Juhan Frank

Numerical Simulations of the Onset and Stability of Dynamical Mass Transfer in Binaries

Hydrodynamical simulations of semidetached, polytropic binary stars are presented in an effort to study the onset and stability of dynamical mass transfer events. Initial, synchronously rotating equilibrium models are constructed using a self-consistent field technique and then evolved with an Eulerian hydrodynamics code in a fully self-consistent manner. We describe code improvements introduced over the past few years that permit us to follow dynamical mass transfer events through more than 30 orbits. Mass transfer evolutions are presented for two different initial configurations: a dynamically unstable binary with initial mass ratio (donor/accretor) q0 = 1.3 that leads to a complete merger in ~10 orbits, and a double-degenerate binary with initial mass ratio q0 = 0.5 that, after some initial unstable growth of mass transfer, tends to separate as the mass transfer rate levels off.

Tearing up the disk: How black holes accrete

We show that in realistic cases of accretion in active galactic nuclei or stellar-mass X-ray binaries, the Lense-Thirring effect breaks the central regions of tilted accretion discs around spinning black holes into a set of distinct planes with only tenuous flows connecting them. If the original misalignment of the outer disc to the spin axis of the hole is

The Stability of Double White Dwarf Binaries Undergoing Direct-Impact Accretion

45^{\circ} \lesssim \theta \lesssim 135^{\circ}

Transients among Binaries with Evolved Low-Mass Companions

, as in

Mass transfer cycles in cataclysmic variables

\sim 70

Evolution of Close White Dwarf Binaries

% of randomly oriented accretion events, the continued precession of these discs sets up partially counter-rotating gas flows. This drives rapid infall as angular momentum is cancelled and gas attempts to circularize at smaller radii. Disc breaking close to the black hole leads to direct dynamical accretion, while breaking further out can drive gas down to scales where it can accrete rapidly. For smaller tilt angles breaking can still occur, and may lead to other observable phenomena such as QPOs. For such effects not to appear, the black hole spin must in practice be negligibly small, or be almost precisely aligned with the disc. Qualitatively similar results hold for any accretion disc subject to a forced differential precession, such as an external disc around a misaligned black hole binary.

Perturbed disks get shocked: Binary black hole merger effects on accretion disks

We present numerical simulations of dynamically unstable mass transfer in a double white dwarf binary with initial mass ratio q = 0.4. The binary components are approximated as polytropes of index n = 3/2, and the initially synchronously rotating, semidetached equilibrium binary is evolved hydrodynamically, with the gravitational potential being computed through the solution of Poissons equation. Upon initiating deep contact in our baseline simulation, the mass transfer rate grows by more than an order of magnitude over approximately 10 orbits, as would be expected for dynamically unstable mass transfer. However, the mass transfer rate then reaches a peak value, the binary expands, and the mass transfer event subsides. The binary must therefore have crossed the critical mass ratio for stability against dynamical mass transfer. Despite the initial loss of orbital angular momentum into the spin of the accreting star, we find that the accretors spin saturates and that angular momentum is returned to the orbit more efficiently than has been previously suspected for binaries in the direct-impact accretion mode. To explore this surprising result, we directly measure the critical mass ratio for stability by imposing artificial angular momentum loss at various rates to drive the binary to an equilibrium mass transfer rate. For one of these driven evolutions, we attain equilibrium mass transfer and deduce that, effectively, qcrit has evolved to approximately 2/3. Despite the absence of a fully developed disk, tidal interactions appear to be effective in returning excess spin angular momentum to the orbit.

Numerical Methods for the Simulation of Dynamical Mass Transfer in Binaries

We show that stable disk accretion should be very rare among low-mass X-ray binaries (LMXBs) and cataclysmic variables whose evolution is driven by the nuclear expansion of the secondary star on the first giant branch. Stable accretion is confined to neutron star systems in which the secondary is still relatively massive and to some supersoft white dwarf accretors. All other systems, including all black hole systems, appear as soft X-ray transients or dwarf novae. All long-period neutron star systems become transient well before most of the envelope mass is transferred and remain transient until envelope exhaustion. This complicates attempts to compare the numbers of millisecond pulsars in the Galactic disk with their LMXB progenitors and means that the pulsar spin rates are fixed in systems that are transient rather than steady, contrary to common assumption. The long-period persistent sources Sco X-2, LMC X-2, Cyg X-2, and V395 Car must have minimum companion masses, M2, of about 0.75 M☉ if they contain neutron stars and still larger M2 if they contain black holes. The neutron star transient GRO J1744-2844 must have M2 0.87 M☉. The existence of any steady source at long periods supports the ideas that (1) the accretion disks in many, if not all, LMXBs are strongly irradiated by the central source and (2) mass transfer is thermally unstable in long-period supersoft X-ray sources.

The transient nature of GRO J1655-40 and its evolutionary state

It is well known that in cataclysmic variables the mass transfer rate must fluctuate about the evolutionary mean on timescales too long to be directly observable. We show that limit-cycle behavior can occur if the radius change of the secondary star is sensitive to the instantaneous mass transfer rate. The only reasonable way in which such a dependence can arise is through irradiation of this star by the accreting component. The system oscillates between high states, in which irradiation causes slow expansion of the secondary and drives an elevated transfer rate, and low states, in which this star contracts.

On the Magnetic Field Evolution in Isolated Neutron Stars

We describe the evolution of double degenerate binary systems, consisting of components obeying the zero-temperature mass-radius relationship for white dwarf stars, from the onset of mass transfer to one of several possible outcomes, including merger, tidal disruption of the donor, or survival as a semidetached AM CVn system. We use a combination of analytic solutions and numerical integrations of the standard orbit-averaged first-order evolution equations, including direct-impact accretion and the evolution of the components due to mass exchange. We include also the effects of mass loss during supercritical (super-Eddington) mass transfer and the tidal and advective exchanges of angular momentum between the binary components. With the caveat that our formalism does not include an explicit treatment of common-envelope phases, our results suggest that a larger fraction of detached double white dwarfs survive the onset of mass transfer than has been hitherto assumed, even if this mass transfer is initially unstable and rises to super-Eddington levels. In addition, as a consequence of the tidal coupling, systems that come into contact near the mass transfer instability boundary undergo a phase of oscillation cycles in their orbital period (and other system parameters). Unless the donor star has a finite entropy such that the effective mass-radius relationship deviates significantly from that of a zero-temperature white dwarf, we expect our results to be valid. Much of the formalism developed here would also apply to other mass-transferring binaries, and in particular to cataclysmic variables and Algol systems.