A B S T R A C TMHD in protostellar discs is modified by the Hall current when the ambipolar diffusion approximation breaks down. Here I examine the Balbus±Hawley (magnetorotational) instability of a weak, vertical magnetic field within a weakly ionized disc. Vertical stratification is neglected, and a linear analysis is undertaken for the case in which the wavevector of the perturbation is parallel to the magnetic field.The growth rate depends on whether the initial magnetic field is parallel or antiparallel to the angular momentum of the disc. The parallel case is less (more) unstable than the antiparallel case if the Hall current is dominated by negative (positive) species. The lessunstable orientation is stable for x & 0X5Y where x is the ratio of a generalized neutral±ion collision frequency to the Keplerian frequency. The other orientation has a formal growth rate of the order of the Keplerian angular frequency even in the limit x 3 0! In this limit the wavelength of the fastest-growing mode tends to infinity, so the minimum level of ionization for instability is determined by the requirement that a wavelength fit within a disc scaleheight. In the ambipolar diffusion case, this requires x . v A ac s ; in the Hall case this imposes a potentially much weaker limit, x . v 2 A ac 2 s X
Magnetic fields likely play a key role in the dynamics and evolution of protoplanetary disks. They have the potential to efficiently transport angular momentum by MHD turbulence or via the magnetocentrifugal acceleration of outflows from the disk surface. Magnetically-driven mixing has implications for disk chemistry and evolution of the grain population, and the effective viscous response of the disk determines whether planets migrate inwards or outwards. However, the weak ionisation of protoplanetary disks means that magnetic fields may not be able to effectively couple to the matter. I examine the magnetic diffusivity in a minimum solar nebula model and present calculations of the ionisation equilibrium and magnetic diffusivity as a function of height from the disk midplane at radii of 1 and 5 AU. Dust grains tend to suppress magnetic coupling by soaking up electrons and ions from the gas phase and reducing the conductivity of the gas by many orders of magnitude. However, once grains have grown to a few microns in size their effect starts to wane and magnetic fields can begin to couple to the gas even at the disk midplane. Because ions are generally decoupled from the magnetic field by neutral collisions while electrons are not, the Hall effect tends to dominate the diffusion of the magnetic field when it is able to partially couple to the gas, except at the disk surfaces where the low density of neutrals permits the ions to remain attached to the field lines.For a standard population of 0.1µm grains the active surface layers have a combined column Σ active ≈ 2 g cm −2 at 1 AU; by the time grains have aggregated to 3 µm, Σ active ≈ 80 g cm −2 . Ionisation in the active layers is dominated by stellar x-rays. In the absence of grains, x-rays maintain magnetic coupling to 10% of
We evaluate the conductivity tensor for molecular gas at densities ranging from 10^4 to 10^15 cm^-3 for a variety of grain models. The Hall contribution to the conductivity has generally been neglected in treatments of the dynamics of molecular gas. We find that it is not important if only 0.1 micron grains are considered, but for a Mathis-Rumpl-Nordsieck grain-size distribution (with or without PAHs) it becomes important for densities between 10^7 and 10^11 cm^-3. If PAHs are included, this range is reduced to 10^9 -- 10^10 cm^-3. The consequences for the magnetic field evolution and dynamics of dense molecular gas are profound. To illustrate this, we consider the propagation of Alfven waves under these conditions. A linear analysis yields a dispersion relation valid for frequencies below the neutral collision frequencies of the charged species. The dispersion relation shows that there is a pair of circularly polarised modes with distinct propagation speeds and damping rates. We note that the gravitational collapse of dense cloud cores may be substantially modified by the Hall term.Comment: MNRAS accepted; 9 pp incl 8 figs, LaTeX, uses epsf.sty mn.st
The central kpc of the Milky Way might be expected to differ significantly from the rest of the Galaxy with regard to gasdynamics and the formation of young stellar objects (YSOs). We probe this possibility with midinfrared observations obtained with Infrared Array Camera and Multiband Imaging Photometer on Spitzer and with Midcourse Space Experiment. We use color-color diagrams and spectral energy distribution (SED) fits to explore the nature of YSO candidates (including objects with 4.5 μm excesses possibly due to molecular emission). There is an asymmetry in the distribution of the candidate YSOs, which tend to be found at negative Galactic longitudes; this behavior contrasts with that of the molecular gas, approximately 2/3 of which is at positive longitudes. The small-scale height of these objects suggests that they are within the Galactic center region and are dynamically young. They lie between two layers of infrared dark clouds and may have originated from these clouds. We identify new sites for this recent star formation by comparing the mid-IR, radio, submillimeter, and methanol maser data. The methanol masers appear to be associated with young, embedded YSOs characterized by 4.5 μm excesses. We use the SEDs of these sources to estimate their physical characteristics; their masses appear to range from ∼10 to ∼20 M . Within the central 400 × 50 pc (|l| < 1.• 3 and |b| < 10 ) the star formation rate (SFR) based on the identification of Stage I evolutionary phase of YSO candidates is about 0.14 M yr −1 . Given that the majority of the sources in the population of YSOs are classified as Stage I objects, we suggest that a recent burst of star formation took place within the last 10 5 yr. This suggestion is also consistent with estimates of SFRs within the last ∼10 7 yr showing a peak around 10 5 yr ago. Lastly, we find that the Schmidt-Kennicutt Law applies well in the central 400 pc of the Galaxy. This implies that star formation does not appear to be dramatically affected by the extreme physical conditions in the Galactic center region.
We have carried out Very Large Array (VLA) continuum observations to study the variability of Sgr A Ã at 43 GHz (k ¼ 7 mm) and 22 GHz (k ¼ 13 mm). A low level of flare activity has been detected with a duration of $2 hr at these frequencies, showing the peak flare emission at 43 GHz leading the 22 GHz peak flare by $20-40 minutes. The overall characteristics of the flare emission are interpreted in terms of the plasmon model of van der Laan by considering the ejection and adiabatic expansion of a uniform, spherical plasma blob due to flare activity. The observed peak of the flare emission with a spectral index, À , of ¼ 1:6 is consistent with the prediction that the peak emission shifts toward lower frequencies in an adiabatically expanding self-absorbed source. We present the expected synchrotron light curves for an expanding blob, as well as the peak frequency emission, as a function of the energy spectral index constrained by the available flaring measurements in near-IR, submillimeter, millimeter, and radio wavelengths. We note that the blob model is consistent with the available measurements; however, we cannot rule out the jet of Sgr A Ã . If expanding material leaves the gravitational potential of Sgr A Ã , the total mass-loss rate of nonthermal and thermal particles is estimated to be 2 ; 10 À8 M yr À1 . We discuss the implication of the mass-loss rate, since this value matches closely the estimated accretion rate based on polarization measurements.
Although Sgr A* is known to be variable in radio, millimeter, near-IR and X-rays, the correlation of the variability across its spectrum has not been fully studied.Here we describe highlights of the results of two observing campaigns in 2004 to investigate the correlation of flare activity in different wavelength regimes, using a total of nine ground and space-based telescopes. We report the detection of several new near-IR flares during the campaign based on HST observations. The level of near-IR flare activity can be as low as ∼ 0.15 mJy at 1.6 µm and continuous up to ∼40% of the total observing time, thus placing better limits than ground-based near-IR observations. Using the NICMOS instrument on the HST, the XMM-Newton and Caltech Submillimeter observatories, we also detect simultaneous bright X-ray and near-IR flare in which we observe for the first time correlated substructures as well as simultaneous submillimeter and near-IR flaring. X-ray emission is arising from the population of near-IR-synchrotron-emitting relativistic particles which scatter submillimeter seed photons within the inner 10 Schwarzschild radii (R sch ) of Sgr A* up to X-ray energies. In addition, using the inverse Compton scattering picture, we explain the high energy 20-120 keV emission from the direction toward Sgr A*, and the lack of one-to-one X-ray counterparts to near-IR flares, by the variation of the magnetic field and the spectral index distributions of this population of nonthermal particles. In this picture, the evidence for the variability of submillimeter emission during a near-IR flare is produced by the low-energy component of the population of particles emitting synchrotron near-IR emission. Based on the measurements of the duration of flares in near-IR and submillimeter wavelengths, we argue that the cooling could be due to adiabatic expansion with the implication that flare activity may drive an outflow.
The high-energy activity in the inner few degrees of the Galactic center is traced by diffuse radio, X-ray, and γ -ray emission. The physical relationship between different components of diffuse gas emitting at multiple wavelengths is a focus of this work. We first present radio continuum observations using the Green Bank Telescope and model the nonthermal spectrum in terms of a broken power-law distribution of ∼GeV electrons emitting synchrotron radiation. We show that the emission detected by Fermi is primarily due to nonthermal bremsstrahlung produced by the population of synchrotron emitting electrons in the GeV energy range interacting with neutral gas. The extrapolation of the electron population measured from radio data to low and high energies can also explain the origin of Fe i 6.4 keV line and diffuse TeV emission, as observed with Suzaku, XMM-Newton, Chandra, and the H.E.S.S. observatories. The inferred physical quantities from modeling multiwavelength emission in the context of bremsstrahlung emission from the inner ∼300×120 pc of the Galactic center are constrained to have the cosmic-ray ionization rate ∼1-10 × 10 −15 s −1 , molecular gas heating rate elevating the gas temperature to 75-200 K, fractional ionization of molecular gas 10 −6 -10 −5 , large-scale magnetic field 10-20 μG, the density of diffuse and dense molecular gas ∼100 and ∼10 3 cm −3 over 300 pc and 50 pc path lengths, and the variability of Fe i Kα 6.4 keV line emission on yearly timescales. Important implications of our study are that GeV electrons emitting in radio can explain the GeV γ -rays detected by Fermi and that the cosmic-ray irradiation model, like the model of the X-ray irradiation triggered by past activity of Sgr A * , can also explain the origin of the variable 6.4 keV emission from Galactic center molecular clouds.
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