Rm Rad Research Articles

Radiation and outflow properties of super-Eddington accretion flows around various mass classes of black holes: Dependence on the accretion rates

Abstract We perform axisymmetric two-dimensional radiation-hydrodynamic simulations of super-Eddington accretion flow and outflow around black holes to examine the properties of radiation and outflow as functions of the black hole mass and the accretion rate on to the black hole ($\dot{M}_{\rm BH}$). We find that the $\dot{m}_{\rm BH} ({\equiv} \dot{M}_{\rm BH}c^2 /L_{\rm Edd})$ dependence of $L_{\rm rad}/L_{\rm Edd}$ and $L_{\rm mech}/L_{\rm Edd}$ found for a stellar-mass black hole can apply to the high-mass cases, where $L_{\rm rad}$ is the radiation luminosity, $L_{\rm mech}$ is the mechanical luminosity, c is the speed of light, and $L_{\rm Edd}$ is the Eddington luminosity. Such universalities can appear in the regime in which electron scattering opacity dominates over absorption opacity. Further, the normalized isotropic mechanical luminosity $L_{\rm mech}^{\rm ISO}/L_{\rm Edd}$ (evaluated by normalized density and velocity at $\theta =10^\circ$) exhibits a broken power-law relationship with ${\dot{m}}_{\rm BH}$; $L_{\rm mech}^{\rm ISO}/ L_{\rm Edd} \propto {\dot{m}}_{\rm BH}^{2.7}$ (or $\propto {\dot{m}}_{\rm BH}^{0.7}$) below (above) ${\dot{m}}_{\rm BH}\sim 400$. This is because the radial velocity stays nearly constant (or even decreases) below (above) the break with increase of $\dot{m}_{\rm BH}$. We also find that the luminosity ratio is $L_{\rm mech}/L_{\rm rad}^{\rm ISO} \sim 0.05$ at ${\dot{m}}_{\rm BH} \sim 100$, which is roughly consistent with the observations of NLS1, 1H 0323+103.

Anisotropies in the spatial distribution and kinematics of dwarf galaxies in the Local Group and beyond

ABSTRACT The mass distribution in the Local Group (LG), dominated by the Andromeda (M31) and Milky Way (MW) pair, is highly anisotropic. We use the APOSTLE simulations to examine how this anisotropy manifests on the spatial distribution and kinematics of dwarf galaxies out to a distance of $d_{\rm MW}\sim 3$ Mpc from the MW. The simulations indicate a preference for dwarfs to be located near the axis defined by the MW-M31 direction, even for dwarfs in the LG periphery (LGP; i.e. at distances $1.25\ \lt\ d_{\rm MW}/$Mpc $\lt\ 3$). The ‘Hubble flow’ in the periphery is also affected; at fixed $d_{\rm MW}$ the mean recession speed, $\langle V_{\rm rad} \rangle$, varies with angular distance to M31, peaking in the anti-M31 direction and reaching a minimum behind M31. The M31-MW mass decelerates the local expansion; the LG ‘turnaround radius’ (i.e. where $\langle V_{\rm rad} \rangle =0$) in APOSTLE is at $r \sim 1.25$ Mpc from the LG barycentre and the pure Hubble flow (where $\langle V_{\rm rad} \rangle \sim H_0*d$) is reached beyond $r\sim 3$ Mpc. The predicted flow is very cold, with a barycentric dispersion of $\lt 40$ km s−1. Comparing these predictions with observations yields mixed results. There is little evidence for a preferred alignment of dwarfs along the MW-M31 direction, but some evidence for an angular anisotropy in $\langle V_{\rm rad} \rangle$. Although the ‘coldness’ of the Hubble flow is consistent with the simulations, it is less decelerated: relative to the MW all galaxies beyond $d_{\rm MW} \sim 1.25$ Mpc seem to be already on a pure Hubble flow. We argue that these oddities may result at least partly from incompleteness and inhomogeneous sky coverage in our current inventory of nearby dwarfs.

Nonlinear electron scattering by electrostatic waves in collisionless shocks

We present a theoretical analysis of electron pitch-angle scattering by ion-acoustic electrostatic fluctuations present in the Earth's bow shock and, presumably, collisionless shocks in general. We numerically simulate electron interaction with a single wave packet to demonstrate the scattering through phase bunching and phase trapping and quantify electron pitch-angle scattering in dependence on the wave amplitude and wave normal angle to the local magnetic field. The iterative mapping technique is used to model pitch-angle scattering of electrons by a large number of wave packets, which have been reported in the Earth's bow shock. Assuming that successive electron scatterings are not correlated, we revealed that the long-term dynamics of electrons is diffusive. The diffusion coefficient depends on the ratio $\varPhi _0/W$ between the wave packet amplitude and electron energy, $D\propto (\varPhi _0/W)^{\nu }$ . A quasi-linear scaling ( $\nu \approx 2$ ) is observed for sufficiently small wave amplitudes, $\varPhi _0\lesssim 10^{-3}W$ , while the diffusion is nonlinear ( $1<\nu <2$ ) above this threshold. We show that pitch-angle diffusion of ${\lesssim }1$ keV electrons in the Earth's bow shock can be nonlinear. The corresponding diffusion coefficient scales with the intensity $E_{w}^{2}$ of the electrostatic fluctuations in a nonlinear fashion, $D\propto E_{w}^{\nu }$ with $\nu <2$ , while its expected values in the Earth's bow shock are $D\sim 0.1\unicode{x2013}100$ $(T_{e}/W)^{\nu -1/2}\,{\rm rad}^{2}\,{\rm s}^{-1}$ . We speculate that in the Earth's quasi-perpendicular bow shock the stochastic shock drift acceleration mechanism with pitch-angle scattering provided by the electrostatic fluctuations can contribute to the acceleration of thermal electrons up to approximately 1 keV. The potential effects of a finite perpendicular coherence scale of the wave packets on the efficiency of electron scattering are discussed.

Wavefront Sensing with a Coupled Cavity for Torsion-Bar Antenna

Torsion-Bar Antenna (TOBA) is a ground-based gravitational wave detector using torsion pendulums. TOBA can detect intermediate-mass black hole binary mergers, gravitational wave stochastic background, and Newtonian noise, and is useful for earthquake early warning. A prototype detector Phase-III TOBA with 35 cm-scale pendulums is under development to demonstrate noise reduction. The target strain sensitivity is set to $1\times10^{-15}\,{/\sqrt{\rm Hz}}$ between 0.1 Hz--10 Hz. A new scheme of wavefront sensing with a coupled cavity was proposed to measure the pendulum rotation as low as $5\times10^{-16}\,{{\rm rad}/\sqrt{\rm Hz}}$ for Phase-III TOBA. In our method, an auxiliary cavity is used to enhance the first-order Hermite--Gaussian mode in a main cavity. Experimental demonstration is ongoing to confirm the feasibility of angular signal amplification and establish a method for locking a coupled cavity. We evaluated the performance of the coupled cavity and concluded that angular signal amplification would be feasible with this sensor. The coupled cavity was successfully locked to the resonance by the Pound--Drever--Hall technique with two modulation frequencies.

The redshift evolution of extragalactic magnetic fields

ABSTRACTFaraday rotation studies of distant radio sources can constrain the evolution and the origin of cosmic magnetism. We use data from the LOFAR Two-Metre Sky Survey: Data Release 2 (LoTSS DR2) to study the dependence of the Faraday rotation measure (RM) on redshift. By focusing on radio sources that are close in terms of their projection on the sky, but physically unrelated (‘random pairs’), we measure the RM difference, ΔRM, between the two sources. Thus, we isolate the extragalactic contribution to ΔRM from other contributions. We present a statistical analysis of the resulting sample of random pairs and find a median absolute RM difference |ΔRM| =(1.79 ± 0.09) ${\rm rad\, m}^{-2}$, with |ΔRM| uncorrelated both with respect to the redshift difference of the pair and the redshift of the nearer source, and a median excess of random pairs over physical pairs of (1.65 ± 0.10) ${\rm rad\, m}^{-2}$. We seek to reproduce this result with Monte Carlo simulations assuming a non-vanishing seed cosmological magnetic field and a redshift evolution of the comoving magnetic field strength that varies as (1 + z)−γ. We find the best-fitting results B0 ≡ Bcomoving(z = 0) ≲ (2.0 ± 0.2) nG and γ ≲ 4.5 ± 0.2 that we conservatively quote as upper limits due to an unmodelled but non-vanishing contribution of local environments to the RM difference. A comparison with cosmological simulations shows our results to be incompatible with primordial magnetogenesis scenarios with uniform seed fields of order nG.

Magnetic field strength in cosmic web filaments

ABSTRACT We used the rotation measure (RM) catalogue derived from the LOFAR Two-metre Sky Survey Data Release 2 (LoTSS DR2) at 144 MHz to measure the evolution with redshift of the extragalactic RM (RRM: Residual RM) and the polarization fraction (p) of sources in low-density environments. We also measured the same at 1.4 GHz by cross-matching with the NRAO VLA Sky Survey RM catalogue. We find that RRM versus redshift is flat at 144 MHz, but, once redshift-corrected, it shows evolution at high significance. Also, p evolves with redshift with a decrement by a factor of ∼8 at z ∼ 2. Comparing the 144-MHz and 1.4-GHz data, we find that the observed RRM and p are most likely to have an origin local to the source at 1.4 GHz, while a cosmic web filament origin is favoured at 144 MHz. If we attribute the entire signal to filaments, we infer a mean rest-frame RRM per filament of RRM$_{\rm 0,f} = 0.71 \pm 0.07 \, \, \rm rad\, m^{-2}$ and a magnetic field per filament of Bf = 32 ± 3 nG. This is in agreement with estimates obtained with a complementary method based on synchrotron emission stacking, and with cosmological simulations if primordial magnetic fields are amplified by astrophysical source field seeding. The measurement of an RRM0, f supports the presence of diffuse baryonic gas in filaments. We also estimated a conservative upper limit of the filament magnetic turbulence of $\sigma _{\rm RRM_{\rm 0,f}} =0.039 \pm 0.001 \, \, \rm rad\, m^{-2}$, concluding that the ordered magnetic field component dominates in filaments.

High-accuracy waveforms for black hole-neutron star systems with spinning black holes

The availability of accurate numerical waveforms is an important requirement for the creation and calibration of reliable waveform models for gravitational wave astrophysics. For black hole-neutron star binaries, very few accurate waveforms are however publicly available. Most recent models are calibrated to a large number of older simulations with good parameter space coverage for low-spin non-precessing binaries but limited accuracy, and a much smaller number of longer, more recent simulations limited to non-spinning black holes. In this paper, we present long, accurate numerical waveforms for three new systems that include rapidly spinning black holes, and one precessing configuration. We study in detail the accuracy of the simulations, and in particular perform for the first time in the context of BHNS binaries a detailed comparison of waveform extrapolation methods to the results of Cauchy Characteristic Extraction. The new waveforms have $<0.1\,{\rm rad}$ phase errors during inspiral, rising to $\sim (0.2-0.4)\,{\rm rad}$ errors at merger, and $\lesssim 1\%$ error in their amplitude. We compute the faithfulness of recent analytical models to these numerical results, and find that models specifically designed for BHNS binaries perform well ($F>0.99$) for binaries seen face-on. For edge-on observations, particularly for precessing systems, disagreements between models and simulations increase, and models that include precession and/or higher-order modes start to perform better than BHNS models that currently lack these features.

Radiative Width of the Hoyle State from γ-Ray Spectroscopy.

The cascading 3.21 and 4.44MeV electric quadrupole transitions have been observed from the Hoyle state at 7.65MeV excitation energy in ^{12}C, excited by the ^{12}C(p,p^{'}) reaction at 10.7MeV proton energy. From the proton-γ-γ triple coincidence data, a value of Γ_{rad}/Γ=6.2(6)×10^{-4} was obtained for the radiative branching ratio. Using our results, together with Γ_{π}^{E0}/Γ from Eriksen etal. [Phys. Rev. C 102, 024320 (2020)PRVCAN2469-998510.1103/PhysRevC.102.024320] and the currently adopted Γ_{π}(E0) values, the radiative width of the Hoyle state is determined as Γ_{rad}=5.1(6)×10^{-3} eV. This value is about 34% higher than the currently adopted value and will impact models of stellar evolution and nucleosynthesis.

Numerical investigation of radiation ablation and acceleration of high-density carbon foils

AbstractThe ablation and acceleration of diamond-like high-density carbon foils irradiated by thermal X-ray radiations are investigated with radiation hydrodynamics simulations. The time-dependent front of the ablation wave is given numerically for radiation temperatures in the range of 100–300 eV. The mass ablation rates and ablation pressures can be derived or implied from the coordinates of ablation fronts, which agree well with reported experiment results of high-density carbon with radiation temperatures Trad in the range of 160–260 eV. It is also found that the $T_{{\rm rad}}^3$ scaling law for ablation rates does not apply to Trad above 260 eV. The trajectories of targets and hydrodynamic efficiencies for different target thicknesses can be derived from the coordinates of ablation fronts using a rocket model and the results agree well with simulations. The peak hydrodynamic efficiencies of the acceleration process are investigated for different foil thicknesses and radiation temperatures. Higher radiation temperatures and target thicknesses result in higher hydrodynamic efficiencies. The simulation results are useful for the design of fusion capsules.

Supercritical Moser–Trudinger inequalities and related elliptic problems

Given $\alpha >0$, we establish the following two supercritical Moser-Trudinger inequalities \[ \sup\limits_{u \in W^{1,n}_{0,{\rm rad}}(B): \int_B |\nabla u|^n dx \leq 1} \int_B \exp\big( (\alpha_n + |x|^\alpha) |u|^{\frac{n}{n-1}} \big) dx < +\infty \] and \[ \sup\limits_{u\in W^{1,n}_{0,{\rm rad}}(B): \int_B |\nabla u|^n dx \leq 1} \int_B \exp\big( \alpha_n |u|^{\frac{n}{n-1} + |x|^\alpha} \big) dx < +\infty, \] where $W^{1,n}_{0,{\rm rad}}(B)$ is the usual Sobolev spaces of radially symmetric functions on $B$ in $\mathbb R^n$ with $n\geq 2$. Without restricting to the class of functions $W^{1,n}_{0,{\rm rad}}(B)$, we should emphasize that the above inequalities fail in $W^{1,n}_{0,{\rm rad}}(B)$. Questions concerning the sharpness of the above inequalities as well as the existence of the optimal functions are also studied. To illustrate the finding, an application to a class of boundary value problems on balls is presented. This is the second part in a set of our works concerning functional inequalities in the supercritical regime.

Measurement of hysteresis loop based on weak measurement.

In this Letter, we propose a technique for hysteresis loop measurement based on weak measurement. By using the photonic spin Hall effect (PSHE) as a probe and combining the quantum weak measurement, the technique's noise can be suppressed greatly. A theoretical model to describe the numerical relation between the amplified shift and Kerr rotation angle is established. Through detecting the amplified shift of the PSHE based on weak measurement, we experimentally measure the hysteresis loops of Ni-Fe alloy film, iron-phthalocyanine (FePc) monolayer film, and Co/FePc double-layer film. The results show that the precision can reach about $ \sim {10^{ - 6}} \;{\rm rad} $∼10-6rad under ordinary experimental conditions, which may have an important application prospect in magneto-optic parameters measurement.

More than just a wrinkle: a wave-like pattern in Ug versus Lz from Gaia data

ABSTRACT We present a newly found wave-like pattern in mean Galactocentric radial velocity ${\overline{U}_\mathrm{ g}}$ versus guiding centre radius Rg or angular momentum Lz of stars in the RV subsample of Gaia DR2. The short-wave pattern has a wavelength of order $1.2 \, {\rm kpc}$ in Rg or $285 \, {\rm kpc}\, {\rm km}\, {\rm s}^{-1}$ in Lz. The pattern shows only weak changes with Galactocentric radius R and little change in strength in particular with the vertical energy Ez of the stars or the distance to the Galactic plane |z|. The pattern is to first order symmetric around the plane, i.e. has no significant odd terms in z. There is a weak phase shift with the pattern moving towards slightly lower Lz (i.e. trailing) with |z| and Ez. However, we observe a highly significant phase shift in Galactic azimuth ϕ, which is different for different peaks. The peak around $L_{z}\sim 2100 \, {\rm kpc}\, {\rm km}\, {\rm s}^{-1}$ only shows a weak change with ϕ, while the rest of the pattern shows a clearly detectable shift of $\text{d} L_{z}/\text{d} \phi = (200 \pm 22) \, {\rm kpc}\, {\rm km}\, {\rm s}^{-1}\, {\rm rad}^{-1}$. If we consider all peaks to belong to the same pattern, this would suggest a wavenumber m = 4. We further find that the wave-like pattern in Ug appears to be related to the ${\overline{W}}$ versus Lz pattern detected in Gaia DR1. A comparison of the ${\overline{U}_\mathrm{ g}}\!-\!L_{z}$ wave pattern with changes of ${\overline{U}_\mathrm{ g}}$ versus R, which have been previously discussed, suggests that the latter can be understood as just the ${\overline{U}_\mathrm{ g}}\!-\!L_{z}$ pattern washed out by blurring (i.e. orbital excursions around their guiding centre) of disc stars.

Green functions and the Dirichlet spectrum

This article has results of four types. We show that the first eigenvalue $\lambda\_{1}(\Omega)$ of the weighted Laplacian of a bounded domain with smooth boundary can be obtained by S. Sato's iteration scheme of the Green operator, taking the limit $\lambda\_{1}(\Omega)=\lim\_{k\to \infty} \Vert G^{k}(f)\Vert\_{L^2}/\Vert G^{k+1}(f)\Vert\_{L^2}$ for any $f\in L^{2}(\Omega, \mu)$, $f > 0$. Then, we study the $L^{1}(\Omega, \mu)$-moment spectrum of $\Omega$ in terms of iterates of the Green operator $G$, extending the work of McDonald–Meyers to the weighted setting. As corollary, we obtain the first eigenvalue of a weighted bounded domain in terms of the $L^{1}(\Omega, \mu)$-moment spectrum, generalizing the work of Hurtado–Markvorsen–Palmer. Finally, we study the radial spectrum $\sigma^{\rm rad}(B\_{h}(o,r))$ of rotationally invariant geodesic balls $B\_{h}(o,r)$ of model manifolds. We prove an identity relating the radial eigenvalues of $\sigma^{\rm rad}(B\_{h}(o,r))$ to an isoperimetric quotient, i.e., $\sum 1/\lambda\_{i}^{\rm rad} = \int V(s)/S(s) ds$, $V(s)={\rm vol}(B\_{h}(o,s))$ and $S(s)={\rm vol}(\partial B\_{h}(o,s))$. We then consider a proper minimal surface $M\subset \mathbb{R}^{3}$ and the extrinsic ball $\Omega=M\cap B\_{\mathbb{R}^{3}}(o,r)$. We obtain upper and lower estimates for the series $\sum \lambda\_i^{-2}(\Omega)$ in terms of the volume ${\rm vol}(\Omega)$ and the radius $r$ of the extrinsic ball $\Omega$.

Generalized compactness limit from an arbitrary viewing angle

A $\gamma$-ray source must have a limited optical depth to pair production. This simple condition, called compactness, implies that gamma-ray bursts (GRBs) must involve a highly relativistic motion ($\Gamma \gtrsim 100$) giving the first and most important clue on their nature. So far, this condition has been discussed under the assumption that the $\gamma$-ray sources are viewed on-axis, that is, by an observer within the beaming cone of the relativistic source. Recently, following the detection of the weak short GRB 170817A, an extensive interest arose in the possibility that some $\gamma$-ray sources are viewed off-axis. We generalize here the compactness formalism for an arbitrary viewing angle taking several possible opacity processes and $\gamma$-ray spectra into account. We find that for a given observables (peak luminosity, temporal variability, and spectra) the minimal Lorentz factor, $\Gamma_{\rm min}$, is obtained, as expected, for an on-axis observer. More remarkably we find that compactness dictates also a maximal viewing angle, $\theta_{\rm max} \simeq 1/2\Gamma_{\rm min}$. Our limit implies for regular GRBs a very small allowed viewing angle ($\lesssim10^{-2}\,\rm rad$), making it extremely unlikely that they are viewed off-axis. For GRB 170817A we confirm earlier results that rule out the possibility that the observed $\gamma$-rays were seen by an on-axis observer as a regular short GRB. The short GRB 150101B was also suggested to be an off-axis event. We show that its maximal viewing angle $\lesssim0.05\,\rm rad$, which is inconsistent with the off-axis model. Finally we show that for low luminosity GRBs, compactness does not exclude by itself an off-axis model, but when combined with other consideration this option is strongly disfavored.

Evolution of Hubble wedges in episodic protostellar outflows

Young low-mass protostars undergo short phases of high accretion and outburst activity leading to lumpy outflows. Recent observations have shown that the position-velocity and mass-velocity diagrams of such outflows exhibit individual bullet-like features; some of these bullets subscribe to a `Hubble Law' velocity relation, and others are manifest as `Hubble wedges'. In order to explore the origin of these features, we have developed a new episodic outflow model for the SPH code {\sc gandalf}, which mimics the accretion and ejection behaviour of FU Ori type stars. We apply this model to simulations of star formation, invoking two types of initial conditions: spherically symmetric cores in solid-body rotation with $\rho\propto r^{-2}$, and spherically symmetric turbulent cores with density proportional to the density of a Bonnor-Ebert sphere. For a wide range of model parameters, we find that episodic outflows lead to self-regulation of the ejected mass and momentum, and we achieve acceptable results, even with relatively low resolution. Using this model, we find that recently ejected outflow bullets produce a `Hubble wedge' in the position-velocity relation. However, once such a bullet hits the leading shock front, it decelerates and aligns with older bullets to form a `Hubble-law'. Bullets can be identified as bumps in the mass-velocity relation, which can be fit with a power-law, $dM/d\upsilon_{_{\rm RAD}}\propto\upsilon_{_{\rm RAD}}^{-1.5}$.

Frequency-domain gravitational waveform models for inspiraling binary neutron stars

We develop a model for frequency-domain gravitational waveforms from inspiraling binary neutron stars. Our waveform model is calibrated by comparison with hybrid waveforms constructed from our latest high-precision numerical-relativity waveforms and the SEOBNRv2T waveforms in the frequency range of $10$--$1000\,{\rm Hz}$. We show that the phase difference between our waveform model and the hybrid waveforms is always smaller than $0.1\, {\rm rad}$ for the binary tidal deformability, ${\tilde \Lambda}$, in the range $300\lesssim{\tilde \Lambda}\lesssim1900$ and for the mass ratio between 0.73 and 1. We show that, for $10$--$1000\,{\rm Hz}$, the distinguishability for the signal-to-noise ratio $\lesssim50$ and the mismatch between our waveform model and the hybrid waveforms are always smaller than 0.25 and $1.1\times10^{-5}$, respectively. The systematic error of our waveform model in the measurement of ${\tilde \Lambda}$ is always smaller than $20$ with respect to the hybrid waveforms for $300\lesssim{\tilde \Lambda}\lesssim1900$. The statistical error in the measurement of binary parameters is computed employing our waveform model, and we obtain results consistent with the previous studies. We show that the systematic error of our waveform model is always smaller than $20\%$ (typically smaller than $10\%$) of the statistical error for events with the signal-to-noise ratio of $50$.

Extracting the orbital axis from gravitational waves of precessing binary systems

We present a new method for extracting the instantaneous orbital axis only from gravitational wave strains of precessing binary systems observed from a particular observer direction. This method enables us to reconstruct the co-precessing frame waveforms only from observed quantities for the ideal case that the signal-to-noise ratio is high enough to analyze the waveforms directly. Specifically, we do not assume knowledge of the time evolution of the instantaneous orbital axis and the co-precessing waveforms before analyzing the data in our method. We test and measure the accuracy of our method using the numerical relativity simulation data of precessing binary black holes taken from the SXS Catalog. We show that the direction of the orbital axis is extracted within $\approx0.02~{\rm rad}$ error from gravitational waves emitted during the inspiral phase. The co-precessing waveforms are also reconstructed with high accuracy; the mismatch (assuming white noise) between them and the original co-precessing waveforms is typically a few times $10^{-3}$ including the merger-ringdown phase, and can be improved by an order of magnitude focusing only on the inspiral waveform. In this method, the co-precessing frame waveforms are not only the purely technical tools for understanding the complex nature of precessing waveforms but also direct observables.

Heat capacity of a self-gravitating spherical shell of radiations

We study the heat capacity of a static system of self-gravitating radiations analytically in the context of general relativity. To avoid the complexity due to a conical singularity at the center, we excise the central part and replace it with a regular spherically symmetric distribution of matters of which specifications we are not interested in. We assume that the mass inside the inner boundary and the locations of the inner and the outer boundaries are given. Then, we derive a formula relating the variations of physical parameters at the outer boundary with those at the inner boundary. Because there is only one free variation at the inner boundary, the variations at the outer boundary are related, which determines the heat capacity. To get an analytic form for the heat capacity, we use the thermodynamic identity $\delta S_{\rm rad} = \beta \delta M_{\rm rad}$ additionally, which is derived from the variational relation of the entropy formula with the restriction that the mass inside the inner boundary does not change. Even if the radius of the inner boundary of the shell goes to zero, in the presence of a central conical singularity, the heat capacity does not go to the form of the regular sphere. An interesting discovery is that another legitimate temperature can be defined at the inner boundary which is different from the asymptotic one $\beta^{-1}$.

Multifrequency VLBA polarimetry of the high-redshift GPS quasar OQ172

Multi-frequency Very Long Baseline Array (VLBA) polarimetry observation of the GHz-Peaked Spectrum (GPS) quasar OQ172 (J1445+0958) has been performed at 1.6, 2.2, 4.8, 8.3 and 15.3 GHz in 2005. Core-jet structures are detected in all bands with the jet strongly bent at about 3 mas from the core. The radio emission of the source is polarised at all five bands. We study the Faraday Rotation in the core and jet components at all five bands, and find good linear fits of Faraday Rotation in the core and jet components at 4.8 and 8.3 GHz. At these two frequencies, the Rotation Measure (RM) is $\sim 2000~\rm rad~m^{-2}$ in the core and $\sim 700~\rm rad~m^{-2}$ in the inner jet components and continues to decrease at the outer jet parts. We find that the depolarisation at 4.8 and 8.3 GHz might be caused by the internal medium in the source. We investigate consistency of the turnover spectra of VLBI components with the Synchrotron Self-Absorption (SSA) and Free-Free Absorption (FFA) models. Although these two models can not be easily distinguished due to the lack of low-frequency data, the physical parameters can be constrained for each model. We find that the large width of the $\rm [OIII]_{5007}$ line is likely caused by a jet interaction with a Narrow Line Region (NLR) medium. The jet bending, significant RM variations, Faraday depolarisation, spectral turnover, and broad line width of $\rm [OIII]_{5007}$ could be closely related, likely caused by the same nucleus medium, presumably NLR.

$$Y(4260)\rightarrow \gamma + X(3872)$$ Y ( 4260 ) → γ + X ( 3872 ) in the diquarkonium picture

The observed Y(4260)\to \gamma + X(3872) decay is a natural consequence of the diquark-antidiquark description of Y and X resonances. In this note we attempt an estimate of the transition rate, \Gamma_{\rm rad}, by a non-relativistic calculation of the electric dipole term of a diquarkonium bound state. We compute \Gamma_{\rm rad} for generic composition values of the isospin of X and Y. Specializing to I=0 for X(3872), we find \Gamma_{\rm rad}= 496~keV for Y(4260) with I=0 and \Gamma_{\rm rad}= 179~keV for I=1. Combining with BESIII data, we derive upper bounds to B(Y\to J/\Psi+\pi+\pi) and to \Gamma(Y\to \mu^+ \mu^-). We expect to confront these results with forthcoming data from electron-positron and hadron colliders.