Local Ignition in Carbon/Oxygen White Dwarfs -- I: One-zone Ignition and Spherical Shock Ignition of Detonations

The details of ignition of Type Ia supernovae remain fuzzy, despite the importance of this input for any large-scale model of the final explosion. Here, we begin a process of understanding the ignition of these hotspots by examining the burning of one zone of material, and then investigate the ignition of a detonation due to rapid heating at single point. We numerically measure the ignition delay time for onset of burning in mixtures of degenerate material and provide fitting formula for conditions of relevance in the Type Ia problem. Using the neon abundance as a proxy for the white dwarf metallicity, we then find that ignition times can decrease by ~20% with addition of even 5% of neon by mass. When temperature fluctuations that successfully kindle a region are very rare, such a reduction in ignition time can increase the probability of ignition by orders of magnitude. If the neon comes largely at the expense of carbon, a similar increase in the ignition time can occur. We then consider the ignition of a detonation by an explosive energy input in one localized zone, eg a Sedov blast wave leading to a shock-ignited detonation. Building on previous work on curved detonations, we find that surprisingly large inputs of energy are required to successfully launch a detonation, leading to required matchheads of ~4500 detonation thicknesses - tens of centimeters to hundreds of meters - which is orders of magnitude larger than naive considerations might suggest. This is a very difficult constraint to meet for some pictures of a deflagration-to-detonation transition, such as a Zel'dovich gradient mechanism ignition in the distributed burning regime.Comment: 29 pages; accepted to ApJ. Comments welcome at http://www.cita.utoronto.ca/~ljdursi/thisweek/ . Updated version addressing referee comment

POTENT Reconstruction from Mark III Velocities

We present an improved POTENT method for reconstructing the velocity and mass density fields from radial peculiar velocities, test it with mock catalogs, and apply it to the Mark III Catalog. Method improvments: (a) inhomogeneous Malmquist bias is reduced by grouping and corrected in forward or inverse analyses of inferred distances, (b) the smoothing into a radial velocity field is optimized to reduce window and sampling biases, (c) the density is derived from the velocity using an improved nonlinear approximation, and (d) the computational errors are made negligible. The method is tested and optimized using mock catalogs based on an N-body simulation that mimics our cosmological neighborhood, and the remaining errors are evaluated quantitatively. The Mark III catalog, with ~3300 grouped galaxies, allows a reliable reconstruction with fixed Gaussian smoothing of 10-12 Mpc/h out to ~60 Mpc/h. We present maps of the 3D velocity and mass-density fields and the corresponding errors. The typical systematic and random errors in the density fluctuations inside 40 Mpc/h are \pm 0.13 and \pm 0.18. The recovered mass distribution resembles in its gross features the galaxy distribution in redshift surveys and the mass distribution in a similar POTENT analysis of a complementary velocity catalog (SFI), including the Great Attractor, Perseus-Pisces, and the void in between. The reconstruction inside ~40 Mpc/h is not affected much by a revised calibration of the distance indicators (VM2, tailored to match the velocities from the IRAS 1.2Jy redshift survey). The bulk velocity within the sphere of radius 50 Mpc/h about the Local Group is V_50=370 \pm 110 km/s (including systematic errors), and is shown to be mostly generated by external mass fluctuations. With the VM2 calibration, V_50 is reduced to 305 \pm 110 km/s.Comment: 60 pages, LaTeX, 3 tables and 27 figures incorporated (may print the most crucial figures only, by commenting out one line in the LaTex source

Gravitational-Wave Stochastic Background from Kinks and Cusps on Cosmic Strings

We compute the contribution of kinks on cosmic string loops to stochastic background of gravitational waves (SBGW).We find that kinks contribute at the same order as cusps to the SBGW.We discuss the accessibility of the total background due to kinks as well as cusps to current and planned gravitational wave detectors, as well as to the big bang nucleosynthesis (BBN), the cosmic microwave background (CMB), and pulsar timing constraints. As in the case of cusps, we find that current data from interferometric gravitational wave detectors, such as LIGO, are sensitive to areas of parameter space of cosmic string models complementary to those accessible to pulsar, BBN, and CMB bounds.Comment: 24 pages, 3 figure

Mechanisms for High-frequency QPOs in Neutron Star and Black Hole Binaries

We explain the millisecond variability detected by Rossi X-ray Timing Explorer (RXTE) in the X-ray emission from a number of low mass X-ray binary systems (Sco X-1, 4U1728-34, 4U1608-522, 4U1636-536, 4U0614+091, 4U1735-44, 4U1820-30, GX5-1 and etc) in terms of dynamics of the centrifugal barrier, a hot boundary region surrounding a neutron star. We demonstrate that this region may experience the relaxation oscillations, and that the displacements of a gas element both in radial and vertical directions occur at the same main frequency, of order of the local Keplerian frequency. We show the importance of the effect of a splitting of the main frequency produced by the Coriolis force in a rotating disk for the interpretation of a spacing between the QPO peaks. We estimate a magnitude of the splitting effect and present a simple formula for the whole spectrum of the split frequencies. It is interesting that the first three lowest-order overtones fall in the range of 200-1200 Hz and match the kHz-QPO frequencies observed by RXTE. Similar phenomena should also occur in Black Hole (BH) systems, but, since the QPO frequency is inversely proportional to the mass of a compact object, the frequency of the centrifugal-barrier oscillations in the BH systems should be a factor of 5-10 lower than that for the NS systems. The X-ray spectrum formed in this region is a result of upscattering of a soft radiation (from a disk and a NS surface) off relatively hot electrons in the boundary layer. We also briefly discuss some alternative QPO models, including a possibility of acoustic oscillations in the boundary layer, the proper stellar rotation, and g-mode disk oscillations.Comment: The paper is coming out in the Astrophysical Journal in the 1st of May issue of 199

A macroscopic multifractal analysis of parabolic stochastic PDEs

It is generally argued that the solution to a stochastic PDE with multiplicative noise---such as $\dot{u}=\frac12 u"+u\xi$, where $\xi$ denotes space-time white noise---routinely produces exceptionally-large peaks that are "macroscopically multifractal." See, for example, Gibbon and Doering (2005), Gibbon and Titi (2005), and Zimmermann et al (2000). A few years ago, we proved that the spatial peaks of the solution to the mentioned stochastic PDE indeed form a random multifractal in the macroscopic sense of Barlow and Taylor (1989; 1992). The main result of the present paper is a proof of a rigorous formulation of the assertion that the spatio-temporal peaks of the solution form infinitely-many different multifractals on infinitely-many different scales, which we sometimes refer to as "stretch factors." A simpler, though still complex, such structure is shown to also exist for the constant-coefficient version of the said stochastic PDE.Comment: 41 page

Cosmological Implications of Neutrinos

The lectures describe several cosmological effects produced by neutrinos. Upper and lower cosmological limits on neutrino mass are derived. The role that neutrinos may play in formation of large scale structure of the universe is described and neutrino mass limits are presented. Effects of neutrinos on cosmological background radiation and on big bang nucleosynthesis are discussed. Limits on the number of neutrino flavors and mass/mixing are given.Comment: 41 page, 7 figures; lectures presented at ITEP Winter School, February, 2002; to be published in the Proceeding

Analytic spectrum of relic gravitational waves modified by neutrino free streaming and dark energy

We include the effect of neutrino free streaming into the spectrum of relic gravitational waves (RGWs) in the currently accelerating universe. For the realistic case of a varying fractional neutrino energy density and a non-vanishing derivative of mode function at the neutrino decoupling, the integro-differential equation of RGWs is solved by a perturbation method for the period from the neutrino decoupling to the matter-dominant stage. Incorporating it to the analytic solution of the whole history of expansion of the universe, the analytic solution of GRWs is obtained, evolving from the inflation up to the current acceleration. The resulting spectrum of GRWs covers the whole range of frequency $(10^{-19}\sim 10^{10})$Hz, and improves the previous results. It is found that the neutrino free-streaming causes a reduction of the spectral amplitude by $\sim 20$ in the range $(10^{-16}\sim 10^{-10})$ Hz, and leaves the other portion of the spectrum almost unchanged. This agrees with the earlier numerical calculations. Examination is made on the difference between the accelerating and non-accelerating models, and our analysis shows that the ratio of the spectral amplitude in accelerating $\Lambda$CDM model over that in CDM model is $\sim 0.7$, and within the various accelerating models of $\Omega_{\Lambda}> \Omega_m$ the spectral amplitude is proportional to $\Omega_m/\Omega_{\Lambda}$ for the whole range of frequency. Comparison with LIGO S5 Runs Sensitivity shows that RGWs are not yet detectable by the present LIGO, and in the future LISA may be able to detect RGWs in some inflationary models.Comment: 22 pages,12 figures, accepeted by PR

e±e^\pm Excesses in the Cosmic Ray Spectrum and Possible Interpretations

The data collected by ATIC, PPB-BETS, FERMI-LAT and HESS all indicate that there is an electron/positron excess in the cosmic ray energy spectrum above $\sim$ 100 GeV, although different instrumental teams do not agree on the detailed spectral shape. PAMELA also reported a clear excess feature of the positron fraction above several GeV, but no excess in anti-protons. Here we review the observational status and theoretical models of this interesting observational feature. We pay special attention to various physical interpretations proposed in the literature, including modified supernova remnant models for the $e^\pm$ background, new astrophysical sources, and new physics (the dark matter models). We suggest that although most models can make a case to interpret the data, with the current observational constraints the dark matter interpretations, especially those invoking annihilation, require much more exotic assumptions than some astrophysical interpretations. Future observations may present some ``smoking-gun'' observational tests to differentiate among different models and to identify the correct interpretation to the phenomenon.Comment: 48 pages, including 10 figures and 1 tabel. Invited review to be published in IJMP

CII* Absorption in Damped Lyman Alpha Systems: (I) Star Formation Rates in a Two-Phase Medium

We describe a technique that for the first time measures star formation rates (SFRs) in damped Lyman alpha systems(DLAs) directly. We assume that massive stars form in DLAs, and that the FUV radiation they emit heats the gas by the grain photoelectric mechanism. We infer the heating rate from the cooling rate measured by the strength of CII* 1335.7 absorption. Since the heating rate is proportional to the dust-to-gas ratio and the SFR per unit area, we deduce the SFR per unit area for DLAs in which both quantities have been measured. We consider models in which the the dust comprises carbonaceous or silicate grains. We present two-phase models where the cold neutral medium (CNM) and warm neutral medium (WNM) are in pressuer equilibrium. In the CNM model the the sightline goes throught the CNM and WNM, while in the WNM model it goes only through the WNM. Since the grain photoelectric heating efficiency is at least 10 times higher in the CNM than in the WNM, CII* absorption mainly arises in the CNM in the CNM model. But in the WNM model all of the CII* absorption arises in the WNM. We use CII* absorption lines to derive the SFR per unit area for a sample of ~ 30 DLAs in which the dust-to-gas ratio has been inferred from element depletion patterns. We show that the resulting SFR per unit area corresponds to an average over the star forming volume of galaxy hosting the DLA rather than to local star formation along the line of sight. We find the average SFR per unit area and equals10$^{-2.2}$ M$_{\odot}$yr$^{-1}$kpc$^{-2}$ for the CNM model and 10$^{-1.3}$ M$_{\odot}$yr$^{-1}$kpc$^{-2}$ for the WNM model. The SFR per unit area in the CNM solution is similar to that measured in the Milky Way ISM.Comment: To Appear in the Astrophysical Journa