The Rapid X-ray Variability Of X-ray Binaries And The Statistics Of GRB Luminosity And Redshift

This thesis includes two parts. The first part (from Chapter1to Chapter4) is about the study of rapid X-ray variability, and the second part(from Chapter5to Chapter7) is about the statistic study of GRB.Observations of X-ray binaries show considerable variability on a wide range of time scales in all wavelengths, and down to less than a millisecond in X-rays. Aperiodic phenomena (QPOs and noise) are potential probes of the strong-gravity dominated flow dynamics. As observationally there are correlated spectral and timing phenomena covering a range of time scales. Some models have been put forward to explain the phenomena by, respectively, orbital motions and accretion-flow instabilities. A brief overview of phenomenology is presented in chapter1. In Chapter2, We study the kHz QPOs and the BLN in the0.5-16Hz range observed simultaneously on the HB and on the upper NB of the brightest LMXB Scorpius X-1with the observations performed with the RXTE. We find that the twin kHz QPO frequencies are positively correlated with the flux variations taking place on the BLN time scales on the HB, in contrast to the anti-correlation held on the time scale of the normal branch oscillation (NBO) on the NB reported previously, suggesting that although they occur in sequence along the color-color tracks, the BLN and the NBO are of different origins. We also show the evidence that the frequency separation between the twin kHz QPOs decreases with the flux by2-3Hz on the BLN time scales, which is consistent with the trend on the longer time scale that the Z source traces the HB. This further suggests that the flux variation associated with the BLN originates from the mass accretion rate variation in the disk accretion flow. We discuss the implications of these results for our understanding of the BLN. In Chapter3, Optical observations of Sco X-1with exposure time around0.5s were performed with the1.56m telescope of the Shanghai Astronomical Observatory in2008. With these observations, we studied the fluctuation of the optical flux on three short timescales (5s,10s,100s), respectively. We found the standard deviations of fluctuations on three timescales differ from that of Gaussian distribution by7σ,5σ and3σ. It suggests that the variation of the intensity on some short timescales differ from pure statistical fluctuation, which indicates intrinsic variability in the optical emission. Finally, we give some discussions and an outlook on study of rapid variabilities in Chapter4.Gamma-ray bursts (GRBs) are observationally short and intense gamma-rays flashes ini-tially (prompt emission) followed by lower wavebands electromagnetic emission (afterglow). The progenitors of long GRBs are believed to be rotating massive stars mainly because of GRB-SN connection, while the progenitors of short GRBs could be compact binaries. A brief overview on the progress in GRB observations and theories will be given in Chapter5. In Chapter6, with a phenomenological investigation on these two complexities:(ⅰ) the evolving connection between GRB rate and cosmic star formation rate and (ⅱ) observational selection effects due to telescope thresholds and redshift measurements, we constrain and discriminate two popular competitive LF models (i.e., broke-power-law LF and single-power-law LF with an exponential cutoff at low luminosities) with Swift GRBs. We find that the broken-power-law LF could be more favored by the observation. For an extra evolution effect expressed by a factor (1+z)δ, if the matallicity of GRB progenitors is lower than～0.1Z(?) as expected by some collapsar models, then there may be no extra evolution effect other than the metallicity evolution (i.e.,δ approaches to be zero). Alternatively, if we remove the theoretical metallicity requirement, then a relationship between the degenerate parameters δ and Zmax can be found, very roughly,δ-2.4(Zmax/Z(?)-0.06). This indicates that an extra evolution could become necessary for relatively high metallicities. In Chapter7, we suggest a phenomenological formula to simultaneously describe the flux-and redshift-dependence of the selection effect. Then, we calibrate the GRB event rate to the star formation rate (SFR) at relatively low redshifts. By extending this calibration to high-redshift range, we further derive a high-redshift star formation history with Swift GRBs.