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Register a new userExtensive population synthesis of isolated neutron stars with field decay
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S.B. Popov
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We perform population synthesis studies of different types of neutron stars taking into account the magnetic field decay. For the first time, we confront our results with observations using {it simultaneously} the Log N -- Log S distribution for nearby isolated neutron stars, the Log N -- Log L distribution for magnetars, and the distribution of radio pulsars in the $P$ -- $dot P$ diagram. We find that our theoretical model is consistent with all sets of data if the initial magnetic field distribution function follows a log-normal law with $<log (B_0/[G]) > sim 13.25$ and $sigma_{log B_0}sim 0.6$. The typical scenario includes about 10% of neutron stars born as magnetars, significant magnetic field decay during the first million years of a NS life. Evolutionary links between different subclasses may exist, although robust conclusions are not yet possible. We apply the obtained field distribution and the model of decay to study long-term evolution of neuton stars till the stage of accretion from the interstellar medium. It is shown that though the subsonic propeller stage can be relatively long, initially highly magnetized neutron stars ($B_0 > sim 10^{13}$ G) reach the accretion regime within the Galactic lifetime if their kick velocities are not too large. The fact that in previous studies made $>$10 years ago, such objects were not considered results in a slight increase of the Accretor fraction in comparison with earlier conclusions. Most of the neutron stars similar to the Magnificent seven are expected to become accreting from the interstellar medium after few billion years of their evolution. They are the main predecestors of accreting isolated neutron stars.
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We perform population synthesis studies of different types of neutron stars (thermally emitting isolated neutron stars, normal radio pulsars, magnetars) taking into account the magnetic field decay and using results from the most recent advances in neutron star cooling theory. For the first time, we confront our results with observations using {it simultaneously} the Log N -- Log S distribution for nearby isolated neutron stars, the Log N -- Log L distribution for magnetars, and the distribution of radio pulsars in the $P$ -- $dot P$ diagram. For this purpose, we fix a baseline neutron star model (all microphysics input), and other relevant parameters to standard values (velocity distribution, mass spectrum, birth rates ...), allowing to vary the initial magnetic field strength. We find that our theoretical model is consistent with all sets of data if the initial magnetic field distribution function follows a log-normal law with $<log (B_0/[G])>sim 13.25$ and $sigma_{log B_0}sim 0.6$. The typical scenario includes about 10% of neutron stars born as magnetars, significant magnetic field decay during the first million years of a NS life (only about a factor of 2 for low field neutron stars but more than an order of magnitude for magnetars), and a mass distribution function dominated by low mass objects. This model explains satisfactorily all known populations. Evolutionary links between different subclasses may exist, although robust conclusions are not yet possible.
We revisit the population synthesis of isolated radio-pulsars incorporating recent advances on the evolution of the magnetic field and the angle between the magnetic and rotational axes from new simulations of the magneto-thermal evolution and magnetosphere models, respectively. An interesting novelty in our approach is that we do not assume the existence of a death line. We discuss regions in parameter space that are more consistent with the observational data. In particular, we find that any broad distribution of birth spin periods with $P_0lesssim 0.5$ s can fit the data, and that if the alignment angle is allowed to vary consistently with the torque model, realistic magnetospheric models are favoured compared to models with classical magneto-dipolar radiation losses. Assuming that the initial magnetic field is given by a lognormal distribution, our optimal model has mean strength $langlelog B_0{rm [G]}rangle approx 13.0-13.2$ with width $sigma (log B_0) = 0.6-0.7$. However, there are strong correlations between parameters. This degeneracy in the parameter space can be broken by an independent estimate of the pulsar birth rate or by future studies correlating this information with the population in other observational bands (X-rays and $gamma$-rays).
Population synthesis studies constitute a powerful method to reconstruct the birth distribution of periods and magnetic fields of the pulsar population. When this method is applied to populations in different wavelengths, it can break the degeneracy in the inferred properties of initial distributions that arises from single-band studies. In this context, we extend previous works to include $X$-ray thermal emitting pulsars within the same evolutionary model as radio-pulsars. We find that the cumulative distribution of the number of X-ray pulsars can be well reproduced by several models that, simultaneously, reproduce the characteristics of the radio-pulsar distribution. However, even considering the most favourable magneto-thermal evolution models with fast field decay, log-normal distributions of the initial magnetic field over-predict the number of visible sources with periods longer than 12 s. We then show that the problem can be solved with different distributions of magnetic field, such as a truncated log-normal distribution, or a binormal distribution with two distinct populations. We use the observational lack of isolated NSs with spin periods P>12 s to establish an upper limit to the fraction of magnetars born with B > 10^{15} G (less than 1%). As future detections keep increasing the magnetar and high-B pulsar statistics, our approach can be used to establish a severe constraint on the maximum magnetic field at birth of NSs.
The fastest-spinning neutron stars in low-mass X-ray binaries, despite having undergone millions of years of accretion, have been observed to spin well below the Keplerian break-up frequency. We simulate the spin evolution of synthetic populations of accreting neutron stars in order to assess whether gravitational waves can explain this behaviour and provide the distribution of spins that is observed. We model both persistent and transient accretion and consider two gravitational-wave-production mechanisms that could be present in these systems: thermal mountains and unstable $r$-modes. We consider the case of no gravitational-wave emission and observe that this does not match well with observation. We find evidence for gravitational waves being able to provide the observed spin distribution; the most promising mechanisms being a permanent quadrupole, thermal mountains and unstable $r$-modes. However, based on the resultant distributions alone it is difficult to distinguish between the competing mechanisms.
Strong magnetic fields play an important role in powering the emission of neutron stars. Nevertheless a full understanding of the interior configuration of the field remains elusive. In this work, we present General Relativistic MagnetoHydroDynamics simulations of the magnetic field evolution in neutron stars lasting 500 ms (5 Alfven crossing times) and up to resolutions of 0.231 km using Athena++. We explore two different initial conditions, one with purely poloidal magnetic field and the other with a dominant toroidal component, and study the poloidal and toroidal field energies, the growth times of the various instability-driven oscillation modes and turbulence. We find that the purely poloidal setup generates a toroidal field which later decays exponentially reaching 1% of the total magnetic energy, showing no evidence of reaching equilibrium. The initially stronger toroidal field setup, on the other hand, loses up to 20% of toroidal energy and maintains this state till the end of our simulation. We also explore the hypothesis, drawn from previous MHD simulations, that turbulence plays an important role in the quasi equilibrium state. An analysis of the spectra in our higher resolution setups reveal, however, that in most cases we are not observing turbulence at small scales, but rather a noisy velocity field inside the star. We also observe that the majority of the magnetic energy gets dissipated as heat increasing the internal energy of the star, while a small fraction gets radiated away as electromagnetic radiation.
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