En-Wei Liang

THE MASS-LUMINOSITY RELATION, ACCRETION RATE-LUMINOSITY RELATION, AND EVOLUTIONARY SEQUENCE OF BLAZARS

A sample of 39 blazars each with a well-established rapid variability timescale and bolometric luminosity has been compiled from the literature. Based on the assumption that central supermassive black holes (SMBHs) are Kerr black holes, the upper limits of the SMBHs were estimated. The masses ranged from 10(7.2) to 10(9.4) M-circle dot, showing a distribution of three subclasses: massive flat-spectrum radio quasars (FSRQs) and smaller mass BL Lac objects occupying separate regions, while medium-mass FSRQs and BL Lac objects bridge the gap. We found that the mass-intrinsic luminosity relations for FSRQs and BL Lac objects are the same. Analysis reveals a relationship of log (L-in/L-circle dot)=1.225 log (M/M-circle dot) + 1.500, which mimics a relationship found in the main sequence. We found that the intrinsic accretion rates are quite different between FSRQs and BL Lac objects. The diagram of the intrinsic accretion rate-luminosity relation shows that FSRQs occur in the earlier, high-luminosity, violent phase of the galactic evolution sequence, while BL Lac objects occur in the low-luminosity, late phase of the galactic evolution sequence. Of note is that the results of the mass-luminosity relation of blazars are consistent with the accretion rate-luminosity relation, and together they prove that active galactic nuclei evolve from FSRQs to BL Lac objects. The evolution diagram of blazars derived in this paper seems to be a Hertzsprung-Russell diagram of star evolution.

Supermassive Black Holes in BL Lacertae Objects: Estimated Masses and Their Relation to Nuclear Luminosity

We compile a sample of 13 BL Lac objects for which rapid optical variabilities are reliably established and luminosities of the nuclei and the host galaxies have been well observed by the Hubble Space Telescope (HST). We present a new method for estimating the masses of the supermassive black holes (SMBHs) at the centers of these objects using the rapid optical variability, and find that the masses of the SMBHs range from 10(7.42) to 10(9.19) M(.). This mass range is quite similar to that of dark compact objects in galaxies. To further investigate the reliability of our method, we also compile another sample with nine high-energy gamma-ray emission sources of BL Lac objects and obtain the masses for the SMBHs in these objects using the Dermer & Gehrels method. We find that the masses derived from these two methods are quite similar. These results strongly imply that the estimation of masses of SMBHs by rapid optical variability is reliable. We examine the correlations of the masses with the luminosities of the nuclei and the host galaxies observed by HST, and find that the masses are significantly correlated with the luminosities of the nuclei, but not correlated with the luminosities of host galaxies at all. In addition, we examine the relation between the observed minimal time-scale of variation and the bolometric luminosities of the objects. We find that they obey the Abromowicz & Nobili relation. These results possibly imply that the luminosities of the nuclei are produced by accretion of the central SMBHs.

The hardness-duration correlation in the two classes of gamma-ray bursts

The well-known hardness-duration correlation of gamma-ray bursts (GRBs) is investigated using data from the 4B catalog. We find that, while the hardness ratio and the duration are obviously correlated for the entire set of the 4B catalog, they are not at all correlated for the two subsets divided at the duration of 2 seconds. However, for other subsets with comparable sizes, the two quantities are significantly correlated. The following conclusions are thus reached: (1) the existence of two classes of GRBs is confirmed; (2) the hardness ratio and the duration are not at all correlated for any of the two classes; (3) different classes of GRBs have different distributions of the hardness ratio and the duration, and it is this difference that causes the correlation between the two quantities for the entire set of bursts.

Correlations between various hardness ratios of gamma-ray bursts

We study correlations between various hardness ratios of gamma-ray bursts (GRBs) and investigate if there are any differences between the short- and long-duration classes of the objects in the distributions of the ratios. The results show that most of the hardness ratios are mutually correlated, but that the ratio defined at the lower energy bands is not correlated with those defined at the higher energy bands, the most significant correlations come from those ratios defined with both the lower and higher energy bands. It a also shown that the short-duration bursts tend to have higher values of hardness ratios. We reach these conclusions that the slope of the higher part of the spectrum of most GRBs is independent of that of the lower part; emissions at higher energy bands from the bursts of both short- and long-duration classes are significantly different for different sources, but radiations at lower energy bands are similar; the spectra of the short-duration bursts is harder than that of the long-duration bursts. A possible interpretation for these results involves Doppler boosting in the relativistic beaming model. In addition, the study reveals that hardness ratios of the long-duration class are more mutually correlated than these of the short-duration class; the data of hardness ratios for the long-duration class are much less scattered than those of the short-duration class. It is found that this difference is at least partially due to measurement errors.

Masses, dimensionless Kerr parameters, and emission regions in GeV gamma-ray-loud blazars

We have compiled sample of 17 GeV gamma-ray-loud blazars, for which rapid optical variability and gamma-ray fluxes are well observed, from the literature. We derive estimates of the masses, the minimum Kerr parameters a(min), and the size of the emission regions of the supermassive black holes (SMBHs) for the blazars in the sample from their minimum optical variability timescales and gamma-ray fluxes. The results show that (1) the masses derived from the optical variability timescale (M(H)) are significantly correlated with the masses from the gamma-ray luminosity (M(H)(KN)); (2) the values of a(min) of the SMBHs with masses M(H)greater than or equal to10(8.3) M(circle dot)(three out of 17 objects) range from similar to0.5 to similar to1.0, suggesting that these SMBHs are likely to be Kerr black holes. For the SMBHs with M(H) 0, the sizes of the emission regions are almost within the horizon (2r(G)) and marginally bound orbit (4r(G)), while for those with a(min)=0 they are in the range (4.3-66.4)r(G), extending beyond the marginally stable orbit (6r(G)). These results may imply that (1) the rotational state, the radiating regions, and the physical processes in the inner regions for the two kinds of SMBH are significantly different and ( 2) the emission mechanisms of GeV gamma-ray blazars are related to the SMBHs in their centers but are not related to the two different kinds of SMBH.

Gamma-ray Emission from the γ-ray-loud BL Lac Objects

Using the HST observation data of BL Lac objects by Urry et al. and gamma-ray observation data, we find that there is a correlation between Fgamma and F-O(nuclei) for gamma-ray-loud BL Lac objects (correlation coefficients: gamma = 0.63, p = 4.0 x 10(-2)), but no correlation between F-gamma and F-O(host), where F-O(nuclei) and F-O(host) are the fluxes of nuclei and host galaxy in V-band. For 19 gamma-ray-loud BL Lac objects with observed spectral index in multi-wavebands, the spectral index correlations between any two bands are as follow: (1) there is a strong correlation between alpha(gamma) and alpha(K) for 15 BL Lac objects (gamma = 0.84, p = 3.11 x 10(-4)); (2) the correlation between alpha(gamma) and alpha(O) for 12 BL Lac objects is gamma = 0.82, p = 1.5 x 10(-3); (3) there is no correlation between alpha(gamma), and alpha(x) for 16 BL Lac objects. The results, together with characteristic double-humped shape of their SEDs, show that the synchrotron self-Compton mechanism might be a main mechanism for the gamma-ray emission of the BL Lac objects. The electrons emitting IR and optical radiation via synchrotron are also responsible for upscattering these photons to gamma-rays, and a variability in IR-optical regime should be accompanied by a change in the gamma-rays.

A Restriction on the Duration and Peak Energy of Gamma-Ray Bursts

Two dimensional distributions of T-90 versus E-peak (or E-break) for three bright GRB samples have been investigated. The result shows that although both T-90 and E-peak (or E-break) each span over a wide range, they are restricted to the region log(T-90) less than or equal to -log(E-peak) + 5.24. This cannot be explained by the current fireball model. It may represent a constraint on the fireball model.