Pulsar Distance Research Articles

Strongly pulsed thermal X-rays from a single extended hot spot on PSR J2021+4026

The radio-quiet pulsar PSR J2021+4026 is mostly known because it is the only rotation-powered pulsar that shows variability in its γ-ray emission. Using XMM-Newton archival data, we first confirmed that its flux is steady in the X-ray band, and then we showed that both the spectral and timing X-ray properties, that is to say the narrow pulse profile, the high pulsed fraction of 80–90%, and its dependence on the energy, can be better reproduced using a magnetized atmosphere model instead of simply a blackbody model. With a maximum likelihood analysis in the energy-phase space, we inferred that the pulsar has, in correspondence of one magnetic pole, a hot spot with a temperature of T ∼ 1 MK and colatitude extension of θ ∼ 20°. For the pulsar distance of 1.5 kpc, this corresponds to a cap of R ∼ 5 − 6 km, which is greater than the standard dimension of the dipolar polar caps. The large pulsed fraction further argues against emission from the entire star surface, as it would be expected in the case of secular cooling. An unpulsed (≲40% pulsed fraction), nonthermal component, probably originating in a wind nebula, is also detected. The pulsar geometry derived with our spectral fits in the X-ray is relatively well constrained (χ = 90° and ξ = 20°–25°) and consistent with what is deduced from γ-ray observations, provided that only one of the two hemispheres is active. The evidence for an extended hot spot in PSR J2021+4026, which was also found in other pulsars of a similar age but not in older objects, suggests a possible age dependence of the emitting size of thermal X-rays.

A comparison of Galactic electron density models using PyGEDM

AbstractGalactic electron density distribution models are crucial tools for estimating the impact of the ionised interstellar medium on the impulsive signals from radio pulsars and fast radio bursts. The two prevailing Galactic electron density models (GEDMs) are YMW16 (Yao et al. 2017, ApJ, 835, 29) and NE2001 (Cordes & Lazio 2002, arXiv e-prints, pp astro–ph/0207156). Here, we introduce a software packagePyGEDMwhich provides a unified application programming interface for these models and the YT20 (Yamasaki & Totani 2020, ApJ, 888, 105) model of the Galactic halo. We usePyGEDMto compute all-sky maps of Galactic dispersion measure (DM) for YMW16 and NE2001 and compare the large-scale differences between the two. In general, YMW16 predicts higher DM values towards the Galactic anticentre. YMW16 predicts higher DMs at low Galactic latitudes, but NE2001 predicts higher DMs in most other directions. We identify lines of sight for which the models are most discrepant, using pulsars with independent distance measurements. YMW16 performs better on average than NE2001, but both models show significant outliers. We suggest that future campaigns to determine pulsar distances should focus on targets where the models show large discrepancies, so future models can use those measurements to better estimate distances along those line of sight. We also suggest that the Galactic halo should be considered as a component in future GEDMs, to avoid overestimating the Galactic DM contribution for extragalactic sources such as FRBs.

A study of dynamical effects in the observed second time-derivative of the spin or orbital frequencies of pulsars

The observed values of the time-derivatives of the spin or orbital frequency of pulsars are affected by their dynamical properties. We derive thorough analytical expressions for such dynamical contributions in terms of the Galactic coordinates, the proper motion, the pulsar distance, and the radial velocity. We find that the effects of the dynamical terms in the second-derivative of frequencies or parameters based on such second derivatives, e.g., braking index, are usually negligible. However, unique pulsars for which the effects of the dynamical terms are significant can exist. In particular, dynamical effects can make the magnitude of the observed value of the braking index to be in the order of thousand while the true value of it is close to the theoretically expected value three, especially if the pulsars lie close to the Galactic centre. Dynamics can also affect the value of the second derivative of the orbital frequency of a binary pulsar at the first decimal place. We also emphasize the fact that our expressions provide more accurate results than pre-existing approximate ones that exclude some of the terms. Comparison with a set of pulsars showed that the median value of the difference between the results obtained by our method and a pre-existing method is about 50 percent.

Radio pulsations from the γ-ray millisecond pulsar PSR J2039–5617

ABSTRACT The predicted nature of the candidate redback pulsar 3FGL J2039.6–5618 was recently confirmed by the discovery of γ-ray millisecond pulsations (Clark et al., hereafter Paper I), which identify this γ-ray source as PSR J2039–5617. We observed this object with the Parkes radio telescope in 2016 and 2019. We detect radio pulsations at 1.4 and 3.1 GHz, at the 2.6 ms period discovered in γ-rays, and also at 0.7 GHz in one 2015 archival observation. In all bands, the radio pulse profile is characterized by a single relatively broad peak which leads the main γ-ray peak. At 1.4 GHz, we found clear evidence of eclipses of the radio signal for about half of the orbit, a characteristic phenomenon in redback systems, which we associate with the presence of intra-binary gas. From the dispersion measure of 24.57 ± 0.03 pc cm−3, we derive a pulsar distance of 0.9 ± 0.2 or 1.7 ± 0.7 kpc, depending on the assumed Galactic electron density model. The modelling of the radio and γ-ray light curves leads to an independent determination of the orbital inclination, and to a determination of the pulsar mass, qualitatively consistent to the results in Paper I.

A model for redistributing heat over the surface of irradiated spider companions

ABSTRACT Spider pulsars are binary systems containing an energetic millisecond pulsar that intensely irradiates a closely orbiting low-mass companion. Modelling their companion’s optical light curves is essential to the study of the orbital properties of the binary, including the determination of the pulsar mass, characterizing the pulsar wind, and the star itself. We aim to generalize the traditional direct heating model of irradiation, whereby energy deposited by the pulsar wind into the stellar envelope is locally re-emitted, by introducing heat redistribution via diffusion and convection within the outer stellar envelope. We approximate the irradiated stellar envelope as a 2D shell. This allows us to propose an effective equation of energy conservation that can be solved at a reduced computational cost. We then implement this model in the icarus software and use evidence sampling to determine the most likely convection and diffusion laws for the light curve of the redback companion of PSR J2215+5135. Redistribution effects concentrate near the terminator line of pulsar irradiation, and can create apparent hot and cold spots. Among the models tested for PSR J2215+5135, we find that all models with heat redistribution are more likely than symmetric direct heating. The best-fitting redistribution model involves diffusion together with a uniformly rotating envelope. However, we caution that all models still present serious systematic effects, and that prior knowledge from pulsar timing, spectroscopy, and distance are key to determine with certainty the most accurate redistribution law. We propose an extension of the direct heating framework that allows for exploring a variety of heat redistribution effects. Future work is necessary to determine the relevant laws from first principles and empirically using complementary observations.

Evidences of low-diffusion bubbles around Galactic pulsars

Recently, a few-degrees extended $\gamma$-ray halo in the direction of Geminga pulsar has been detected by HAWC, Milagro and Fermi-LAT. These observations can be interpreted with positrons ($e^+$) and electrons ($e^-$) accelerated by Geminga pulsar wind nebula (PWN), released in a Galactic environment with a low diffusion coefficient ($D_0$), and inverse Compton scattering (ICS) with the interstellar radiation fields. We inspect here how the morphology of the ICS $\gamma$-ray flux depends on the energy, the pulsar age and distance, and the strength and extension of the low-diffusion bubble. In particular we show that $\gamma$-ray experiments with a peak of sensitivity at TeV energies are the most promising ones to detect ICS halos. We perform a study of the sensitivity of HAWC, HESS and the future CTA experiment finding that, with efficiencies of the order of a few %, the first two experiments should have already detected a few tens of ICS halos while the latter will increase the number of detections by a factor of 4. We then consider a sample of sources associated to PWNe and detected in the HESS Galactic plane survey and in the second HAWC catalog. We use the information available in these catalogs for the $\gamma$-ray spatial morphology and flux of these sources to inspect the value of $D_0$ around them and the $e^{\pm}$ injection spectrum. All sources are detected as extended with a $\gamma$-ray emission extended about $15-80$ pc. Assuming that most of the $e^{\pm}$ accelerated by these sources have been released in the interstellar medium, the diffusion coefficient is $2-30 \cdot 10^{26}$ cm$^2$/s at 1 TeV, i.e. two orders of magnitude smaller than the value considered to be the average in the Galaxy. These observations imply that Galactic PWNe have low-diffusion bubbles with a size of at least 80 pc.

The dynamics of Galactic centre pulsars: constraining pulsar distances and intrinsic spin-down

Through high-precision radio timing observations, we show that five recycled pulsars in the direction of the Galactic Centre (GC) have anomalous spin period time derivative ($\dot P$) measurements -- PSRs J1748$-$3009, J1753$-$2819, J1757$-$2745, and J1804$-$2858 show negative values of $\dot P$ and PSR J1801$-$3210 is found to have an exceptionally small value of $\dot P$. We attribute these observed $\dot P$ measurements to acceleration of these pulsars along their lines-of-sight (LOSs) due to the Galactic gravitational field. Using models of the Galactic mass distribution and pulsar velocities, we constrain the distances to these pulsars, placing them on the far-side of the Galaxy, providing the first accurate distance measurements to pulsars located in this region and allowing us to consider the electron density along these LOSs. We find the new electron density model YMW16 to be more consistent with these observations than the previous model NE2001. The LOS dynamics further constrain the model-dependent intrinsic $\dot P$ values for these pulsars and they are consistent with measurements for other known pulsars. In the future, the independent distance measurements to these and other pulsars near the GC would allow us to constrain the Galactic gravitational potential more accurately.

Modelling annual and orbital variations in the scintillation of the relativistic binary PSR J1141−6545

ABSTRACT We have observed the relativistic binary pulsar PSR J1141−6545 over a period of ∼6 yr using the Parkes 64 m radio telescope, with a focus on modelling the diffractive intensity scintillations to improve the accuracy of the astrometric timing model. The long-term scintillation, which shows orbital and annual variations, allows us to measure parameters that are difficult to measure with pulsar timing alone. These include: the orbital inclination i, the longitude of the ascending node Ω, and the pulsar system transverse velocity. We use the annual variations to resolve the previous ambiguity in the sense of the inclination angle. Using the correct sense, and a prior probability distribution given by a constraint from pulsar timing (i = 73 ± 3°), we find Ω = 24.8 ± 1.8° and we estimate the pulsar distance to be $D=10^{+4}_{-3}$ kpc. This then gives us an estimate of this pulsar’s proper motion of μαcos δ = 2.9 ± 1.0 mas yr−1 in right ascension and μδ = 1.8 ± 0.6 mas yr−1 in declination. Finally, we obtain measurements of the spatial structure of the interstellar electron-density fluctuations, including: the spatial scale and anisotropy of the diffraction pattern, the distribution of scattering material along the line of sight, and spatial variation in the strength of turbulence from epoch to epoch. We find that the scattering is dominated by a thin screen at a distance of (0.724 ± 0.008)D, with an anisotropy axial ratio Ar = 2.14 ± 0.11.

Searching a Thousand Radio Pulsars for Gamma-Ray Emission

Abstract Identifying as many gamma-ray pulsars as possible in the Fermi Large Area Telescope (LAT) data helps test pulsar emission models by comparing predicted and observed properties for a large, varied sample with as little selection bias as possible. It also improves extrapolations from the observed population to estimate the contribution of unresolved pulsars to the diffuse gamma-ray emission. We use a recently developed method to determine the probability that a given gamma-ray photon comes from a known position in the sky, convolving the photon’s energy with the LAT’s energy-dependent point-spread function, without the need for an accurate spatial and spectral model of the gamma-ray sky around the pulsar. The method is simple and fast and, importantly, provides probabilities, or weights, for gamma-rays from pulsars too faint for phase-integrated detection. We applied the method to over a thousand pulsars for which we obtained rotation ephemerides from radio observations, and discovered gamma-ray pulsations from 16 pulsars, 12 young and 4 recycled. PSR J2208+4056 has spindown power erg s−1, about three times lower than the previous observed gamma-ray emission “deathline.” PSRs J2208+4056 and J1816−0755 have radio interpulses, constraining their geometry and perhaps enhancing their gamma-ray luminosity. We discuss whether the deathline is an artifact of selection bias due to the pulsar distance.

PSR J2234+0611: A New Laboratory for Stellar Evolution

Abstract We report the timing results for PSR J2234+0611, a 3.6 ms pulsar in a 32 day, eccentric (e = 0.13) orbit with a helium white dwarf. The precise timing and eccentric nature of the orbit allow measurements of an unusual number of parameters: (a) a precise proper motion of 27.10(3) mas yr−1 and a parallax of 1.05(4) mas resulting in a pulsar distance of 0.95(4) kpc; enabling an estimate of the transverse velocity, 123(5) km s−1. Together with previously published spectroscopic measurements of the systemic radial velocity, this allows a 3D determination of the system’s velocity; (b) precise measurements of the rate of advance of periastron yields a total system mass of M ⊙; (c) a Shapiro delay measurement, h 3 = 82 ± 14 ns, despite the orbital inclination not being near 90°; combined with the measurement of the total mass yields a pulsar mass of and a companion mass of (d) we measure precisely the secular variation of the projected semimajor axis and detect a significant annual orbital parallax; together these allow a determination of the 3D orbital geometry of the system, including an unambiguous orbital inclination ( ) and a position angle for the line of nodes ( ). We discuss the component masses to investigate the hypotheses previously advanced to explain the origin of eccentric MSPs. The unprecedented determination of the 3D position, motion, and orbital orientation of the system, plus the precise pulsar and WD masses and the latter’s optical detection make this system a unique test of our understanding of white dwarfs and their atmospheres.

Binary Pulsar Distances and Velocities from Gaia Data Release 2

Abstract The second data release from the Gaia mission (Gaia DR2) includes, among its billion entries, astrometric parameters for binary companions to a number of known pulsars, including white dwarf companions to millisecond pulsars (MSPs) and the non-degenerate components of so-called “black widow” and “redback” systems. We find 22 such counterparts in DR2, of which 12 have statistically significant measurements of parallax. These DR2 optical proper motions and parallaxes provide new measurements of the distances and transverse velocities of the associated pulsars. For the most part, the results agree with existing radio interferometric and pulsar timing-based astrometry, as well as other distance estimates based on photometry or associations, and for some pulsars they provide the best known distance and velocity estimates. In particular, two of these pulsars have no previous distance measurement: PSR J1227−4853, for which Gaia measures a parallax of 0.62 ± 0.16 mas, and PSR J1431−4715, with a Gaia parallax of 0.64 ± 0.16 mas. Using the Gaia distance measurements, we find that dispersion-measure-based distance estimates calculated using the Cordes & Lazio and Yao et al. Galactic electron density models are on average slightly underestimated, which may be a selection effect due to the over-representation of pulsars at high Galactic latitudes in the present Gaia sample. While the Gaia DR2 results do not quite match the precision that can be achieved by dedicated pulsar timing or radio interferometry, taken together they constitute a small but important improvement to the pulsar distance scale, and the subset of MSPs with distances measured by Gaia may help improve the sensitivity of pulsar timing arrays to nanohertz gravitational waves.

How to estimate distance and velocity from parallax and proper motion

AbstractIf the observed parallax ϖ′ has a gaussian measurement error σ, there is a 68% probability that the actual parallax ϖ is in the range ϖ′ − σ < ϖ < ϖ′ + σ (the frequentist approach). The probability distribution within this range is not known from ϖ′ and σ alone, and in particular, we cannot state that the most probable distance D is given by D = 1/ϖ′. To obtain a probability distribution, we need to know or assume a distribution of pulsar distances. Similar assumptions are also required to estimate the velocity distribution of radio pulsars.

The Magnetoionic Universe: Timing, Bursts, and SETI

AbstractPropagation effects have been central to pulsar research and indeed were an integral part of the pulsar discovery and its prologue. I will summarize the early deduction process for establishing pulsar distances and refinements to the distance scale and modeling of the Galaxy in electron density and magnetic field. This will lead to the analogous current situation of understanding distances and media for extragalactic radio bursts. The role of magnetoionic media in precision pulsar timing and surveys for transients will be summarized. Finally, going full circle, searches for extraterrestrial intelligence (LGMs) also require attention to propagation effects.

B-ducted Heating of Black Widow Companions

Abstract The companions of evaporating binary pulsars (black widows and related systems) show optical emission suggesting strong heating. In a number of cases, large observed temperatures and asymmetries are inconsistent with direct radiative heating for the observed pulsar spindown power and expected distance. Here we describe a heating model in which the pulsar wind sets up an intrabinary shock (IBS) against the companion wind and magnetic field, and a portion of the shock particles duct along this field to the companion magnetic poles. We show that a variety of heating patterns, and improved fits to the observed light curves, can be obtained at expected pulsar distances and luminosities, at the expense of a handful of model parameters. We test this “IBS-B” model against three well-observed binaries and comment on the implications for system masses.

Locating the intense interstellar scattering towards the inner Galaxy

We use VLBA+VLA observations to measure the sizes of the scatter-broadened images of 6 of the most heavily scattered known pulsars: 3 within the Galactic Centre (GC) and 3 elsewhere in the inner Galactic plane. By combining the measured sizes with temporal pulse broadening data from the literature and using the thin-screen approximation, we locate the scattering medium along the line of sight to these 6 pulsars. At least two scattering screens are needed to explain the observations of the GC sample. We show that the screen inferred by previous observations of SGR J1745-2900 and Sgr A*, which must be located far from the GC, falls off in strength on scales < 0.2 degree. A second scattering component closer to (< 2 kpc) or even (tentatively) within (< 700 pc) the GC produces most or all of the temporal broadening observed in the other GC pulsars. Outside the GC, the scattering locations for all three pulsars are ~2 kpc from Earth, consistent with the distance of the Carina-Sagittarius or Scutum spiral arm. For each object the 3D scattering origin coincides with a known HII region (and in one case also a supernova remnant), suggesting that such objects preferentially cause the intense interstellar scattering seen towards the Galactic plane. We show that the HII regions should contribute > 25% of the total dispersion measure (DM) towards these pulsars, and calculate reduced DM distances. Those distances for other pulsars lying behind HII regions may be similarly overestimated.

Determination of the Sun's offset from the Galactic plane using pulsars

We derive the Sun's offset from the local mean Galactic plane($z_\odot$) using the observed $z$ distribution of young pulsars. Pulsar distances are obtained from measurements of annual parallax, HI absorption spectra or associations where available and otherwise from the observed pulsar dispersion and a model for the distribution of free electrons in the Galaxy. We fit the cumulative distribution function for a ${\rm sech}^2(z)$ distribution function, representing an isothermal self-gravitating disk, with uncertainties being estimated using the bootstrap method. We take pulsars having characteristic age $\tau_c<10^{6.5}$~yr and located within 4.5~kpc of the Sun, omitting those within the local spiral arm and those significantly affected by the Galactic warp, and solve for $z_\odot$ and the scale height, $H$, for different cutoffs in $\tau_c$. We compute these quantities using just the independently determined distances, and these together with DM-based distances separately using the YMW16 and NE2001 Galactic electron density models. We find that an age cutoff at $10^{5.75}$~yr with YMW16 DM-distances gives the best results with a minimum uncertainty in $z_\odot$ and an asymptotically stable value for $H$ showing that, at this age and below, the observed pulsar $z$-distribution is dominated by the dispersion in their birth locations. From this sample of 115 pulsars, we obtain $z_\odot=13.4\pm$4.4~pc and $H=56.9\pm$6.5~pc, similar to estimated scale heights for OB stars and open clusters. Consistent results are obtained using the independent-only distances and using the NE2001 model for the DM-based distances.

A NEW ELECTRON-DENSITY MODEL FOR ESTIMATION OF PULSAR AND FRB DISTANCES

ABSTRACT We present a new model for the distribution of free electrons in the Galaxy, the Magellanic Clouds, and the intergalactic medium (IGM) that can be used to estimate distances to real or simulated pulsars and fast radio bursts (FRBs) based on their dispersion measure (DM). The Galactic model has an extended thick disk representing the so-called warm interstellar medium, a thin disk representing the Galactic molecular ring, spiral arms based on a recent fit to Galactic H ii regions, a Galactic Center disk, and seven local features including the Gum Nebula, Galactic Loop I, and the Local Bubble. An offset of the Sun from the Galactic plane and a warp of the outer Galactic disk are included in the model. Parameters of the Galactic model are determined by fitting to 189 pulsars with independently determined distances and DMs. Simple models are used for the Magellanic Clouds and the IGM. Galactic model distances are within the uncertainty range for 86 of the 189 independently determined distances and within 20% of the nearest limit for a further 38 pulsars. We estimate that 95% of predicted Galactic pulsar distances will have a relative error of less than a factor of 0.9. The predictions of YMW16 are compared to those of the TC93 and NE2001 models showing that YMW16 performs significantly better on all measures. Timescales for pulse broadening due to interstellar scattering are estimated for (real or simulated) Galactic and Magellanic Cloud pulsars and FRBs.

Observations of the γ-ray pulsar J1932+1916 in X-rays

We present the analysis of the archival Suzaku and Swift X-ray observations of the young γ-ray pulsar J1932+1916 field. The data revealed a point-like object at the γ-ray position of the pulsar and diffuse X-ray emission around it. Spectra of the point-like source and diffuse emission are well-described by absorbed power-law models with spectral parameters typical for pulsar plus pulsar wind nebula systems. Therefore, we suggest that Suzaku and Swift detected the X-ray counterpart of PSR J1932+1916. Assuming this interpretation, we constrain the distance to the pulsar in the range of 2–6 kpc. We also suggest possible association of the pulsar with the nearby supernova remnant G54.4–0.3 and discuss its implications for the pulsar proper motion, age and distance.

TheNuSTARview of the non-thermal emission from PSR J0437−4715

We present a hard X-ray NuSTAR observation of PSR J0437-4715, the nearest millisecond pulsar. The known pulsations at the apparent pulse period ~5.76 ms are detected at energies up to 20 keV. We measure a photon index $\Gamma= 1.65\pm0.24$ (90% confidence) for the power law fit to the non-thermal emission. It had been shown that spectral models with two or three thermal components fit the XMM-Newton spectrum of PSR J0437-4715, depending on the slope of the power-law component, and the amount of absorption of soft X-rays. The new constraint on the high-energy emission provided by NuSTAR removes ambiguities regarding the thermal components of the emission below 3 keV. We performed a simultaneous spectral analysis of the XMM-Newton and NuSTAR data to confirm that three thermal components and a power law are required to fit the 0.3-20 keV emission of PSR J0437-4715. Adding a ROSAT-PSPC spectrum further confirmed this result and allowed us to better constrain the temperatures of the three thermal components. A phase-resolved analysis of the NuSTAR data revealed no significant change in the photon index of the high-energy emission. This NuSTAR observation provides further impetus for future observations with the NICER mission (Neutron Star Interior Composition Explorer) whose sensitivity will provide much stricter constraints on the equation of state of nuclear matter by combining model fits to the pulsar's phase-folded lightcurve with the pulsar's well-defined mass and distance from radio timing observations.

Detection and localization of continuous gravitational waves with pulsar timing arrays: the role of pulsar terms

A pulsar timing array is a Galactic-scale detector of nanohertz gravitational waves (GWs). Its target signals contain two components: the `Earth term' and the `pulsar term' corresponding to GWs incident on the Earth and pulsar respectively. In this work we present a Frequentist method for the detection and localization of continuous waves that takes into account the pulsar term and is significantly faster than existing methods. We investigate the role of pulsar terms by comparing a full-signal search with an Earth-term-only search for non-evolving black hole binaries. By applying the method to synthetic data sets, we find that (i) a full-signal search can slightly improve the detection probability (by about five percent); (ii) sky localization is biased if only Earth terms are searched for and the inclusion of pulsar terms is critical to remove such a bias; (iii) in the case of strong detections (with signal-to-noise ratio $\gtrsim$ 30), it may be possible to improve pulsar distance estimation through GW measurements.