Population Of Neutron Stars Research Articles

The EXOD search for faint transients in XMM-Newton observations: Method and discovery of four extragalactic Type I X-ray bursters

Context. The observations carried out with XMM-Newton have produced a very extensive X-ray source catalogue in which the standard pipeline determines the variability of sufficiently bright sources through χ2 and fractional variability tests. Faint sources, however, are not automatically checked for variability, and this means that faint, short timescale transients are overlooked. From dedicated X-ray searches, as well as optical and radio archive searches, we know that some such dim sources can still be identified with high confidence. Aims. Our goal is to find new faint, fast transients in XMM-Newton EPIC-pn observations. To that end we created the EPIC-pn XMM-Newton outburst detector (EXOD) algorithm, which we run on the EPIC-pn full-frame data available in the 3XMM-DR8 catalogue. Methods. In EXOD, we computed the variability of the whole field of view by first binning in time the counts detected in each pixel of the detector. We next computed the difference between the median and maximal number of counts in each time bin and pixel to detect variability. We applied EXOD to 5751 observations in the full frame mode and compared the variability of the detected sources to the standard χ2 and Kolmogorov–Smirnov (KS) variability tests. Results. The algorithm is able to detect periodic and aperiodic variability, with both short and long flares. Of the sources detected by EXOD, 60−95% are also shown to be variable by the standard χ2 and KS tests. EXOD computes the variability over the entire field of view faster than the light curve generation takes for all the individual sources. We detect a total of 2961 X-ray variable sources. After removing the spurious detections, we obtain a net number of 2536 variable sources. Of these we investigate the nature of 35 sources with no previously confirmed classification. Amongst the new sources, we find stellar flares and AGNs, in addition to four extragalactic type I X-ray bursters that double the known neutron-star population in M 31. Conclusions. This algorithm is a powerful tool for the prompt detection of interesting variable sources in XMM-Newton observations. EXOD also detects fast transients that other variability tests would classify as non-variable due to their short duration and low number of counts. This is of increasing importance for the multi-messenger detection of transient sources. Finally, EXOD allows us to identify the nature of compact objects through their variability and to detect rare compact objects. We demonstrate this through the discovery of four extragalactic neutron-star low-mass X-ray binaries, doubling the number of known neutron stars in M 31.

The Galactic population and properties of young, highly energetic pulsars

ABSTRACT The population of young, non-recycled pulsars with spin-down energies $\dot{E} \gt 10^{35}$ erg s−1 is sampled predominantly at γ-ray and radio wavelengths. A total of 137 such pulsars are known, with partial overlap between the sources detectable in radio and γ-rays. We use a very small set of assumptions in an attempt to test whether the observed pulsar sample can be explained by a single underlying population of neutron stars. For radio emission we assume a canonical conal beam with a fixed emission height of 300 km across all spin periods and a luminosity law which depends on $\dot{E}^{0.25}$. For γ-ray emission we assume the outer-gap model and a luminosity law which depends on $\dot{E}^{0.5}$. We synthesize a population of fast-spinning pulsars with a birth rate of one per 100 yr. We find that this simple model can reproduce most characteristics of the observed population with two caveats. The first is a deficit of γ-ray pulsars at the highest $\dot{E}$ which we surmise to be an observational selection effect due to the difficulties of finding γ-ray pulsars in the presence of glitches without prior knowledge from radio frequencies. The second is a deficit of radio pulsars with interpulse emission, which may be related to radio emission physics. We discuss the implications of these findings.

Subtracting compact binary foreground sources to reveal primordial gravitational-wave backgrounds

Detection of primordial gravitational-wave backgrounds generated during the early universe phase transitions is a key science goal for future ground-based detectors. The rate of compact binary mergers is so large that their cosmological population produces a confusion background that could masquerade the detection of potential primordial stochastic backgrounds. In this paper we study the ability of current and future detectors to resolve the confusion background to reveal interesting primordial backgrounds. The current detector network of LIGO and Virgo and the upcoming KAGRA and LIGO-India will not be able to resolve the cosmological compact binary source population and its sensitivity to stochastic background will be limited by the confusion background of these sources. We find that a network of three (and five) third generation (3G) detectors of Cosmic Explorer and Einstein Telescope will resolve the confusion background produced by binary black holes leaving only about 0.013\% (respectively, 0.00075\%) unresolved; in contrast, as many as 25\% (respectively, 7.7\%) of binary neutron star sources remain unresolved. Consequently, the binary black hole population will likely not limit observation of primordial backgrounds but the binary neutron star population will limit the sensitivity of 3G detectors to $\Omega_{\rm GW} \sim 10^{-11}$ at 10 Hz (respectively, $\Omega_{\rm GW} \sim 3\times 10^{-12}$).

Physics in Ultra-Strong Magnetic Fields

AbstractSeveral populations of neutron stars have surface magnetic fields above the critical strength of 4.4 × 1013 G where the electron cyclotron energy equals its rest mass. These include high-field rotation-powered pulsars, X-ray dim isolated neutron stars (XDIN), and magnetars. In such ultra-strong fields, quantum effects in physical processes as well as additional exotic Quantum Electrodynamic processes only occurring at these high field strengths have a significant influence on the emitted radiation. Although very strong magnetic fields play a critical role both inside and outside of neutron stars, I will review primarily processes that operate in the neutron star magnetospheres and how they influence the observed radiation.

Modelling double neutron stars: radio and gravitational waves

ABSTRACT We have implemented prescriptions for modelling pulsars in the rapid binary population synthesis code Compact Object Mergers: Population Astrophysics and Statistics. We perform a detailed analysis of the double neutron star (DNS) population, accounting for radio survey selection effects. The surface magnetic field decay time-scale (∼1000 Myr) and mass-scale (∼0.02 M⊙) are the dominant uncertainties in our model. Mass accretion during common envelope evolution plays a non-trivial role in recycling pulsars. We find a best-fitting model that is in broad agreement with the observed Galactic DNS population. Though the pulsar parameters (period and period derivative) are strongly biased by radio selection effects, the observed orbital parameters (orbital period and eccentricity) closely represent the intrinsic distributions. The number of radio observable DNSs in the Milky Way at present is about 2500 in our model, corresponding to approximately 10 per cent of the predicted total number of DNSs in the Galaxy. Using our model calibrated to the Galactic DNS population, we make predictions for DNS mergers observed in gravitational waves. The DNS chirp mass distribution varies from 1.1 to 2.1 M⊙ and the median is found to be 1.14 M⊙. The expected effective spin χeff for isolated DNSs is ≲0.03 from our model. We predict that 34 per cent of the current Galactic isolated DNSs will merge within a Hubble time, and have a median total mass of 2.7 M⊙. Finally, we discuss implications for fast radio bursts and post-merger remnant gravitational waves.

Gravitational waves or deconfined quarks: What causes the premature collapse of neutron stars born in short gamma-ray bursts?

We infer the collapse times of long-lived neutron stars into black holes using the X-ray afterglows of 18 short gamma-ray bursts. We then apply hierarchical inference to infer properties of the neutron star equation of state and dominant spin-down mechanism. We measure the maximum non-rotating neutron star mass $M_\mathrm{TOV} = 2.31 ^{+0.36}_{-0.21} M_{\odot}$ and constrain the fraction of remnants spinning down predominantly through gravitational-wave emission to $\eta = 0.69 ^{+0.21}_{-0.39}$ with $68 \%$ uncertainties. In principle, this method can determine the difference between hadronic and quark equation of states. In practice, however, the data is not yet informative with indications that these neutron stars do not have hadronic equation of states at the $1\sigma$ level. These inferences all depend on the underlying progenitor mass distribution for short gamma-ray bursts produced by binary neutron star mergers. The recently announced gravitational-wave detection of GW190425 suggests this underlying distribution is different from the locally-measured population of double neutron stars. We show that $M_\mathrm{TOV}$ and $\eta$ constraints depend on the fraction of binary mergers that form through a distribution consistent with the locally-measured population and a distribution that can explain GW190425. The more binaries that form from the latter distribution, the larger $M_\mathrm{TOV}$ needs to be to satisfy the X-ray observations. Our measurements above are marginalised over this unknown fraction. If instead, we assume GW190425 is not a binary neutron star merger, i.e the underlying mass distribution of double neutron stars is the same as observed locally, we measure $M_\mathrm{TOV} = 2.26 ^{+0.31}_{-0.17} M_{\odot}$.

Updated parameter estimates for GW190425 using astrophysical arguments and implications for the electromagnetic counterpart

ABSTRACT The progenitor system of the compact binary merger GW190425 had a total mass of $3.4^{+0.3}_{-0.1}$ M⊙ (90th-percentile confidence region) as measured from its gravitational wave signal. This mass is significantly different from the Milky Way (MW) population of binary neutron stars (BNSs) that are expected to merge in a Hubble time and from that of the first BNS merger, GW170817. Here, we explore the expected electromagnetic (EM) signatures of such a system. We make several astrophysically motivated assumptions to further constrain the parameters of GW190425. By simply assuming that both components were NSs, we reduce the possible component masses significantly, finding $m_{1}=1.85^{+0.27}_{-0.19}$ M⊙ and $m_{2}=1.47^{+0.16}_{-0.18}$ M⊙. However, if the GW190425 progenitor system was an NS–black hole (BH) merger, we find best-fitting parameters $m_{1}=2.19^{+0.21}_{-0.17}$ M⊙ and $m_{2}=1.26^{+0.10}_{-0.08}$ M⊙. For a well-motivated BNS system where the lighter NS has a mass similar to the mass of non-recycled NSs in MW BNS systems, we find $m_{1}=2.03^{+0.15}_{-0.14}$ M⊙ and m2 = 1.35 ± 0.09 M⊙, corresponding to only 7 per cent mass uncertainties. For all scenarios, we expect a prompt collapse of the resulting remnant to a BH. Examining detailed models with component masses similar to our best-fitting results, we find the EM counterpart to GW190425 is expected to be significantly redder and fainter than that of GW170817. We find that almost all reported search observations were too shallow to detect the expected counterpart to GW190425. If the LIGO–Virgo Collaboration promptly provides the chirp mass, the astronomical community can adapt their observations to improve the likelihood of detecting a counterpart for similarly ‘high-mass’ BNS systems.

Studying strong phase transitions in neutron stars with gravitational waves

The composition of neutron stars at the extreme densities reached in their cores is currently unknown. Besides nuclear matter of normal neutrons and protons, the cores of neutron stars might harbor exotic matter such as deconfined quarks. In this paper we study strong hadron-quark phase transitions in the context of gravitational wave observations of inspiraling neutron stars. We consider upcoming detections of neutron star coalescences and model the neutron star equations of state with phase transitions through the Constant-Speed-of-Sound parametrization. We use the fact that neutron star binaries with one or more hadron-quark hybrid stars can exhibit qualitatively different tidal properties than binaries with hadronic stars of the same mass, and hierarchically model the masses and tidal properties of simulated populations of binary neutron star inspiral signals. We explore the parameter space of phase transitions and discuss under which conditions future observations of binary neutron star inspirals can identify this effect and constrain its properties, in particular the threshold density at which the transition happens and the strength of the transition. We find that if the detected population of binary neutron stars contains both hadronic and hybrid stars, the onset mass and strength of a sufficiently strong phase transition can be constrained with 50-100 detections. If the detected neutron stars are exclusively hadronic or hybrid, then it is possible to place lower or upper limits on the transition density and strength.

Detecting double neutron stars with LISA

ABSTRACT We estimate the properties of the double neutron star (DNS) population that will be observable by the planned space-based interferometer Laser Interferometer Space Antenna (LISA). By following the gravitational radiation-driven evolution of DNSs generated from rapid population synthesis of massive binary stars, we estimate that around 35 DNSs will accumulate a signal-to-noise ratio above 8 over a 4-yr LISA mission. The observed population mainly comprises Galactic DNSs (94 per cent), but detections in the LMC (5 per cent) and SMC (1 per cent) may also be expected. The median orbital frequency of detected DNSs is expected to be 0.8 mHz, and many of them will be eccentric (median eccentricity of 0.11). LISA is expected to localize these DNSs to a typical angular resolution of 2°. We expect the best-constrained DNSs to have eccentricities known to a few parts in a thousand, chirp masses measured to better than 1 per cent fractional uncertainty, and sky localization at the level of a few arcminutes. The orbital properties will provide insights into DNS progenitors and formation channels. The localizations may allow neutron star natal kick magnitudes to be constrained through the Galactic distribution of DNSs, and make it possible to follow up the sources with radio pulsar searches. LISA is also expected to resolve ∼104 Galactic double white dwarfs, many of which may have binary parameters that resemble DNSs; we discuss how the combined measurement of binary eccentricity, chirp mass, and sky location may aid the identification of a DNS.

The overarching framework of core-collapse supernova explosions as revealed by 3D fornax simulations

ABSTRACT We have conducted 19 state-of-the-art 3D core-collapse supernova simulations spanning a broad range of progenitor masses. This is the largest collection of sophisticated 3D supernova simulations ever performed. We have found that while the majority of these models explode, not all do, and that even models in the middle of the available progenitor mass range may be less explodable. This does not mean that those models for which we did not witness explosion would not explode in Nature, but that they are less prone to explosion than others. One consequence is that the ‘compactness’ measure is not a metric for explodability. We find that lower-mass massive star progenitors likely experience lower-energy explosions, while the higher-mass massive stars likely experience higher-energy explosions. Moreover, most 3D explosions have a dominant dipole morphology, have a pinched, wasp-waist structure, and experience simultaneous accretion and explosion. We reproduce the general range of residual neutron-star masses inferred for the galactic neutron-star population. The most massive progenitor models, however, in particular vis à vis explosion energy, need to be continued for longer physical times to asymptote to their final states. We find that while the majority of the inner ejecta have Ye = 0.5, there is a substantial proton-rich tail. This result has important implications for the nucleosynthetic yields as a function of progenitor. Finally, we find that the non-exploding models eventually evolve into compact inner configurations that experience a quasi-periodic spiral SASI mode. We otherwise see little evidence of the SASI in the exploding models.

Radio afterglows of binary neutron star mergers: a population study for current and future gravitational wave observing runs

Following the historical observations of GW170817 and its multi-wavelength afterglow, more radio afterglows from neutron star mergers are expected in the future as counterparts to gravitational wave inspiral signals. Our aim is to describe these events using our current knowledge of the population of neutron star mergers based on gamma-ray burst science, and taking into account the sensitivities of current and future gravitational wave and radio detectors. We combined analytical models for the merger gravitational wave and radio afterglow signals to a population model prescribing the energetics, circum-merger density and other relevant parameters of the mergers. We reported the expected distributions of observables (distance, orientation, afterglow peak time and flux, etc.) for future events and studied how these can be used to further probe the population of binary neutron stars, their mergers and related outflows during future observing campaigns. In the case of the O3 run of the LIGO-Virgo Collaboration, the radio afterglow of one third of gravitational-wave-detected mergers should be detectable (and detected if the source is localized thanks to the kilonova counterpart) by the Very Large Array. Furthermore, these events should have viewing angles similar to that of GW170817. These findings confirm the radio afterglow as a powerful insight into these events, although some key afterglow-related techniques, such as very long baseline interferometry imaging of the merger remnant, may no longer be feasible as the gravitational wave horizon increases.

Double Neutron Star Populations and Formation Channels

Abstract In the past five years, the number of known double neutron stars (DNSs) in the Milky Way has roughly doubled. We argue that the observed sample can be split into three distinct subpopulations based on their orbital characteristics: (i) short-period, low-eccentricity binaries; (ii) wide binaries; and (iii) short-period, high-eccentricity binaries. These subpopulations also exhibit distinct spin period and spindown rate properties. We focus on subpopulation (iii), which contains the Hulse–Taylor binary. Contrary to previous analysis, we demonstrate that, if they are the product of isolated binary evolution, the P orb and e distribution of these systems requires that the second-born NSs must have been formed with small natal kicks (≲25 km s−1) and have pre-SN masses narrowly distributed around 3.2 M ⊙. These constraints challenge binary evolution theory and further predict closely aligned spin and orbital axes, inconsistent with the Hulse–Taylor binary’s measured spin–orbit misalignment angle of ≈20°. Motivated by the similarity of these DNSs to B2127+11C, a DNS residing in the globular cluster M15, we argue that this subpopulation is consistent with being formed in, and then ejected from, globular clusters. This scenario provides a pathway for the formation and merger of DNSs in stellar environments without recent star formation, as observed in the host galaxy population of short gamma-ray bursts and the recent detection by LIGO of a merging DNS in an old stellar population.

Detecting axion dark matter with radio lines from neutron star populations

It has been suggested that radio telescopes may be sensitive to axion dark matter that resonantly converts to radio photons in the magnetospheres surrounding neutron stars (NSs). In this work, we closely examine this possibility by calculating the radiated power from and projected sensitivity to axion dark matter conversion in ensembles of NSs within astrophysical systems like galaxies and globular clusters. We use population synthesis and evolution models to describe the spatial distributions of NSs within these systems and the distributions of NS properties. Focusing on three specific targets for illustration, the Galactic Center of the Milky Way, the globular cluster M54 in the Sagittarius dwarf galaxy, and the Andromeda galaxy, we show that narrow-band radio observations with telescopes such as the Green Bank Telescope and the future Square Kilometer Array may be able to probe the quantum chromodynamics axion over roughly two orders of magnitude in mass, starting at a fraction of a $\mu$eV.

Time Domain Studies of Neutron Star and Black Hole Populations: X-ray Identification of Compact Object Types

We present requirements for next generation X-ray telescopes that will enable measurements of time domain properties of X-ray binaries to identify black holes and neutron stars.

Relativistic fireball reprise: radio suppression at the onset of short magnetar bursts

There is growing evidence that a clear distinction between magnetars and radio pulsars may not exist, implying the population of neutron stars that exhibit both radio pulsations and bursting activities could be potentially large. In this situation, new insights into the burst mechanism could be gained by combining the temporal behavior of radio pulsations. We present a general model for radio suppression by relativistic $e^{\pm}$ plasma outflows at the onset of magnetar flares. A sudden ejection of magnetic energy into the magnetosphere would generate a fireball plasma, which is promptly driven to expand at relativistic speed. This would make the plasma cutoff frequency significantly higher than the rest frame radio frequency, resulting in the suppression of radio waves. We analytically show that any GHz radio emission arising from the magnetosphere is suppressed for $\sim100\ {\rm s}$, depending on the total fireball energy. On the other hand, thermal radiation is expected from the hot spot(s) on the stellar surface created by an inflow of dense plasma, which could be the origin of short bursts. Since our hypothesis predicts radio suppression in coincidence with short bursts, this could be an indirect method to constrain the occurrence rate of short bursts at the faint end that remain undetected by X-ray detectors. Furthermore, ultra-fast gamma-ray flashes from the fireball photosphere is also expected as a smoking gun, although the onboard detection is challenging due to its extremely short duration $\sim\mu$s. Finally, our model is applied to the radio pulsar with magnetar-like activities, PSR J1119-6127 in light of recent observations. Implications for fast radio bursts and the possibility of plasma lensing are also discussed.

On GW170817 and the Galactic Binary Neutron Star Population

Abstract GW170817/GRB170817A, a short gamma-ray burst arising from a low-mass compact object merger was the first multimessenger discovery of a compact binary system outside the local galactic neighborhood. From gravitational-wave (GW) measurements, we know GW170817 has a wide range of plausible component masses, depending also on less well-constrained properties such as the spin and tidal deformability of the component stars. The kilonova light curve—and hence the total ejecta mass from a given source—depends on the relative contribution of dynamical ejecta and other sources such as disk winds. Electromagnetic observations and model fitting of the ejecta properties from the subsequent kilonova detection provided values of the ejecta mass from the merger. These values, when combined with the GW measurement disfavor an equal-mass configuration, with the level of disagreement dependent on the assumed amount of ejecta mass of dynamical origin. Within the confines of our own galaxy, several binary neutron star (BNS) systems along with measurements of their component masses have been made. If those distributions are indicative of a universal distribution, the joint measurement of the component masses of GW170817 represents an outlier. This tension is not easily resolvable from physical arguments, as the proposed pathways that form BNSs do not often produce very asymmetrical pairs. Even accounting for the uncertainty associated with the total mass of the dynamical ejecta, this tension suggests that the distribution of BNS masses in the galaxy is not indicative of those in other galaxies.

Neutron-star spindown and magnetic inclination-angle evolution

A rotating fluid star, endowed with a magnetic field, can undergo a form of precessional motion: a sum of rigid-body free precession and a non-rigid response. On secular timescales this motion is dissipated by bulk and shear viscous processes in the stellar interior and magnetospheric braking in the exterior, changing the inclination angle between the rotation and magnetic axes. Using our recent solutions for the non-rigid precessional dynamics, and viscous dissipation integrals derived in this paper, we make the only self-consistent calculation to date of these dissipation rates. We present the first results for the full coupled evolution of spindown and inclination angle for a model of a late-stage proto-neutron star with a strong toroidal magnetic field, allowing for both electromagnetic torques and internal dissipation when evolving the inclination angle. We explore this coupled evolution for a range of initial inclination angles, rotation rates and magnetic field strengths. For fixed initial inclination angle, our results indicate that the neutron-star population naturally evolves into two classes: near-aligned and near-orthogonal rotators -- with typical pulsars falling into the latter category. Millisecond magnetars can evolve into the near-aligned rotators which mature magnetars appear to be, but only for small initial inclination angle and internal toroidal fields stronger than roughly $5\times 10^{15}$ G. Once any model has evolved to either an aligned or orthogonal state, there appears to be no further evolution away from this state at later times.

Characterization of binary black holes by heterogeneous gravitational-wave networks

Gravitational waves detected by advanced ground-based detectors have allowed studying the Universe in a way which is fully complementary to electromagnetic observations. As more sources are detected, it will be possible to measure properties of the local population of black holes and neutron stars, including their mass and spin distributions. Once at design sensitivity, existing instruments will be able to detect heavy binary black holes at redshifts of $\ensuremath{\sim}1$. Significant upgrades in the current facilities could increase the sensitivity by another factor of few, further extending reach and signal-to-noise ratio. More is required to access the most remote corners of the Universe. Third-generation gravitational-wave detectors have been proposed, which could observe most of the binary black holes merging anywhere in the Universe. In this paper, we check if, and to which extent, it makes sense to keep previous-generation detectors up and running once a significantly more sensitive detector is online. First, we focus on a population of binary black holes with redshifts distributed uniformly in comoving volume. We show that measurement of extrinsic parameters, such as sky position, inclination and luminosity distance can significantly benefit from the presence of a less sensitive detector. Conversely, intrinsic parameters such as detector-frame masses and spins are largely unaffected. Measurement of the source-frame masses is instead improved, owing to the improvement of the distance measurement. Then, we focus on nearby events. We simulated sources similar to GW150914 and GW151226 and check how well their parameters can be measured by various networks. Here, too, we find that the main difference is a better estimation of the sky position, although even a single triangular-shaped third-generation detector can estimate their sky position to $1\text{ }\text{ }{\mathrm{deg}}^{2}$ or better.

Rotational and X-ray luminosity evolution of high-B radio pulsars

In continuation of our earlier work on the long-term evolution of the so-called high–B radio pulsars (HBRPs) with measured braking indices, we have investigated the long-term evolution of the remaining five HBRPs for which braking indices have not been measured yet. This completes our source-by-source analyses of HBRPs in the fallback disc model that was also applied earlier to anomalous X-ray pulsars (AXPs), soft gamma repeaters (SGRs), and dim isolated neutron stars (XDINs). Our results show that the X-ray luminosities and the rotational properties of these rather different neutron star populations can be acquired by neutron stars with fallback discs as a result of differences in their initial conditions, namely the initial disc mass, initial period and the dipole field strength. For the five HBRPs, unlike for AXPs, SGRs and XDINs, our results do not constrain the dipole field strengths of the sources. We obtain evolutionary paths leading to the properties of HBRPs in the propeller phase with dipole fields sufficiently strong to produce pulsed radio emission.

The glitch activity of neutron stars

We present a statistical study of the glitch population and the behaviour of the glitch activity across the known population of neutron stars. An unbiased glitch database was put together based on systematic searches of radio timing data of 898 rotation-powered pulsars obtained with the Jodrell Bank and Parkes observatories. Glitches identified in similar searches of 5 magnetars were also included. The database contains 384 glitches found in the rotation of 141 of these neutron stars. We confirm that the glitch size distribution is at least bimodal, with one sharp peak at approximately $20\, \rm{\mu\,Hz}$, which we call large glitches, and a broader distribution of smaller glitches. We also explored how the glitch activity $\dot{\nu}_{\rm{g}}$, defined as the mean frequency increment per unit of time due to glitches, correlates with the spin frequency $\nu$, spin-down rate $|\dot{\nu}|$, and various combinations of these, such as energy loss rate, magnetic field, and spin-down age. It is found that the activity is insensitive to the magnetic field and that it correlates strongly with the energy loss rate, though magnetars deviate from the trend defined by the rotation-powered pulsars. However, we find that a constant ratio $\dot\nu_{\rm{g}}/|\dot\nu| = 0.010 \pm 0.001$ is consistent with the behaviour of all rotation-powered pulsars and magnetars. This relation is dominated by large glitches, which occur at a rate directly proportional to $|\dot{\nu}|$. The only exception are the rotation-powered pulsars with the highest values of $|\dot{\nu}|$, such as the Crab pulsar and PSR B0540$-$69, which exhibit a much smaller glitch activity, intrinsically different from each other and from the rest of the population. The activity due to small glitches also shows an increasing trend with $|\dot\nu|$, but this relation is biased by selection effects.