Bound on the multiplicity of almost complete intersections

Let $R$ be a polynomial ring over a field of characteristic zero and let $I \subset R$ be a graded ideal of height $N$ which is minimally generated by $N+1$ homogeneous polynomials. If $I=(f_1,...,f_{N+1})$ where $f_i$ has degree $d_i$ and $(f_1,...,f_N)$ has height $N$, then the multiplicity of $R/I$ is bounded above by $\prod_{i=1}^N d_i - \max\{1, \sum_{i=1}^N (d_i-1) - (d_{N+1}-1) \}$.Comment: 7 pages; to appear in Communications in Algebr

Observational Prospects for Afterglows of Short Duration Gamma-ray Bursts

If the efficiency for producing $\gamma$-rays is the same in short duration (\siml 2 s) Gamma-Ray Bursts (GRBs) as in long duration GRBs, then the average kinetic energy of short GRBs must be $\sim 20$ times less than that of long GRBs. Assuming further that the relativistic shocks in short and long duration GRBs have similar parameters, we show that the afterglows of short GRBs will be on average 10--40 times dimmer than those of long GRBs. We find that the afterglow of a typical short GRB will be below the detection limit (\siml 10 \microJy) of searches at radio frequencies. The afterglow would be difficult to observe also in the optical, where we predict R \simg 23 a few hours after the burst. The radio and optical afterglow would be even fainter if short GRBs occur in a low-density medium, as expected in NS-NS and NS-BH merger models. The best prospects for detecting short-GRB afterglows are with early (\siml 1 day) observations in X-rays.Comment: 5 pages, 2 figures, submitted to ApJ lette

A global picture of quantum de Sitter space

Perturbative gravity about a de Sitter background motivates a global picture of quantum dynamics in `eternal de Sitter space,' the theory of states which are asymptotically de Sitter to both future and past. Eternal de Sitter physics is described by a finite dimensional Hilbert space in which each state is precisely invariant under the full de Sitter group. This resolves a previously-noted tension between de Sitter symmetry and finite entropy. Observables, implications for Boltzmann brains, and Poincare recurrences are briefly discussed.Comment: 17 pages, 1 figure. v2: minor changes, references added. v3: minor changes to correspond to PRD versio

A Signature of Cosmic Strings Wakes in the CMB Polarization

We calculate a signature of cosmic strings in the polarization of the cosmic microwave background (CMB). We find that ionization in the wakes behind moving strings gives rise to extra polarization in a set of rectangular patches in the sky whose length distribution is scale-invariant. The length of an individual patch is set by the co-moving Hubble radius at the time the string is perturbing the CMB. The polarization signal is largest for string wakes produced at the earliest post-recombination time, and for an alignment in which the photons cross the wake close to the time the wake is created. The maximal amplitude of the polarization relative to the temperature quadrupole is set by the overdensity of free electrons inside a wake which depends on the ionization fraction $f$ inside the wake. The signal can be as high as $0.06 {\rm \mu K}$ in degree scale polarization for a string at high redshift (near recombination) and a string tension $\mu$ given by $G \mu = 10^{-7}$.Comment: 8 pages, 3 figure

Polarization in the prompt emission of gamma-ray bursts and their afterglows

Synchrotron is considered the dominant emission mechanism in the production of gamma-ray burst photons in the prompt as well as in the afterglow phase. Polarization is a characteristic feature of synchrotron and its study can reveal a wealth of information on the properties of the magnetic field and of the energy distribution in gamma-ray burst jets. In this paper I will review the theory and observations of gamma-ray bursts polarization. While the theory is well established, observations have prove difficult to perform, due to the weakness of the signal. The discriminating power of polarization observations, however, cannot be overestimated.Comment: 16 pages, 9 figures, accepted for publication in the New Journal of Physics focus issue on Gamma Ray Burst

X-ray Polarization Signatures of Compton Scattering in Magnetic Cataclysmic Variables

Compton scattering within the accretion column of magnetic cataclysmic variables (mCVs) can induce a net polarization in the X-ray emission. We investigate this process using Monte Carlo simulations and find that significant polarization can arise as a result of the stratified flow structure in the shock-ionized column. We find that the degree of linear polarization can reach levels up to ~8% for systems with high accretion rates and low white-dwarf masses, when viewed at large inclination angles with respect to the accretion column axis. These levels are substantially higher than previously predicted estimates using an accretion column model with uniform density and temperature. We also find that for systems with a relatively low-mass white dwarf accreting at a high accretion rate, the polarization properties may be insensitive to the magnetic field, since most of the scattering occurs at the base of the accretion column where the density structure is determined mainly by bremsstrahlung cooling instead of cyclotron cooling.Comment: 7 pages, 8 figures, accepted by MNRA

Cosmic Renaissance: The First Sources of Light

I review recent progress in understanding the formation of the first stars and quasars. The initial conditions for their emergence are given by the now firmly established model of cosmological structure formation. Numerical simulations of the collapse and fragmentation of primordial gas indicate that the first stars formed at redshifts z ~ 20 - 30, and that they were predominantly very massive, with M_* > 100 M_sun. Important uncertainties, however, remain. Paramount among them is the accretion process, which builds up the final stellar mass by incorporating part of the diffuse, dust-free envelope into the central protostellar core. The first quasars, on the other hand, are predicted to have formed later on, at z ~ 10, in more massive dark matter halos, with total masses, ~ 10^8 M_sun, characteristic of dwarf galaxies.Comment: 16 pages, 7 figures, invited review, to appear in PASP, Feb. 200

Cosmological Hysteresis and the Cyclic Universe

A Universe filled with a homogeneous scalar field exhibits `Cosmological hysteresis'. Cosmological hysteresis is caused by the asymmetry in the equation of state during expansion and contraction. This asymmetry results in the formation of a hysteresis loop: $\oint pdV$, whose value can be non-vanishing during each oscillatory cycle. For flat potentials, a negative value of the hysteresis loop leads to the increase in amplitude of consecutive cycles and to a universe with older and larger successive cycles. Such a universe appears to possess an arrow of time even though entropy production is absent and all of the equations respect time-reversal symmetry ! Cosmological hysteresis appears to be widespread and exists for a large class of scalar field potentials and mechanisms for making the universe bounce. For steep potentials, the value of the hysteresis loop can be positive as well as negative. The expansion factor in this case displays quasi-periodic behaviour in which successive cycles can be both larger as well as smaller than previous ones. This quasi-regular pattern resembles the phenomenon of BEATS displayed by acoustic systems. Remarkably, the expression relating the increase/decrease in oscillatory cycles to the quantum of hysteresis appears to be model independent. The cyclic scenario is extended to spatially anisotropic models and it is shown that the anisotropy density decreases during successive cycles if the hysteresis loop is negative.Comment: 31 pages, 8 figures. Matches version published in Phys Rev D85, 123542 (2012

Measuring the Virial Temperature of Galactic Halos Through Electron Scattering of Quasar Emission Lines

Semi-analytic models of galaxy formation postulate the existence of virialized gaseous halos around galaxies at high redshifts. A small fraction of the light emitted by any high-redshift quasar is therefore expected to scatter off the free electrons in the halo of its host galaxy. The broadening of the scattered emission lines of the quasar can be used to measure the temperature of these electrons. For gas in virial equilibrium, the velocity width of the scattered line profile is larger by a factor of (m_p/m_e)^{1/2}=43 than the velocity dispersion of the host galaxy and reaches >10,000 km/s for the massive galaxies and groups in which bright quasars reside. In these systems, the scattered width exceeds the intrinsic width of the quasar lines and hence can be used to measure the virial temperature of the quasar host. The high degree of polarization of the scattered radiation can help filter out the extended scattered light from the central emission by the quasar and its host galaxy. The signal-to-noise ratio of the spectral broadening can be enhanced by matching the full spectrum of the scattered radiation to a template of the unscattered quasar spectrum. Although the central fuzz around low-redshift quasars is dominated by starlight, the fuzz around high-redshift quasars might be dominated by scattering before galaxies have converted most of their gas reservoirs into stars.Comment: 10 pages, 1 figures, submitted to ApJ Letter

The Pulsar Wind Nebula Around PSR B1853+01 in the Supernova Remnant W44

We present radio observations of a region in the vicinity of the young pulsar PSR B1853+01 in the supernova remnant W44. The pulsar is located at the apex of an extended feature with cometary morphology. We argue on the basis of its morphology and its spectral index and polarization properties that this is a synchrotron nebula produced by the spin down energy of the pulsar. The geometry and physical parameters of this pulsar-powered nebula and W44 are used to derive three different measures of the pulsar's transverse velocity. A range of estimates between 315 and 470 km/s are derived, resulting in a typical value of 375 km/s. The observed synchrotron spectrum from radio to X-ray wavelengths is used to put constraints on the energetics of the nebula and to derive the parameters of the pulsar wind.Comment: ApJ Let (in press