Convergence of random zeros on complex manifolds

We show that the zeros of random sequences of Gaussian systems of polynomials of increasing degree almost surely converge to the expected limit distribution under very general hypotheses. In particular, the normalized distribution of zeros of systems of m polynomials of degree N, orthonormalized on a regular compact subset K of C^m, almost surely converge to the equilibrium measure on K as the degree N goes to infinity.Comment: 16 page

Discovery of a supernova associated with GRB 031203: SMARTS Optical-Infrared Lightcurves from 0.2 to 92 days

Optical and infrared monitoring of the afterglow site of gamma-ray burst (GRB) 031203 has revealed a brightening source embedded in the host galaxy, which we attribute to the presence of a supernova (SN) related to the GRB ("SN 031203"). We present details of the discovery and evolution of SN 031203 from 0.2 to 92 days after the GRB, derived from SMARTS consortium photometry in I and J bands. A template type Ic lightcurve, constructed from SN 1998bw photometry, is consistent with the peak brightness of SN 031203 although the lightcurves are not identical. Differential astrometry reveals that the SN, and hence the GRB, occurred less than 300 h_71^-1 pc (3-sigma) from the apparent galaxy center. The peak of the supernova is brighter than the optical afterglow suggesting that this source is intermediate between a strong GRB and a supernova.Comment: 11 pages, 3 figures, submitted to ApJ Letter

Astrometric Microlensing Constraints on a Massive Body in the Outer Solar System with Gaia

A body in Solar orbit beyond the Kuiper belt exhibits an annual parallax that exceeds its apparent proper motion by up to many orders of magnitude. Apparent motion of this body along the parallactic ellipse will deflect the angular position of background stars due to astrometric microlensing ("induced parallax"). By synoptically sampling the astrometric position of background stars over the entire sky, constraints on the existence (and basic properties) of a massive nearby body may be inferred. With a simple simulation, we estimate the signal-to-noise for detecting such a body -- as function of mass, heliocentric distance, and ecliptic latitude -- using the anticipated sensitivity and temporal cadences from Gaia (launch 2011). A Jupiter-mass (M_Jup) object at 2000 AU is detectable by Gaia over the whole sky above 5-sigma, with even stronger constraints if it lies near the ecliptic plane. Hypotheses for the mass (~3M_Jup), distance (~20,000 AU) and location of the proposed perturber ("Planet X") which gives rise to long-period comets may be testable.Comment: 17 pages, 6 figures. Figures revised, new figure added, minor text revisions. Accepted to ApJ, to appear in the Dec 10, 2005 issue (v635

The impact of health on professionally active people's incomes in Poland. Microeconometric analysis

The outcome of the research confirms the occurrence of positive interaction between professionally active people's incomes and the self-assessed state of health. People declaring a bad state of health have incomes by 20% on average lower than people who enjoy good health (assuming that the remaining characteristics of the surveyed person are the same). In case of men, the impact of health state on incomes is slightly greater than in case of women.Wyniki badań potwierdzają istnienie pozytywnej zależności dochodów osób aktywnych zawodowo od stanu zdrowia mierzonego jego samooceną. Osoby deklarujące zły stan zdrowia osiągają dochody przeciętnie o 20% niższe niż osoby, które cieszą się dobrym stanem zdrowia (przy założeniu, że pozostałe charakterystyki badanej osoby są takie same). W przypadku mężczyzn zależność dochodów od stanu zdrowia jest nieznacznie silniejsza niż w przypadku kobiet

Multi-color Optical and NIR Light Curves of 64 Stripped-Envelope Core-Collapse Supernovae

We present a densely-sampled, homogeneous set of light curves of 64 low redshift (z < 0.05) stripped-envelope supernovae (SN of type IIb, Ib, Ic and Ic-bl). These data were obtained between 2001 and 2009 at the Fred L. Whipple Observatory (FLWO) on Mt. Hopkins in Arizona, with the optical FLWO 1.2-m and the near-infrared PAIRITEL 1.3-m telescopes. Our dataset consists of 4543 optical photometric measurements on 61 SN, including a combination of UBVRI, UBVr'i', and u'BVr'i', and 2142 JHKs near-infrared measurements on 25 SN. This sample constitutes the most extensive multi-color data set of stripped-envelope SN to date. Our photometry is based on template-subtracted images to eliminate any potential host galaxy light contamination. This work presents these photometric data, compares them with data in the literature, and estimates basic statistical quantities: date of maximum, color, and photometric properties. We identify promising color trends that may permit the identification of stripped-envelope SN subtypes from their photometry alone. Many of these SN were observed spectroscopically by the CfA SN group, and the spectra are presented in a companion paper (Modjaz et al. 2014). A thorough exploration that combines the CfA photometry and spectroscopy of stripped-envelope core-collapse SN will be presented in a follow-up paper.Comment: 26 pages, 17 figures, 8 tables. Revised version resubmitted to ApJ Supplements after referee report. Additional online material is available through http://cosmo.nyu.edu/SNYU

On the Conditions for Neutron-Rich Gamma-Ray Burst Outflows

We calculate the structure and neutron content of neutrino-heated MHD winds driven from the surface of newly-formed magnetars (``proto-magnetars'') and from the midplane of hyper-accreting disks, two of the possible central engines for gamma-ray bursts (GRBs) and hyper-energetic supernovae (SNe). Both the surface of proto-magnetars and the midplane of neutrino-cooled accretion flows (NDAFs) are electron degenerate and neutron-rich (neutron-to-proton ratio n/p >> 1). If this substantial free neutron excess is preserved to large radii in ultra-relativistic outflows, several important observational consequences may result. Weak interaction processes, however, can drive n/p to ~1 in the nondegenerate regions that obtain just above the surfaces of NDAFs and proto-magnetars. Our calculations show that mildly relativistic neutron-rich outflows from NDAFs are possible in the presence of a strong poloidal magnetic field. However, we find that neutron-rich winds possess a minimum mass-loss rate that likely precludes simultaneously neutron-rich and ultra-relativistic (Lorentz factor > 100) NDAF winds accompanying a substantial accretion power. In contrast, proto-magnetars are capable of producing neutron-rich long-duration GRB outflows ~10-30 seconds following core bounce for sub-millisecond rotation periods; such outflows would, however, accompany only extremely energetic events, in which the GRB + SN energy budget exceeds ~ 4e52 ergs. Neutron-rich highly relativistic outflows may also be produced during some short-duration GRBs by geometrically thick accretion disks formed from compact object mergers. The implications for r-process nucleosynthesis, optical transients due to non-relativistic neutron-rich winds, and Nickel production in proto-magnetar and NDAF winds are also briefly discussed.Comment: 24 pages, 7 figures, submitted to Ap

Early optical observations of GRBs by the TAROT telescopes: period 2001-2008

The TAROT telescopes (Telescopes a Action Rapide pour les Objets Transitoires) are two robotic observatories designed to observe the prompt optical emission counterpart and the early afterglow of gamma ray bursts (GRBs). We present data acquired between 2001 and 2008 and discuss the properties of the optical emission of GRBs, noting various interesting results. The optical emission observed during the prompt GRB phase is rarely very bright: we estimate that 5% to 20% of GRBs exhibit a bright optical flash (R<14) during the prompt gamma-ray emission, and that more than 50% of the GRBs have an optical emission fainter than R=15.5 when the gamma-ray emission is active. We study the apparent optical brightness distribution of GRBs at 1000 s showing that our observations confirm the distribution derived by other groups. The combination of these results with those obtained by other rapid slewing telescopes allows us to better characterize the early optical emission of GRBs and to emphasize the importance of very early multi-wavelength GRB studies for the understanding of the physics of the ejecta.Comment: 13 pages, 2 color figures, 5 b&w figures. Accepted for publication in Astronomical Journa

The Afterglow, Energetics and Host Galaxy of the Short-Hard Gamma-Ray Burst 051221a

We present detailed optical, X-ray and radio observations of the bright afterglow of the short gamma-ray burst 051221a obtained with Gemini, Swift/XRT, and the Very Large Array, as well as optical spectra from which we measure the redshift of the burst, z=0.5464. At this redshift the isotropic-equivalent prompt energy release was about 1.5 x 10^51 erg, and using the standard afterglow synchrotron model we find that the blastwave kinetic energy is similar, E_K,iso ~ 8.4 x 10^51 erg. An observed jet break at t ~ 5 days indicates that the opening angle is ~ 7 degrees and the total beaming-corrected energy is therefore ~ 2.5 x 10^49 erg, comparable to the values inferred for previous short GRBs. We further show that the burst experienced an episode of energy injection by a factor of 3.4 between t=1.4 and 3.4 hours, which was accompanied by reverse shock emission in the radio band. This result provides continued evidence that the central engines of short GRBs may be active significantly longer than the duration of the burst and/or produce a wide range of Lorentz factors. Finally, we show that the host galaxy of GRB051221a is actively forming stars at a rate of about 1.6 M_solar/yr, but at the same time exhibits evidence for an appreciable population of old stars (~ 1 Gyr) and near solar metallicity. The lack of bright supernova emission and the low circumburst density (n ~ 10^-3 cm^-3) continue to support the idea that short bursts are not related to the death of massive stars and are instead consistent with a compact object merger. Given that the total energy release is a factor of ~ 10 larger than the predicted yield for a neutrino annihilation mechanism, this suggests that magnetohydrodynamic processes may be required to power the burst.Comment: Final version (to appear in ApJ on 20 September 2006