The Study On The Variations Of The Flux Density And Spectral Index Of Millisecond Pulsars

The pulsar is a high-speed rotating neutron star with a high density in the universe.We study the radiation mechanism of the pulsar by the variation of the flux density.It is found that the flux density of pulsar has long-term variation.Some astronomers believe that this phenomenon is due to the scintillation of the interstellar medium and the other people think that it due to the own attribute of the pulse.Recently,most astronomers believe that the change is caused by the refraction interstellar scintillation.In general,the flux density of the pulsar decreases with increasing frequency and showing a power-law spectrum.It is a non-thermal radiation spectrum,is the spectral index.This is a typical feature of high-energy electron synchronous curvature radiation and the radiation signal has a high of linear polarization.But so far,the spectral indexes change and the scope of specific scope are not studied very much.In this paper,we use the data of PSR J1045-4509,PSR J1643-1224,PSR J1824-2452 and PSR J1939+2134,which are observed by the Parkes Observatory in Australia.Firstly,we derived the 4 millisecond pulsars in three bands at the mean flux density changes over time.We present that the flux density of the millisecond pulsars showed a long-term change in each frequency band(10cm,20 cm 50cm),which we believe may be due to refraction interstellar scintillation.The flux density decreases with the increasing frequency.Secondly,we calculated the structure functions of the mean flux density of these millisecond pulsars at 10 cm,20 cm and 50 cm.we found that the structure functions of the mean flux density increased with time scale in each frequency band and followed by a saturation value.We have obtained the slope of the structure function for each millisecond pulsar,the scintillation time scale and the spectral index of the kolmogorov turbulence spectrum of the scattering medium.We found that the scintillation time scale of millisecond pulsars decreases with increasing frequency of observation.The ? values are distributed between 3 to 4,and the average is 3.68,which is in good agreement with the theoretical ? = 11/3.Therefore,we get that the long-term variation of the flux density of these pulsars is mainly caused by the turbulence of the continuous scattering medium in the large scale range.The spectral indices of previous studies are the average spectral indices of the total profile of each pulsar,but we have calculated the spectral indices of the above four millisecond pulsars in three bands,and we obtained the relationship between the spectral indices and the time,the average value,distribution range of spectral indices,and distribution of spectral indices over all bands.We find that the spectral index of the millisecond pulsar is in good agreement with the power-law relationship in most cases,but there are a few inverse spectra that show that the spectrum deviates from the power-law spectrum in the observation.We think this may be caused by the observation error.We also found that the spectral index calculated using the data at all bands at the same time is more stable than the spectral index calculated by the individual sub-bands.