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

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

Pulsar timing analysis in the presence of correlated noise

Pulsar timing observations are usually analysed with least-square-fitting procedures under the assumption that the timing residuals are uncorrelated (statistically "white"). Pulsar observers are well aware that this assumption often breaks down and causes severe errors in estimating the parameters of the timing model and their uncertainties. Ad hoc methods for minimizing these errors have been developed, but we show that they are far from optimal. Compensation for temporal correlation can be done optimally if the covariance matrix of the residuals is known using a linear transformation that whitens both the residuals and the timing model. We adopt a transformation based on the Cholesky decomposition of the covariance matrix, but the transformation is not unique. We show how to estimate the covariance matrix with sufficient accuracy to optimize the pulsar timing analysis. We also show how to apply this procedure to estimate the spectrum of any time series with a steep red power-law spectrum, including those with irregular sampling and variable error bars, which are otherwise very difficult to analyse.Comment: Accepted by MNRA

Low-Frequency Spectral Turn-Overs in Millisecond Pulsars Studied from Imaging Observations

Measurements of pulsar flux densities are of great importance for understanding the pulsar emission mechanism and for predictions of pulsar survey yields and the pulsar population at large. Typically these flux densities are determined from phase-averaged "pulse profiles", but this method has limited applicability at low frequencies because the observed pulses can easily be spread out by interstellar effects like scattering or dispersion, leading to a non-pulsed continuum component that is necessarily ignored in this type of analysis. In particular for the class of the millisecond pulsars (MSPs) at frequencies below 200MHz, such interstellar effects can seriously compromise de- tectability and measured flux densities. In this paper we investigate MSP spectra based on a complementary approach, namely through investigation of archival con- tinuum imaging data. Even though these images lose sensitivity to pulsars since the on-pulse emission is averaged with off-pulse noise, they are insensitive to effects from scattering and provide a reliable way to determine the flux density and spectral indices of MSPs based on both pulsed and unpulsed components. Using the 74MHz VLSSr as well as the 325MHz WENSS and 1.4GHz NVSS catalogues, we investigate the imaging flux densities of MSPs and evaluate the likelihood of spectral turn-overs in this population. We determine three new MSP spectral indices and identify six new MSPs with likely spectral turn-overs.Comment: 10 pages, 4 figures, 3 tables, accepted for publication in MNRA

Limits on the Mass, Velocity and Orbit of PSR J1933−-6211

We present a high-precision timing analysis of PSR J1933$-$6211, a millisecond pulsar (MSP) with a 3.5-ms spin period and a white dwarf (WD) companion, using data from the Parkes radio telescope. Since we have accurately measured the polarization properties of this pulsar we have applied the matrix template matching approach in which the times of arrival are measured using full polarimetric information. We achieved a weighted root-mean-square timing residuals (rms) of the timing residuals of 1.23 $\rm \mu s$, 15.5$\%$ improvement compared to the total intensity timing analysis. After studying the scintillation properties of this pulsar we put constraints on the inclination angle of the system. Based on these measurements and on $\chi^2$ mapping we put a 2-$\sigma$ upper limit on the companion mass (0.44 M$_\odot$). Since this mass limit cannot reveal the nature of the companion we further investigate the possibility of the companion to be a He WD. Applying the orbital period-mass relation for such WDs, we conclude that the mass of a He WD companion would be about 0.26$\pm$0.01 M$_\odot$ which, combined with the measured mass function and orbital inclination limits, would lead to a light pulsar mass $\leqslant$ 1.0 M$_\odot$. This result seems unlikely based on current neutron star formation models and we therefore conclude that PSR J1933$-$6211 most likely has a CO WD companion, which allows for a solution with a more massive pulsar

The impact of a stochastic gravitational-wave background on pulsar timing parameters

Gravitational waves are predicted by Einstein's theory of general relativity as well as other theories of gravity. The rotational stability of the fastest pulsars means that timing of an array of these objects can be used to detect and investigate gravitational waves. Simultaneously, however, pulsar timing is used to estimate spin period, period derivative, astrometric, and binary parameters. Here we calculate the effects that a stochastic background of gravitational waves has on pulsar timing parameters through the use of simulations and data from the millisecond pulsars PSR J0437--4715 and PSR J1713+0747. We show that the reported timing uncertainties become underestimated with increasing background amplitude by up to a factor of $\sim10$ for a stochastic gravitational-wave background amplitude of $A=5\times 10^{-15}$, where $A$ is the amplitude of the characteristic strain spectrum at one-year gravitational wave periods. We find evidence for prominent low-frequency spectral leakage in simulated data sets including a stochastic gravitational-wave background. We use these simulations along with independent Very Long Baseline Interferometry (VLBI) measurements of parallax to set a 2--sigma upper limit of $A\le9.1\times 10^{-14}$. We find that different supermassive black hole assembly scenarios do not have a significant effect on the calculated upper limits. We also test the effects that ultralow--frequency (10$^{-12}$--10$^{-9}$ Hz) gravitational waves have on binary pulsar parameter measurements and find that the corruption of these parameters is less than those due to $10^{-9}$--$10^{-7}$ Hz gravitational waves.Comment: 16 pages, 7 figures, accepted to MNRA

A possible signature of cosmic neutrino decoupling in the nHz region of the spectrum of primordial gravitational waves

In this paper we study the effect of cosmic neutrino decoupling on the spectrum of cosmological gravitational waves (GWs). At temperatures T>>1 MeV, neutrinos constitute a perfect fluid and do not hinder GW propagation, while for T<<1 MeV they free-stream and have an effective viscosity that damps cosmological GWs by a constant amount. In the intermediate regime, corresponding to neutrino decoupling, the damping is frequency-dependent. GWs entering the horizon during neutrino decoupling have a frequency f ~ 1 nHz, corresponding to a frequency region that will be probed by Pulsar Timing Arrays (PTAs). In particular, we show how neutrino decoupling induces a spectral feature in the spectrum of cosmological GWs just below 1 nHz. We briefly discuss the conditions for a detection of this feature and conclude that it is unlikely to be observed by PTAs.Comment: 11 pages, 2 figures. V2: References Adde