arXiv subjects

I. Cognard

Publications and source records attributed to I. Cognard.

At least 37 records · Page 2Linked to original sources

arXiv2024

Practical approaches to analyzing PTA data: Cosmic strings with six pulsars

We search for a stochastic gravitational wave background (SGWB) generated by a network of cosmic strings using six millisecond pulsars from Data Release 2 (DR2) of the European Pulsar Timing Array (EPTA). We perform a Bayesian analysis considering two models for the network of cosmic string loops, and compare it to a simple power-law model which is expected from the population of supermassive black hole binaries. Our main strong assumption is that the previously reported common red noise process is a SGWB. We find that the one-parameter cosmic string model is slightly favored over a power-law model thanks to its simplicity. If we assume a two-component stochastic signal in the data (supermassive black hole binary population and the signal from cosmic strings), we get a $95\%$ upper limit on the string tension of $\log_{10}(Gμ) < -9.9$ ($-10.5$) for the two cosmic string models we consider. In extended two-parameter string models, we were unable to constrain the number of kinks. We test two approximate and fast Bayesian data analysis methods against the most rigorous analysis and find consistent results. These two fast and efficient methods are applicable to all SGWBs, independent of their source, and will be crucial for analysis of extended data sets.

gr-qc↗

arXiv2024

A targeted radio pulsar survey of redback candidates with MeerKAT

Redbacks are millisecond pulsar binaries with low mass, irradiated companions. These systems have a rich phenomenology that can be used to probe binary evolution models, pulsar wind physics, and the neutron star mass distribution. A number of high-confidence redback candidates have been identified through searches for variable optical and X-ray sources within the localisation regions of unidentified but pulsar-like Fermi-LAT gamma-ray sources. However, these candidates remain unconfirmed until pulsations are detected. As part of the TRAPUM project, we searched for radio pulsations from six of these redback candidates with MeerKAT. We discovered three new radio millisecond pulsars, PSRs J0838$-$2527, J0955$-$3947 and J2333$-$5526, confirming their redback nature. PSR J0838$-$2827 remained undetected for two years after our discovery despite repeated observations, likely due to evaporated material absorbing the radio emission for long periods of time. While, to our knowledge, this system has not undergone a transition to an accreting state, the disappearance, likely caused by extreme eclipses, illustrates the transient nature of spider pulsars and the heavy selection bias in uncovering their radio population. Radio timing enabled the detection of gamma-ray pulsations from all three pulsars, from which we obtained 15-year timing solutions. All of these sources exhibit complex orbital period variations consistent with gravitational quadrupole moment variations in the companion stars. These timing solutions also constrain the binary mass ratios, allowing us to narrow down the pulsar masses. We find that PSR J2333$-$5526 may have a neutron star mass in excess of 2 M$_{\odot}$.

astro-ph.HE↗

arXiv2024

A 350-MHz Green Bank Telescope Survey of Unassociated Fermi LAT Sources: Discovery and Timing of Ten Millisecond Pulsars

We have searched for radio pulsations towards 49 Fermi Large Area Telescope (LAT) 1FGL Catalog $γ$-ray sources using the Green Bank Telescope at 350 MHz. We detected 18 millisecond pulsars (MSPs) in blind searches of the data; 10 of these were discoveries unique to our survey. Sixteen are binaries, with eight having short orbital periods $P_B < 1$ day. No radio pulsations from young pulsars were detected, although three targets are coincident with apparently radio-quiet $γ$-ray pulsars discovered in LAT data. Here, we give an overview of the survey and present radio and $γ$-ray timing results for the 10 MSPs discovered. These include the only isolated MSP discovered in our survey and six short-$P_B$ binary MSPs. Of these, three have very low-mass companions ($M_c$ $\ll$ 0.1M$_{\odot}$) and hence belong to the class of black widow pulsars. Two have more massive, non-degenerate companions with extensive radio eclipses and orbitally modulated X-ray emission consistent with the redback class. Significant $γ$-ray pulsations have been detected from nine of the discoveries. This survey and similar efforts suggest that the majority of Galactic $γ$-ray sources at high Galactic latitudes are either MSPs or relatively nearby non-recycled pulsars, with the latter having on average a much smaller radio/$γ$-ray beaming ratio as compared to MSPs. It also confirms that past surveys suffered from an observational bias against finding short-$P_B$ MSP systems.

astro-ph.HE↗

arXiv2023

The second data release from the European Pulsar Timing Array: VI. Challenging the ultralight dark matter paradigm

Pulsar Timing Array experiments probe the presence of possible scalar or pseudoscalar ultralight dark matter particles through decade-long timing of an ensemble of galactic millisecond radio pulsars. With the second data release of the European Pulsar Timing Array, we focus on the most robust scenario, in which dark matter interacts only gravitationally with ordinary baryonic matter. Our results show that ultralight particles with masses $10^{-24.0}~\text{eV} \lesssim m \lesssim 10^{-23.3}~\text{eV}$ cannot constitute $100\%$ of the measured local dark matter density, but can have at most local density $ρ\lesssim 0.3$ GeV/cm$^3$.

astro-ph.HE↗

arXiv2023

Constraining the magnetic field geometry of the millisecond pulsar PSR~J0030+0451 from joint radio, thermal X-ray and $γ$-ray emission

With the advent of multi-wavelength electromagnetic observations of neutron stars, spanning many decades in photon energies, from radio wavelengths up to X-rays and $γ$-rays, it becomes possible to significantly constrain the geometry and the location of the associated emission regions. In this work, we use results from the modelling of thermal X-ray observations of PSR~J0030+0451 from the NICER mission and phase-aligned radio and $γ$-ray pulse profiles to constrain the geometry of an off-centred dipole able to reproduce the light-curves in these respective bands simultaneously. To this aim, we deduce a configuration with a simple dipole off-centred from the location of the centre of the thermal X-ray hot spots and show that the geometry is compatible with independent constraints from radio and $γ$-ray pulsations only, leading to a fixed magnetic obliquity of $α\approx 75°$ and a line of sight inclination angle of $ζ\approx 54°$. We demonstrate that an off-centred dipole cannot be rejected by accounting for the thermal X-ray pulse profiles. Moreover, the crescent shape of one spot is interpreted as the consequence of a small scale surface dipole on top of the large scale off-centred dipole.

astro-ph.HE↗

arXiv2023

Comparing recent PTA results on the nanohertz stochastic gravitational wave background

The Australian, Chinese, European, Indian, and North American pulsar timing array (PTA) collaborations recently reported, at varying levels, evidence for the presence of a nanohertz gravitational wave background (GWB). Given that each PTA made different choices in modeling their data, we perform a comparison of the GWB and individual pulsar noise parameters across the results reported from the PTAs that constitute the International Pulsar Timing Array (IPTA). We show that despite making different modeling choices, there is no significant difference in the GWB parameters that are measured by the different PTAs, agreeing within $1σ$. The pulsar noise parameters are also consistent between different PTAs for the majority of the pulsars included in these analyses. We bridge the differences in modeling choices by adopting a standardized noise model for all pulsars and PTAs, finding that under this model there is a reduction in the tension in the pulsar noise parameters. As part of this reanalysis, we "extended" each PTA's data set by adding extra pulsars that were not timed by that PTA. Under these extensions, we find better constraints on the GWB amplitude and a higher signal-to-noise ratio for the Hellings and Downs correlations. These extensions serve as a prelude to the benefits offered by a full combination of data across all pulsars in the IPTA, i.e., the IPTA's Data Release 3, which will involve not just adding in additional pulsars, but also including data from all three PTAs where any given pulsar is timed by more than as single PTA.

astro-ph.HE↗

arXiv2023

The second data release from the European Pulsar Timing Array I. The dataset and timing analysis

Pulsar timing arrays offer a probe of the low-frequency gravitational wave spectrum (1 - 100 nanohertz), which is intimately connected to a number of markers that can uniquely trace the formation and evolution of the Universe. We present the dataset and the results of the timing analysis from the second data release of the European Pulsar Timing Array (EPTA). The dataset contains high-precision pulsar timing data from 25 millisecond pulsars collected with the five largest radio telescopes in Europe, as well as the Large European Array for Pulsars. The dataset forms the foundation for the search for gravitational waves by the EPTA, presented in associated papers. We describe the dataset and present the results of the frequentist and Bayesian pulsar timing analysis for individual millisecond pulsars that have been observed over the last ~25 years. We discuss the improvements to the individual pulsar parameter estimates, as well as new measurements of the physical properties of these pulsars and their companions. This data release extends the dataset from EPTA Data Release 1 up to the beginning of 2021, with individual pulsar datasets with timespans ranging from 14 to 25 years. These lead to improved constraints on annual parallaxes, secular variation of the orbital period, and Shapiro delay for a number of sources. Based on these results, we derived astrophysical parameters that include distances, transverse velocities, binary pulsar masses, and annual orbital parallaxes.

astro-ph.HE↗

arXiv2023

The second data release from the European Pulsar Timing Array II. Customised pulsar noise models for spatially correlated gravitational waves

The nanohertz gravitational wave background (GWB) is expected to be an aggregate signal of an ensemble of gravitational waves emitted predominantly by a large population of coalescing supermassive black hole binaries in the centres of merging galaxies. Pulsar timing arrays, ensembles of extremely stable pulsars, are the most precise experiments capable of detecting this background. However, the subtle imprints that the GWB induces on pulsar timing data are obscured by many sources of noise. These must be carefully characterized to increase the sensitivity to the GWB. In this paper, we present a novel technique to estimate the optimal number of frequency coefficients for modelling achromatic and chromatic noise and perform model selection. We also incorporate a new model to fit for scattering variations in the pulsar timing package temponest and created realistic simulations of the European Pulsar Timing Array (EPTA) datasets that allowed us to test the efficacy of our noise modelling algorithms. We present an in-depth analysis of the noise properties of 25 millisecond pulsars (MSPs) that form the second data release (DR2) of the EPTA and investigate the effect of incorporating low-frequency data from the Indian PTA collaboration. We use enterprise and temponest packages to compare noise models with those reported with the EPTA DR1. We find that, while in some pulsars we can successfully disentangle chromatic from achromatic noise owing to the wider frequency coverage in DR2, in others the noise models evolve in a more complicated way. We also find evidence of long-term scattering variations in PSR J1600$-$3053. Through our simulations, we identify intrinsic biases in our current noise analysis techniques and discuss their effect on GWB searches. The results presented here directly help improve sensitivity to the GWB and are already being used as part of global PTA efforts.

astro-ph.HE↗

arXiv2023

The second data release from the European Pulsar Timing Array III. Search for gravitational wave signals

We present the results of the search for an isotropic stochastic gravitational wave background (GWB) at nanohertz frequencies using the second data release of the European Pulsar Timing Array (EPTA) for 25 millisecond pulsars and a combination with the first data release of the Indian Pulsar Timing Array (InPTA). We analysed (i) the full 24.7-year EPTA data set, (ii) its 10.3-year subset based on modern observing systems, (iii) the combination of the full data set with the first data release of the InPTA for ten commonly timed millisecond pulsars, and (iv) the combination of the 10.3-year subset with the InPTA data. These combinations allowed us to probe the contributions of instrumental noise and interstellar propagation effects. With the full data set, we find marginal evidence for a GWB, with a Bayes factor of four and a false alarm probability of $4\%$. With the 10.3-year subset, we report evidence for a GWB, with a Bayes factor of $60$ and a false alarm probability of about $0.1\%$ ($\gtrsim 3σ$ significance). The addition of the InPTA data yields results that are broadly consistent with the EPTA-only data sets, with the benefit of better noise modelling. Analyses were performed with different data processing pipelines to test the consistency of the results from independent software packages. The inferred spectrum from the latest EPTA data from new generation observing systems is rather uncertain and in mild tension with the common signal measured in the full data set. However, if the spectral index is fixed at 13/3, the two data sets give a similar amplitude of ($2.5\pm0.7)\times10^{-15}$ at a reference frequency of $1\,{\rm yr}^{-1}$. By continuing our detection efforts as part of the International Pulsar Timing Array (IPTA), we expect to be able to improve the measurement of spatial correlations and better characterise this signal in the coming years.

astro-ph.HE↗

arXiv2023

Variable Scintillation Arcs of Millisecond Pulsars observed with the Large European Array for Pulsars

We present the first large sample of scintillation arcs in millisecond pulsars, analysing 12 sources observed with the Large European Array for Pulsars (LEAP), and the Effelsberg 100\,m telescope. We estimate the delays from multipath propagation, measuring significant correlated changes in scattering timescales over a 10-year timespan. Many sources show compact concentrations of power in the secondary spectrum, which in PSRs J0613$-$0200 and J1600$-$3053 can be tracked between observations, and are consistent with compact scattering at fixed angular positions. Other sources such as PSRs J1643$-$1224 and J0621+1002 show diffuse, asymmetric arcs which are likely related to phase-gradients across the scattering screen. PSR B1937+21 shows at least three distinct screens which dominate at different times and evidence of varying screen axes or multi-screen interactions. We model annual and orbital arc curvature variations in PSR J0613$-$0200, providing a measurement of the longitude of ascending node, resolving the sense of the orbital inclination, where our best fit model is of a screen with variable axis of anisotropy over time, corresponding to changes in the scattering of the source. Unmodeled variations of the screen's axis of anisotropy are likely to be a limiting factor in determining orbital parameters with scintillation, requiring careful consideration of variable screen properties, or independent VLBI measurements. Long-term scintillation studies such as this serve as a complementary tool to pulsar timing, to measure a source of correlated noise for pulsar timing arrays, solve pulsar orbits, and to understand the astrophysical origin of scattering screens.

astro-ph.HE↗

arXiv2023

Radio timing constraints on the mass of the binary pulsar PSR J1528-3146

PSR J1528-3146 is a 60.8 ms pulsar orbiting a heavy white dwarf (WD) companion, with an orbital period of 3.18 d. This work aimed at characterizing the pulsar's astrometric, spin and orbital parameters by analyzing timing measurements conducted at the Parkes, MeerKAT and Nançay radio telescopes over almost two decades. The measurement of post-Keplerian perturbations to the pulsar's orbit can be used to constrain the masses of the two component stars of the binary, and in turn inform us on the history of the system. We analyzed timing data from the Parkes, MeerKAT and Nançay radio telescopes collected over $\sim$16 yrs, obtaining a precise rotation ephemeris for PSR J1528-3146. A Bayesian analysis of the timing data was carried out to constrain the masses of the two components and the orientation of the orbit. We further analyzed the polarization properties of the pulsar, in order to constrain the orientations of the magnetic axis and of the line-of-sight with respect to the spin axis. We measured a significant rate of advance of periastron for the first time, and put constraints on the Shapiro delay in the system and on the rate of change of the projected semi-major axis of the pulsar's orbit. The Bayesian analysis yielded measurements for the pulsar and companion masses of respectively $M_p = 1.61_{-0.13}^{+0.14}$ M$_\odot$ and $M_c = 1.33_{-0.07}^{+0.08}$ M$_\odot$ (68\% C.L.), confirming that the companion is indeed massive. This companion mass as well as other characteristics of PSR J1528$-$3146 make this pulsar very similar to PSR J2222-0137, a 32.8 ms pulsar orbiting a WD whose heavy mass ($\sim 1.32$ M$_\odot$) was unique among pulsar-WD systems until now. Our measurements therefore suggest common evolutionary scenarios for PSRs J1528-3146 and J2222-0137.

astro-ph.HE↗

arXiv2023

The MSPSR$π$ catalogue: VLBA astrometry of 18 millisecond pulsars

With unparalleled rotational stability, millisecond pulsars (MSPs) serve as ideal laboratories for numerous astrophysical studies, many of which require precise knowledge of the distance and/or velocity of the MSP. Here, we present the astrometric results for 18 MSPs of the "MSPSR$π$" project focusing exclusively on astrometry of MSPs, which includes the re-analysis of 3 previously published sources. On top of a standardized data reduction protocol, more complex strategies (i.e., normal and inverse-referenced 1D interpolation) were employed where possible to further improve astrometric precision. We derived astrometric parameters using sterne, a new Bayesian astrometry inference package that allows the incorporation of prior information based on pulsar timing where applicable. We measured significant ($>3\,σ$) parallax-based distances for 15 MSPs, including $0.81\pm0.02\,$kpc for PSR J1518+4904 -- the most significant model-independent distance ever measured for a double neutron star system. For each MSP with a well-constrained distance, we estimated its transverse space velocity and radial acceleration. Among the estimated radial accelerations, the updated ones of PSR J1012+5307 and PSR J1738+0333 impose new constraints on dipole gravitational radiation and the time derivative of Newton's gravitational constant. Additionally, significant angular broadening was detected for PSR J1643-1224, which offers an independent check of the postulated association between the HII region Sh 2-27 and the main scattering screen of PSR J1643-1224. Finally, the upper limit of the death line of $γ$-ray-emitting pulsars is refined with the new radial acceleration of the hitherto least energetic $γ$-ray pulsar PSR J1730-2304.

astro-ph.HE↗

arXiv2023

Searching for continuous Gravitational Waves in the second data release of the International Pulsar Timing Array

The International Pulsar Timing Array 2nd data release is the combination of datasets from worldwide collaborations. In this study, we search for continuous waves: gravitational wave signals produced by individual supermassive black hole binaries in the local universe. We consider binaries on circular orbits and neglect the evolution of orbital frequency over the observational span. We find no evidence for such signals and set sky averaged 95% upper limits on their amplitude h 95 . The most sensitive frequency is 10nHz with h 95 = 9.1 10-15 . We achieved the best upper limit to date at low and high frequencies of the PTA band thanks to improved effective cadence of observations. In our analysis, we have taken into account the recently discovered common red noise process, which has an impact at low frequencies. We also find that the peculiar noise features present in some pulsars data must be taken into account to reduce the false alarm. We show that using custom noise models is essential in searching for continuous gravitational wave signals and setting the upper limit.

gr-qc↗

arXiv2023

A new pulsar timing model for scalar-tensor gravity with applications to PSR J2222-0137 and pulsar-black hole binaries

Context. Scalar-tensor gravity (STG) theories are well-motivated alternatives to general relativity (GR). One class of STG theories, the Damour-Esposito-Farese (DEF) gravity, has a massless scalar field with two arbitrary coupling parameters. We are interested in this theory because, despite its simplicity, it predicts a wealth of different phenomena, such as dipolar gravitational wave emission and spontaneous scalarization of neutron stars (NSs). These phenomena of DEF gravity can be tested by timing binary radio pulsars. Aims. We aim to develop a new binary pulsar timing model DDSTG to enable more precise tests of STG theories based on a minimal set of binary parameters. The expressions for post-Keplerian (PK) parameters in DEF gravity are self-consistently incorporated into the model. The new technique takes into account all possible correlations between PK parameters naturally. Methods. Grids of physical parameters of NSs are calculated in the framework of DEF gravity for a set of 11 equations of state. The automatic Differentiation (AutoDiff) technique is employed, which aids in the calculation of gravitational form factors of NSs with higher precision than in previous works. The pulsar timing program TEMPO is selected as a framework for the realization of the DDSTG model. The implemented model is applicable to any type of pulsar companions. Results. We apply the DDSTG model to the most recently published observational data for PSR J2222-0137. The obtained limits on DEF gravity parameters for this system confirm and improve previous results. New limits are also the most reliable because DEF gravity is directly fitted to the data. We argue that future observations of PSR J2222-0137 can significantly improve the limits and that PSR-BH systems have the potential to place the tightest limits in certain areas of the DEF gravity parameter space.

astro-ph.HE↗

arXiv2023

Removal and replacement of interference in tied-array radio pulsar observations using the spectral kurtosis estimator

We describe how to implement the spectral kurtosis method of interference removal (zapping) on a digitized signal of averaged power values. Spectral kurtosis is a hypothesis test, analogous to the t-test, with a null hypothesis that the amplitudes from which power is formed belong to a `good' distribution -- typically Gaussian with zero mean -- where power values are zapped if the hypothesis is rejected at a specified confidence level. We derive signal-to-noise ratios (SNRs) as a function of amount of zapping for folded radio pulsar observations consisting of a sum of signals from multiple telescopes in independent radio-frequency interference (RFI) environments, comparing four methods to compensate for lost data with coherent (tied-array) and incoherent summation. For coherently summed amplitudes, scaling amplitudes from non-zapped telescopes achieves a higher SNR than replacing zapped amplitudes with artificial noise. For incoherently summed power values, the highest SNR is given by scaling power from non-zapped telescopes to maintain a constant mean. We use spectral kurtosis to clean a tied-array radio pulsar observation by the Large European Array for Pulsars (LEAP): the signal from one telescope is zapped with time and frequency resolutions of 6.25 $μ$s and 0.16 MHz, removing interference along with 0.27 per cent of `good' data, giving an uncertainty of 0.25 $μ$s in pulse time of arrival (TOA) for PSR J1022+1001. We use a single-telescope observation to demonstrate recovery of the pulse profile shape, with 0.6 per cent of data zapped and a reduction from 1.22 to 0.70 $μ$s in TOA uncertainty.

astro-ph.IM↗

arXiv2023

Neutron star mass estimates from gamma-ray eclipses in spider millisecond pulsar binaries

Reliable neutron star mass measurements are key to determining the equation-of-state of cold nuclear matter, but these are rare. "Black Widows" and "Redbacks" are compact binaries consisting of millisecond pulsars and semi-degenerate companion stars. Spectroscopy of the optically bright companions can determine their radial velocities, providing inclination-dependent pulsar mass estimates. While inclinations can be inferred from subtle features in optical light curves, such estimates may be systematically biased due to incomplete heating models and poorly-understood variability. Using data from the Fermi Large Area Telescope, we have searched for gamma-ray eclipses from 49 spider systems, discovering significant eclipses in 7 systems, including the prototypical black widow PSR B1957$+$20. Gamma-ray eclipses require direct occultation of the pulsar by the companion, and so the detection, or significant exclusion, of a gamma-ray eclipse strictly limits the binary inclination angle, providing new robust, model-independent pulsar mass constraints. For PSR B1957$+$20, the eclipse implies a much lighter pulsar ($M_{\rm psr} = 1.81 \pm 0.07\,M_{\odot}$) than inferred from optical light curve modelling.

astro-ph.HE↗

arXiv2022

The TRAPUM L-band survey for pulsars in Fermi-LAT gamma-ray sources

More than 100 millisecond pulsars (MSPs) have been discovered in radio observations of gamma-ray sources detected by the Fermi Large Area Telescope (LAT), but hundreds of pulsar-like sources remain unidentified. Here we present the first results from the targeted survey of Fermi-LAT sources being performed by the Transients and Pulsars with MeerKAT (TRAPUM) Large Survey Project. We observed 79 sources identified as possible gamma-ray pulsar candidates by a Random Forest classification of unassociated sources from the 4FGL catalogue. Each source was observed for 10 minutes on two separate epochs using MeerKAT's L-band receiver (856-1712 MHz), with typical pulsed flux density sensitivities of $\sim$100$\,μ$Jy. Nine new MSPs were discovered, eight of which are in binary systems, including two eclipsing redbacks and one system, PSR J1526$-$2744, that appears to have a white dwarf companion in an unusually compact 5 hr orbit. We obtained phase-connected timing solutions for two of these MSPs, enabling the detection of gamma-ray pulsations in the Fermi-LAT data. A follow-up search for continuous gravitational waves from PSR J1526$-$2744 in Advanced LIGO data using the resulting Fermi-LAT timing ephemeris yielded no detection, but sets an upper limit on the neutron star ellipticity of $2.45\times10^{-8}$. We also detected X-ray emission from the redback PSR J1803$-$6707 in data from the first eROSITA all-sky survey, likely due to emission from an intra-binary shock.

astro-ph.HE↗

arXiv2022

The LOFAR Tied-Array All-Sky Survey: Timing of 35 radio pulsars and an overview of the properties of the LOFAR pulsar discoveries

The LOFAR Tied-Array All-Sky Survey (LOTAAS) is the most sensitive untargeted radio pulsar survey performed at low radio frequencies (119--151\,MHz) to date and has discovered 76 new radio pulsars, among which the 23.5-s pulsar J0250+5854, up until recently the slowest-spinning radio pulsar known. Here, we report on the timing solutions of 35 pulsars discovered by LOTAAS, which include a nulling pulsar and a mildly recycled pulsar, and thereby complete the full timing analysis of the LOTAAS pulsar discoveries. We give an overview of the findings from the full LOTAAS sample of 76 pulsars, discussing their pulse profiles, radio spectra and timing parameters. We found that the pulse profiles of some of the pulsars show profile variations in time or frequency and while some pulsars show signs of scattering, a large majority display no pulse broadening. The LOTAAS discoveries have on average steeper radio spectra and have longer spin periods ($1.4\times$) as well as lower spin-down rates ($3.1\times$) compared to the known pulsar population. We discuss the cause of these differences, and attribute them to a combination of selection effects of the LOTAAS survey as well as previous pulsar surveys, though can not rule out that older pulsars tend to have steeper radio spectra.

astro-ph.HE↗