Metal Cooling in Simulations of Cosmic Structure Formation

The addition of metals to any gas can significantly alter its evolution by increasing the rate of radiative cooling. In star-forming environments, enhanced cooling can potentially lead to fragmentation and the formation of low-mass stars, where metal-free gas-clouds have been shown not to fragment. Adding metal cooling to numerical simulations has traditionally required a choice between speed and accuracy. We introduce a method that uses the sophisticated chemical network of the photoionization software, Cloudy, to include radiative cooling from a complete set of metals up to atomic number 30 (Zn) that can be used with large-scale three-dimensional hydrodynamic simulations. Our method is valid over an extremely large temperature range (10 K < T < 10^8 K), up to hydrogen number densities of 10^12 cm^-3. At this density, a sphere of 1 Msun has a radius of roughly 40 AU. We implement our method in the adaptive mesh refinement (AMR) hydrodynamic/N-body code, Enzo. Using cooling rates generated with this method, we study the physical conditions that led to the transition from Population III to Population II star formation. While C, O, Fe, and Si have been previously shown to make the strongest contribution to the cooling in low-metallicity gas, we find that up to 40% of the metal cooling comes from fine-structure emission by S, when solar abundance patterns are present. At metallicities, Z > 10^-4 Zsun, regions of density and temperature exist where gas is both thermally unstable and has a cooling time less than its dynamical time. We identify these doubly unstable regions as the most inducive to fragmentation. At high redshifts, the CMB inhibits efficient cooling at low temperatures and, thus, reduces the size of the doubly unstable regions, making fragmentation more difficult.Comment: 19 pages, 12 figures, significant revision, including new figure

The X-ray Ridge Surrounding Sgr A* at the Galactic Center

We present the first detailed simulation of the interaction between the supernova explosion that produced Sgr A East and the wind-swept inner ~ 2-pc region at the Galactic center. The passage of the supernova ejecta through this medium produces an X-ray ridge ~ 9'' to 15'' to the NE of the supermassive black hole Sagittarius A* (Sgr A*). We show that the morphology and X-ray intensity of this feature match very well with recently obtained Chandra images, and we infer a supernova remnant age of less than 2,000 years. This young age--a factor 3--4 lower than previous estimates--arises from our inclusion of stellar wind effects in the initial (pre-explosion) conditions in the medium. The supernova does not clear out the central ~ 0.2-pc region around Sgr~A* and does not significantly alter the accretion rate onto the central black hole upon passage through the Galactic center.Comment: 10 pages, 3 figures, submitted to ApJ

Probing the Density in the Galactic Center Region: Wind-Blown Bubbles and High-Energy Proton Constraints

Recent observations of the Galactic center in high-energy gamma-rays (above 0.1TeV) have opened up new ways to study this region, from understanding the emission source of these high-energy photons to constraining the environment in which they are formed. We present a revised theoretical density model of the inner 5pc surrounding Sgr A* based on the fact that the underlying structure of this region is dominated by the winds from the Wolf-Rayet stars orbiting Sgr A*. An ideal probe and application of this density structure is this high energy gamma-ray emission. We assume a proton-scattering model for the production of these gamma-rays and then determine first whether such a model is consistent with the observations and second whether we can use these observations to further constrain the density distribution in the Galactic center.Comment: 36 pages including 17 figures, submitted to ApJ, comments welcom

Super stellar clusters with a bimodal hydrodynamic solution: an Approximate Analytic Approach

We look for a simple analytic model to distinguish between stellar clusters undergoing a bimodal hydrodynamic solution from those able to drive only a stationary wind. Clusters in the bimodal regime undergo strong radiative cooling within their densest inner regions, which results in the accumulation of the matter injected by supernovae and stellar winds and eventually in the formation of further stellar generations, while their outer regions sustain a stationary wind. The analytic formulae are derived from the basic hydrodynamic equations. Our main assumption, that the density at the star cluster surface scales almost linearly with that at the stagnation radius, is based on results from semi-analytic and full numerical calculations. The analytic formulation allows for the determination of the threshold mechanical luminosity that separates clusters evolving in either of the two solutions. It is possible to fix the stagnation radius by simple analytic expressions and thus to determine the fractions of the deposited matter that clusters evolving in the bimodal regime blow out as a wind or recycle into further stellar generations.Comment: 5 pages, 4 figures, accepted by A&

The effect of 12C + 12C rate uncertainties on s-process yields

The slow neutron capture process in massive stars (the weak s-process) produces most of the s-only isotopes in the mass region 60 < A < 90. The nuclear reaction rates used in simulations of this process have a profound effect on the final s-process yields. We generated 1D stellar models of a 25 solar mass star varying the 12C + 12C rate by a factor of 10 and calculated full nucleosynthesis using the post-processing code PPN. Increasing or decreasing the rate by a factor of 10 affects the convective history and nucleosynthesis, and consequently the final yields.Comment: Conference proceedings for the Nuclear Physics in Astrophysics IV conference, 8-12 June 2009. 4 pages, 3 figures. Accepted for publication to the Journal of Physics: Conference Serie

The Sgr B2 X-ray Echo of the Galactic Center Supernova Explosion that Produced Sgr A East

The possible impact Sgr A East is having on the Galactic center has fueled speculation concerning its age and the energetics of the supernova explosion that produced it. We have carried out the first in-depth analysis of the remnant's evolution and its various interactions: with the stellar winds flowing out from the inner ~2 pc, with the supermassive black hole, Sgr A*, and with the 50 km/s molecular cloud behind and to the East of the nucleus. We have found that a rather "standard" supernova explosion with energy ~1.5e51 ergs is sufficient to create the remnant we see today, and that the latter is probably only ~1,700 years old. The X-ray Ridge between ~9" and 15" to the NE of Sgr A* appears to be the product of the current interaction between the remaining supernova ejecta and the outflowing winds. Perhaps surprisingly, we have also found that the passage of the remnant across the black hole would have enhanced the accretion rate onto the central object by less than a factor 2. Such a small increase cannot explain the current Fe fluorescence observed from the molecular cloud Sgr B2; this fluorescence would have required an increase in Sgr A*'s luminosity by 6 orders of magnitude several hundred years ago. Instead, we have uncovered what appears to be a more plausible scenario for this transient irradiation--the interaction between the expanding remnant and the 50 km/s molecular cloud. The first impact would have occurred about 1,200 years after the explosion, producing a 2-200 keV luminosity of ~1e39 ergs/s. During the intervening 300-400 years, the dissipation of kinetic energy subsided considerably, leading to the much lower luminosity (~1e36 ergs/s at 2-10 keV) we see today.Comment: 27 pages (including 9 figures), submitted to ApJ, for hi-res/color figures, see http://qso.lanl.gov/~cl

Discovery of a superluminal Fe K echo at the Galactic Center: The glorious past of Sgr A* preserved by molecular clouds

We present the result of a study of the X-ray emission from the Galactic Centre (GC) Molecular Clouds (MC) within 15 arcmin from Sgr A*. We use XMM-Newton data (about 1.2 Ms of observation time) spanning about 8 years. The MC spectra show all the features characteristic of reflection: i) intense Fe Kalpha, with EW of about 0.7-1 keV, and the associated Kbeta line; ii) flat power law continuum and iii) a significant Fe K edge (tau~0.1-0.3). The diffuse low ionisation Fe K emission follows the MC distribution, nevertheless not all MC are Fe K emitters. The long baseline monitoring allows the characterisation of the temporal evolution of the MC emission. A complex pattern of variations is shown by the different MC, with some having constant Fe K emission, some increasing and some decreasing. In particular, we observe an apparent super-luminal motion of a light front illuminating a Molecular nebula. This might be due to a source outside the MC (such as Sgr A* or a bright and long outburst of a X-ray binary), while it cannot be due to low energy cosmic rays or a source located inside the cloud. We also observe a decrease of the X-ray emission from G0.11-0.11, behaviour similar to the one of Sgr B2. The line intensities, clouds dimensions, columns densities and positions with respect to Sgr A*, are consistent with being produced by the same Sgr A* flare. The required high luminosity (about 1.5~10^39 erg/s) can hardly be produced by a binary system, while it is in agreement with a flare of Sgr A* fading about 100 years ago. The low intensity of the Fe K emission coming from the 50 and the 20 km/s MC places an upper limit of 10^36 erg/s to the mean luminosity of Sgr A* in the last 60-90 years. The Fe K emission and variations from these MC might have been produced by a single flare of Sgr A*.Comment: ApJ in press 17 pages, 14 Figures, 3 table

Characterizing the universal rigidity of generic frameworks

A framework is a graph and a map from its vertices to E^d (for some d). A framework is universally rigid if any framework in any dimension with the same graph and edge lengths is a Euclidean image of it. We show that a generic universally rigid framework has a positive semi-definite stress matrix of maximal rank. Connelly showed that the existence of such a positive semi-definite stress matrix is sufficient for universal rigidity, so this provides a characterization of universal rigidity for generic frameworks. We also extend our argument to give a new result on the genericity of strict complementarity in semidefinite programming.Comment: 18 pages, v2: updates throughout; v3: published versio

The effect of 12C +12C rate uncertainties on the evolution and nucleosynthesis of massive stars

Over the last 40 years, the 12C +12C fusion reaction has been the subject of considerable experimental efforts to constrain uncertainties at temperatures relevant for stellar nucleosynthesis. Recent studies have indicated that the reaction rate may be higher than that currently used in stellar models. In order to investigate the effect of an enhanced carbon-burning rate on massive star structure and nucleosynthesis, new stellar evolution models and their yields are presented exploring the impact of three different 12C +12C reaction rates. Non-rotating stellar models considering five different initial masses, 15, 20, 25, 32 and 60 M⊙, at solar metallicity, were generated using the Geneva Stellar Evolution Code (genec) and were later post-processed with the NuGrid Multi-zone Post-Processing Network tool (mppnp). A dynamic nuclear reaction network of ∼1100 isotopes was used to track the s-process nucleosynthesis. An enhanced 12C +12C reaction rate causes core carbon burning to be ignited more promptly and at lower temperature. This reduces the neutrino losses, which increases the core carbon-burning lifetime. An increased carbon-burning rate also increases the upper initial mass limit for which a star exhibits a convective carbon core (rather than a radiative one). Carbon-shell burning is also affected, with fewer convective-shell episodes and convection zones that tend to be larger in mass. Consequently, the chance of an overlap between the ashes of carbon-core burning and the following carbon shell convection zones is increased, which can cause a portion of the ashes of carbon-core burning to be included in the carbon shell. Therefore, during the supernova explosion, the ejecta will be enriched by s-process nuclides synthesized from the carbon-core s-process. The yields were used to estimate the weak s-process component in order to compare with the Solar system abundance distribution. The enhanced rate models were found to produce a significant proportion of Kr, Sr, Y, Zr, Mo, Ru, Pd and Cd in the weak component, which is primarily the signature of the carbon-core s-process. Consequently, it is shown that the production of isotopes in the Kr-Sr region can be used to constrain the 12C +12C rate using the current branching ratio for α- and p-exit channel