A Physical Link Between Jet Formation and Hot Plasma in Active Galactic Nuclei

Recent observations suggest that in black hole X-ray binaries jet/outflow formation is related to the hot plasma in the vicinity of the black hole, either in the form of an advection-dominated accretion flow at low accretion rates or in a disk corona at high accretion rates. We test the viability of this scenario for supermassive black holes using two samples of active galactic nuclei distinguished by the presence (radio-strong) and absence (radio-weak) of well-collimated, relativistic jets. Each is centered on a narrow range of black hole mass but spans a very broad range of Eddington ratios, effectively simulating, in a statistical manner, the behavior of a single black hole evolving across a wide spread in accretion states. Unlike the relationship between the radio and optical luminosity, which shows an abruptly break between high- and low-luminosity sources at an Eddington ratio of ~1, the radio emission-a measure of the jet power-varies continuously with the hard X-ray (2-10 keV) luminosity, roughly as L_R \propto L_X^(0.6-0.75). This relation, which holds for both radio-weak and radio-strong active galaxies, is similar to the one seen in X-ray binaries. Jet/outflow formation appears to be closely linked to the conditions that give rise to the hot, optically thin coronal emission associated with accretion flows, both in the regime of low and high accretion rates.Comment: Accepted by ApJ, 8 pages, 3 figure

Sobolev Calibration of Imperfect Computer Models

Calibration refers to the statistical estimation of unknown model parameters in computer experiments, such that computer experiments can match underlying physical systems. This work develops a new calibration method for imperfect computer models, Sobolev calibration, which can rule out calibration parameters that generate overfitting calibrated functions. We prove that the Sobolev calibration enjoys desired theoretical properties including fast convergence rate, asymptotic normality and semiparametric efficiency. We also demonstrate an interesting property that the Sobolev calibration can bridge the gap between two influential methods: $L_2$ calibration and Kennedy and O'Hagan's calibration. In addition to exploring the deterministic physical experiments, we theoretically justify that our method can transfer to the case when the physical process is indeed a Gaussian process, which follows the original idea of Kennedy and O'Hagan's. Numerical simulations as well as a real-world example illustrate the competitive performance of the proposed method

A generalized hand-eye calibration dual quaternion matrix equation

In the field of robotics research, a crucial applied problem is the hand-eye calibration issue. The corresponding matrix equation $AX=YB$ in hand-eye calibration can be equivalently transformed into the dual quaternion equation $q_Aq_X=q_Yq_B$. However, the dual quaternion equation $q_Aq_X=q_Yq_B$ is merely a specific case of the more general dual quaternion matrix equation $AX-YB=C$, which also holds significant applications in system and control theory. Therefore, we in this paper establish the solvability conditions of the dual quaternion matrix equation $AX-YB=C$ and provide a general expression for its solutions when it is solvable. As an application, we investigate the analytical solutions of the dual quaternion matrix equation $AX=YB$. Finally, we validate the main results of this paper through a numerical example

Accretion-modified stellar-mass black hole distribution and milli-Hz gravitational wave backgrounds from galaxy centre

Gas accretion of embedded stellar-mass black holes\,(sBHs) or stars in the accretion disk of active galactic nuclei\,(AGNs) will modify the mass distribution of these sBHs and stars, which will also affect the migration of the sBHs/stars. With the introduction of the mass accretion effect, we simulate the evolution of the sBH/star distribution function in a consistent way by extending the Fokker-Planck equation of sBH/star distributions to the mass-varying scenario, and explore the mass distribution of sBHs in the nuclear region of the galaxy centre. We find that the sBHs can grow up to several tens solar mass and form heavier sBH binaries, which will be helpful for us to understand the black-hole mass distribution as observed by the current and future ground-based gravitational wave detectors\,(e.g., LIGO/VIRGO, ET and Cosmic Explorer). We further estimate the event rate of extreme mass-ratio inspirals\,(EMRI) for sBH surrounding the massive black hole and calculate the stochastic gravitational wave\,(GW) background of the EMRIs. We find that the background can be detected in future space-borne GW detectors after considering the sBHs embedded in the AGN disk, while the mass accretion has a slight effect on the GW background.Comment: 15 pages, 8 figures, Accepted by MNRA