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Register a new userThe Probability Distribution of Binary Pulsar Coalescence Rate Estimates. II. Neutron Star-White Dwarf Binaries
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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.
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Estimates of the Galactic coalescence rate (R) of close binaries with two neutron stars (NS-NS) are known to be uncertain by large factors (about two orders of magnitude) mainly due to the small number of systems detected as binary radio pulsars. We present an analysis method that allows us to estimate the Galactic NS-NS coalescence rate using the current observed sample and, importantly, to assign a statistical significance to these estimates and to calculate the allowed ranges of values at various confidence levels. The method involves the simulation of selection effects inherent in all relevant radio pulsar surveys and a Bayesian statistical analysis for the probability distribution of the rate. The most likely values for the total Galactic coalescence rate (R_peak) lie in the range 2-60 per Myr depending on different pulsar population models. For our reference model 1, where the most likely estimates of pulsar population properties are adopted, we obtain R_tot = 8_{-5}^{+9} per Myr at a 68% statistical confidence level. The corresponding range of expected detection rates of NS-NS inspiral are 3_{-2}^{+4}x10^{-3} per yr for the initial LIGO and 18_{-11}^{+21} per yr for the advanced LIGO.
We present an analysis method that allows us to estimate the Galactic formation of radio pulsar populations based on their observed properties and our understanding of survey selection effects. More importantly, this method allows us to assign a statistical significance to such rate estimates and calculate the allowed ranges of values at various confidence levels. Here, we apply the method to the question of the double neutron star (NS-NS) coalescence rate using the current observed sample, and we find calculate the most likely value for the total Galactic coalescence rate to lie in the range 3-22 Myr^{-1}, for different pulsar population models. The corresponding range of expected detection rates of NS--NS inspiral are (1-9)x10^{-3} yr^{-1} for the initial LIGO, and 6-50 yr^{-1} for the advanced LIGO. Based on this newly developed statistical method, we also calculate the probability distribution for the expected number of pulsars that could be observed by the Parkes Multibeam survey, when acceleration searches will alleviate the effects of Doppler smearing due to orbital motions. We suggest that the Parkes survey will probably detect 1-2 new binary pulsars like PSRs B1913+16 and/or B1534+12.
We estimate the coalescence rate of close binaries with two neutron stars (NS) and discuss the prospects for the detection of NS-NS inspiral events by ground-based gravitational-wave observatories, such as LIGO. We derive the Galactic coalescence rate using the observed sample of close NS-NS binaries (PSR B1913+16 and PSR B1534+12) and examine in detail each of the sources of uncertainty associated with the estimate. Specifically, we investigate (i) the dynamical evolution of NS-NS binaries in the Galactic potential and the vertical scale height of the population, (ii) the pulsar lifetimes, (iii) the effects of the faint end of the radio pulsar luminosity function and their dependence on the small number of observed objects, (iv) the beaming fraction, and (v) the extrapolation of the Galactic rate to extragalactic distances expected to be reachable by LIGO. We find that the dominant source of uncertainty is the correction factor (up to about 200) for faint (undetectable) pulsars. All other sources are much less important, each with uncertainty factors smaller than 2. Despite the relatively large uncertainty, the derived coalescence rate is approximately consistent with previously derived upper limits, and is more accurate than rates obtained from population studies. We obtain a most conservative lower limit for the LIGO II detection rate of 2 events per year. Our upper limit on the detection rate lies between 300 to more than 1000 events per year.
In this paper we consider the population of eccentric binaries with a neutron star and a white dwarf that has been revealed in our galaxy in recent years through binary pulsar observations. We apply our statistical analysis method (Kim, Kalogera, & Lorimer 2003)and calculate the Galactic formation rate of these binaries empirically. We then compare our results with rate predictions based on binary population synthesis from various research groups and for various ranges of model input parameters. For our reference moel, we find the Galactic formation rate of these eccentric systems to be ~7 per Myr, about an order of magnitude smaller than results from binary evolution estimations. However, the empirical estimates are calculated with no correction for pulsar beaming, and therefore they should be taken as lower limits. Despite uncertainties that exceed an order of magnitude, there is significant overlap of the various rate calculations. This consistency lends confidence that our current understanding of the formation of these eccentric NS-WD binaries is reasonable.
This manuscript is an updated version of Kalogera et al. (2004) published in ApJ Letters to correct our calculation of the Galactic DNS in-spiral rate. The details of the original erratum submitted to ApJ Letters are given in page 6 of this manuscript. We report on the newly increased event rates due to the recent discovery of the highly relativistic binary pulsar J0737--3039 (Burgay et al. 2003). Using a rigorous statistical method, we present the calculations reported by Burgay et al., which produce a in-spiral rate for Galactic double neutron star (DNS) systems that is higher by a factor of 5-7 compared to estimates made prior to the new discovery. Our method takes into account known pulsar-survey selection effects and biases due to small-number statistics. This rate increase has dramatic implications for gravitational wave detectors. For the initial Laser Interferometer Gravitational-Wave Observatory (LIGO) detectors, the most probable detection rates for DNS in-spirals are one event per 10-630 yr; at 95% confidence, we obtain rates up to one per 3 yr. For the advanced LIGO detectors, the most probable rates are 10-500 events per year. These predictions, for the first time, bring the expectations for DNS detections by the initial LIGO detectors to the astrophysically relevant regime. We also use our models to predict that the large-scale Parkes Multibeam pulsar survey with acceleration searches could detect an average of four binary pulsars similar to those known at present.
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