency QPO's, and point out the existence of a new pair of modes which can be in an approximate 3:2 ratio for arbitrary black hole spins and angular momentum distributions, provided the torus is radiation pressure dominated. This mode pair consists of the axisymmetric vertical epicyclic mode and the lowest order axisymmetric breathing mode.
59 citations
TL;DR: In this paper, the authors consider the thermal structure and radii of strongly irradiated gas giant planets over a range in mass and irradiating flux, and find that the cooling rate of the planet is sensitive to the surface boundary condition, which depends on the detailed manner in which starlight is absorbed and energy redistributed by fluid motion.
Abstract: We consider the thermal structure and radii of strongly irradiated gas giant planets over a range in mass and irradiating flux. The cooling rate of the planet is sensitive to the surface boundary condition, which depends on the detailed manner in which starlight is absorbed and energy redistributed by fluid motion. We parametrize these effects by imposing an isothermal boundary condition $T \equiv T_{\rm deep}$ below the photosphere, and then constrain $T_{\rm deep}$ from the observed masses and radii. We compute the dependence of luminosity and core temperature on mass, $T_{\rm deep}$ and core entropy, finding that simple scalings apply over most of the relevant parameter space. These scalings yield analytic cooling models which exhibit power-law behavior in the observable age range $0.1-10 {\rm Gyr}$, and are confirmed by time-dependent cooling calculations. We compare our model to the radii of observed transiting planets, and derive constraints on $T_{\rm deep}$. Only HD 209458 has a sufficiently accurate radius measurement that $T_{\rm deep}$ is tightly constrained; the lower error bar on the radii for other planets is consistent with no irradiation. More accurate radius and age measurements will allow for a determination of the correlation of $T_{\rm deep}$ with the equilibrium temperature, informing us about both the greenhouse effect and day-night asymmetries.
53 citations
TL;DR: In this article, the authors investigate the impact of diversity on the range of Teff for which g-mode pulsations are unstable in accreting white dwarfs in cataclysmic variables with a large range of effective temperatures.
Abstract: The detection of g-mode pulsations in accreting white dwarfs (WDs) in cataclysmic variables (CVs) with a large range of effective temperatures (Teff) has shown these WDs to be a more diverse class than their isolated counterparts, the ZZ Ceti and DB pulsators. The simplest contrast of CV to isolated pulsators is an envelope of solar-like composition (of various helium enrichments if the donor is evolved) rather than pristine hydrogen or helium. A range of WD masses is expected, from low-mass He core WDs to massive WDs. We investigate the impact of this diversity on the range of Teff for which g-modes are unstable. Motivated by earlier theoretical studies, we compare a fiducial g-mode period to the thermal time at the base of the convection zones created by H and first He (H/He I) ionization or second He (He II) ionization zones. We find that (for solar composition envelopes), relative to a fiducial WD mass 0.6 M☉, the blue edge for a 0.4 M☉ He core WD shifts downward by ≈1000 K, while that for a massive ≈1.2 M☉ WD shifts upward by ≈2000 K. Surprisingly, increasing Y by only 10% relative to solar creates an "intermediate" instability strip near 15,000 K.
52 citations
TL;DR: In this article, the authors investigated the impact of the diversity of donor stars and accreting white dwarfs (WDs) on the range of effective temperatures for which g-modes are unstable.
Abstract: (Abridged) The Cataclysmic Variable (CV) population harbors a diverse range of donor stars and accreting white dwarfs (WDs). A range of WD masses is expected, from low mass Helium core WDs, to massive WDs which have previously accreted at rates high enough for Hydrogen to burn steadily. Furthermore, a wide range of Helium enrichment is expected in the accreted material depending on the degree to which the donor star is evolved. We investigate the impact of this diversity on the range of effective temperatures ($T_{\rm eff}$) for which g-modes are unstable. The critical $T_{\rm eff}$ below which modes are unstable ("blue edge") depends on both surface gravity, $g$, and He abundance, $Y$. The Hydrogen/first Helium ionization instability strip is more sensitive to $g$ than $Y$. We find that (for solar composition envelopes), relative to a fiducial WD mass $0.6 M_\odot$, the blue edge for a $0.4 M_\odot$ He core WD shifts downward by $\approx 1000 {\rm K}$, while that for a massive $\approx 1.2 M_\odot$ WD shifts upward by $\approx 2000 {\rm K}$. The second Helium ionization instability strip exhibits strong dependences on both $g$ and $Y$. Surprisingly, increasing $Y$ by only 10% relative to solar creates an instability strip near $15,000 {\rm K}$. Hence CV's below the period gap with evolved donor stars of $Y\ga 0.4$ may have an "intermediate" instability strip well outside of the isolated DA and DB variables. This "intermediate" instability strip also occurs for low mass He WD with solar composition envelopes. The lack of pulsations in CV's with $T_{\rm eff}$ in the pure Hydrogen ZZ Ceti instability strip is also easily explained.
42 citations
TL;DR: In this article, it was shown that axisymmetric acoustic modes and radial epicyclic motions driven by MRI turbulence give rise to narrow, distinct peaks in the temporal power spectrum.
Abstract: Quasi-periodic oscillations (QPOs) in the X-ray light curves of accreting neutron star and black hole binaries have been widely interpreted as being due to standing wave modes in accretion disks. These disks are thought to be highly turbulent due to the magnetorotational instability (MRI). We study wave excitation by MRI turbulence in the shearing box geometry. We demonstrate that axisymmetric acoustic modes and radial epicyclic motions driven by MRI turbulence give rise to narrow, distinct peaks in the temporal power spectrum. Inertial waves, on the other hand, do not give rise to distinct peaks which rise significantly above the continuum noise spectrum set by MRI turbulence, even when the fluid motions are projected onto the eigenfunctions of the modes. This is a serious problem for QPO models based on inertial waves.
41 citations
TL;DR: In this article, it was shown that axisymmetric sound waves and radial epicyclic motions driven by MRI turbulence give rise to narrow, distinct peaks in the temporal power spectrum.
Abstract: Quasi-periodic oscillations (QPOs) in the X-ray lightcurves of accreting neutron star and black hole binaries have been widely interpreted as being due to standing wave modes in accretion disks. These disks are thought to be highly turbulent due to the magnetorotational instability (MRI). We study wave excitation by MRI turbulence in the shearing box geometry. We demonstrate that axisymmetric sound waves and radial epicyclic motions driven by MRI turbulence give rise to narrow, distinct peaks in the temporal power spectrum. Inertial waves, on the other hand, do not give rise to distinct peaks which rise significantly above the continuum noise spectrum set by MRI turbulence, even when the fluid motions are projected onto the eigenfunctions of the modes. This is a serious problem for QPO models based on inertial waves.
2 citations
TL;DR: In this paper, a non-dissipative hydrodynamical mechanism that can stabilize the spin of the accretor in an ultra-compact double white dwarf binary was proposed.
Abstract: We study a non-dissipative hydrodynamical mechanism that can stabilize the spin of the accretor in an ultra-compact double white dwarf binary. This novel synchronization mechanism relies on a nonlinear wave interaction spinning down the background star. The essential physics of the synchronization mechanism is summarized as follows. As the compact binary coalesces due to gravitational wave emission, the largest star eventually fills its Roche lobe and accretion starts. The accretor then spins up due to infalling material and eventually reaches a spin frequency where a normal mode of the star is resonantly driven by the gravitational tidal field of the companion. If the resonating mode satisfies a set of specific criteria, which we elucidate in this paper, it exchanges angular momentum with the background star at a rate such that the spin of the accretor locks at this resonant frequency, even though accretion is ongoing. Some of the accreted angular momentum that would otherwise spin up the accretor is fed back into the orbit through this resonant tidal interaction.
Two modes capable of stabilizing the accretor's spin are the l=4,m=2 and l=5,m=3 CFS unstable hybrid r-modes, which stabilize the spin of the accretor at frequency 2.6 and 1.5 times the binary's orbital frequency respectively. Since the stabilization mechanism relies on continuously driving a mode at resonance, its lifetime is limited since eventually the mode amplitude saturates due to non-linear mode-mode coupling. Rough estimates of the lifetime of the effect lie from a few orbits to millions of years.