Greg Ushomirsky

Lithium Depletion in Fully Convective Pre-Main-Sequence Stars

We present an analytic calculation of the thermonuclear depletion of lithium in contracting, fully con- vective, preEmain-sequence stars of mass Previous numerical work relies on still uncertain M ( 0.5 M _ . physics (atmospheric opacities and convection, in particular) to calculate the e†ective temperature as a unique function of stellar mass. We assume that the starIs e†ective temperature, is -xed during T eff , Hayashi contraction and allow its actual value to be a free parameter constrained by observation. Using this approximation, we compute lithium burning analytically and explore the dependence of lithium depletion on M, and composition. Our calculations yield the radius, age, and luminosity of a preE T eff , main-sequence star as a function of lithium depletion. This allows for more direct comparisons with observations of lithium-depleted stars. Our results agree with those numerical calculations that explicitly determine stellar structure during Hayashi contraction. In agreement with Basri, Marcy, & Graham, we show that the absence of lithium in the Pleiades star HHJ 3 implies that it is older than 100 Myr. We also suggest a generalized method for dating Galactic clusters younger than 100 Myr (i.e., those with contracting stars of and for constraining the masses of lithium-depleted stars. M Z 0.08 M _ ) Subject headings: nuclear reactions, nucleosynthesis, abundances E stars: evolution E stars: interiors E stars: preEmain-sequence

Viscous Boundary-Layer Damping of r-Modes in Neutron Stars

Recent work has raised the exciting possibility that r-modes (Rossby waves) in rotating neutron star cores might be strong gravitational-wave sources. We estimate the effect of a solid crust on their viscous damping rate and show that the dissipation rate in the viscous boundary layer between the oscillating fluid and the nearly static crust is more than 105 times higher than that from the shear throughout the interior. This increases the minimum frequency for the onset of the gravitational r-mode instability to at least 500 Hz when the core temperature is less than 1010 K. It eliminates the conflict between the r-mode instability and the accretion-driven spin-up scenario for millisecond radio pulsars and makes it unlikely that the r-mode instability is active in accreting neutron stars. For newborn neutron stars, the formation of a solid crust shortly after birth affects their gravitational-wave spin-down and hence their detectability by ground-based interferometric gravitational-wave detectors.

Crust–core coupling and r‐mode damping in neutron stars: a toy model

R-modes in neutron stars with crusts are damped by viscous friction at the crust-core boundary. The magnitude of this damping, evaluated by Bildsten and Ushomirsky (BU) under the assumption of a perfectly rigid crust, sets the maximum spin frequency for a neutron star spun up by accretion in a Low-Mass X-ray binary (LMXB). In this paper we explore the mechanical coupling between the core r-modes and the elastic crust, using a toy model of a constant density neutron star with a constant shear modulus crust. We find that, at spin frequencies in excess of ~50 Hz, the r-modes strongly penetrate the crust. This reduces the relative motion (slippage) between the crust and the core compared to the rigid crust limit. We therefore revise down, by as much as a factor of 10^2-10^3, the damping rate computed by BU, significantly reducing the maximal possible spin frequency of neutron star with a solid crust. The dependence of the crust-core slippage on the spin frequency is complicated, and is very sensitive to the physical thickness of the crust. If the crust is sufficiently thick, the curve of the critical spin frequency for the onset of the r-mode instability becomes multi-valued for some temperatures; this is related to the avoided crossings between the r-mode and the higher-order torsional modes in the crust. The critical frequencies are comparable to the observed spins of neutron stars in LMXBs and millisecond pulsars.

Constraints on the Steady State r-Mode Amplitude in Neutron Star Transients

Recent observations suggest that neutron stars in low-mass X-ray binaries rotate within a narrow range of spin frequencies clustered around 300 Hz. A proposed explanation for this remarkable fact is that gravitational radiation from a steady state r-mode oscillation in the neutron stars core halts the spin-up due to accretion. For the neutron star transients, balancing the time-averaged accretion torque with gravitational wave emission from steady state, constant amplitude r-mode pulsations implies a quiescent luminosity too bright to be consistent with observations (in particular of Aql X-1). The viscous dissipation (roughly 10 MeV per accreted nucleon for a spin of 300 Hz) from such an r-mode makes the core sufficiently hot to power a thermal luminosity ~1034 ergs s-1 when accretion halts. This is the minimum quiescent luminosity that the neutron star must emit when viscous heating in the core is balanced by radiative cooling from the surface, as is the case when the core of the star is superfluid. We therefore conclude that either the accretion torque is much less than (GMR)1/2 or a steady state r-mode does not limit the spin rate of the neutron star transients. Future observations with Chandra and XMM promise to further constrain the amount of viscous dissipation in the neutron star core.

Rapid Rotation and Nonradial Pulsations: κ-Mechanism Excitation of g-Modes in B Stars

Several classes of stars (most notably O and B main-sequence stars, as well as accreting white dwarfs and neutron stars) rotate quite rapidly, at spin frequencies greater than the typical g-mode frequencies. We discuss how rapid rotation modifies the κ-mechanism excitation and observability of g-mode oscillations. We find that, by affecting the timescale match between the mode period and the thermal time at the driving zone, rapid rotation stabilizes some of the g-modes that are excited in a nonrotating star and, conversely, excites g-modes that are damped in the absence of rotation. The fluid velocities and temperature perturbations are strongly concentrated near the equator for most g-modes in rapidly rotating stars, which means that a favorable viewing angle may be required to observe the pulsations. Moreover, the stability of modes of the same l but different m is affected differently by rotation. We illustrate this by considering g-modes in slowly pulsating B-type stars as a function of the rotation rate.

Non-linear r-modes in a spherical shell: issues of principle

ABSTRA C T We use a simple physical model to study the non-linear behaviour of the r-mode instability. We assume that r-modes (Rossby waves) are excited in a thin spherical shell of rotating incompressible fluid. For this case, exact Rossby wave solutions of arbitrary amplitude are known. We find that these non-linear Rossby waves carry zero physical angular momentum and positive physical energy, which is contrary to the folklore belief that the r-mode angular momentum and energy are negative. We think that the origin of the confusion lies in the difference between physical and canonical quantities. Within our model, we confirm the differential drift reported in 2000 by Rezzolla, Lamb & Shapiro. Radiation reaction is introduced into the model by assuming that the fluid is electrically charged; r-modes are coupled to electromagnetic radiation through current (magnetic) multipole moments. We study the coupled equations of charged fluid and Maxwell field dynamics and find the following. To linear order in the mode amplitude, r-modes are subject to the CFS instability, as expected. Radiation reaction decreases the angular velocity of the shell and causes differential rotation (which is distinct from but similar in magnitude to the differential drift reported by Rezzolla et al.) prior to saturation of the r-mode growth. This is contrary to the phenomenological treatments to date, which assumed that, prior to the saturation of the r-mode amplitude, the loss of stellar angular momentum is accounted for by the r-mode growth. This establishes, for the first time, that radiation reaction leads not only to overall loss of angular momentum, but also to differential rotation. Finally, we show that for the la 2 r-mode the electromagnetic radiation reaction is equivalent to the gravitational radiation reaction in the lowest post-Newtonian order. Based on our electromagnetic calculations, we conclude that inertial frame dragging, both from the background rotation and from the r-mode itself, will modify the r-mode frequency by a factor of ,RSch=Rstar (where RSch is the Schwarzschild radius), in qualitative agreement with Kojima’s result from 1998.