arXiv subjects

Andrew Melatos

Publications and source records attributed to Andrew Melatos.

At least 19 recordsLinked to original sources

arXiv2026

Search for Long-Transient Gravitational Waves from Supernova SN2023ixf using GFH-v2 Pipeline

We present a directed search for long-transient gravitational waves from the possible newborn magnetar remnant of SN2023ixf, a nearby Type II core-collapse supernova in the M101 galaxy. The analysis uses LIGO Hanford and Livingston data from Engineering Run 15, using coincident data lying within the on-source window associated with the supernova. We target signals from a rapidly rotating, non-axisymmetric neutron star whose spin-down is dominated by gravitational-wave emission, producing a power-law decrease in frequency and a corresponding decrease in strain amplitude. The search is performed with the GFH-v2 pipeline, based on the Generalized Frequency Hough transform. No candidate survives the coincidence and follow-up analysis. We therefore set upper limits on the maximum detectable distance as a function of initial frequency and ellipticity. For the highest ellipticity interval, the 90% upper limits reach distances of about 1-2.5~Mpc across most of the analysed band. Although these limits are below the distance to M101, the search provides the first application of GFH-v2 to a nearby core-collapse supernova and characterizes its performance on real detector data.

astro-ph.IM↗

arXiv2026

Relaxation of magnetically-confined mountains on accreting neutron stars through cross-field mass transport

Hydromagnetic instabilities modify the structure of a magnetically confined mountain on an accreting neutron star, once the accreted mass exceeds a critical value. Ideal magnetohydrodynamics and flux freezing break down, and mass diffuses across magnetic field lines locally, wherever instabilities are excited. Here a self-consistent, iterative, numerical scheme is used to evolve an axisymmetric magnetic mountain through a quasistatic sequence of Grad-Shafranov equilibria as a function of the accreted mass, $M_{\rm a}$, modified by instability-driven cross-field mass transport obeying the semi-analytic, Kulsrud-Sunyaev recipe. The results are compared to an artificially stabilised mountain, in which flux freezing does not break down, and there is no cross-field mass transport. It is shown that cross-field mass transport prevents instabilities from demolishing the mountain. Instead, the mass-flux distribution adjusts locally to nullify the instabilities and preserve a nonzero mass quadrupole moment indefinitely in the absence of ohmic dissipation.

astro-ph.HE↗

arXiv2026

A Convolutional Neural Network-Derived Catalog of Solar Flares from Soft X-Ray Observations

A convolutional neural network (CNN) is used to construct a new catalog for solar flares based on high resolution (1-s cadence) Geostationary Operational Environmental Satellites (GOES) soft X-ray data. The CNN is trained to identify flare rise episodes. From 1 January 2018 to 22 August 2025, the algorithm detects 111,580 flare candidates, compared with 14,612 events in the corresponding GOES catalog. For each candidate, the probability of being a true positive is quantified by Bayesian inference based on the peak flux, rise time, and temporal coincidence with cataloged events where available. The flare size and waiting-time distributions are studied and compared with the GOES catalog. The CNN catalog shows a steeper power-law index for raw peak fluxes (-2.59 -\+ 0.02) than GOES (-2.25 -\+ 0.04), indicating the CNN's higher sensitivity to small events. After background correction, the indices are -1.97 -\+ 0.02 (CNN) and -2.05 -\+ 0.04 (GOES). The CNN catalog extends the power-law distribution of flare peak fluxes by one order of magnitude at the small-flux end compared with the GOES background-subtracted catalog. A Bayesian blocks analysis of the waiting-time distributions from the GOES and CNN catalogs indicates broad consistency with a piecewise Poisson process. We find that previously reported correlations between flare sizes and waiting times are significantly influenced by obscuration, that is, under-counting weaker or overlapping flares during periods of elevated flux. The new CNN catalog provides a foundation for complete and consistent studies of solar flare statistics.

astro-ph.SR↗

arXiv2026

Discovering pulsars in compact binaries with a hidden Markov model

Discovering radio pulsars in compact binaries, whose orbital periods $P_{\rm b}$ satisfy $P_{\rm b} \lesssim 1 \, \rm{day}$, is computationally challenging, because the time-dependent pulse frequency $f_{\rm p}(t)$ is strongly Doppler modulated by the binary motion. Here we present a new, fast, semi-coherent detection scheme based on a hidden Markov model (HMM) combined with a maximum likelihood matched filter, the Schuster periodogram. The HMM scheme complements traditional acceleration searches by dividing $f_{\rm p}(t)$ into piecewise-constant blocks and tracking the block-to-block evolution efficiently using dynamic programming. Monte Carlo simulations show that the new method can detect compact binaries with flux densities $S \geq 0.50 \, \rm{mJy}$ and orbital periods $P_{\rm b} \geq 0.012 \, \rm{day}$ under observing conditions (e.g.\ cadence) typical of radio pulsar surveys, with and without impulsive, narrowband radio frequency interference. The new method is fast; it employs the classic Viterbi algorithm to solve the HMM recursively. The central processing unit run time scales nominally as $T_{\rm run} \approx 2.8 \, N_B (N_T/10^2) (N_Q \ln N_Q/10^4 \ln 10^4) \, {\rm s}$ for $N_B$ subbands, $N_T$ coherent segments, and $N_Q$ frequency bins.

astro-ph.HE↗

arXiv2025

Is there a retrograde accretion disk around 4U 1626$-$67? Tracking torque reversals with a state-space model

X-ray timing studies of the persistent, Galactic, accretion-powered pulsar 4U 1626$-$67 reveal torque reversals, during which the pulse frequency $\nu(t)$ alternates between multiyear episodes of secular acceleration and deceleration, separated by transitions lasting $\lesssim 150 \, \rm{days}$. Here an unscented Kalman filter is applied to track the $\nu(t)$ fluctuations observed in 22.7 years (3340 samples) of publicly available Compton Gamma-Ray Observatory and Fermi Gamma-Ray Space Telescope data to test the canonical picture of magnetocentrifugal accretion for consistency with prograde-prograde and retrograde-prograde accretion disk configurations on either side of the 2008 torque reversal. It is found that the retrograde-prograde model is preferred, with a log Bayes factor equal to 0.44 and maximum a posteriori log likelihood ratio equal to 2.5. The mass accretion rate $Q(t)$ and magnetocentrifugal fastness $\omega(t)$ transition smoothly between episodes of deceleration and acceleration; $Q(t)$ shifts by $\leq 0.34 \, {\rm dex}$ across the reversal, and one measures $\omega(t) \approx 0.25$ and $\omega(t) \approx 0.30$ during deceleration and acceleration, respectively. The angular acceleration $\dot{\Omega}(t)$ satisfies $-9 \lesssim \dot{\Omega}(t)/(10^{-12} \, \rm{rad \, s^{-2}}) \lesssim -5$ and $2 \lesssim \dot{\Omega}(t)/(10^{-12} \, \rm{rad \, s^{-2}}) \lesssim 9$ before and after the 2008 reversal, respectively, compared to $\dot{\Omega} \approx -3.0 \times 10^{-12} \, \rm{rad \, s^{-2}}$ before reversal and $\dot{\Omega} \approx 2.5 \times 10^{-12} \, \rm{rad \, s^{-2}}$ after reversal, as inferred from previous long-term X-ray timing and spectral analysis of 4U 1626$-$67.

astro-ph.HE↗

arXiv2025

Hierarchical Bayesian estimation of population-level torque law parameters from $68$ young radio pulsars observed with the Murriyang telescope

Abridged. The measured braking index, $n=\nu \ddot{\nu}/\dot{\nu}^2$, of a rotation-powered pulsar with spin frequency $\nu$ and braking torque $K \nu^{n_{\rm pl}}$, features secular and stochastic anomalies arising from $\dot{K} \neq 0$ and random torque noise respectively. Previous studies quantified the variance $\langle n^{2} \rangle = (n_{\rm pl}+\dot{K}_{\rm dim})^{2}+\sigma_{\rm dim}^{2}$, where the secular anomaly, $\dot{K}_{\rm dim}$, is inversely proportional to the characteristic time-scale $\tau_{K}$ over which $K$ varies; the stochastic anomaly, $\sigma_{\rm dim}^{2} = \sigma_{\ddot{\nu}}^{2}\nu^{2}\gamma_{\ddot{\nu}}^{-2}\dot{\nu}^{-4}T_{\rm obs}^{-1}$, is a function of the timing noise amplitude $\sigma_{\ddot{\nu}}$, a damping time-scale $\gamma_{\ddot{\nu}}^{-1}$ and the total observing time $T_{\rm obs}$; and the average is taken over an ensemble of random realizations of the noise process. Here, we use a hierarchical Bayesian scheme, based on the formula for $\langle n^{2} \rangle$, to infer the population-level distribution of $n_{\rm pl}+\dot{K}_{\rm dim}$ for a sample of $68$ young radio pulsars, observed for $\gtrsim 10~{\rm years}$ with Murriyang, the 64-m Parkes radio telescope. Upon assuming that the $n_{\rm pl}+\dot{K}_{\rm dim}$ values are drawn from a population-level Gaussian, $N(\mu_{\rm pl}, \sigma_{\rm pl})$, the Bayesian scheme returns the mean $\mu_{\rm pl} = 9.95^{+5.58}_{-5.26}$ and standard deviation $\sigma_{\rm pl}=10.89^{+5.14}_{-3.69}$. At a per-pulsar level it returns posterior medians satisfying $-13.86 \leq n_{\rm pl}+\dot{K}_{\rm dim} \leq 30.38$. The secular anomaly dominates the stochastic anomaly, with posterior medians satisfying $|n_{\rm pl} + \dot{K}_{\rm dim}| \geq \sigma_{\rm dim}$ in 10 out of 68 objects.

astro-ph.HE↗

arXiv2025

Measuring the crust-superfluid coupling time-scale for 105 UTMOST pulsars with a Kalman filter

Crust-superfluid coupling plays an important role in neutron star rotation, particularly with respect to timing noise and glitches. Here, we present new timing-noise-based estimates of the crust-superfluid coupling time-scale $\tau$ for 105 radio pulsars in the UTMOST dataset, by Kalman filtering the pulse times of arrival. The 105 objects are selected because they favor a two-component, crust-superfluid model over a one-component model with log Bayes factor $\ln \mathfrak{B}_{\rm BF} \geq 5$. The median estimate of $\tau$ ranges from $10^{4.6\pm0.4}$\,s for PSR J2241$-$5236 to $10^{7.7^{+0.7}_{-0.4}}$\,s for PSR J1644$-$4559 among 28 out of 105 objects with sharply peaked $\tau$ posteriors. A hierarchical Bayesian analysis is performed on 101 out of 105 objects that are canonical (i.e.\ neither recycled nor magnetars) and reside in the populous core of the $\Omega_{\rm c}$-$\dot{\Omega}_{\rm c}$ plane. It returns the population-level scaling $\tau \propto \Omega_{\rm c}^{0.19^{+0.50}_{-0.52}} |\dot{\Omega}_{\rm c}|^{0.18^{+0.18}_{-0.19}}$, where $\Omega_{\rm c}$ and $\dot{\Omega}_{\rm c}$ are the angular velocity and spin-down rate of the crust respectively. The variances of the stochastic crust and superfluid torques are also estimated hierarchically, with $Q_{\rm c} \propto \Omega_{\rm c}^{1.23^{+0.80}_{-0.75}} |\dot{\Omega}_{\rm c}|^{0.49^{+0.27}_{-0.32}}$ and $Q_{\rm s} \propto \Omega_{\rm c}^{0.71^{+0.76}_{-0.78}} |\dot{\Omega}_{\rm c}|^{1.27^{+0.30}_{-0.28}}$ respectively. Implications for the physical origin of crust-superfluid coupling, e.g.\ through mutual friction, are discussed briefly.

astro-ph.HE↗

arXiv2025

Myopic Entropy Scheduling for Ramsey Magnetometry

This paper presents an entropy based adaptive measurement sequence strategy for quantum sensing of magnetic fields. To physically ground our ideas we consider a sensor employing a nitrogen vacancy center in diamond, however our approach is applicable to other quantum sensor arrangements. The sensitivity and accuracy of these sensors typically rely on long sequences of rapidly occurring measurements. We introduce a new technique for designing these measurement sequences aimed at reducing the number of measurements required for a specified accuracy as measured by entropy, by selecting measurement parameters that optimally reduce entropy at each measurement. We compare, via simulation, the efficiency and sensitivity of our new method with several existing measurement sequence design strategies. Our results show quantifiable improvements in sensing performance. We also show analytically that our entropy reduction approach, reduces, under certain simplified conditions, to a well-known and widely used measurement strategy.

quant-ph↗

arXiv2025

Argus: JAX state-space filtering for gravitational wave detection with a pulsar timing array

Argus is a high-performance Python package for detecting and characterising nanohertz gravitational waves in pulsar timing array data. The package provides a complete Bayesian inference framework based on state-space models, using Kalman filtering for efficient likelihood evaluation. Argus leverages JAX for just-in-time compilation, GPU acceleration, and automatic differentiation, facilitating rapid Bayesian inference with gradient-based samplers. The state-space approach provides a computationally efficient alternative to traditional frequency-domain methods, offering linear scaling with the number of pulse times-of-arrival, and natural handling of non-stationary processes.

astro-ph.IM↗

arXiv2025

Luminosity distance dispersion in Swiss-cheese cosmology as a function of the hole size distribution

The luminosity distance-redshift ($D_{\rm L}$--$z$) relation derived from Type Ia supernovae (SNe Ia) yields evidence for a nonzero cosmological constant. SNe Ia analyses typically fit to the functional form $D_{\rm L}(z)$ derived theoretically from the homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) metric. Yet, the metric in the epoch relevant to SNe Ia measurements deviates slightly from FLRW due to gravitational clumping of mass into large-scale structures like filaments and voids, whose sizes span many orders of magnitude. The small deviation is modeled typically by scalar perturbations to the FLRW metric. Each line of sight to a SNe Ia passes through a random sequence of structures, so $D_{\rm L}$ differs stochastically from one line of sight to the next. Here, we calculate the $D_{\rm L}$ dispersion in an exact Lemaitre-Tolman-Bondi Swiss-cheese universe with a power-law hole size distribution, as a function of the lower cut-off $R_{\rm min}$ and logarithmic slope $\gamma$. We find that the standard deviation of $D_{\rm L}$ scales as $\sigma_{D_{\rm L}} \propto z^{2.25\pm0.01} (R_{\rm min}/24\pm1\,{\rm Mpc})^{(0.157\pm0.003)\left[\gamma - (1.16\pm0.02)\right]}$ for redshifts in the range $0.5 \lesssim z \lesssim 2.1$. The scaling shows that the $D_{\rm L}$ dispersion is dominated by a few large voids rather than the many small voids.

astro-ph.CO↗

arXiv2025

Dedicated-frequency analysis of gravitational-wave bursts from core-collapse supernovae with minimal assumptions

Gravitational-wave (GW) emissions from core-collapse supernovae (CCSNe) provide insights into the internal processes leading up to their explosions. Theory predicts that CCSN explosions are driven by hydrodynamical instabilities like the standing accretion shock instability (SASI) or neutrino-driven convection, and simulations show that these mechanisms emit GWs at low frequencies ($\lesssim 0.25 \,{\rm kHz}$). Thus the detection of low-frequency GWs, or lack thereof, is useful for constraining explosion mechanisms in CCSNe. This paper introduces the dedicated-frequency framework, which is designed to follow-up GW burst detections using bandpass analyses. The primary aim is to study whether low-frequency (LF) follow-up analyses, limited to $\leq 256 \,{\rm Hz}$, constrain CCSN explosion models in practical observing scenarios. The analysis dataset comprises waveforms from five CCSN models with different strengths of low-frequency GW emissions induced by SASI and/or neutrino-driven convection, injected into the Advanced LIGO data from the Third Observing Run (O3). Eligible candidates for the LF follow-up must satisfy a benchmark detection significance and are identified using the coherent WaveBurst (cWB) algorithm. The LF follow-up analyses are performed using the BayesWave algorithm. Both cWB and BayesWave make minimal assumptions about the signal's morphology. The results suggest that the successful detection of a CCSN in the LF follow-up analysis constrains its explosion mechanism. The dedicated-frequency framework also has other applications. As a demonstration, the loudest trigger from the SN 2019fcn supernova search is followed-up using a high-frequency (HF) analysis, limited to $\geq 256 \,{\rm Hz}$. The trigger has negligible power below $256 \, {\rm Hz}$, and the HF analysis successfully enhances its detection significance.

astro-ph.HE↗

arXiv2025

Using Gaussian Mixtures to Model Evolving Multi-Modal Beliefs Across Social Media

We use Gaussian mixtures to model formation and evolution of multi-modal beliefs and opinion uncertainty across social networks. In this model, opinions evolve by Bayesian belief update when incorporating exogenous factors (signals from outside sources, e.g., news articles) and by non-Bayesian mixing dynamics when incorporating endogenous factors (interactions across social media). The modeling enables capturing the richness of behavior observed in multi-modal opinion dynamics while maintaining interpretability and simplicity of scalar models. We present preliminary results on opinion formation and uncertainty to investigate the effect of stubborn individuals (as social influencers). This leads to a notion of centrality based on the ease with which an individual can disrupt the flow of information across the social network.

eess.SY↗

arXiv2025

How trust networks shape students' opinions about the proficiency of artificially intelligent assistants

The rising use of educational tools controlled by artificial intelligence (AI) has provoked a debate about their proficiency. While intrinsic proficiency, especially in tasks such as grading, has been measured and studied extensively, perceived proficiency remains underexplored. Here it is shown through Monte Carlo multi-agent simulations that trust networks among students influence their perceptions of the proficiency of an AI tool. A probabilistic opinion dynamics model is constructed, in which every student's perceptions are described by a probability density function (PDF), which is updated at every time step through independent, personal observations and peer pressure shaped by trust relationships. It is found that students infer correctly the AI tool's proficiency $\theta_{\rm AI}$ in allies-only networks (i.e.\ high trust networks). AI-avoiders reach asymptotic learning faster than AI-users, and the asymptotic learning time for AI-users decreases as their number increases. However, asymptotic learning is disrupted even by a single partisan, who is stubbornly incorrect in their belief $\theta_{\rm p} \neq \theta_{\rm AI}$, making other students' beliefs vacillate indefinitely between $\theta_{\rm p}$ and $\theta_{\rm AI}$. In opponents-only (low trust) networks, all students reach asymptotic learning, but only a minority infer $\theta_{\rm AI}$ correctly. AI-users have a small advantage over AI-avoiders in reaching the right conclusion. In mixed networks, students may exhibit turbulent nonconvergence and intermittency, or achieve asymptotic learning, depending on the relationships between partisans and AI-users. The educational implications of the results are discussed briefly in the context of designing robust usage policies for AI tools, with an emphasis on the unintended and inequitable consequences which arise sometimes from counterintuitive network effects.

physics.soc-ph↗

arXiv2025

Discerning media bias within a network of political allies: an analytic condition for disruption by partisans

An individual's opinion concerning political bias in the media is shaped by exogenous factors (independent analysis of media outputs) and endogenous factors (social activity, e.g. peer pressure by political allies and opponents in a network). Previous numerical studies show, that persuadable agents in allies-only networks are disrupted from asymptotically learning the intrinsic bias of a media organization, when the network is populated by one or more obdurate agents (partisans), who are not persuadable themselves but exert peer pressure on other agents. Some persuadable agents asymptotically learn a false bias, while others vacillate indefinitely between a false bias and the true bias, a phenomenon called turbulent nonconvergence which also emerges in opponents-only and mixed networks without partisans. Here we derive an analytic instability condition, which demarcates turbulent nonconvergence from asymptotic learning as a function of key network properties, for an idealized model of media bias featuring a biased coin. The condition is verified with Monte Carlo simulations as a function of network size, sparsity, and partisan fraction. It is derived in a probabilistic framework, where an agent's opinion is uncertain and is described by a probability density function, which is multimodal in general, generalizing previous studies which assume that an agent's opinion is certain (i.e. described by one number). The results and their social implications are interpreted briefly in terms of the social science theory of structural balance.

physics.soc-ph↗

arXiv2025

How much spin wandering can continuous gravitational wave search algorithms handle?

The canonical signal model in continuous gravitational wave searches is deterministic, and stable over the long integration times needed to separate a putative signal from the noise, e.g. with a matched filter. However, there exist plausible physical mechanisms that give rise to "spin-wandering", i.e. small stochastic variations in the frequency of the gravitational wave. Stochastic variations degrade the sensitivity of matched filters which assume a deterministic frequency evolution. Suites of synthetic spin-wandering injections are performed to infer the loss in sensitivity depth $D_{\rm SW}$ when compared to the depth for a canonical signal $D_{\rm det}$. For a fiducial spin-wandering signal that wanders by $\lesssim5 \times 10^{-6}\,$Hz per day, the depth ratio is $D_{\rm det} / D_{\rm SW}=4.39^{+0.23}_{-0.27}$, $1.51^{+0.02}_{-0.03}$, $1.75^{+0.04}_{-0.04}$, and $1.07^{+0.01}_{-0.02}$ for the coherent $F$-statistic, semi-coherent $F$-statistic, CrossCorr, and HMM-Viterbi algorithms respectively. Increasing the coherence time of the semi-coherent algorithms does not necessarily increase their sensitivity to spin-wandering signals.

gr-qc↗

arXiv2025

Multi-detector characterization of gravitational-wave burst tensor polarizations with the BayesWave algorithm

Einstein's theory of general relativity predicts that gravitational waves (GWs) are tensor-polarized, with two modes of polarization: plus ($h_+$) and cross ($h_\times$). The unmodeled GW burst analysis pipeline, \textit{BayesWave}, offers two tensor-polarized signal models: the elliptical polarization model ($E$) and the relaxed polarization model ($R$). Future expansion of the global GW detector network will enable more accurate studies of GW polarizations with GW bursts. Here a multi-detector analysis is conducted to compare the performance of $E$ and $R$ in characterizing elliptical and nonelliptical GW polarizations, using nonprecessing and precessing binary black holes (BBHs) respectively as representative synthetic sources. It is found that both models reconstruct the elliptical nonprecessing BBH signals accurately, but $E$ has a higher Bayesian evidence than $R$ as it is has fewer model parameters. The same is true for precessing BBHs that are reconstructed equally well by both models. However, for some events with high precession and especially with three or more detectors, the reconstruction accuracy and evidence of $R$ surpass $E$. The analysis is repeated for BBH events from the third LIGO-Virgo-KAGRA observing run, and the results show that $E$ is preferred over $R$ for existing detections. Although $E$ is generally preferred for its simplicity, it insists on elliptical polarizations, whereas $R$ can measure generic GW polarization content in terms of Stokes parameters. The accuracy of $R$ in recovering polarization content improves as the detector network expands, and the performance is independent of the GW signal morphology.

gr-qc↗

arXiv2025

Observing Rayleigh-Taylor stable and unstable accretion through a Kalman filter analysis of X-ray pulsars in the Small Magellanic Cloud

Global, three-dimensional, magnetohydrodynamic simulations of Rayleigh-Taylor instabilities at the disk-magnetosphere boundary of rotating, magnetized, compact stellar objects reveal that accretion occurs in three regimes: the stable regime, the chaotic unstable regime, and the ordered unstable regime. Here we track stochastic fluctuations in the pulse period $P(t)$ and aperiodic X-ray luminosity $L(t)$ time series of 24 accretion-powered pulsars in the Small Magellanic Cloud using an unscented Kalman filter to analyze Rossi X-ray Timing Explorer data. We measure time-resolved histories of the magnetocentrifugal fastness parameter $ω(t)$ and we connect $ω(t)$ with the three Rayleigh-Taylor accretion regimes. The 24 objects separate into two distinct groups, with 10 accreting in the stable regime, and 14 accreting in the ordered unstable regime. None of the 24 objects except SXP 293 visit the chaotic unstable regime for sustained intervals, although several objects visit it sporadically. The Kalman filter output also reveals a positive temporal cross-correlation between $ω(t)$ and the independently measured pulse amplitude $A(t)$, which agrees with simulation predictions regarding the pulse-forming behavior of magnetospheric funnel flows in the three accretion regimes.

astro-ph.HE↗

arXiv2025

Hierarchical Bayesian estimation of population-level torque law parameters from anomalous pulsar braking indices

Abridged. Stochastic fluctuations in the spin frequency $ν$ of a rotation-powered pulsar affect how accurately one measures the power-law braking index, $n_{\rm pl}$, defined through $\dotν=Kν^{n_{\rm pl}}$, and can lead to measurements of anomalous braking indices, with $\vert n \vert = \vert ν\ddotν/ \dotν^{2} \vert \gg1$, where the overdot symbolizes a derivative with respect to time. Previous studies show that the variance of the measured $n$ obeys the predictive, falsifiable formula $\langle n^{2} \rangle = n_{\rm pl}^{2}+σ^{2}_{\ddotν}ν^{2}γ_{\ddotν}^{-2}\dotν^{-4}T_{\rm obs}^{-1}$ for $\dot{K}=0$, where $σ_{\ddotν}$ is the timing noise amplitude, $γ_{\ddotν}^{-1}$ is a stellar damping time-scale, and $T_{\rm obs}$ is the total observing time. Here we combine this formula with a hierarchical Bayesian scheme to infer the population-level distribution of $n_{\rm pl}$ for a pulsar population of size $M$. The scheme is validated using synthetic data. For a plausible test population with $M=100$ and injected $n_{\rm pl}$ values drawn from a population-level Gaussian with mean $μ_{\rm pl}=4$ and standard deviation $σ_{\rm pl}=0.5$, intermediate between electromagnetic braking and mass quadrupole gravitational radiation reaction, the Bayesian scheme infers $μ_{\rm pl}=3.89^{+0.24}_{-0.23}$ and $σ_{\rm pl}=0.43^{+0.21}_{-0.14}$. The $M=100$ per-pulsar posteriors for $n_{\rm pl}$ and $σ^{2}_{\ddotν}γ_{\ddotν}^{-2}$ contain $87\%$ and $69\%$, respectively, of the injected values within their $90\%$ credible intervals. Comparable accuracy is achieved for (i) population sizes spanning the range $50 \leq M \leq 300$, and (ii) wide priors satisfying $μ_{\rm pl} \leq 10^{3}$ and $σ_{\rm pl} \leq 10^{2}$, which accommodate plausible spin-down mechanisms with $\dot{K}\neq0$.

astro-ph.HE↗