Phase Lag and Coherence Function of X-ray emission from Black Hole Candidate XTE J1550-564

We report the results from measuring the phase lag and coherence function of X-ray emission from black hole candidate (BHC) XTE J1550-564. These X-ray temporal properties have been recognized to be increasingly important in providing important diagnostics of the dynamics of accretion flows around black holes. For XTE J1550-564, we found significant hard lag --- the X-ray variability in high energy bands {\em lags} behind that in low energy bands --- associated both with broad-band variability and quasi-periodic oscillation (QPO). However, the situation is more complicated for the QPO: while hard lag was measured for the first harmonic of the signal, the fundamental component showed significant {\em soft} lag. Such behavior is remarkably similar to what was observed of microquasar GRS 1915+105. The phase lag evolved during the initial rising phase of the 1998 outburst. The magnitude of both the soft and hard lags of the QPO increases with X-ray flux, while the Fourier spectrum of the broad-band lag varies significantly in shape. The coherence function is relatively high and roughly constant at low frequencies, and begins to drop almost right after the first harmonic of the QPO. It is near unity at the beginning and decreases rapidly during the rising phase. Also observed is that the more widely separated the two energy bands are the less the coherence function between the two. It is interesting that the coherence function increases significantly at the frequencies of the QPO and its harmonics. We discuss the implications of the results on the models proposed for BHCs.Comment: To appear in ApJ Letter

Testing the Universal Structured Jet Models of Gamma-Ray Bursts by BATSE Observations

Assuming that the observed gamma-ray burst (GRB) rate as a function of redshift is proportional to a corrected star formation rate, we derive the empirical distribution of the viewing angles of long BATSE GRBs, $P^{\rm em}(\theta)$, and the distribution of these bursts in the plane of $\theta$ against redshift, $P^{\rm em}(\theta, z)$, by using a tight correlation between $E_{\gamma}$) and $E_{\rm p}^{'}$). Our results show that $P^{\rm em}(\theta)$ is well fitted by a log-normal distribution centering at $\log \theta/{\rm rad}=-0.76$ with a width of $\sigma_{\log \theta}=0.57$. We test different universal structured jet models by comparing model predictions with our empirical results. To make the comparisons reasonable, an "effective" threshold, which corresponds to the sample selection criteria of the long GRB sample, is used. We find that the predictions of a two-Gaussian jet model are roughly consistent with our empirical results. A brief discussion shows that cosmological effect on the $E_{\gamma}-E_{\rm p}^{'}$ relation does not significantly affect our results, but sample selection effects on this relationship might significantly influence our results.Comment: 5 pages, 6 figures, accepted for publication in A