An empirical Bayesian analysis applied to the globular cluster pulsar population

We describe an empirical Bayesian approach to determine the most likely size of an astronomical population of sources of which only a small subset are observed above some limiting flux density threshold. The method is most naturally applied to astronomical source populations at a common distance (e.g.,stellar populations in globular clusters), and can be applied even to populations where a survey detects no objects. The model allows for the inclusion of physical parameters of the stellar population and the detection process. As an example, we apply this method to the current sample of radio pulsars in Galactic globular clusters. Using the sample of flux density limits on pulsar surveys in 94 globular clusters published by Boyles et al., we examine a large number of population models with different dependencies. We find that models which include the globular cluster two-body encounter rate, $\Gamma$, are strongly favoured over models in which this is not a factor. The optimal model is one in which the mean number of pulsars is proportional to $\exp(1.5 \log \Gamma)$. This model agrees well with earlier work by Hui et al. and provides strong support to the idea that the two-body encounter rate directly impacts the number of neutron stars in a cluster. Our model predicts that the total number of potentially observable globular cluster pulsars in the Boyles et al. sample is 1070$^{+1280}_{-700}$, where the uncertainties signify the 95% confidence interval. Scaling this result to all Galactic globular clusters, and to account for radio pulsar beaming, we estimate the total population to be 2280$^{+2720}_{-1490}$.Comment: 8 pages, 6 figures, 3 tables, corrected a few minor formatting errors which have also been submitted as an erratum to MNRA

Why the distance of PSR J0218+4232 does not challenge pulsar emission theories

Recent VLBI measurements of the astrometric parameters of the millisecond pulsar J0218+4232 by Du et al. have suggested this pulsar is as distant as 6.3 kpc. At such a large distance, the large {\gamma}-ray flux observed from this pulsar would make it the most luminous {\gamma}-ray pulsar known. This luminosity would exceed what can be explained by the outer gap and slot-gap pulsar emission models, potentially placing important and otherwise elusive constraints on the pulsar emission mechanism. We show that the VLBI parallax measurement is dominated by the Lutz-Kelker bias. When this bias is corrected for, the most likely distance for this pulsar is 3.15(+0.85/-0.60) kpc. This revised distance places the luminosity of PSR J0218+4232 into a range where it does not challenge any of the standard theories of the pulsar emission mechanism.Comment: 3 pages, 2 figures, 1 table. Accepted for publication in MNRA

Isolated pulsar spin evolution on the P-Pdot Diagram

We look at two contrasting spin-down models for isolated radio pulsars and, accounting for selection effects, synthesize observable populations. While our goal is to reproduce all of the observable characteristics, in this paper we pay particular attention to the form of the spin period vs. period derivative (P-Pdot) diagram and its dependence on various pulsar properties. We analyse the initial spin period, the braking index, the magnetic field, various beaming models, as well as the pulsar's luminosity. In addition to considering the standard magnetic dipole model for pulsar spin-down, we also consider the recent hybrid model proposed by Contopoulos & Spitkovsky. The magnetic dipole model, however, does a better job of reproducing the observed pulsar population. We conclude that random alignment angles and period dependent luminosity distributions are essential to reproduce the observed P-Pdot diagram. We also consider the time decay of alignment angles, and attempt to reconcile various models currently being studied. We conclude that, in order to account for recent evidence for the alignment found by Weltevrede & Johnston, the braking torque on a neutron star should not depend strongly on the inclination. Our simulation code is publically available and includes a web-based interface to examine the results and make predictions for yields of current and future surveys.Comment: 9 pages, 4 figure

Strengthening the role of civil society in water sector governance towards climate change adaptation in African cities – Durban, Maputo, Nairobi

Water resources management is one of the most important climate change-related issues on international, national and urban public policy agendas. Income inequality in South Africa, Mozambique, and Kenya is among the largest in the world; in all three countries, equity struggles related to water are growing in social, political and ecological significance, which is both a symptom and a cause of urban vulnerabilities related to climate change. Democratic mediation of these conflicts, and sustainable long-term management of water resources in the face of climate change, requires public participation. But those most affected by water issues such as scarcity and flooding are also those least likely to be able to participate in governance and policy institutions. In particular, members of economically disadvantaged groups – especially women, in general – tend to be gravely impacted by poor water management, but also face great difficulties in participating effectively in governance bodies. This project responded to that particular need, and has developed practical strategies for strengthening urban governments in planning investments in climate change adaptation. The project linked university researchers with community-based NGOs conducting environmental education and organizing participatory workshops in low-income urban areas with pressing climate change and water-related problems; built on proven methods of community-university collaboration to strengthen urban watershed governance; increased equity in public participation processes related to urban climate change adaptation; and fostered progressive local, national and international policy development on climate change-related water management – while training students, university researchers, NGO staff members, and community participants. The major research outcome of the project is its contribution to understanding effective ways of strengthening local governments, NGOs and civil society organizations involved in environmental education and organizing for improved public participation in watershed governance and climate change adaptation in African urban areas.This research was supported by the International Development Research Centre, grant number IDRC GRANT NO. 106002-00

Lutz-Kelker bias in pulsar parallax measurements

Lutz & Kelker showed that parallax measurements are systematically overestimated because they do not properly account for the larger volume of space that is sampled at smaller parallax values. We apply their analysis to neutron stars, incorporating the bias introduced by the intrinsic radio luminosity function and a realistic Galactic population model for neutron stars. We estimate the bias for all published neutron star parallax measurements and find that measurements with less than ~95% certainty, are likely to be significantly biased. Through inspection of historic parallax measurements, we confirm the described effects in optical and radio measurements, as well as in distance estimates based on interstellar dispersion measures. The potential impact on future tests of relativistic gravity through pulsar timing and on X-ray--based estimates of neutron star radii is briefly discussed.Comment: 9 pages, 3 tables, 1 figure. Accepted for publication in MNRA

The pulsar spectral index distribution

The flux density spectra of radio pulsars are known to be steep and, to first order, described by a power-law relationship of the form S_{\nu} \propto \nu^{\alpha}, where S_{\nu} is the flux density at some frequency \nu and \alpha is the spectral index. Although measurements of \alpha have been made over the years for several hundred pulsars, a study of the intrinsic distribution of pulsar spectra has not been carried out. From the result of pulsar surveys carried out at three different radio frequencies, we use population synthesis techniques and a likelihood analysis to deduce what underlying spectral index distribution is required to replicate the results of these surveys. We find that in general the results of the surveys can be modelled by a Gaussian distribution of spectral indices with a mean of -1.4 and unit standard deviation. We also consider the impact of the so-called "Gigahertz-peaked spectrum" pulsars. The fraction of peaked spectrum sources in the population with significant turn-over at low frequencies appears to be at most 10%. We demonstrate that high-frequency (>2 GHz) surveys preferentially select flatter-spectrum pulsars and the converse is true for lower-frequency (<1 GHz) surveys. This implies that any correlations between \alpha and other pulsar parameters (for example age or magnetic field) need to carefully account for selection biases in pulsar surveys. We also expect that many known pulsars which have been detected at high frequencies will have shallow, or positive, spectral indices. The majority of pulsars do not have recorded flux density measurements over a wide frequency range, making it impossible to constrain their spectral shapes. We also suggest that such measurements would allow an improved description of any populations of pulsars with 'non-standard' spectra.Comment: 8 pages, 5 figures. Accepted by MNRA

Gravitational wave background from rotating neutron stars

The background of gravitational waves produced by the ensemble of rotating neutron stars (which includes pulsars, magnetars and gravitars) is investigated. A formula for \Omega(f) (commonly used to quantify the background) is derived, properly taking into account the time evolution of the systems since their formation until the present day. Moreover, the formula allows one to distinguish the different parts of the background: the unresolvable (which forms a stochastic background) and the resolvable. Several estimations of the background are obtained, for different assumptions on the parameters that characterize neutron stars and their population. In particular, different initial spin period distributions lead to very different results. For one of the models, with slow initial spins, the detection of the background can be rejected. However, other models do predict the detection of the background by the future ground-based gravitational wave detector ET. A robust upper limit for the background of rotating neutron stars is obtained; it does not exceed the detection threshold of two cross-correlated Advanced LIGO interferometers. If gravitars exist and constitute more than a few percent of the neutron star population, then they produce an unresolvable background that could be detected by ET. Under the most reasonable assumptions on the parameters characterizing a neutron star, the background is too faint. Previous papers have suggested neutron star models in which large magnetic fields (like the ones that characterize magnetars) induce big deformations in the star, which produce a stronger emission of gravitational radiation. Considering the most optimistic (in terms of the detection of gravitational waves) of these models, an upper limit for the background produced by magnetars is obtained; it could be detected by ET, but not by BBO or DECIGO.Comment: 25 pages, 15 figure

Low-Mass X-Ray Binaries, Millisecond Radio Pulsars, and the Cosmic Star Formation Rate

We report on the implications of the peak in the cosmic star-formation rate (SFR) at redshift z ~ 1.5 for the resulting population of low-mass X-ray binaries(LMXB) and for that of their descendants, the millisecond radio pulsars (MRP). Since the evolutionary timescales of LMXBs, their progenitors, and their descendants are thought be significant fractions of the time-interval between the SFR peak and the present epoch, there is a lag in the turn-on of the LMXB population, with the peak activity occurring at z ~ 0.5 - 1.0. The peak in the MRP population is delayed further, occurring at z < 0.5. We show that the discrepancy between the birthrate of LMXBs and MRPs, found under the assumption of a stead-state SFR, can be resolved for the population as a whole when the effects of a time-variable SFR are included. A discrepancy may persist for LMXBs with short orbital periods, although a detailed population synthesis will be required to confirm this. Further, since the integrated X-ray luminosity distribution of normal galaxies is dominated by X-ray binaries, it should show strong luminosity evolution with redshift. In addition to an enhancement near the peak (z ~ 1.5) of the SFR due to the prompt turn-on of the relatively short-lived massive X-ray binaries and young supernova remnants, we predict a second enhancement by a factor ~10 at a redshift between ~ 0.5 and ~ 1 due to the delayed turn-on of the LMXB population. Deep X-ray observations of galaxies out to z ~ 1 by AXAF will be able to observe this enhancement, and, by determining its shape as a function of redshift, will provide an important new method for constraining evolutionary models of X-ray binaries.Comment: 13 pages, including 1 figure. Accepted for publication in ApJ Letter

Observations of 20 millisecond pulsars in 47 Tucanae at 20 cm

We have used a new observing system on the Parkes radio telescope to carry out a series of pulsar observations of the globular cluster 47 Tucanae at 20-cm wavelength. We detected all 11 previously known pulsars, and have discovered nine others, all of which are millisecond pulsars in binary systems. We have searched the data for relatively short orbital period systems, and found one pulsar with an orbital period of 96 min, the shortest of any known radio pulsar. The increased rate of detections with the new system resulted in improved estimates of the flux density of the previously known pulsars, determination of the orbital parameters of one of them, and a coherent timing solution for another one. Five of the pulsars now known in 47 Tucanae have orbital periods of a few hours and implied companion masses of only ~ 0.03 Msun. Two of these are eclipsed at some orbital phases, while three are seen at all phases at 20 cm but not always at lower frequencies. Four and possibly six of the other binary systems have longer orbital periods and companion masses ~ 0.2 Msun, with at least two of them having relatively large orbital eccentricities. All 20 pulsars have rotation periods in the range 2-8 ms.Comment: 15 pages, 6 embedded EPS figures, to be published in The Astrophysical Journa