Observability of zero-angular-momentum sources near Kerr black holes

We revisit monochromatic and isotropic photon emissions from the zero-angular-momentum sources (ZAMSs) near a Kerr black hole. We investigate the escape probability of the photons that can reach to infinity and study the energy shifts of these escaping photons, which could be expressed as the functions of the source radius and the black hole spin. We study the cases for generic source radius and black hole spin, but we pay special attention to the near-horizon (near-)extremal Kerr ((near-)NHEK) cases. We reproduce the relevant numerical results using a more efficient method and get new analytical results for (near-)extremal cases. The main non-trivial results are: in the NHEK region of a (near-)extremal Kerr black hole, the escape probability for a ZAMS tends to $$\frac{7}{24}\approx 29.17\%$$ 7 24 ≈ 29.17 % , independent of the NHEK radius; at the innermost of the photon shell (IPS) in the near-NHEK region, the escape probability for a ZAMS tends to $$\begin{aligned} \frac{5}{12} -\frac{1}{\sqrt{7}} + \frac{2}{\sqrt{7}\pi }\arctan \frac{1}{\sqrt{7}}\approx 12.57\% . \end{aligned}$$ 5 12 - 1 7 + 2 7 π arctan 1 7 ≈ 12.57 % .

The source parameters of earthquakes of Bishkek geodynamic proving ground (Northern Tien Shan)

Based on the method of polarity of signs of P-waves, the focal mechanisms of 1674 earthquakes with M ≥ 1.6, which occurred on the territory of the Bishkek geodynamic proving ground (BGPG) from 1994 to 2020, were determined. Some characteristics of the complete catalogue are presented. Quantitative distributions by the type of mechanisms and diagrams of azimuths of the main stress axes are constructed. A variety of focal mechanism of earthquake is observed, most of them are reverse fault, oblique reverse fault, and horizontal strike-slip fault. The compression axis for most of the events has a north-northwest direction and a sub-horizontal position. For 183, dynamic parameters (DP, source parameters) were obtained: spectral density Ω0, corner frequency f0, scalar seismic moment M0, source radius (Brune radius) r, and stress drop Δσ. The correlations between DP and energy characteristic (magnitude) and scalar seismic moment are investigated. The smallest correlation coefficient was obtained for stress drop.

Liverpool-Maidanak monitoring of the Einstein Cross in 2006–2019

Quasar microlensing offers a unique opportunity to resolve tiny sources in distant active galactic nuclei and study compact object populations in lensing galaxies. We therefore searched for microlensing-induced variability of the gravitationally lensed quasar QSO 2237+0305 (Einstein Cross) using 4374 optical frames taken with the 2.0 m Liverpool Telescope and the 1.5 m Maidanak Telescope. These gVrRI frames over the 2006–2019 period were homogeneously processed to generate accurate long-term multi-band light curves of the four quasar images A–D. Through difference light curves, we found strong microlensing signatures. We then focused on the analytical modelling of two putative caustic-crossing events in image C, finding compelling evidence that this image experienced a double caustic crossing. Additionally, our overall results indicate that a standard accretion disc accounts reasonably well for the brightness profile of UV continuum emission sources and for the growth in source radius when the emission wavelength increases: Rλ ∝ λα, α = 1.33 ± 0.09. However, we caution that numerical microlensing simulations are required before firm conclusions can be reached on the UV emission scenario because the VRI-band monitoring during the first caustic crossing and one of our two α indicators lead to a few good solutions with α ≈ 1.

Microlensing of radially pulsating stars

ABSTRACT In this paper, we study the microlensing of radially pulsating stars. It is possible to discern and characterize the properties of distant, faint pulsating stars using high-cadence microlensing observations. By combining the stellar variability period with microlensing, we can obtain the source distance, type and radius, and we can better determine the lens parameters. Considering the variations in the radius and surface temperature of radially pulsating stars periodically, their microlensing light curves can be obtained by multiplying the magnification factor with a variable finite size effect by the intrinsic brightness curves of the pulsing source. The variable finite size of the source due to pulsation can be significant for transit and single microlensing with caustic-crossing features. This type of deviation in the magnification factor is considerable when the ratio of the source radius to the projected lens–source distance is in the range of ρ⋆/u ∈ [0.4, 10] and when its duration is short and of the same order as the time of crossing the source radius. Other deviations due to variable source intensity and its area make coloured and periodic deviations, which are asymmetric with respect to the signs of the pulsation phase. The positive phase makes deviations with larger amplitude than the negative phase. These deviations dominate in filters with short wavelengths (e.g. the B band). The position of the magnification peaks in the microlensing of variable stars varies and this displacement differs in different filters.

On the stress drop in North Eurasia earthquakes source-sites versus specific seismic energy

A generalization of the results on the stress drop and the specific seismic energy for the earthquakes in Northern Eurasia has been made. The relationship of these parameters with the seismic moment and the magnitude has been analyzed. Detailed studies for the Northern Tien Shan (Bishkek geodynamic polygon) were carried out, the values of the dynamic parameters of the sources for 183 earthquakes of various energy classes (K = 8.7–14.8) were obtained: angular frequency, spectral density parameter, scalar seismic moment, source radius, stress drop level, seismic energy and specific seismic energy. Two models have been used to compute the source radius and the stress drop – the Brune approach and the improved Madariaga–Kaneko–Shearer model. For relatively weak events, a power-law dependence (regression) of the stress drop on the scalar seismic moment M0 has been identified, that complies with the results on the power-law dependence of the specific seismic energy on M0 in a number of other regions of Northern Eurasia. The relationship between the type of source movement and the stress drop level has been noted as well.

Control of light gas releases in ventilated tunnels

The release of buoyant harmful gases within enclosed spaces, such as tunnels and corridors, may engender specific health, industrial and transportation risks. For safety, a simple ventilation strategy for these spaces is to impose a flow along the tunnel, whose velocity is defined as ‘critical’, that confines the front of harmful buoyant gases immediately downstream of the source of emission. Determining the critical velocity as a function of the geometrical and dynamical conditions at the source is a fundamental fluid mechanics problem which has yet to be elucidated; this problem concerns the dynamics of non-Boussinesq releases relating to large differences between the densities of the buoyant and the ambient fluids. We have investigated this problem theoretically, by means of a simplified model of a top-hat plume in a cross-flow, and in complementary experiments by means of tests in a reduced-scale ventilated tunnel, examining releases from circular sources. Experimental results reveal: (i) the existence of two flow regimes depending on the plume Richardson number at the source $\unicode[STIX]{x1D6E4}_{i}$, one for momentum-dominated releases, $\unicode[STIX]{x1D6E4}_{i}\ll 1$, and a second for buoyancy-dominated releases, $\unicode[STIX]{x1D6E4}_{i}\gg 1$, with a smooth transition between the two; and (ii) the presence of relevant non-Boussinesq effects only for momentum-dominated releases. All these features can be conveniently predicted by the plume-based model, whose validity is, strictly speaking, limited to releases issuing from ‘small’ sources in ‘weak’ ventilation flows. Analytical solutions of the model are generally in good agreement with the experimental data, even for values of the governing parameters that are beyond the range of validity for the model. The solutions aid to clarify the effect of the source radius, and reveal interesting behaviours in the limits $\unicode[STIX]{x1D6E4}_{i}\rightarrow 0$ and $\unicode[STIX]{x1D6E4}_{i}\rightarrow \infty$. These findings support the adoption of simplified models to simulate light gas releases in confined ventilated spaces.

S-WAVE SPECTRAL ANALYSIS AND ESTIMATION OF SPECTRAL PARAMETERS IN NORTHWESTERN GREECE

During a 12-month period (August 1998 - June 1999), a dense microseismic network of 44 portable seismographs, was installed in Epirus - Northwestern Greece, by the Seismological Laboratory, of the University of Patras and recorded 1368 earthquakes. We selected a subset of 200 well recorded events, with duration magnitude ranging from 1.61 to 2.92 and focal depths ranging from a few hundred meters to 35km; the majority was in the 0-10km range. This study uses this high quality dataset to (i)calculate the earthquake spectra and source parameters; (ii) perform linear regression between Seismic Moment (M0) and the source parameters Source Radius (r), Stress Drop (Δσ) and Displacement (s); (iii) correlate source parameter’s distribution with the tectonics of the area. Finally, we compare the derived empirical laws with similar studies.

Scaling arguments for the fluxes in turbulent miscible fountains

For established axisymmetric turbulent miscible Boussinesq fountains in quiescent uniform environments, expressions are developed for the fluxes of volume, momentum and buoyancy at the outflow from the fountain: the outflow referring to the counterflow at the horizontal plane of the source. The fluxes are expressed in terms of the fountain source conditions and two dimensionless functions of the source Froude number, ${\rm Fr}_{0}$: a radial function (relating a horizontal scale of the outflow to the source radius) and a volume flux function (relating the outflow and source volume fluxes). The forms taken by these two functions at low ${\rm Fr}_{0}$ and high ${\rm Fr}_{0}$ are deduced, thereby providing the outflow fluxes and outflow Froude number solely in terms of the source conditions. For high ${\rm Fr}_{0}$, the outflow Froude number, ${\rm Fr}_{out}$, is shown to be invariant, indicating (by analogy with plumes for which the ‘far-field’ Froude number is invariant with source Froude number) that the outflow may be regarded as ‘far-field’ since the fluxes within the fountain have adjusted to attain a balance which is independent of the source conditions. Based on ${\rm Fr}_{out}$, the fluxes in the plume that forms beyond the fountain outflow are deduced. Finally, from the results of previously published studies, we show that the scalings deduced for fountains are valid for $0.0025 \lesssim {\rm Fr}_{0} \lesssim 1.0 $ for low ${\rm Fr}_{0}$ and $ {\rm Fr}_{0} \gtrsim 3.0 $ for high ${\rm Fr}_{0}$.

Steady free surface flows induced by a submerged ring source or sink

The steady axisymmetric flow induced by a ring sink (or source) submerged in an unbounded inviscid fluid is computed and the resulting deformation of the free surface is obtained. Solutions are obtained analytically in the limit of small Froude number (and hence small surface deformation) and numerically for the full nonlinear problem. The small Froude number solutions are found to have the property that if the non-dimensional radius of the ring sink is less than $\rho = \sqrt{2} $, there is a central stagnation point on the surface surrounded by a dip which rises to the stagnation level in the far distance. However, as the radius of the ring sink increases beyond $\rho = \sqrt{2} $, a surface stagnation ring forms and moves outward as the ring sink radius increases. It is also shown that as the radius of the sink increases, the solutions in the vicinity of the ring sink/source change continuously from those due to a point sink/source ($\rho = 0$) to those due to a line sink/source ($\rho \ensuremath{\rightarrow} \infty $). These properties are confirmed by the numerical solutions to the full nonlinear equations for finite Froude numbers. At small values of the Froude number and sink or source radius, the nonlinear solutions look like the approximate solutions, but as the flow rate increases a limiting maximum Froude number solution with a secondary stagnation ring is obtained. At large values of sink or source radius, however, this ring does not form and there is no obvious physical reason for the limit on solutions. The maximum Froude numbers at which steady solutions exist for each radius are computed.