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Register a new userRelating Braking Indices of Young Pulsars to the Dynamics of Superfluid Cores
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Added by
Geanderson Carvalho Mr
Publication date
2018
fields
Physics
and research's language is
English
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Pulsars are stars that emit electromagnetic radiation in well-defined time intervals. The frequency of such pulses decays with time as is quantified by the {it braking index} ($n$). In the canonical model $n = 3$ for all pulsars, but observational data show that $n eq 3$, indicating a limitation of the model. In this work we present a new approach to study the frequency decay of the rotation of a pulsar, based on an adaptation of the canonical one. We consider the pulsar a star that rotates in vacuum and has a strong magnetic field but, differently from the canonical model, we assume that its moment of inertia changes in time due to a uniform variation of a displacement parameter in time. We found that the braking index results smaller than the canonical value as a consequence of an increase in the stars displacement parameter, whose variation is small enough to allow plausible physical considerations that can be applied to a more complex model for pulsars in the future. In particular, this variation is of the order of neutron vortices creep in rotating superfluids. When applied to pulsar data our model yielded values for the stars braking indices close to the observational ones. The application of this approach to a more complex star model, where pulsars are assumed to have superfluid interiors, is the next step in probing it. We hypothesize that the slow expansion of the displacement parameter might mimic the motion of core superfluid neutron vortices in realistic models.
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Recently, Parthsarathy et al. analysed long-term timing observations of 85 young radio pulsars. They found that 11 objects have braking indices ranging $sim 10-100$, far from the classical value $n=3$. They also noted a mild correlation between measured value of $n$ and characteristic age of a radio pulsar. In this article we systematically analyse possible physical origin of large braking indices. We find that a small fraction of these measurements could be caused by gravitational acceleration from an unseen ultra-wide companion of a pulsar or by precession. Remaining braking indices cannot be explained neither by pulsar obliquity angle evolution, nor by complex high-order multipole structure of the poloidal magnetic field. The most plausible explanation is a decay of the poloidal dipole magnetic field which operates on a time scale $sim 10^4-10^5$ years in some young objects, but has significantly longer time scale in other radio pulsars. This decay can explain both amplitude of measured $n$ and some correlation between $n$ and characteristic age. The decay can be caused by either enhanced crystal impurities in the crust of some isolated radio pulsars, or more likely, by enhanced resistivity related to electron scattering off phonons due to slow cooling of low-mass neutron stars. If this effect is indeed the main cause of the rapid magnetic field decay manifesting as large braking indices, we predict that pulsars with large braking indices are hotter in comparison to those with $napprox 3$.
The departure of all measured pulsar braking indexes from the canonical dipole value 3 has been attributed to several causes in the past. Careful monitoring of the Crab pulsar has revealed permanent changes in the spin-down rate which are most likely the accumulation of small jumps in the angle $alpha$ between the magnetic and spin axis. Recently, a large permanent change in the braking index of the in the Crab twin pulsar B0540-69 has been reported, and an analogous phenomenon seen in the high-field pulsar PSR 1846-0258 has been seen following a glitch, while another similar event (in PSR J119-6127) needs to be confirmed. We argue in this work that a common physical origin of all these observations can be attributed to the counter-alignment of the axis without serious violations of the observed features and with very modest inferred values of the hypothesized jump in the $alpha$ angle. In addition, detected increases of the X-ray luminosities after the events are an additional ingredient for this interpretation. We argue that a component of a time-dependent torque has been identified, being an important ingredient towards a full solution of observed pulsar timing behavior which is in search of a consistent modeling.
Braking indices of pulsars present a scientific challenge as their theoretical calculation is still an open problem. In this paper we report results of a study regarding such calculation which adapts the canonical model (which admits that pulsars are rotating magnetic dipoles) basically by introducing a compensating component in the energy conservation equation of the system. This component would correspond to an effective force that varies with the first power of the tangential velocity of the pulsars crust. We test the proposed model using data available and predict braking indices values for different stars. We comment on the high braking index recently measured of the pulsar J1640-4631.
The current understanding of the spin evolution of young pulsars is reviewed through a compilation of braking index measurements. An immediate conclusion is that the spin evolution of all pulsars with a measured braking index is not purely caused by a constant magnetic dipole. The case of PSR J1734-3333 and its upward movement towards the magnetars is used as a guide to try to understand why pulsars evolve with n < 3. Evolution between different pulsar families, driven by the emergence of a hidden internal magnetic field, appears as one possible picture.
The observed braking index n_{obs} which had been determined for a few young pulsars, had been found to differ from the expected value for a rotating magnetic dipole model. Also, the observational jerk parameter, determined for two of these pulsars, disagree with the theoretical prediction m_{obs} = 15 in both cases. We propose a simple model able to account for these differences, based on a growth of the torque function K = -(dot Omega)/(Omega^{n}), under the constraint that n_{obs} is a constant. We show that there is observational evidence supporting the latter hypotesis, and derive initial values for several physical quantities for the four pulsars whose n_{obs} have been measured.
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