Phil Arras

Modules for Experiments in Stellar Astrophysics (MESA): Planets, Oscillations, Rotation, and Massive Stars

We substantially update the capabilities of the open source software package Modules for Experiments in Stellar Astrophysics (MESA), and its one-dimensional stellar evolution module, MESA star. Improvements in MESA stars ability to model the evolution of giant planets now extends its applicability down to masses as low as one-tenth that of Jupiter. The dramatic improvement in asteroseismology enabled by the space-based Kepler and CoRoT missions motivates our full coupling of the ADIPLS adiabatic pulsation code with MESA star. This also motivates a numerical recasting of the Ledoux criterion that is more easily implemented when many nuclei are present at non-negligible abundances. This impacts the way in which MESA star calculates semi-convective and thermohaline mixing. We exhibit the evolution of 3-8 M ? stars through the end of core He burning, the onset of He thermal pulses, and arrival on the white dwarf cooling sequence. We implement diffusion of angular momentum and chemical abundances that enable calculations of rotating-star models, which we compare thoroughly with earlier work. We introduce a new treatment of radiation-dominated envelopes that allows the uninterrupted evolution of massive stars to core collapse. This enables the generation of new sets of supernovae, long gamma-ray burst, and pair-instability progenitor models. We substantially modify the way in which MESA star solves the fully coupled stellar structure and composition equations, and we show how this has improved the scaling of MESAs calculational speed on multi-core processors. Updates to the modules for equation of state, opacity, nuclear reaction rates, and atmospheric boundary conditions are also provided. We describe the MESA Software Development Kit that packages all the required components needed to form a unified, maintained, and well-validated build environment for MESA. We also highlight a few tools developed by the community for rapid visualization of MESA star results.

The Role of Planet Accretion in Creating the Next Generation of Red Giant Rapid Rotators

Rapid rotation in field red giant stars is a relatively rare but well-studied phenomenon; here we investigate the potential role of planet accretion in spinning up these stars. Using Zahns theory of tidal friction and stellar evolution models, we compute the decay of a planets orbit into its evolving host star and the resulting transfer of angular momentum into the stellar convective envelope. This experiment assesses the frequency of planet ingestion and rapid rotation on the red giant branch (RGB) for a sample of 99 known exoplanet host stars. We find that the known exoplanets are indeed capable of creating rapid rotators; however, the expected fraction due to planet ingestion is only ~ 10% of the total seen in surveys of present-day red giants. Of the planets ingested, we find that those with smaller initial semimajor axes are more likely to create rapid rotators because these planets are accreted when the stellar moment of inertia is smallest. We also find that many planets may be ingested prior to the RGB phase, contrary to the expectation that accretion would generally occur when the stellar radii expand significantly as giants. Finally, our models suggest that the rapid rotation signal from ingested planets is most likely to be seen on the lower RGB, which is also where alternative mechanisms for spin-up, e.g., angular momentum dredged up from the stellar core, do not operate. Thus, rapid rotators on the lower RGB are the best candidates to search for definitive evidence of systems that have experienced planet accretion.

Ellipsoidal Oscillations Induced by Substellar Companions: A Prospect for the Kepler Mission

Hundreds of substellar companions to solar-type stars will be discovered with the Kepler satellite. Keplers extreme photometric precision gives access to low-amplitude stellar variability contributed by a variety of physical processes. We discuss in detail the periodic flux modulations arising from the tidal force on the star due to a substellar companion. An analytic expression for the variability is derived in the equilibrium-tide approximation. We demonstrate analytically and through numerical solutions of the linear, nonadiabatic stellar oscillation equations that the equilibrium-tide formula works extremely well for stars of mass <1.4 M☉ with thick surface convection zones. More massive stars with largely radiative envelopes do not conform to the equilibrium-tide approximation and can exhibit flux variations 10 times larger than naive estimates. Over the full range of stellar masses considered, we treat the oscillatory response of the convection zone by adapting a prescription that A. J. Brickhill developed for pulsating white dwarfs. Compared to other sources of periodic variability, the ellipsoidal light curve has a distinct dependence on time and system parameters. We suggest that ellipsoidal oscillations induced by giant planets may be detectable from as many as ~100 of the 105 Kepler target stars. For the subset of these stars that show transits and have radial-velocity measurements, all system parameters are well constrained, and measurement of ellipsoidal variation provides a consistency check, as well as a test of the theory of forced stellar oscillations in a challenging regime.

Tidal asteroseismology: Kepler’s KOI-54

We develop a general framework for interpreting and analysing high-precision light curves from eccentric stellar binaries. Although our methods are general, we focus on the recently discovered Kepler system KOI-54, a face-on binary of two A stars with e= 0.83 and an orbital period of 42 days. KOI-54 exhibits strong ellipsoidal variability during its periastron passage; its light curve also contains ∼20 pulsations at perfect harmonics of the orbital frequency, and another ∼10 non-harmonic pulsations. Analysis of such data is a new form of asteroseismology in which oscillation amplitudes and phases rather than frequencies contain information that can be mined to constrain stellar properties. We qualitatively explain the physics of mode excitation and the range of harmonics expected to be observed. To quantitatively model observed pulsation spectra, we develop and apply a linear, tidally forced, non-adiabatic stellar oscillation formalism including the Coriolis force. We produce temporal power spectra for KOI-54 that are semi-quantitatively consistent with the observations. Both stars in the KOI-54 system are expected to be rotating pseudo-synchronously, with resonant non-axisymmetric modes providing a key contribution to the total torque; such resonances present a possible explanation for the two largest-amplitude harmonic pulsations observed in KOI-54, although we find problems with this interpretation. We show in detail that the non-harmonic pulsations observed in KOI-54 can be explained by non-linear three-mode coupling. The methods developed in this paper can be generalized in the future to determine the best-fitting stellar parameters given pulsation data. We also derive an analytic model of KOI-54’s ellipsoidal variability, including both tidal distortion and stellar irradiation, which can be used to model other similar systems.

Pulsations in Hydrogen Burning Low Mass Helium White Dwarfs

Helium core white dwarfs (WDs) with mass M {approx}< 0.20 M {sub sun} undergo several Gyr of stable hydrogen burning as they evolve. We show that in a certain range of WD and hydrogen envelope masses, these WDs may exhibit g-mode pulsations similar to their passively cooling, more massive carbon/oxygen core counterparts, the ZZ Cetis. Our models with stably burning hydrogen envelopes on helium cores yield g-mode periods and period spacings longer than the canonical ZZ Cetis by nearly a factor of 2. We show that core composition and structure can be probed using seismology since the g-mode eigenfunctions predominantly reside in the helium core. Though we have not carried out a fully nonadiabatic stability analysis, the scaling of the thermal time in the convective zone with surface gravity highlights several low-mass helium WDs that should be observed in search of pulsations: NLTT 11748, SDSS J0822+2753, and the companion to PSR J1012+5307. Seismological studies of these He core WDs may prove especially fruitful, as their luminosity is related (via stable hydrogen burning) to the hydrogen envelope mass, which eliminates one model parameter.

MASSIVE SATELLITES OF CLOSE-IN GAS GIANT EXOPLANETS

We study the orbits, tidal heating and mass loss from satellites around close-in gas giant exoplanets. The focus is on large satellites which are potentially observable by their transit signature. We argue that even Earth-size satellites around hot Jupiters can be immune to destruction by orbital decay; detection of such a massive satellite would strongly constrain theories of tidal dissipation in gas giants, in a manner complementary to orbital circularization. The stars gravity induces significant periodic eccentricity in the satellites orbit. The resulting tidal heating rates, per unit mass, are far in excess of Ios and dominate radioactive heating out to planet orbital periods of months for reasonable satellite tidal Q. Inside planet orbital periods of about a week, tidal heating can completely melt the satellite. Lastly, we compute an upper limit to the satellite mass loss rate due to thermal evaporation from the surface, valid if the satellites atmosphere is thin and vapor pressure is negligible. Using this upper limit, we find that although rocky satellites around hot Jupiters with orbital periods less than a few days can be significantly evaporated in their lifetimes, detectable satellites suffer negligible mass loss at longer orbital periods.

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 factorQt and tidal heating rate during a g-mode resonance lock, and verify our results numerically. We find thatQt 10 7 for orbital periods . 1 ‐ 2 hr in C/O WDs, andQt 10 9 for Porb . 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 , rivaling the luminosities of our fiducial WD models. Recent observations of the 13minute 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 Porb 10 min even in the presence of a tidal torque concentrated near the WD surface.

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 ωa excites a pair of secondary waves of frequency ωb + ωc ≃ ωa. Here we consider a nonresonant form of three-wave interaction in which a low-frequency primary wave excites a highfrequency p-mode and a low-frequency g-mode such that ωb + ωc ≫ ωa. We show that a p-mode can couple so strongly to a g-mode of similar radial wavelength that this type of nonresonant 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 fgw & 20 Hz and drive short wavelength p-g mode pairs to significant energies on very short timescales (much less than the orbital decay time due to gravitational radiation). 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 p-g instability and therefore we cannot say precisely how it influences the evolution of 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 will: (i) induce significant orbital phase errors (�φ & 1 radian) that accumulate primarily at low frequencies (fgw . 50 Hz) and (ii) heat the neutron star core to a temperature of T ∼ 10 10 K. Since there are at least ∼ 100 unstable p-g daughter pairs, �φ and T are potentially much larger than these values. Tides might therefore significantly influence the gravitational wave signal and electromagnetic emission from coalescing neutron star binaries at much larger orbital separations than previously thought.

The radial velocity signature of tides raised in stars hosting exoplanets

Close-in, massive exoplanets raise significant tides in their stellar hosts. We compute the radial velocity (RV) signal due to this fluid motion in the equilibrium tide approximation. The predicted radial velocities in the observed sample of exoplanets exceed 1 m/s for 17 systems, with the largest predicted signal being � 30 m s 1 for WASP-18 b. Tidally-induced RV’s are thus detectable with present methods. Both tidal fluid flow and the epicyclic motion of a slightly eccentric orbit produce an RV signal at twice the orbital frequency. If care is not taken, the tidally induced RV may, in some cases, be confused with a finite orbital eccentricity. Indeed, WASP-18 b is reported to have an eccentric orbit with small e = 0.009 and pericenter longitude ω = π/2. Whereas such a close alignment of the orbit and line of sight to the observer requires fine tuning, this phase in the RV signal is naturally explained by the tidal velocity signature of an e = 0 orbit. Additionally, the equilibrium tide estimate for the amplitude is in rough agreement with the data. Thus the reported eccentricity for WASP-18 b is instead likely a signature of the tidally-induced RV in the stellar host. Measurement of both the orbital and tidal velocity for non-transiting planets may allow planet mass and inclination to be separately determined solely from radial velocity data. We suggest that high precision fitting of RV data should include the tidal velocity signal in those cases where it may affect the determination of orbital parameters.

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 Lyα 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.