Pulsar B0531 + 21 in the Crab Nebula

The Crab Nebula and its pulsar PSR B0531 + 21 is the space laboratory for the study of fundamental physical processes. From the beginning of the current century up to date, the giant pulses of the pulsar in the Crab Nebula are regu-larly observed on the Large Phased Array of the Pushchino Radio Astronomy Observatory of the Lebedev Physical Institute at a frequency 111 MHz. The connection between the scattering time scale of radio pulses and the dispersion measure of the pulsar, which was established earlier together with Jodrell Bank, is confirmed. The observed variations in the scattering of radio pulses and their partial correlation with the dispersion measure are explained by the eclipse of the pulsar by dense plasma clouds with fluctuations in the electron density significantly exceeding the corresponding fluctuations in the interstellar medium. The question of a possible connection between period failers (glitches), dispersion measure variations, radio pulses scattering and gam-ma-ray flares is discussed.


Introduction
The Crab Nebula was first observed in 1731 by the English physicist and amateur astronomer John Bevis. It is included in the catalog of nebulae compiled by Charles Monsieur in 1758 as object M1. The Crab Nebula was so named by Lord Ross in 1844. Observing the nebula with high resolution, he noticed a structure similar to a crab claw. It is believed that it is a remnant of the hydrogen-rich type II supernova explosion, observed in China in 1054. In 1949, radio astronomers Bolton, Stanley, and Slee identified the Crab Nebula as a radio source. Buhler great detail. It is therefore one of our prime laboratories to study non-thermal processes in the Universe. Many discoveries have been made in the Crab and then been seen in other non-thermal sources (including active galactic nuclei, A gamma ray bursts and X-ray binaries) such as polarized synchrotron radiation or pulsed optical emission (Shklovsky 1953, Cocke et al. 1969). True to this legacy two remarkable discoveries have been made in the last years. Very high-energy (VHE & 100 GeV) gamma-ray emission has been detected from the pulsar, and high-energy (HE & 100 MeV) gamma-ray flares have been discovered from the nebula. These phenomena have not been observed in any other pulsar wind nebula to date".
The Crab Nebula pulsar PSR B0531 + 21 (Crab Pulsar) was discovered by Staeilin and Reifenstein in 1968 as a radio source of giant pulses (GPs) 1 , rather than as a periodic source [2]. Fourier analysis did this later.  [7]. In particular, we show that the scattering of GPs of the Crab pulsar depends not only on the DM, but also on the degree of plasma inhomogeneity. The possible relationship between step changes in the rotation speed ("glitch"), the DM variations and scattering time scale is discussed. Results of the search for a connection between gamma-ray flares and disturbances in the pulsar magnetosphere are given.

Observations and Results
Systematic observations of the Crab Pulsar at a frequency of 111 MHz are carried out on LPA radio telescope from September 2002 up to date. The observations were initially carried out using a 128-channel spectrum analyzer with a channel bandwidth of 20 kHz, a total bandwidth 2560 kHz, and a readout inter- GPs are analyzed using a special program that allows us to determine the scat- 1 The working definition of giant pulses is a flux density in a single pulse which is more than 10 times the mean flux density. International Journal of Astronomy and Astrophysics tering time scale pulsar radio pulses by simulating the passage of a pulse through a scattering medium. A theoretical scattering pulse profile was generated by successively convolving a gaussian profile, representing the intrinsic pulse, with: 1) an impulse scattering function of the form exp(−t/τ sc ); 2) a gaussian function representing the effects of interstellar dispersion across the filter bandpass; 3) an exponential function representing the post-detector RC time constant. The theoretical profile was least-squares fitted to the observed profile, with τ sc as the adjustable parameter [8].
The scattering values for each GP were averaged over five days of observations. The mean scattering parameters were compared with dispersion measures derived from data obtained at Jodrell Bank Observatory (JBO) 3 . The monthly JBO data were interpolated to the comparison data.      The scattering time scale τ sc depends on: the electron density n e ; the relative inhomogeneity of the medium Δn e /n e ; the dispersion measure DM, (or the distance between the source and the observer d); the frequency of the radio signal ν [10].
In an environment, where the parameter Δn e /n e is almost constant, the scattering at a given frequency is proportional to the square of the DM: This is what is observed for most pulsars [19]. The scattering variations in the first approximation are proportional to the variations of DM: It follows from the Formula (2) that the scattering can be different with the same DM.
In the Crab Nebula, the parameter (Δn e /n e ) is subject to significant changes, so the variations of the τ sc parameter depend not only on the dispersion measure, but also on the degree of plasma inhomogeneity (Δn e /n e ): The spectrum of electron density fluctuations B. Ja. Losovsky International Journal of Astronomy and Astrophysics is the turbulence coefficient [20]; q-spatial frequency, q = 2π/l-where l is the character scale of turbulence α-spectral index of the electron-density irregularity.
where β-spectral index of pulse broadening ( ) Here ν is the frequency in GHz, Δν is the decorrelation bandwidth in MHz, d is in kpc.

Measurements of
The scattering τ sc and the decorrelation bandwidth Δν are related by the ratio 2πτ sc Δν = 1. In particular, for the frequency ν = 111 MHz and τ sc = 1/(2πΔν) turbulence level 2 2 0.00198 where τ sc is in milliseconds. We accepted mean scattering parameter τ sc = 10 ms for the passive period and τ sc = 100 ms for the active period. Error estimated as 20%.
According to Yao et al. [22] distance to Crab pulsar d = 1.311 kpc (Err = 14%) In 2002-2007, during a quiet period 2 n C = 0.0115 ± 0.0038 m −7 . The variations of DM measure ΔDM were 0.035, which at a radius of nebular 1.7 pc corresponds to Δn e ~ 0.02 cm −3 and this is consistent with the estimate [18].
If, according to [23], the value of the dispersion measure of the Crab nebula can be taken as 4 pc/cm 3 , then n e ~ 2 cm −3 and Δn e /n e ~ 0.01. Turbulence in the disturbed region higher than in quiet ones and much higher than in the interstellar medium.

Discussion
Pulsars The braking index n is expected to be 3 in the case of braking by pure dipole radiation and 1 in the case of pulsar wind dominated torque. Deviations from value 3 for Crab pulsar (n ~ 2.5) indicates, than the part of the torque on the pulsar is due to the outflow of particles.
Jumping irregularities in the rotation of the pulsar (glitches) can be of two types: discrete glitches and slow glitches. Both types of glitches cause accelerated rotation of the pulsar, which occurs against the background of secular deceleration of the neutron star. With discrete glitches, the frequency increases suddenly, and then follows an exponential decrease in frequency to the previous value.
Slow glitches are associated with slow frequency fluctuations.
The hypothesis about the connection of random irregularities of period with processes in the magnetosphere was firstly expressed Manchester and Taylor in the book "PULSARS" [10]. There are some models, describing the origin of glitches. One model treats glitches as star quakes, caused by the rearrangement of the flattened crust, which tends to become spherical, as the star's rotation slows down. Another model considers a neutron star as a reservoir, filled with a superfluid, the mass of which, when the pulsar's rotation slows down, transmits the angular momentum to the crust, which leads to a glitch [24].
The problem of the relationship between glitches, scattering changes, dispersion measures and gamma-ray bursts is discussed in detail Cadez et al. [25].
They devoted their work to the study of the pulsar in the Crab nebula, using radio data from the Jodrell Bank Observatory from 1998 to 2014 together with optical observations of the pulsar, using the ultra-fast photon counter, mounted on the Copernico telescope at the Astrophysical Observatory in Asiago (Italy) in 2008 and at the Southern European Telescope at La Silla observatory (Chile) in 2009. Analysis of the data showed, that jumps in the braking index are associated with large glitches, when the relative change in the rotational speed of the pulsar exceeds 10 −8 . A similar conclusion was obtained by Lyne et al. with the mean value n = 2.34 [26]. Different braking index values 2.45 and 2.57 are also reported between glitches by Kou and Tong [27]. The delay in the variations of the dispersion measure relative to the variations of the braking index is ~1010 days and is explained by the time of ionization of the nebula by the pulsar wind ( Figure 4).
The model of Cadez et al. [25] suggests, that glitches and subsequent varia-  increase in the dispersion measure. Intermediary models have been discussed by Kou and Tong [27]. They consider that glitches are related to changes in interior of the neutron stars, but may lead to some effect in the outer magnetosphere. In turn, plasma instabilities in the nebula can disrupt the configuration of magnetic field lines, when fields of opposite polarity are pressed together, and cause gamma-ray flare, similar to flares in the solar corona. The same opinion says Buhler and Blangdford [1]: "The gamma-ray flares are therefore likely connected to explosive reconnection events triggered by current instabilities". Striany et al. also support this idea [28], but they note: "However, evidence for magnetic field reconnection events in the Crab Nebula is elusive, and no optical or X-ray emission in coincidence with the gamma-ray flaring has been unambiguously detected to date (e.g., Weisskopf et al. 2012)". According to our data ( Figure 3) gamma-flares have tendency to concentrate during the period of enhanced disturbances in the Crab Nebula, that can be considered as support of this model. As for the correlation between of pulsar glitches and gamma-ray flares Buhler and Blandford [1] write: "The time scale of the recurrence of pulsar glitches is similar to the recurrence of the gamma-ray flares, however, there is no obvious correlation in time between these two events".

Conclusions
The scattering of the Crab pulsar radio emission at a frequency of 111 MHz ac- Turbulence in the disturbed region is higher than in quiet ones and much be higher than in the interstellar medium.
Various types of pulsar radio emission irregularities can be explained by physical processes occurring in the pulsar's magnetosphere. Perturbations in the pulsar's magnetosphere can lead to ejection of charged particles into the Nebula, lead to instability of the plasma, disrupt the configuration of the magnetic field lines and cause gamma-ray flares. According to our data gamma-flares have tendency to take place during the period of enhanced disturbances in the Crab Nebula that can be considered as support of this model. New observations are needed to support this hypothesis.

Funding
This work was supported by the research program of the Presidium of the Russian Academy of Sciences "Non-stationary phenomena in the objects of the Universe"