In this paper, we investigate the influences of two continuum radiation pressures of the central engines on the black hole mass estimates for 40 active galactic nuclei (AGNs) with high accretion rates. The two continuum radiation pressure forces, usu
ally believed negligible or not considered, are from the free electron Thomson scattering, and the recombination and re-ionization of hydrogen ions that continue to absorb ionizing photons to compensate for the recombination. The masses counteracted by the two radiation pressures $M_{rm{RP}}$ depend sensitively on the percent of ionized hydrogen in the clouds $beta$, and are not ignorable compared to the black hole virial masses $M_{rm{RM}}$, estimated from the reverberation mapping method, for these AGNs. As $beta$ increases, $M_{rm{RP}}$ also does. The black hole masses $M_{rm{bullet}}$ could be underestimated at least by a factor of 30--40 percent for some AGNs accreting around the Eddington limit, regardless of redshifts of sources $z$. Some AGNs at $z < 0.3$ and quasars at $z ga 6.0$ have the same behaviors in the plots of $M_{rm{RP}}$ versus $M_{rm{RM}}$. The complete radiation pressures will be added as AGNs match $M_{rm{RP}}ga 0.3 M_{rm{RM}}$ due to the two continuum radiation pressures. Compared to $M_{rm{RM}}$, $M_{rm{bullet}}$ might be extremely underestimated if considering the complete radiation pressures for the AGNs accreting around the Eddington limit.
In this paper, we investigated the issue of black hole masses and minimum timescales of jet emission for blazars. We proposed a sophisticated model that sets an upper limit to the central black hole masses $M_{bullet}$ with the minimum timescales $De
lta t^{rm{ob}}_{rm{min}}$ of variations observed in blazars. The value of $Delta t^{rm{ob}}_{rm{min}}$ presents an upper limit to the size of blob in jet. The blob is assumed to be generated in the jet-production region in the vicinity of black hole, and then the expanding blob travels outward along the jet. We applied the model to 32 blazars, 29 of which were detected in gamma rays by satellites, and these $Delta t^{rm{ob}}_{rm{min}}$ are on the order of hours with large variability amplitudes. In general, these $M_{bullet}$ estimated with this method are not inconsistent with those masses reported in the literatures. This model is natural to connect $M_{bullet}$ with $Delta t^{rm{ob}}_{rm{min}}$ for blazars, and seems to be applicable to constrain $M_{bullet}$ in the central engines of blazars.
In the paper, we investigate correlation between broad-line and radio variations for broad-line radio galaxy 3C 120. By the z-transformed discrete correlation function method and the model-independent flux randomization/random subset selection (FR/RS
S) Monte Carlo method, we find that the broad Hbeta line variations lead the 15 GHz variations. The FR/RSS method shows that the Hbeta line variations lead the radio variations by a factor of tau_{ob}=0.34 +/- 0.01 yr. This time lag can be used to locate the position of emitting region of radio outbursts in jet, on the order of ~ 5 light-years, from the central engine. This distance is much larger than the size of broad-line region. The large separation of the radio outburst emitting region from the broad-line region will observably influence the gamma-ray emission in 3C 120.
We demonstrated for the first time the characterization of absolute frequency stability of three reference cavities by cross beating three laser beams which are independently locked to these reference cavities. This method shows the individual featur
e of each reference cavity, while conventional beatnote measurement between two cavities can only provide an upper bound. This method allows for numerous applications such as optimizing the performance of the reference cavity for optical clockwork.
We provide a simple solution to the $mu/B_mu$ problem in the gauge-mediated Next-to-Minimal Supersymmetric Standard Model. In this model the messenger sector contains one pair of $3+bar 3$ and one pair of $2+bar 2$ messengers. These two messenger pai
rs couple to different gauge singlets in the hidden sector in which supersymmetry (SUSY) is broken. Such a gauge-mediation structure can naturally arise in many backgrounds. Because of the two effective SUSY breaking scales $frac{< F_i>}{< M_i>}$ in the messenger sector, the renormalization group evolutions of the soft SUSY breaking parameters can be properly modified, leading to a negative enough singlet soft mass square $m_N^2(Lambda_{EW})$ and hence reasonable $mu/B_mu$ values. In most of the perturbative (up to the GUT scale) parameter region, as a result, the electroweak scale is stabilized and phenomenologically interesting mass spectra of particles and superparticles are obtained. In addition, this model favors large values of $tanbeta$: $5 sim 50$ and a heavy scalar spectrum. With the relatively large $tanbeta$, the light $U(1)_R$ pseudoscalar (mainly appearing in the low-scale gauge-mediated SUSY breaking models) becomes extremely singlet-like, and is no longer a problem in this model. These features apply to all cases of low-, intermediate- and high-scale gauge-mediated SUSY breaking.
