Pulsar Luminosity Function Research Articles

Probing the Pulsar Explanation of the Galactic-Center GeV Excess Using Continuous Gravitational-Wave Searches.

Over 10years ago, Fermi observed an excess of GeV gamma rays from the Galactic Center whose origin is still under debate. One explanation for this excess involves annihilating dark matter, another requires an unresolved population of millisecond pulsars concentrated at the Galactic Center. In this work, we use the results from LIGO and Virgo's most recent all-sky search for quasimonochromatic, persistent gravitational-wave signals from isolated neutron stars, which is estimated to be about 20%-50% of the population, to determine whether unresolved millisecond pulsars could actually explain this excess. First, we choose a luminosity function that determines the number of millisecond pulsars required to explain the observed excess. Then, we consider two models for deformations on millisecond pulsars to determine their ellipticity distributions, which are directly related to their gravitational-wave radiation. Lastly, based on null results from the O3 frequency-Hough all-sky search for continuous gravitational waves, we find that a large set of the parameter space in the pulsar luminosity function can be excluded. We also evaluate how these exclusion regions may change with respect to various model choices. Our results are the first of their kind and represent a bridge between gamma-ray astrophysics, gravitational-wave astronomy, and dark-matter physics.

Radio Pulse Profiles and Polarization of the Terzan 5 Pulsars

Terzan 5 is a rich globular cluster within the galactic bulge containing 39 known millisecond pulsars, the largest known population of any globular cluster. These faint pulsars do not have sufficient signal-to-noise ratio (S/N) to measure reliable flux density or polarization information from individual observations in general. We combined over 5.2 days of archival data, at 1500 and 2000 MHz, taken with the Green Bank Telescope over the past 12 years. We created high-S/N profiles for 32 of the pulsars and determined precise rotation measures (RMs) for 28. We used the RMs, pulsar positions, and dispersion measures to map the projected parallel component of the Galactic magnetic field toward the cluster. The 〈B ∣∣〉 shows a rough gradient of ∼6 nG arcsec−1 (∼160 nG pc−1) or, fractionally, a change of ∼20% in the R.A. direction across the cluster, implying Galactic magnetic field variability at sub-parsec scales. We also measured average flux densities S ν for the pulsars, ranging from ∼10 μJy to ∼2 mJy, and an average spectral index α = −1.35, where S ν ∝ ν α . This spectral index is flatter than most known pulsars, likely a selection effect due to the high frequencies used in pulsar searches to mitigate dispersion and scattering. We used flux densities from each observation to constrain the scintillation properties toward the cluster, finding strong refractive modulation on timescales of months. The inferred pulsar luminosity function is roughly power law, with slope at the high-luminosity end. At the low-luminosity end, there are incompleteness effects, implying that Terzan 5 contains many more pulsars.

Probing the Pulsar Population of Terzan 5 via Spectral Modeling

Abstract Terzan 5 is the only Galactic globular cluster that has plausibly been detected at very high energies by the High Energy Stereoscopic System. It has an unexpectedly asymmetric very high energy morphology that is offset from the cluster center, in addition to a large-scale, offset radio structure and compact diffuse X-ray emission associated with this cluster. We present new data from the Fermi Large Area Telescope on this source. We model the updated broadband spectral energy distribution, attributing this to cumulative pulsed emission from a population of embedded millisecond pulsars, as well as unpulsed emission from the interaction of their leptonic winds with the ambient magnetic and soft-photon fields. In particular, our model invokes unpulsed synchrotron and inverse Compton components to model the radio and TeV data and cumulative pulsed curvature radiation to fit the Fermi data, and it explains the hard Chandra X-ray spectrum via a “new” cumulative synchrotron component from electron–positron pairs within the pulsar magnetospheres that has not been implemented before. We find reasonable spectral fits for plausible model parameters. We also derive constraints on the millisecond pulsar luminosity function using the diffuse X-ray data and the Chandra sensitivity. Future higher-quality spectral and spatial data will help discriminate between competing scenarios (such as dark matter annihilation, white dwarf winds, or hadronic interactions) proposed for the broadband emission, as well as constraining degenerate model parameters.

Future Prospects for Ground-based Gravitational-wave Detectors: The Galactic Double Neutron Star Merger Rate Revisited

Abstract We present the Galactic merger rate for double neutron star (DNS) binaries using an observed sample of eight DNS systems merging within a Hubble time. This sample includes the recently discovered, highly relativistic DNS systems J1757−1854 and J1946+2052, and is approximately three times the sample size used in previous estimates of the Galactic merger rate by Kim et al. Using this sample, we calculate the vertical scale height for DNS systems in the Galaxy to be z 0 = 0.4 ± 0.1 kpc. We calculate a Galactic DNS merger rate of Myr−1 at the 90% confidence level. The corresponding DNS merger detection rate for Advanced LIGO (Laser Interferometer Gravitational-wave Observatory) is , where D r is the range distance. Using this merger detection rate and the predicted range distance of 120–170 Mpc for the third observing run of LIGO, we predict, accounting for 90% confidence intervals, that LIGO–Virgo will detect anywhere between zero and two DNS mergers. We explore the effects of the underlying pulsar population properties on the merger rate and compare our merger detection rate with those estimated using different formation and evolutionary scenario of DNS systems. As we demonstrate, reconciling the rates is sensitive to assumptions about the DNS population, including its radio pulsar luminosity function. Future constraints from further gravitational wave DNS detections and pulsar surveys anticipated in the near future should permit tighter constraints on these assumptions.

Do pulsar radio fluxes violate the inverse-square law?

Singleton et al (2009) have argued that the flux of pulsars measured at 1400 MHz shows an apparent violation of the inverse-square law with distance ($r$), and it is consistent with $1/r$ scaling. They deduced this from the fact that the convergence error obtained in reconstructing the luminosity function of pulsars using an iterative maximum likelihood procedure is about $10^5$ times larger for a distance exponent of two (corresponding to the inverse-square law) compared to an exponent of one. When we applied the same technique to this pulsar dataset with two different values for the trial luminosity function in the zeroth iteration, we find that neither of them can reproduce a value of $10^5$ for the ratio of the convergence error between these distance exponents. We then reconstruct the differential pulsar luminosity function using Lynden-Bell's $C^{-}$ method after positing both an inverse-linear and an inverse-square scalings with distance. We show this method cannot help in discerning between the two exponents. Finally, when we tried to estimate the power law exponent with a Bayesian regression procedure, we do not get a best-fit value of one for the distance exponent. The model residuals obtained from our fitting procedure are larger for the inverse-linear law compared to the inverse-square law. Moreover, the observed pulsar flux cannot be parameterized only by power-law functions of distance, period, and period derivative. Therefore, we conclude from our analysis using multiple methods that there is no evidence that the pulsar radio flux at 1400 MHz violates the inverse-square law.

The Galactic Centre pulsar population

Abstract The recent discovery of a magnetar in the Galactic Centre region has allowed Spitler et al. to characterize the interstellar scattering in that direction. They find that the temporal broadening of the pulse profile of the magnetar is substantially less than that predicted by models of the electron density of that region. This raises the question of what the plausible limits for the number of potentially observable pulsars – i.e. the number of pulsars beaming towards the Earth – in the Galactic Centre are. In this Letter, using reasonable assumptions – namely (i) the luminosity function of pulsars in the Galactic Centre region is the same as that in the field, (ii) the region has had a constant pulsar formation rate, (iii) the spin and luminosity evolution of magnetars and pulsars are similar and (iv) the scattering in the direction of the Galactic Centre magnetar is representative of the entire inner parsec – we show that the potentially observable population of pulsars in the inner parsec has a conservative upper limit of ∼200 and that it is premature to conclude that the number of pulsars in this region is small. We also show that the observational results so far are consistent with this number and make predictions for future radio pulsar surveys of the Galactic Centre.

A search for radio pulsars and fast transients in M31 using the Westerbork Synthesis Radio Telescope

We present the results of the most sensitive and comprehensive survey yet undertaken for radio pulsars and fast transients in the Andromeda galaxy (M31) and its satellites, using the Westerbork Synthesis Radio Telescope (WSRT) at a central frequency of 328 MHz. We used the WSRT in a special configuration called 8gr8 (eight-grate) mode, which provides a large instantaneous field-of-view, about 5 square degrees per pointing, with good sensitivity, long dwell times (up to 8 hours per pointing), and good spatial resolution (a few arc minutes) for locating sources. We have searched for both periodicities and single pulses in our data, aiming to detect bright, persistent radio pulsars and rotating radio transients (RRATs) of either Galactic or extragalactic origin. Our searches did not reveal any confirmed periodic signals or bright single bursts from (potentially) cosmological distances. However, we do report the detection of several single pulse events, some repeating at the same dispersion measure, which could potentially originate from neutron stars in M31. One in particular was seen multiple times, including a burst of six pulses in 2000 seconds, at a dispersion measure of 54.7 pc cm^-3, which potentially places the origin of this source outside of our Galaxy. Our results are compared to a range of hypothetical populations of pulsars and RRATs in M31 and allow us to constrain the luminosity function of pulsars in M31. They also show that, unless the pulsar population in M31 is much dimmer than in our Galaxy, there is no need to invoke any violation of the inverse square law of the distance for pulsar fluxes.

The effect of PSR J0737-3039 on the DNS merger rate and implications for gravity-wave detection

We present the current estimates of the Galactic merger rate of double-neutron-star (DNS) systems. Using a statistical analysis method, we calculate the probability distribution function (PDF) of the rate estimates, which allows us to assign confidence intervals to the rate estimates. We calculate the Galactic DNS merger rate based on the three known systems B1913+16, B1534+12, and J0737-3039. The discovery of J0737-3039 increases the estimated DNS merger rate by a factor ∼6 than what is previously known. The most likely values of DNS merger rate lie in the range 3–190 Myr −1 depending on different pulsar models. Motivated by a strong correlation between the peak rate estimates and a pulsar luminosity function, we calculate a global probability distribution as a single representation of the parameter space covered by different pulsar population models. We compare the global PDF with the observed supernova Ib/c rate, which sets an upper limit on the DNS merger rate. Finally, we remark on implications of new discoveries such as of J1756-2251, the 4th DNS in the Galactic disk, and J1906+0746, a possible DNS system.

Integrated radio luminosities of pulsars

The integrated radio luminosities of 311 long-period (P > 0.1 s) and 27 short-period (P < 0.1 s) pulsars have been calculated using a new compilation of radio spectra. The luminosities are in the range 1027 − 1030 erg/s for 88% of the long-period pulsars and 1028 − 1031 erg/s for 88% of the short-period pulsars. We find a high correlation between the luminosity L and the estimate L 1 = S 400 d 2 from the catalog of Taylor et al. The factor η for the transformation of the rotational energy of the neutron star into radio emission increases-decreases with increasing period for long-period and short-period pulsars. The mean value of η is −3.73 for the long-period and −4.85 for short-period pulsars. No dependence was found between L and the pulsar’s kinematic age t k = |z|/〈v z〉, where |z| and 〈v z〉 = 300 km/s are the pulsars’ height above the plane of the Galaxy and mean velocity. A dependence of L on the rate of rotational energy losses Ė was found for both groups of pulsars. It is shown that L ∝ Ė 1/3 for the entire sample. The pulsar luminosity function is constructed, and the total number and birth rate of pulsars in the Galaxy are calculated.

A survey for pulsars in EGRET error boxes

As part of an effort to associate the unidentified EGRET gamma-ray sources with pulsars, error boxes for 19 sources were searched using Arecibo at 327-MHz. The sources were chosen to be out-of-plane and possibly associated with the Gould belt, a nearby starburst region with an enhanced production rate of core-collapse supernovae. The search revealed one new 597-ms pulsar, J2243+1518, within the error box of the EGRET source 3EG J2243+1509. The spin-down energy loss rate of the new pulsar is not nearly sufficient to power the gamma-ray source and so the pulsar is very unlikely to be associated. Simulations we have carried out show that any pulsars at Gould belt distances should have been detected by the survey. This suggests that either the EGRET sources associated with the Gould belt are not pulsars, or that the minimum of the pulsar luminosity function is lower than the ~1.5 mJy kpc^2 inferred from the population of normal pulsars.

The Coalescence Rate of Double Neutron Star Systems

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.

Deep Radio Imaging of Globular Clusters and the Cluster Pulsar Population

We have obtained deep multifrequency radio observations of seven globular clusters using the Very Large Array and the Australia Telescope Compact Array. Five of these, NGC 6440, NGC 6539, NGC 6544, NGC 6624, and Terzan 5, had previously been detected by Fruchter & Goss in a shallower survey for steep-spectrum radio sources in globular clusters. The sixth, the rich globular cluster Liller 1, had heretofore been undetected in the radio, and the seventh, 47 Tucanae, was not included in our original survey. High-resolution 6 and 20 cm images of three of the clusters, NGC 6440, NGC 6539, and NGC 6624, reveal only point sources coincident with pulsars which have been discovered subsequent to our first imaging survey; 21 and 18 cm images reveal several point sources within a few core radii of the center of 47 Tuc. Two of these are identified pulsars, and a third, which is variable and has a steep spectrum, is also most likely a pulsar previously identified by a pulsed survey. However, the 6, 20, and 90 cm images of NGC 6544, Liller 1, and Terzan 5 display strong steep-spectrum emission which cannot be associated with known pulsars. The 90 cm flux densities of Terzan 5, Liller 1, and NGC 6544 are 35, 9, and 6 mJy, respectively, implying that a number of bright pulsars in these clusters have been hidden from pulsed searches. The image of the rich cluster Terzan 5 displays numerous point sources within 30'', or 4 core radii, of the cluster center. The density of these objects rises rapidly toward the core, where an elongated region of emission is found. This feature may be due to the presence of a higher density of point sources than can be resolved by the 1'' resolution of our data. The brightest individual sources, as well as the extended emission, possess the steep spectra expected of pulsars. Furthermore, the flux distribution of the sources agrees well with the standard pulsar luminosity function. The total luminosity and number of objects observed suggest that Terzan 5 contains more pulsars than any other Galactic globular cluster.

DO OB Runaway Stars Have Pulsar Companions?

We have conducted a VLA search for radio pulsars at the positions of 44 nearby OB runaway stars. The observations involved both searching images for point sources of continuum emission and a time series analysis. Our mean flux sensitivity to pulsars slower than 50 ms was 0.2 mJy. No new pulsars were found in the survey. The size of the survey, combined with the high sensitivity of the observations, sets a significant constraint on the probability, $f_p$, of a runaway OB star having an observable pulsar companion. We find $f_p \le 6.5$\% with 95\% confidence, if the general pulsar luminosity function is applicable to OB star pulsar companions. If a pulsar beaming fraction of \onethird is assumed, then we estimate that fewer than 20\% of runaway OB stars have neutron star companions, unless pulsed radio emission is frequently obscured by the OB stellar wind. Our result is consistent with the dynamical (or cluster) ejection model for the formation of OB runaways. The supernova ejection model is not ruled out, but is constrained by these observations to allow only a small binary survival fraction, which may be accommodated if neutron stars acquire significant natal kicks. According to Leonard, Hills and Dewey (1994), a 20\% survival fraction corresponds to a 3-d kick velocity of 420 km s$^{-1}$. This value is in close agreement with recent revisions of the pulsar velocity distribution.

Deep radio observations of the rich globular clusters Terzan 5 and Liller 1

We have obtained deep 6, 20 and 90 cm observation of two of the richest globular clusters in the galaxy, Terzan 5 and Liller 1. In addition to the well known eclipsing pulsar, PSR1744-24A, our 20 cm image of Terzan 5 displays numerous point sources within 30″, or 4 core radii of the cluster center. The density of these objects rises rapidly toward the core, where an elongated region of emission is found. This feature may be due to the presence of a higher density of point sources than can be resolved by the 1″ resolution of our data. Observations at 6 and 90 cm show that the brightest individual sources, as well as the extended emission, possess the steep spectra expected of pulsars. Furthermore, we find that the strength of the sources in the 20 cm image agrees well with the standard pulsar luminosity function. The total luminosity and number of objects observed in Terzan 5 suggest that this cluster may contain 100 pulsars — probably more than any other Galactic cluster. Although we do not resolve individual sources in Liller 1, comparison of our images with other observations suggests that we are again observing the sum of emission from a number of objects. The 90 cm flux densities of Terzan 5 and Liller 1 are 35 and 9 mJy, respectively, implying that a number of bright pulsars in these clusters have been hidden from pulsed searches, perhaps by a combination of dispersion smearing, scattering and doppler broadening.

Neutron stars and millisecond pulsars from accretion-induced collapse in globular clusters

This paper examines the limits on the number of millisecond pulsars which could be formed in globular clusters by the generally accepted scenario (in which a neutron star is created by the supernova of an initially massive star and subsequently captures a companion to form a low-mass X-ray binary which eventually becomes a millisecond pulsar). It is found that, while the number of observed low-mass X-ray binaries can be adequately explained in this way, the reasonable assumption that the pulsar luminosity function in clusters extends below the current observational limits down to the luminosity of the faintest millisecond pulsars in the field suggests a cluster population of millisecond pulsars which is substantially larger than the standard model can produce. Alleviating this problem by postulating much shorter lifetimes for the X-ray binaries requires massive star populations sufficiently large that the mass loss resulting from their evolution would be likely to unbind the cluster. It is argued that neutron star formation in globular clusters by accretion-induced collapse of white dwarfs may resolve the discrepancy in birthrates.

Effect of long-term intensity variations on pulsar searches and the pulsar luminosity function

Long-term intensity data for five pulsars are used to obtain the probability density distribution of intensities for each pulsar, and it is found that they are described satisfactorily by chi-squared distributions. Based on these distributions, the number of new pulsars expected to be found on repeatedly searching the same region of the sky with the same sensitivity is given. Nearly 25 percent more new pulsars are expected to be found on the first repeat search. It is also shown that the luminosity function deduced from either a single survey or surveys with very different sensitivities is not affected by the omission of flux density variations in the calculation of selection effects. Finally, a method is proposed for deriving the luminosity function by combining the different searches of a given area on the basis of a probabilistic approach to the evaluation of selection effects.

Space distribution and birth-rate of pulsars

Using the data of the 321 pulsars so far known the Galactic distribution and the luminosity function of pulsars have been investigated. The total number of pulsars in our Galaxy is found to be 9 × 10 4. If the mean age of pulsars is 1.8 × 10 6 years, the birth-rate of pulsars in the Galaxy will be one every 20 years. This rate is not in contradiction with the birth-rate of supernovae.

A Search of the Galactic Plane for High Dispersion Pulsars

A search of the Southern galactic plane using two ‘dispersion removers ’ extends the useful sensitivity of the Molonglo pulsar searches to dispersion measures of 400 cm–3pc. Only two pulsars of dispersion measure exceeding 200 cm–3pc were discovered, suggesting that the slope of the pulsar luminosity function becomes very steep at high luminosities. Calibration data for all the Molonglo searches are presented, so that selection effects among the 29 pulsars discovered at Molonglo can be assessed.