Buoyancy Instabilities in Degenerate, Collisional, Magnetized Plasmas

In low-collisionality plasmas, anisotropic heat conduction due to a magnetic field leads to buoyancy instabilities for any nonzero temperature gradient. We study analogous instabilities in degenerate {\it collisional} plasmas, i.e., when the electron collision frequency is large compared to the electron cyclotron frequency. Although heat conduction is nearly isotropic in this limit, the small residual anisotropy ensures that collisional degenerate plasmas are also convectively unstable independent of the sign of the temperature gradient. We show that the range of wavelengths that are unstable is independent of the magnetic field strength, while the growth time increases with decreasing magnetic field strength. We discuss the application of these collisional buoyancy instabilities to white dwarfs and neutron stars. Magnetic tension and the low specific heat of a degenerate plasma significantly limit their effectiveness; the most promising venues for growth are in the liquid oceans of young, weakly magnetized neutron stars ($B \lesssim 10^9$ G) and in the cores of young, high magnetic field white dwarfs ($B \sim 10^9$ G).Comment: 8 pages, 1 figure, 1 table, submitted to MNRA

Turbulence and Mixing in the Intracluster Medium

The intracluster medium (ICM) is stably stratified in the hydrodynamic sense with the entropy $s$ increasing outwards. However, thermal conduction along magnetic field lines fundamentally changes the stability of the ICM, leading to the "heat-flux buoyancy instability" when $dT/dr>0$ and the "magnetothermal instability" when $dT/dr<0$. The ICM is thus buoyantly unstable regardless of the signs of $dT/dr$ and $ds/dr$. On the other hand, these temperature-gradient-driven instabilities saturate by reorienting the magnetic field (perpendicular to $\hat{\bf r}$ when $dT/dr>0$ and parallel to $\hat{\bf r}$ when $dT/dr<0$), without generating sustained convection. We show that after an anisotropically conducting plasma reaches this nonlinearly stable magnetic configuration, it experiences a buoyant restoring force that resists further distortions of the magnetic field. This restoring force is analogous to the buoyant restoring force experienced by a stably stratified adiabatic plasma. We argue that in order for a driving mechanism (e.g, galaxy motions or cosmic-ray buoyancy) to overcome this restoring force and generate turbulence in the ICM, the strength of the driving must exceed a threshold, corresponding to turbulent velocities $\gtrsim 10 -100 {km/s}$. For weaker driving, the ICM remains in its nonlinearly stable magnetic configuration, and turbulent mixing is effectively absent. We discuss the implications of these findings for the turbulent diffusion of metals and heat in the ICM.Comment: 8 pages, 2 figs., submitted to the conference proceedings of "The Monster's Fiery Breath;" a follow up of arXiv:0901.4786 focusing on the general mixing properties of the IC

Relativistic Jets and Long-Duration Gamma-ray Bursts from the Birth of Magnetars

We present time-dependent axisymmetric magnetohydrodynamic simulations of the interaction of a relativistic magnetized wind produced by a proto-magnetar with a surrounding stellar envelope, in the first $\sim 10$ seconds after core collapse. We inject a super-magnetosonic wind with $\dot E = 10^{51}$ ergs s$^{-1}$ into a cavity created by an outgoing supernova shock. A strong toroidal magnetic field builds up in the bubble of plasma and magnetic field that is at first inertially confined by the progenitor star. This drives a jet out along the polar axis of the star, even though the star and the magnetar wind are each spherically symmetric. The jet has the properties needed to produce a long-duration gamma-ray burst (GRB). At $\sim 5$ s after core bounce, the jet has escaped the host star and the Lorentz factor of the material in the jet at large radii $\sim 10^{11}$ cm is similar to that in the magnetar wind near the source. Most of the spindown power of the central magnetar escapes via the relativistic jet. There are fluctuations in the Lorentz factor and energy flux in the jet on $\sim 0.01-0.1$ second timescale. These may contribute to variability in GRB emission (e.g., via internal shocks).Comment: 5 pages, 3 figures, accepted in MNRAS letter, presented at the conference "Astrophysics of Compact Objects", 1-7 July, Huangshan, Chin

A Kinetic Alfven wave cascade subject to collisionless damping cannot reach electron scales in the solar wind at 1 AU

(Abridged) Turbulence in the solar wind is believed to generate an energy cascade that is supported primarily by Alfv\'en waves or Alfv\'enic fluctuations at MHD scales and by kinetic Alfv\'en waves (KAWs) at kinetic scales $k_\perp \rho_i\gtrsim 1$. Linear Landau damping of KAWs increases with increasing wavenumber and at some point the damping becomes so strong that the energy cascade is completely dissipated. A model of the energy cascade process that includes the effects of linear collisionless damping of KAWs and the associated compounding of this damping throughout the cascade process is used to determine the wavenumber where the energy cascade terminates. It is found that this wavenumber occurs approximately when $|\gamma/\omega|\simeq 0.25$, where $\omega(k)$ and $\gamma(k)$ are, respectively, the real frequency and damping rate of KAWs and the ratio $\gamma/\omega$ is evaluated in the limit as the propagation angle approaches 90 degrees relative to the direction of the mean magnetic field.Comment: Submitted to Ap

Feedback-regulated star formation in molecular clouds and galactic discs

We present a two-zone theory for feedback-regulated star formation in galactic discs, consistently connecting the galaxy-averaged star formation law with star formation proceeding in giant molecular clouds (GMCs). Our focus is on galaxies with gas surface density Sigma_g>~100 Msun pc^-2. In our theory, the galactic disc consists of Toomre-mass GMCs embedded in a volume-filling ISM. Radiation pressure on dust disperses GMCs and most supernovae explode in the volume-filling medium. A galaxy-averaged star formation law is derived by balancing the momentum input from supernova feedback with the gravitational weight of the disc gas. This star formation law is in good agreement with observations for a CO conversion factor depending continuously on Sigma_g. We argue that the galaxy-averaged star formation efficiency per free fall time, epsilon_ff^gal, is only a weak function of the efficiency with which GMCs convert their gas into stars. This is possible because the rate limiting step for star formation is the rate at which GMCs form: for large efficiency of star formation in GMCs, the Toomre Q parameter obtains a value slightly above unity so that the GMC formation rate is consistent with the galaxy-averaged star formation law. We contrast our results with other theories of turbulence-regulated star formation and discuss predictions of our model. Using a compilation of data from the literature, we show that the galaxy-averaged star formation efficiency per free fall time is non-universal and increases with increasing gas fraction, as predicted by our model. We also predict that the fraction of the disc gas mass in bound GMCs decreases for increasing values of the GMC star formation efficiency. This is qualitatively consistent with the smooth molecular gas distribution inferred in local ultra-luminous infrared galaxies and the small mass fraction in giant clumps in high-redshift galaxies.Comment: 23 pages, 10 figures. To appear in MNRA

Spherical Accretion with Anisotropic Thermal Conduction

We study the effects of anisotropic thermal conduction on magnetized spherical accretion flows using global axisymmetric MHD simulations. In low collisionality plasmas, the Bondi spherical accretion solution is unstable to the magnetothermal instability (MTI). The MTI grows rapidly at large radii where the inflow is subsonic. For a weak initial field, the MTI saturates by creating a primarily radial magnetic field, i.e., by aligning the field lines with the background temperature gradient. The saturation is quasilinear in the sense that the magnetic field is amplified by a factor of $\sim 10-30$ independent of the initial field strength (for weak fields). In the saturated state, the conductive heat flux is much larger than the convective heat flux, and is comparable to the field-free (Spitzer) value (since the field lines are largely radial). The MTI by itself does not appreciably change the accretion rate $\dot M$ relative to the Bondi rate $\dot M_B$. However, the radial field lines created by the MTI are amplified by flux freezing as the plasma flows in to small radii. Oppositely directed field lines are brought together by the converging inflow, leading to significant resistive heating. When the magnetic energy density is comparable to the gravitational potential energy density, the plasma is heated to roughly the virial temperature; the mean inflow is highly subsonic; most of the energy released by accretion is transported to large radii by thermal conduction; and the accretion rate $\dot M \ll \dot M_B$. The predominantly radial magnetic field created by the MTI at large radii in spherical accretion flows may account for the stable Faraday rotation measure towards Sgr A* in the Galactic Center.Comment: accepted in MNRAS with some modifications suggested by the referee; 15 pages, 16 figure