Guaranteeing Spatial Uniformity in Diffusively-Coupled Systems

We present a condition that guarantees spatially uniformity in the solution trajectories of a diffusively-coupled compartmental ODE model, where each compartment represents a spatial domain of components interconnected through diffusion terms with like components in different compartments. Each set of like components has its own weighted undirected graph describing the topology of the interconnection between compartments. The condition makes use of the Jacobian matrix to describe the dynamics of each compartment as well as the Laplacian eigenvalues of each of the graphs. We discuss linear matrix inequalities that can be used to verify the condition guaranteeing spatial uniformity, and apply the result to a coupled oscillator network. Next we turn to reaction-diffusion PDEs with Neumann boundary conditions, and derive an analogous condition guaranteeing spatial uniformity of solutions. The paper contributes a relaxed condition to check spatial uniformity that allows individual components to have their own specific diffusion terms and interconnection structures

An Adaptive Algorithm for Synchronization in Diffusively Coupled Systems

We present an adaptive algorithm that guarantees synchronization in diffusively coupled systems. We first consider compartmental systems of ODEs, where each compartment represents a spatial domain of components interconnected through diffusion terms with like components in different compartments. Each set of like components may have its own weighted undirected graph describing the topology of the interconnection between compartments. The link weights are updated adaptively according to the magnitude of the difference between neighboring agents connected by the link. We next consider reaction-diffusion PDEs with Neumann boundary conditions, and derive an analogous algorithm guaranteeing spatial homogenization of solutions. We provide a numerical example demonstrating the results

Cosmic-Ray Heating of Molecular Gas in the Nuclear Disk: Low Star Formation Efficiency

Understanding the processes occurring in the nuclear disk of our Galaxy is interesting in its own right, as part of the Milky Way Galaxy, but also because it is the closest galactic nucleus. It has been more than two decades since it was recognized that the general phenomenon of higher gas temperature in the inner few hundred parsecs by comparison with local clouds in the disk of the Galaxy. This is one of the least understood characteristics of giant molecular clouds having a much higher gas temperature than dust temperature in the inner few degrees of the Galactic center. We propose that an enhanced flux of cosmic-ray electrons, as evidenced recently by a number of studies, are responsible for directly heating the gas clouds in the nuclear disk, elevating the temperature of molecular gas ($\sim$ 75K) above the dust temperature ($\sim$ 20K). In addition we report the detection of nonthermal radio emission from Sgr B2-F based on low-frequency GMRT and VLA observations. The higher ionization fraction and thermal energy due to the impact of nonthermal electrons in star forming sites have important implications in slowing down star formation in the nuclear disk of our galaxy and nuclei of galaxies.Comment: 12 pages, one figure, ApJL (in press

Shocked molecular gas towards the SNR G359.1-0.5 and the Snake

We have found a bar of shocked molecular hydrogen (H2) towards the OH(1720 MHz) maser located at the projected intersection of supernova remnant (SNR) G359.1-0.5 and the nonthermal radio filament, known as the Snake. The H2 bar is well aligned with the SNR shell and almost perpendicular to the Snake. The OH(1720 MHz) maser is located inside the sharp western edge of the H2 emission, which is consistent with the scenario in which the SNR drives a shock into a molecular cloud at that location. The spectral-line profiles of 12CO, HCO+ and CS towards the maser show broad-line absorption, which is absent in the 13CO spectra and most probably originates from the pre-shock gas. A density gradient is present across the region and is consistent with the passage of the SNR shock while the H2 filament is located at the boundary between the pre--shocked and post-shock regions.Comment: 8 pages, 12 figures, accepted by the MNRAS, typos fixe

An Inverse Compton Scattering Origin of X-ray Flares from Sgr A*

The X-ray and near-IR emission from Sgr A* is dominated by flaring, while a quiescent component dominates the emission at radio and sub-mm wavelengths. The spectral energy distribution of the quiescent emission from Sgr A* peaks at sub-mm wavelengths and is modeled as synchrotron radiation from a thermal population of electrons in the accretion flow, with electron temperatures ranging up to $\sim 5-20$\,MeV. Here we investigate the mechanism by which X-ray flare emission is produced through the interaction of the quiescent and flaring components of Sgr A*. The X-ray flare emission has been interpreted as inverse Compton, self-synchrotron-Compton, or synchrotron emission. We present results of simultaneous X-ray and near-IR observations and show evidence that X-ray peak flare emission lags behind near-IR flare emission with a time delay ranging from a few to tens of minutes. Our Inverse Compton scattering modeling places constraints on the electron density and temperature distributions of the accretion flow and on the locations where flares are produced. In the context of this model, the strong X-ray counterparts to near-IR flares arising from the inner disk should show no significant time delay, whereas near-IR flares in the outer disk should show a broadened and delayed X-ray flare.Comment: 22 pages, 6 figures, 2 tables, AJ (in press

Properties of the Compact HII Region Complex G-0.02-0.07

We present new extinction maps and high-resolution Paschen alpha images of G-0.02-0.07, a complex of compact HII regions located adjacent to the M-0.02-0.07 giant molecular cloud, 6 parsecs in projection from the center of the Galaxy. These HII regions, which lie in projection just outside the boundary of the Sgr A East supernova remnant, represent one of the most recent episodes of star formation in the central parsecs of the Galaxy. The 1.87 micron extinctions of regions A, B and C are almost identical, approximately 1.5 magnitudes. Region D, in contrast, has a peak 1.87 micron extinction of 2.3 magnitudes. Adopting the Nishiyama et al. (2008) extinction law, we find these extinctions correspond to visual extinctions of A_V = 44.5 and A_V = 70, respectively. The similar and uniform extinctions of regions A, B and C are consistent with that expected for foreground extinction in the direction of the Galactic center, suggesting that they lie at the front side of the M-0.02-0.07 molecular cloud. Region D is more compact, has a higher extinction and is thus suspected to be younger and embedded in a dense core in a compressed ridge on the western edge of this cloud.Comment: 21 pages, 11 figures, submitted to ApJ, comments welcom

Magnetic field near the central region of the Galaxy: Rotation measure of extragalactic sources

To determine the properties of the Faraday screen and the magnetic field near the central region of the Galaxy, we measured the Faraday rotation measure (RM) towards 60 background extragalactic source components through the -6 deg < l <6 deg, -2 deg < b < 2 deg region of the Galaxy using the 4.8 and 8.5 GHz bands of the ATCA and VLA. Here we use the measured RMs to estimate the systematic and the random components of the magnetic fields. The measured RMs are found to be mostly positive for the sample sources in the region. This is consistent with either a large scale bisymmetric spiral magnetic fields in the Galaxy or with fields oriented along the central bar of the Galaxy. The outer scale of the RM fluctuation is found to be about 40 pc, which is much larger than the observed RM size scales towards the non-thermal filaments (NTFs). The RM structure function is well-fitted with a power law index of 0.7 +/- 0.1 at length scales of 0.3 to 100 pc. If Gaussian random processes in the ISM are valid, the power law index is consistent with a two dimensional Kolmogorov turbulence. If there is indeed a strong magnetic field within 1 degree (radius 150 pc) from the GC, the strength of the random field in the region is estimated to be 20 microGauss. Given the highly turbulent magnetoionic ISM in this region, the strength of the systematic component of the magnetic fields would most likely be close to that of the random component. This suggests that the earlier estimated milliGauss magnetic field near the NTFs is localised and does not pervade the central 300 pc of the Galaxy.Comment: 9 pages, 6 figures, accepted for publication in A&

High Spectral and Spatial Resolution Observations of Shocked Molecular Hydrogen at the Galactic Center

The presence of OH (1720 MHz) masers, and the absence of counterparts at 1665/1667 MHz has proved to be a clear diagnostic of shocked molecular gas associated with Galactic supernova remnants. This suggests that shocked molecular gas should be associated with the OH (1720 MHz) masers that have been detected in the circumnuclear disk (CND) and Sgr A East at the Galactic center. In order to test this hypothesis, we observed the H$_2$ 1--0 S(1) and Br $\gamma$ lines using NICMOS on the HST and UNSWIRF on the AAT, near the regions where OH (1720 MHz) masers are detected in the CND and Sgr A East. We present the distribution of H$_2$ in the North and South lobes of the CND and in Sgr A East. H$_2$ emission accompanies almost all of the maser spots detected at the Galactic center. In particular, we find a striking filamentary structure near the Northwest of the CND and evidence that shocked molecular gas is associated with the 70 \kms molecular cloud at the Galactic center. We argue that the emission from the CND could arise in gas heated by the dissipation of the random motion of clumps by collisions or the dissipation of turbulence in a more homogeneous medium. In addition, highly red-shifted gas of up to 140 \kms\ close to the eastern edge of the Sgr A East shell is detected. These observations combined with OH (1720 MHz) results suggest that the H$_2$ gas is shocked and accelerated by the expansion of Sgr A East into the 50 and the 70 \kms cloud and into the lobes of the CND.Comment: 31 pages plus 14 figures, ApJ (in press