Effects of Luminosity Functions Induced by Relativistic Beaming on Statistics of Cosmological Gamma-Ray Bursts

We study the effects of the beaming-induced luminosity function on statistics of observed GRBs, assuming the cosmological scenario. We select and divide the BATSE 4B data into 588 long bursts (T$_{90}>2.5$ sec) and 149 short bursts (T$_{90}<2.5$ sec), and compare the statistics calculated in each subgroup. The of the long bursts is $ 0.2901\pm 0.0113$, and that of the short bursts is $0.4178\pm 0.0239$, which is a Euclidean value. For luminosity function models, we consider a cylindrical-beam and a conic-beam. We take into account the spatial distribution of GRB sources as well. A broad luminosity function is naturally produced when one introduces beaming of GRBs. We calculate the maximum detectable redshift of GRBs, $z_{\rm max}$. The estimated $z_{\rm max}$ for the cylindrical-beam case is as high as $\sim 14$ for the long bursts and $\sim 3$ for the short bursts. The large $z_{\rm max}$ value for the short bursts is rather surprising in that the for this subgroup is close to the so-called Euclidean value, 0.5. We calculate the fraction of bursts whose redshifts are larger than a certain redshift $z'$, i.e. $f_{\rm > z'}$. When we take $z'=3.42$ and apply the luminosity function derived for the cylindrical-beam, the expected $f_{\rm > z'}$ is $\sim 75$ for long bursts. When we increase the opening angle of the conic beam to $\Delta \theta =3^\circ.0$, $f_{\rm > z'}$ decreases to $\sim 20$ at ${\rm z'=3.42}$. We conclude that the beaming-induced luminosity functions are compatible with the redshift distribution of observed GRBs and that the apparent Euclidean value of $$ may not be due to the Euclidean space distribution but to the luminosity distribution.Comment: Accepted for publication in the Astronomical Journal (vol. 548, Feb. 20 2001

Gravitational lensing aided luminosity distance estimation for compact binary coalescences

The luminosity distance is a key observable of gravitational-wave observations. We demonstrate how one can correctly retrieve the luminosity distance of compact binary coalescences if the gravitational-wave signal is strongly lensed. We perform a proof-of-concept parameter estimation for the luminosity distance supposing (i) strong lensing produces two lensed gravitational-wave signals, (ii) the advanced LIGO-Virgo network detects both lensed signals as independent events, and (iii) the two events are identified as strongly lensed signals originated from a single compact binary coalescence. Focusing on the maximum magnification allowed in the given lensing scenario, we find that the strong lensing can improve the precision of the distance estimation by up to a factor of two compared to that can be expected for the signal experiencing no lensing. Our results imply that strong lensing of gravitational waves can be helpful for better constraining the distance to the source, and furthermore, the Hubble constant.Comment: 7 pages, 4 figures, 2 table

Gravitational waves from BH-NS binaries: Effective Fisher matrices and parameter estimation using higher harmonics

Inspiralling black hole-neutron star (BH-NS) binaries emit a complicated gravitational wave signature, produced by multiple harmonics sourced by their strong local gravitational field and further modulated by the orbital plane's precession. Some features of this complex signal are easily accessible to ground-based interferometers (e.g., the rate of change of frequency); others less so (e.g., the polarization content); and others unavailable (e.g., features of the signal out of band). For this reason, an ambiguity function (a diagnostic of dissimilarity) between two such signals varies on many parameter scales and ranges. In this paper, we present a method for computing an approximate, effective Fisher matrix from variations in the ambiguity function on physically pertinent scales which depend on the relevant signal to noise ratio. As a concrete example, we explore how higher harmonics improve parameter measurement accuracy. As previous studies suggest, for our fiducial BH-NS binaries and for plausible signal amplitudes, we see that higher harmonics at best marginally improve our ability to measure parameters. For non-precessing binaries, these Fisher matrices separate into intrinsic (mass, spin) and extrinsic (geometrical) parameters; higher harmonics principally improve our knowledge about the line of sight. For the precessing binaries, the extra information provided by higher harmonics is distributed across several parameters. We provide concrete estimates for measurement accuracy, using coordinates adapted to the precession cone in the detector's sensitive band.Comment: 19 pages, 11 figure

The KaVA and KVN Pulsar Project

We present our work towards using the Korean VLBI (Very Long Baseline Interferometer) Network (KVN) and VLBI Exploration of Radio Astronomy (VERA) arrays combined into the KVN and VERA Array (KaVA) for observations of radio pulsars at high frequencies ($\simeq$22-GHz). Pulsar astronomy is generally focused at frequencies approximately 0.3 to several GHz and pulsars are usually discovered and monitored with large, single-dish, radio telescopes. For most pulsars, reduced radio flux is expected at high frequencies due to their steep spectrum, but there are exceptions where high frequency observations can be useful. Moreover, some pulsars are observable at high frequencies only, such as those close to the Galactic Center. The discoveries of a radio-bright magnetar and a few dozen extended Chandra sources within 15 arc-minute of the Galactic Center provide strong motivations to make use of the KaVA frequency band for searching pulsars in this region. Here, we describe the science targets and report progresses made from the KVN test observations for known pulsars. We then discuss why KaVA pulsar observations are compelling.Comment: To appear in PASJ KaVA Special Issu

The Probability Distribution of Binary Pulsar Coalescence Rate Estimates. II. Neutron Star-White Dwarf Binaries

We consider the statistics of pulsar binaries with white dwarf companions (NS-WD). Using the statistical analysis method developed by Kim et al. (2003) we calculate the Galactic coalescence rate of NS-WD binaries due to gravitational-wave emission. We find that the most likely values for the total Galactic coalescence rate (R_tot) of NS-WD binaries lie in the range 0.2--10 per Myr depending on different assumed pulsar population models. For our reference model, we obtain R_tot=4.11_(-2.56)^(+5.25) per Myr at a 68% statistical confidence level. These rate estimates are not corrected for pulsar beaming and as such they are found to be about a factor of 20 smaller than the Galactic coalescence rate estimates for double neutron star systems. Based on our rate estimates, we calculate the gravitational-wave background due to coalescing NS-WD binaries out to extragalactic distances within the frequency band of the Laser Interferometer Space Antenna. We find the contribution from NS-WD binaries to the gravitational-wave background to be negligible.Comment: 20 pages, 2 figures, 2 tables, Accepted for publication in Ap