Many variables are pulsation variables.They can be divided into several types or subtypes depend on the pulsation period.The pulsation variables with period less than one day have three types:RR Lyr type stars,delta Sct type stars and beta Cep type stars.The observation and research of RR Lyr type stars have long history,and the understanding of this type stars is well.The studies of delta Sct type stars are pop because of their short pulsation period and different pulsation modes.The number of beta Cep type stars is not many and only about 100 ones were found.The research on the period of this type is few. In this paper,we used the O-C method,analyzed some stars of delta Sct type and obtained the results as follow: 1.We proposed a new fitting formulae to fit the periodic change which caused by the light travel time effect in the O-C curve.And our new method can fit the data well even when the eccentricity of the orbit is high. 2.After observed and analyzed the SX Phe type star DY Peg,we found a continuous decrease of period at a rate of -8.8*10^-12days/day and a periodic change with about 41.7yrs.The periodic component could be introduced as the existence of a companion which is likely a brown dwarf. 3.After observed and analyzed the delta Sct type stars AN Lyn,we found a continuous increase of period at a rate of 1.44*10^-10days/day which was larger than the values of other delta Sct type stars.Periodic change with 23.2yrs existing in the O-C curve indicated a companion with mass greater than 0.936Msun.We considered it may be a compact object.The phenomenon of the periodic change of pulsation amplitude of AN Lyn were also discussed and explained. 4.According the the statistical study of the period change of more than 100 RRab type stars,we found most stars with high value of period change show low metallicity which were less than -1.0,and presumed that the metallicity would re- strict the change of the pulsation period.We also found a possible relation between the metallicity and pulsation period,and the upper limit of mean magnitude for the RR Lyr type star with the same amplitude.
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