arXiv subjects

Phil Arras

Publications and source records attributed to Phil Arras.

At least 37 records · Page 2Linked to original sources

arXiv2019

I-Love-Q Relations for Realistic White Dwarfs

The space-borne gravitational wave interferometer, LISA, is expected to detect signals from numerous binary white dwarfs. At small orbital separation, rapid rotation and large tidal bulges may allow for the stellar internal structure to be probed through such observations. Finite-size effects are encoded in quantities like the moment of inertia ($I$), tidal Love number (Love), and quadrupole moment ($Q$). The universal relations among them (I-Love-Q relations) can be used to reduce the number of parameters in the gravitational-wave templates. We here study I-Love-Q relations for more realistic white dwarf models than used in previous studies. In particular, we extend previous works by including (i) differential rotation and (ii) internal temperature profiles taken from detailed stellar evolution calculations. We use the publicly available stellar evolution code MESA to generate cooling models of both low- and high-mass white dwarfs. We show that differential rotation causes the I-Q relation (and similarly the Love-Q relation) to deviate from that of constant rotation. We also find that the introduction of finite temperatures causes the white dwarf to move along the zero-temperature mass sequence of I-Q values, moving towards values that suggest a lower mass. We further find that after only a few Myrs, high-mass white dwarfs are well-described by the zero-temperature model, suggesting that the relations with zero-temperature may be good enough in most practical cases. Low-mass, He-core white dwarfs with thick hydrogen envelopes may undergo long periods of H burning which sustain the stellar temperature and allow deviations from the I-Love-Q relations for longer times.

gr-qc↗

arXiv2019

The full $\mathit{Kepler}$ phase curve of the eclipsing hot white dwarf binary system KOI-964

We analyze the full $\mathit{Kepler}$ phase curve of KOI-964, a binary system consisting of a hot white dwarf on an eclipsing orbit around an A-type host star. Using all 18 quarters of long-cadence photometry, we carry out a joint light curve fit and obtain improved phase curve amplitudes, occultation depths, orbital parameters, and transit ephemeris over the previous results of Carter et al. 2011. A periodogram of the residuals from the phase curve fit reveals an additional stellar variability signal from the host star with a characteristic period of $0.620276\pm0.000011$ days and a full amplitude of $24\pm2$ ppm. We also present new Keck/HIRES radial velocity observations which we use to measure the orbit and obtain a mass ratio of $q=0.106\pm0.012$. Combining this measurement with the results of a stellar isochrone analysis, we find that the masses of the host star and white dwarf companion are $2.23\pm0.12\,M_{\odot}$ and $0.236^{+0.028}_{-0.027}\,M_{\odot}$, respectively. The effective temperatures of the two components are $9940^{+260}_{-230}$ K and $15080\pm400$ K, respectively, and we determine the age of the system to be $0.21^{+0.11}_{-0.08}$ Gyr. We use the measured system properties to compute predicted phase curve amplitudes and find that while the measured Doppler boosting and mutual illumination components agree well with theory, the ellipsoidal distortion amplitude is significantly underestimated. We detail possible explanations for this discrepancy, including interactions between the dynamical tide of the host star and the tidal bulge and possible non-synchronous rotation of the host star.

astro-ph.SR↗

arXiv2019

Nonlinear Mixed Modes in Red Giants

Turbulent motions in the convective envelope of red giants excite a rich spectrum of solar-like oscillation modes. Observations by CoRoT and Kepler have shown that the mode amplitudes increase dramatically as the stars ascend the red giant branch, i.e., as the frequency of maximum power, $ν_\mathrm{max}$, decreases. Most studies nonetheless assume that the modes are well described by the linearized fluid equations. We investigate to what extent the linear approximation is justified as a function of stellar mass $M$ and $ν_\mathrm{max}$, focusing on dipole mixed modes with frequency near $ν_\mathrm{max}$. A useful measure of a mode's nonlinearity is the product of its radial wavenumber and its radial displacement, $k_r ξ_r$ (i.e., its shear). We show that $k_r ξ_r \propto ν_\mathrm{max}^{-9/2}$, implying that the nonlinearity of mixed modes increases significantly as a star evolves. The modes are weakly nonlinear ($k_r ξ_r > 10^{-3}$) for $ν_\mathrm{max} \lesssim 150 \, μ\mathrm{Hz}$ and strongly nonlinear ($k_r ξ_r > 1$) for $ν_\mathrm{max} \lesssim 30 \, μ\mathrm{Hz}$, with only a mild dependence on $M$ over the range we consider ($1.0 - 2.0 M_\odot$). A weakly nonlinear mixed mode can excite secondary waves in the stellar core through the parametric instability, resulting in enhanced, but partial, damping of the mode. By contrast, a strongly nonlinear mode breaks as it propagates through the core and is fully damped there. Evaluating the impact of nonlinear effects on observables such as mode amplitudes and linewidths requires large mode network simulations. We plan to carry out such calculations in the future and investigate whether nonlinear damping can explain why some red giants exhibit dipole modes with unusually small amplitudes, known as depressed modes.

astro-ph.SR↗

arXiv2018

Orbital Decay in Binaries Containing Post-Main Sequence Stars

The orbital decay of binaries containing a primary sub-giant or red giant star and a stellar or substellar companion is investigated. The tide raised in the primary by the companion leads to an exchange of angular momentum between the orbit and the stellar spin, causing the orbit to contract and the primary to spin up. The rate of orbital decay is computed including both the equilibrium tide, damped by turbulent viscosity in the convective envelope, and the dynamical tide, assumed to be a traveling internal-gravity wave in the radiative core. For close binaries, the tidal forcing period is expected to be much shorter than the eddy turnover timescale in the convective envelope, and the prescription for "reduced" viscosity is an important consideration. The dynamical tide tends to dominate for the closest orbits, while the equilibrium tide dominates for more distant orbits, with the crossover point depending on the stellar mass. The spin up of the primary to synchronous rotation occurs for sufficiently massive secondaries, and this greatly slows the orbital decay until the Darwin instability occurs. A parameter survey is presented for orbital decay as a function of primary and secondary mass, as well as turbulent viscosity prescription. These results are summarized with analytic formulae and numerical results for the age-dependent critical separation, $a_{\rm crit}$, inside of which orbital decay is rapid, and few systems are expected to be observed. The calculations of $a_{\rm crit}$ are compared with APOGEE binaries, as well as solar mass exoplanet host stars.

astro-ph.SR↗

arXiv2018

Urca reactions during neutron star inspiral

We study the impact of nonlinear bulk viscosity due to Urca reactions driven by tidally-induced fluid motion during binary neutron star inspiral. Fluid compression is computed for low radial order oscillation modes through an adiabatic, time-dependent solution of the mode amplitudes. Optically thin neutrino emission and heating rates are then computed from this adiabatic fluid motion. Calculations use direct and modified Urca reactions operating in a $M=1.4\, M_\odot$ neutron star, which is constructed using the Skyrme Rs equation of state. We find that the energy pumped into low order oscillation modes is not efficiently thermalized even by direct Urca reactions, with core temperatures reaching only $T \simeq 10^8\, {\rm K}$ during the inspiral. Although this is an order of magnitude larger than the heating due to shear viscosity considered by previous studies, it reinforces the result that the stars are quite cold at merger. Upon excitation of the lowest order g-mode, the chemical potential imbalance reaches $β> 1\, {\rm MeV}$ at orbital frequencies $ν_{\rm orb} > 200\, {\rm Hz}$, implying significant charged-current optical depths and Fermi blocking. To asses the importance of neutrino degeneracy effects, the neutrino transfer equation is solved in the static approximation for the three-dimensional density distribution, and the reaction rates are then computed including Fermi-blocking. We find that the heating rate is suppressed by factors of a few for $ν_{\rm orb} > 200\, {\rm Hz}$. The spectrum of emitted $ν_e$ and $\barν_e$, including radiation transfer effects, is presented for a range of orbital separations.

astro-ph.HE↗

arXiv2018

Formation of Extremely Low-mass White Dwarfs Binaries

Motivated by the discovery of a handful of pulsating, extremely low mass white dwarfs (ELM WDs, mass $M \lesssim 0.17\, M_\odot$) which likely have WD companions, this paper discusses binary formation models for these systems. Formation of an ELM WD by unstable mass transfer (MT) or a common envelope (CE) event is unlikely. Stable Roche-lobe overflow with conservative MT produces only $M \gtrsim 0.2\, M_\odot$. This paper discusses the formation of ELM WD using angular momentum losses by magnetic braking. The initially more massive star becomes the companion WD through a CE event. The initially less massive star becomes the ELM WD as an evolved donor in a Cataclysmic Variable binary. Evolutionary models are constructed using the Modules for Experiments in Stellar Astrophysics (MESA), with ELM WD progenitors in the range $M_d=1.0-1.5\, M_\odot$ and WD companions in the range $M_{\rm a} \simeq 0.4-0.9\, M_\odot$. A prescription to reduce magnetic braking for thin surface convection zones is included. Upon the thinning of the evolved donor's envelope, the donor star shrinks out of contact and MT ceases, revealing the ELM WD. Systems with small masses have previously been suggested as possible AM CVN's. Systems with large masses, up to the limit $M \simeq 0.18\, M_\odot$ at which shell flashes occur on the WD cooling track, will tend to expand out to orbital periods $P_{\rm orb} \gtrsim 15\, {\rm hr}$. In between this range, ELM WD may become pulsators both as pre-WD and on the WD cooling track. Brickhill's criterion for convective mode driving is used to estimate the location of the blue edge of the g-mode instability strip.

astro-ph.SR↗

arXiv2017

A Model of the H$α$ and Na Transmission Spectrum of HD 189733b

This paper presents a detailed hydrostatic model of the upper atmosphere of HD 189733b, with the goal of constraining its temperature, particle densities, and radiation field over the pressure range $10^{-4}-10\, μ\rm bar$, where the observed H$α$ transmission spectrum is produced. The atomic hydrogen level population is computed including both collisional and radiative transition rates. The Ly$α$ resonant scattering is computed using a Monte-Carlo simulation. The model transmission spectra are in broad agreement with the data. Excitation of the H(2$\ell$) population is mainly by Ly$α$ radiative excitation due to the large Ly$α$ intensity. The density of H(2$\ell$) is nearly flat over two decades in pressure, and is optically thick to H$α$. Additional models computed for a range of the stellar Lyman continuum (LyC) flux suggest that the variability in H$α$ transit depth may be due to the variability in the stellar LyC. Since metal lines provide the dominant cooling of this part of the atmosphere, the atmosphere structure is sensitive to the density of species such as Mg and Na which may themselves be constrained by observations. Since the H$α$ and Na D lines have comparable absorption depths, we argue that the center of the Na D lines are also formed in the atomic layer where the H$α$ line is formed.

astro-ph.EP↗

arXiv2017

Tidal Dissipation in WASP-12

WASP-12 is a hot Jupiter system with an orbital period of $P= 1.1\textrm{ day}$, making it one of the shortest-period giant planets known. Recent transit timing observations by Maciejewski et al. (2016) and Patra et al. (2017) find a decreasing period with $P/|\dot{P}| = 3.2\textrm{ Myr}$. This has been interpreted as evidence of either orbital decay due to tidal dissipation or a long term oscillation of the apparent period due to apsidal precession. Here we consider the possibility that it is orbital decay. We show that the parameters of the host star are consistent with either a $M_\ast \simeq 1.3 M_\odot$ main sequence star or a $M_\ast \simeq 1.2 M_\odot$ subgiant. We find that if the star is on the main sequence, the tidal dissipation is too inefficient to explain the observed $\dot{P}$. However, if it is a subgiant, the tidal dissipation is significantly enhanced due to nonlinear wave breaking of the dynamical tide near the star's center. The subgiant models have a tidal quality factor $Q_\ast'\simeq 2\times10^5$ and an orbital decay rate that agrees well with the observed $\dot{P}$. It would also explain why the planet survived for $\simeq 3\textrm{ Gyr}$ while the star was on the main sequence and yet is now inspiraling on a 3 Myr timescale. Although this suggests that we are witnessing the last $\sim 0.1\%$ of the planet's life, the probability of such a detection is a few percent given the observed sample of $\simeq 30$ hot Jupiters in $P<3\textrm{ day}$ orbits around $M_\ast>1.2 M_\odot$ hosts.

astro-ph.EP↗

arXiv2017

Using long-term millisecond pulsar timing to obtain physical characteristics of the bulge globular cluster Terzan 5

Over the past decade the discovery of three unique stellar populations and a large number of confirmed pulsars within the globular cluster Terzan 5 has raised questions over its classification. Using the long-term radio pulsar timing of 36 millisecond pulsars in the cluster core, we provide new measurements of key physical properties of the system. As Terzan 5 is located within the galactic bulge, stellar crowding and reddening make optical and near infrared observations difficult. Pulsar accelerations, however, allow us to study the intrinsic characteristics of the cluster independent of reddening and stellar crowding and probe the mass density profile without needing to quantify the mass to light ratio. Relating the spin and orbital periods of each pulsar to the acceleration predicted by a King model, we find a core density of $1.58\times$10$^6$ M$_\odot$ pc$^{-3}$, a core radius of 0.16 pc, a pulsar density profile $n\propto r^{-3.14}$, and a total mass of M$_{\rm T}$($R_\perp<$1.0 pc)$\simeq3.0\times$10$^5$ M$_\odot$ assuming a cluster distance of 5.9 kpc. Using this information we argue against Terzan 5 being a disrupted dwarf galaxy and discuss the possibility of Terzan 5 being a fragment of the Milky Way's proto-bulge. We also discuss whether low-mass pulsars were formed via electron capture supernovae or exist in a core full of heavy white dwarfs and hard binaries. Finally we provide an upper limit for the mass of a possible black hole at the core of the cluster of 3.0$\times$10$^4$ M$_\odot$.

astro-ph.SR↗

arXiv2016

A New Model of Roche-lobe Overflow for Short-Period Gaseous Planets and Binary Stars

Some close-in gaseous exoplanets are nearly in Roche-lobe contact, and previous studies show tidal decay can drive hot Jupiters into contact during the main sequence of their host stars. Improving upon a previous model, we present a revised model for mass transfer in a semi-detached binary system that incorporates an extended atmosphere around the donor and allows for an arbitrary mass ratio. We apply this new formalism to hypothetical, confirmed, and candidate planetary systems to estimate mass loss rates and compare with models of evaporative mass loss. Overflow may be significant for hot Neptunes out to periods of $\sim$ 2 days, while for hot Jupiters, it may only be important inward of 0.5 days. We find that CoRoT-24 b may be losing mass at a rate of more than an Earth mass in a Gyr. The hot Jupiter WASP-12 b may lose an Earth mass in a Myr, while the putative planet orbiting a T-Tauri star PTFO8-8695 might shed its atmosphere in a few Myrs. We point out that the orbital expansion that can accompany mass transfer may be less effective than previously considered because the gas accreted by the host star removes some of the system's angular momentum from the orbit, but simple scaling arguments suggest that the Roche-lobe overflow might remain stable. Consequently, the recently discovered small planets in ultra-short-periods ($<$ 1 day) may not be the remnants of hot Jupiters/Neptunes. The new model presented here has been incorporated into Modules for Experiments in Stellar Astrophysics (MESA).

astro-ph.EP↗

arXiv2016

Tidal Decay and Stable Roche-Lobe Overflow of Short-Period Gaseous Exoplanets

Many gaseous exoplanets in short-period orbits are on the verge or are in the process of Roche-lobe overflow (RLO). Moreover, orbital stability analysis shows tides can drive many hot Jupiters to spiral inevitably toward their host stars. Thus, the coupled processes of orbital evolution and RLO likely shape the observed distribution of close-in exoplanets and may even be responsible for producing some of the short-period rocky planets. However, the exact outcome for an overflowing planet depends on its internal response to mass loss, and the accompanying orbital evolution can act to enhance or inhibit RLO. In this study, we apply the fully-featured and robust Modules for Experiments in Stellar Astrophysics (MESA) suite to model RLO of short-period gaseous planets. We show that, although the detailed evolution may depend on several properties of the planetary system, it is largely determined by the core mass of the overflowing gas giant. In particular, we find that the orbital expansion that accompanies RLO often stops and reverses at a specific maximum period that depends on the core mass. We suggest that RLO may often strand the remnant of a gas giant near this orbital period, which provides an observational prediction that can corroborate the hypothesis that short-period gas giants undergo RLO. We conduct a preliminary comparison of this prediction to the observed population of small, short-period planets and find some planets in orbits that may be consistent with this picture. To the extent that we can establish some short-period planets are indeed the remnants of gas giants, that population can elucidate the properties of gas giant cores, the properties of which remain largely unconstrained.

astro-ph.EP↗

arXiv2016

Investigation of the environment around close-in transiting exoplanets using CLOUDY

It has been suggested that hot stellar wind gas in a bow shock around an exoplanet is sufficiently opaque to absorb stellar photons and give rise to an observable transit depth at optical and UV wavelengths. In the first part of this paper, we use the CLOUDY plasma simulation code to model the absorption from X-ray to radio wavelengths by 1-D slabs of gas in coronal equilibrium with varying densities ($10^{4}-10^{8} \, {\rm cm^{-3}}$) and temperatures ($2000-10^{6} \ {\rm K}$) illuminated by a solar spectrum. For slabs at coronal temperatures ($10^{6} \ {\rm K}$) and densities even orders of magnitude larger than expected for the compressed stellar wind ($10^{4}-10^{5} \, {\rm cm^{-3}}$), we find optical depths orders of magnitude too small ($> 3\times10^{-7}$) to explain the $\sim3\%$ UV transit depths seen with Hubble. Using this result and our modeling of slabs with lower temperatures ($2000-10^4 {\rm K}$), the conclusion is that the UV transits of WASP-12b and HD 189733b are likely due to atoms originating in the planet, as the stellar wind is too highly ionized. A corollary of this result is that transport of neutral atoms from the denser planetary atmosphere outward must be a primary consideration when constructing physical models. In the second part of this paper, additional calculations using CLOUDY are carried out to model a slab of planetary gas in radiative and thermal equilibrium with the stellar radiation field. Promising sources of opacity from the X-ray to radio wavelengths are discussed, some of which are not yet observed.

astro-ph.EP↗

arXiv2016

Axisymmetric Simulations of Hot Jupiter-Stellar Wind Hydrodynamic Interaction

Gas giant exoplanets orbiting at close distances to the parent star are subjected to large radiation and stellar wind fluxes. In this paper, hydrodynamic simulations of the planetary upper atmosphere and its interaction with the stellar wind are carried out to understand the possible flow regimes and how they affect the Lyman-alpha transmission spectrum. Following Tremblin and Chiang, charge exchange reactions are included to explore the role of energetic atoms as compared to thermal particles. In order to understand the role of the tail as compared to the leading edge of the planetary gas, the simulations were carried out under axisymmetry, and photoionization and stellar wind electron impact ionization reactions were included to limit the extent of the neutrals away from the planet. By varying the planetary gas temperature, two regimes are found. At high temperature, a supersonic planetary wind is found, which is turned around by the stellar wind and forms a tail behind the planet. At lower temperatures, the planetary wind is shut off when the stellar wind penetrates inside where the sonic point would have been. In this regime mass is lost by viscous interaction at the boundary between planetary and stellar wind gases. Absorption by cold hydrogen atoms is large near the planetary surface, and decreases away from the planet as expected. The hot hydrogen absorption is in an annulus and typically dominated by the tail, at large impact parameter, rather than by the thin leading edge of the mixing layer near the substellar point.

astro-ph.EP↗

arXiv2016

Seismology of Rapidly Rotating Accreting White Dwarfs

A number of White Dwarfs (WDs) in cataclysmic binaries have shown brightness variations consistent with non-radial oscillations as observed in isolated WDs. A few objects have been well-characterized with photometric campaigns in the hopes of gleaning information about the mass, spin, and possibly internal structural characteristics. The novel aspect of this work is the possiblity to measure or constrain the interior structure and spin rate of WDs which have spent gigayears accreting material from their companion, undergoing thousands of nova outbursts in the process. In addition, variations in the surface temperature affect the site of mode driving, and provide unique and challenging tests for mode driving theories previously applied to isolated WD's. Having undergone long-term accretion, these WDs are expected to have been spun up. Spin periods in the range 60-100 seconds have been measured by other means for two objects, GW Lib and V455 And. Compared to typical mode frequencies, the spin frequency may be similar or higher, and the Coriolis force can no longer be treated as a small perturbation on the fluid motions. We present the results of a non-perturbative calculation of the normal modes of these WDs, using interior thermal structures appropriate to accreting systems. This includes a discussion of the surface brightness distributions, which are strongly modified from the non-rotating case. Using the measured spin period of approximately 100 seconds, we show that the observed pulsations from GW Lib are consistent with the three lowest azimuthal order rotationally modified modes that have the highest frequency in the stellar frame. The high frequencies are needed for the convective driving, but are then apparently shifted to lower frequencies by a combination of their pattern motion and the WD rotation.

astro-ph.SR↗

arXiv2015

An instability due to the nonlinear coupling of p-modes to g-modes: Implications for coalescing neutron star binaries

A weakly nonlinear fluid wave propagating within a star can be unstable to three-wave interactions. The resonant parametric instability is a well-known form of three-wave interaction in which a primary wave of frequency $ω_a$ excites a pair of secondary waves of frequency $ω_b+ω_c \simeq ω_a$. Here we consider a nonresonant form of three-wave interaction in which a low-frequency primary wave excites a high-frequency p-mode and a low-frequency g-mode such that $ω_b+ω_c >>ω_a$. We show that a p-mode can couple so strongly to a g-mode of similar radial wavelength that this type of interaction is unstable even if the primary wave amplitude is small. As an application, we analyze the stability of the tide in coalescing neutron star binaries to p-g mode coupling. We find that the equilibrium tide and dynamical tide are both p-g unstable at gravitational wave frequencies f_{gw} > 20 Hz and drive p-g pairs to significant energies on very short timescales (much less than the orbital decay time). Resonant parametric coupling to the tide is, by contrast, either stable or drives modes at a much smaller rate. We do not solve for the saturation of the instability and therefore cannot say precisely how it influences neutron star binaries. However, we show that if even a single daughter mode saturates near its wave breaking amplitude, the p-g instability of the equilibrium tide: (i) induces significant orbital phase errors ($Δϕ$ > 1 radian) that accumulate primarily at low frequencies (f_{gw} < 50 Hz) and (ii) heats the neutron star core to T~10^{10} K. Since there are >100 unstable daughters, $Δϕ$ and T are potentially much larger than these values. Tides might therefore significantly influence the gravitational wave signal and electromagnetic emission from neutron star binaries at much larger orbital separations than previously thought.

astro-ph.SR↗

arXiv2014

Dynamical resonance locking in tidally interacting binary systems

We examine the dynamics of resonance locking in detached, tidally interacting binary systems. In a resonance lock, a given stellar or planetary mode is trapped in a highly resonant state for an extended period of time, during which the spin and orbital frequencies vary in concert to maintain the resonance. This phenomenon is qualitatively similar to resonance capture in planetary dynamics. We show that resonance locks can accelerate the course of tidal evolution in eccentric systems and also efficiently couple spin and orbital evolution in circular binaries. Previous analyses of resonance locking have not treated the mode amplitude as a fully dynamical variable, but rather assumed the adiabatic (i.e. Lorentzian) approximation valid only in the limit of relatively strong mode damping. We relax this approximation, analytically derive conditions under which the fixed point associated with resonance locking is stable, and further check these analytic results using numerical integrations of the coupled mode, spin, and orbital evolution equations. These show that resonance locking can sometimes take the form of complex limit cycles or even chaotic trajectories. We provide simple analytic formulae that define the binary and mode parameter regimes in which resonance locks of some kind occur (stable, limit cycle, or chaotic). We briefly discuss the astrophysical implications of our results for white dwarf and neutron star binaries as well as eccentric stellar binaries.

astro-ph.SR↗

arXiv2014

Magnetohydrodynamic Simulations of Hot Jupiter Upper Atmospheres

Two-dimensional simulations of hot Jupiter upper atmospheres including the planet's magnetic field are presented. The goal is to explore magnetic effects on the layer of the atmosphere that is ionized and heated by stellar EUV radiation, and the imprint of these effects on the Ly$α$ transmission spectrum. The simulations are axisymmetric, isothermal, and include both rotation and azimuth-averaged stellar tides. Mass density is converted to atomic hydrogen density through the assumption of ionization equilibrium. The three-zone structure -- polar dead zone, mid-latitude wind zone, and equatorial dead zone -- found in previous analytic calculations is confirmed. For a magnetic field comparable to that of Jupiter, the equatorial dead zone, which is confined by the magnetic field and corotates with the planet, contributes at least half of the transit signal. For even stronger fields, the gas escaping in the mid-latitude wind zone is found to have a smaller contribution to the transit depth than the equatorial dead zone. Transmission spectra computed from the simulations are compared to HST STIS and ACS data for HD 209458b and HD 189733b, and the range of model parameters consistent with the data is found. The central result of this paper is that the transit depth increases strongly with magnetic field strength when the hydrogen ionization layer is magnetically dominated, for dipole magnetic field $B_0 > 10\ {\rm G}$. Hence transit depth is sensitive to magnetic field strength, in addition to standard quantities such as the ratio of thermal to gravitational binding energies.

astro-ph.EP↗

arXiv2013

Tidal resonance locks in inspiraling white dwarf binaries

We calculate the tidal response of helium and carbon/oxygen (C/O) white dwarf (WD) binaries inspiraling due to gravitational wave emission. We show that resonance locks, previously considered in binaries with an early-type star, occur universally in WD binaries. In a resonance lock, the orbital and spin frequencies evolve in lockstep, so that the tidal forcing frequency is approximately constant and a particular normal mode remains resonant, producing efficient tidal dissipation and nearly synchronous rotation. We show that analogous locks between the spin and orbital frequencies can occur not only with global standing modes, but even when damping is so efficient that the resonant tidal response becomes a traveling wave. We derive simple analytic formulas for the tidal quality factor Q and tidal heating rate during a g-mode resonance lock, and verify our results numerically. We find that Q ~ 10^7 for orbital periods ~ 1 - 2 hr in C/O WDs, and Q ~ 10^9 for P_orb ~ 3 - 10 hr in helium WDs. Typically tidal heating occurs sufficiently close to the surface that the energy should be observable as surface emission. Moreover, near an orbital period of ~ 10 min, the tidal heating rate reaches ~ 10^{-2} L_\sun, rivaling the luminosities of our fiducial WD models. Recent observations of the 13-minute double-WD binary J0651 are roughly consistent with our theoretical predictions. Tides naturally tend to generate differential rotation; however, we show that the fossil magnetic field strength of a typical WD can maintain solid-body rotation down to at least P_orb ~ 10 min even in the presence of a tidal torque concentrated near the WD surface.

astro-ph.SR↗