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New physics beyond the Standard Model (BSM) with an extra neutral boson can be constrained from the observation of SN1987A, since the production of this neutral boson in a supernova (SN) could accelerate the SN cooling and potentially lead to a period of the neutrino burst incompatible with the observation. The constraint to the model is formulated by the condition $L_{\rm NB}\leq 3\times 10^{52}$ erg/s according to G. Raffelt with $L_{\rm NB}$ the luminosity of BSM neutral boson. Computing the above luminosity in the large coupling case, the so-called trapping regime, is non-trivial since the luminosity is a competition between the large production rate and the efficient absorption or decay rate of the neutral boson. We illustrate such a subtlety using $U(1)_{L_\mu-L_\tau}$ model as an example where the $Z^{\prime}$ luminosity, $L_{Z^{\prime}}$, from the neutrinosphere is calculated. We calculate $Z'$ production, absorption, and decay rates through pair-coalescence, semi-Compton, loop-bremsstrahlung from proton-neutron scattering, and their inverse processes in a benchmark SN simulation with muons. We point out that, as the coupling constant $g_{Z'}$ increases, $L_{Z^{\prime}}$ shall be approaching a constant plateau value for a given $m_{Z'}$ instead of monotonically decreasing down to zero as obtained in the previous literature. We demonstrate that this plateau phenomenon can be understood by physical arguments and justified by numerical calculations. With a different result on $L_{Z^{\prime}}$ from the previous one, we discuss impacts on the constraints to $U(1)_{L_\mu-L_\tau}$ parameter space by SN1987A. The implication of our result to the similar constraint on a generic BSM model with an extra neutral boson is also discussed., Comment: 35 pages, 10 figures

Radio data can give stringent constraints for annihilating dark matter. In general, radio observations can detect very accurate radio flux density with high resolution and different frequencies for nearby galaxies. We are able to obtain the radio flux density as a function of distance from the galactic center and frequencies $S(r,\nu)$. In this article, we demonstrate a comprehensive radio analysis of the M33 galaxy, combining the radio flux density profile $S(r)$ and the frequency spectrum $S(\nu)$ to get the constraints of dark matter annihilation parameters. By analyzing the archival radio data obtained from the Effelsberg telescope, we show that the dark matter annihilation contributing to the radio flux density might be insignificant in the disk region of the M33 galaxy. Moreover, by including the baryonic radio contribution, we constrain the $2\sigma$ conservative upper limits of the annihilation cross section, which can be complementary to the existing constraints based on neutrino, cosmic-ray, and gamma-ray observations. Our results indicate that analyzing the galactic multi-frequency radio flux profiles can give useful and authentic constraints on dark matter for the leptophilic annihilation channels., Comment: Accepted publication in ApJ

Small radio telescope in 21cm was used for studying the partial solar eclipse, with magnitude 0.89, in Hong Kong on 21st June, 2020. The radio telescope SPIDER 300A was designed and constructed by the Radio2Space Company, Italy. Radio flux density time curves (light curve) and a two-dimension mapping of the eclipse is presented in this paper. Standard radio data reduction methods were used to obtain the intensity time curve. We also adopted the semi-pipeline method for the reduction of data to obtain the same results as with the built-in software of the radio telescope SPIDER 300A. The total solar radio flux of the eclipse was found to reduce by maximum 55 +/- 5 percent, while the maximum eclipsed area of the same eclipse is 86.08%. Other radio observations of solar eclipses in Hong Kong are also discussed in this paper, including SPIDER 300A observation of partial solar eclipse on 26th December 2019 (APPENDIX A); and small radio telescope (SRT), developed by the Haystack Observatory, MIT, USA, observation of 2020 eclipse (APPENDIX B)., Comment: Accepted to publish in RoAJ 18 pages, 11 figures, 3 Appendix

The Adomian Decomposition Method (ADM) is a very effective approach for solving broad classes of nonlinear partial and ordinary differential equations, with important applications in different fields of applied mathematics, engineering, physics and biology. It is the goal of the present paper to provide a clear and pedagogical introduction to the Adomian Decomposition Method and to some of its applications. In particular, we focus our attention to a number of standard first-order ordinary differential equations (the linear, Bernoulli, Riccati, and Abel) with arbitrary coefficients, and present in detail the Adomian method for obtaining their solutions. In each case we compare the Adomian solution with the exact solution of some particular differential equations, and we show their complete equivalence. The second order and the fifth order ordinary differential equations are also considered. An important extension of the standard ADM, the Laplace-Adomian Decomposition Method is also introduced through the investigation of the solutions of a specific second order nonlinear differential equation. We also present the applications of the method to the Fisher-Kolmogorov second order partial nonlinear differential equation, which plays an important role in the description of many physical processes, as well as three important applications in astronomy and astrophysics, related to the determination of the solutions of the Kepler equation, of the Lane-Emden equation, and of the general relativistic equation describing the motion of massive particles in the spherically symmetric and static Schwarzschild geometry., Comment: 41 pages, no figures, accepted for publication in the Romanian Astronomical Journal

Some recent studies have examined the gamma-ray flux profile of our Galaxy to determine the signal of dark matter annihilation. However, the results are controversial and no confirmation is obtained. In this article, we study the radio flux density profile of the M31 galaxy and show that it could manifest a possible signal of dark matter annihilation. By comparing the likelihoods between the archival observed radio flux density profile data and the predicted radio flux density profile contributed by dark matter and stellar emission, we can constrain the relevant dark matter parameters. Specifically, for the thermal annihilation cross section via the $b\bar{b}$ channel, the best-fit value of dark matter mass is $\sim 30$ GeV, which is consistent with the results of many recent studies. We expect that this method would become another useful way to constrain dark matter, which is complementary to the traditional radio analyses and the other indirect detections., Comment: Accepted in MNRAS

The Schr\"{o}dinger-Newton system is a nonlinear system obtained by coupling together the linear Schr\"{o}dinger equation of quantum mechanics with the Poisson equation of Newtonian mechanics. In the present work we will investigate the effects of a cosmological constant (dark energy or vacuum fluctuation) on the Schr\"{o}dinger-Newton system, by modifying the Poisson equation through the addition of a new term. The corresponding Schr\"{o}dinger-Newton-$\Lambda$ system cannot be solved exactly, and therefore for its study one must resort to either numerical or semianalytical methods. In order to obtain a semianalytical solution of the system we apply the Adomian Decomposition Method, a very powerful method used for solving a large class of nonlinear ordinary and partial differential equations. Moreover, the Adomian series are transformed into rational functions by using the Pad\'{e} approximants. The semianalytical approximation is compared with the full numerical solution, and the effects of the dark energy on the structure of the Newtonian quantum system are investigated in detail., Comment: 17 pages, 7 figures, accepted for publication in Modern Physics Letters A

In the past decade, the properties of annihilating dark matter models were examined by various kinds of data, including the data of gamma rays, radio waves, X-ray, positrons, electrons, antiprotons and neutrinos. In particular, most of the studies focus on the data of our Galaxy, nearby galaxies (e.g. M31 galaxy) or nearby galaxy clusters (e.g. Fornax cluster). In this article, we examine the archival radio continuum spectral data of a relatively high-redshift galaxy cluster (A697 cluster) to constrain the properties of annihilating dark matter. We find that leptophilic annihilation channels ($e^+e^-$, $\mu^+\mu^-$ and $\tau^+\tau^-$) can give very good fits to the radio continuum spectrum of the A697 cluster., Comment: Submitted to ApJ. arXiv admin note: text overlap with arXiv:1912.03640

We study the dynamics of vortices with arbitrary topological charges in weakly interacting Bose-Einstein condensates using the Adomian Decomposition Method to solve the nonlinear Gross-Pitaevskii equation in polar coordinates. The solutions of the vortex equation are expressed in the form of infinite power series. The power series representations are compared with the exact numerical solutions of the Gross-Pitaevskii equation for the uniform and the harmonic potential, respectively. We find that there is a good agreement between the analytical and the numerical results., Comment: 10 pages, 2 figures, accepted for publication in Romanian Reports in Physics

In the past few years, some studies claimed that annihilating dark matter with mass $\sim 10-100$ GeV can explain the GeV gamma-ray excess in our Galaxy. However, recent analyses of the Fermi-LAT and radio observational data rule out the possibility of the thermal relic annihilating dark matter with mass $m \le 100$ GeV for some popular annihilation channels. By using the new observed radio data of the Andromeda galaxy, we rule out the existence of $\sim 100-300$ GeV thermal relic annihilating dark matter for ten annihilation channels. The lower limits of annihilating dark matter mass are improved to larger than 330 GeV for the most conservative case, which is a few times larger than the current best constraints. Moreover, these limits strongly disfavor the benchmark model of weakly interacting massive particle (WIMP) produced through the thermal freeze-out mechanism., Comment: Accepted in ApJ

The biharmonic equation, as well as its nonlinear and inhomogeneous generalizations, plays an important role in engineering and physics. In particular the focusing biharmonic nonlinear Schr\"{o}dinger equation, and its standing wave solutions, have been intensively investigated. In the present paper we consider the applications of the Laplace-Adomian and Adomian Decomposition Methods for obtaining semi-analytical solutions of the generalized biharmonic equations of the type $\Delta ^{2}y+\alpha \Delta y+\omega y+b^{2}+g\left( y\right) =f$, where $\alpha $, $\omega $ and $b$ are constants, and $g$ and $f$ are arbitrary functions of $y$ and the independent variable, respectively. After introducing the general algorithm for the solution of the biharmonic equation, as an application we consider the solutions of the one-dimensional and radially symmetric biharmonic standing wave equation $\Delta ^{2}R+R-R^{2\sigma +1}=0$, with $\sigma = {\rm constant}$. The one-dimensional case is analyzed by using both the Laplace-Adomian and the Adomian Decomposition Methods, respectively, and the truncated series solutions are compared with the exact numerical solution. The power series solution of the radial biharmonic standing wave equation is also obtained, and compared with the numerical solution., Comment: 20 pages, 4 figures

We study the equations of motion of the massive and massless particles in the Schwarzschild geometry of general relativity by using the Laplace-Adomian Decomposition Method, which proved to be extremely successful in obtaining series solutions to a wide range of strongly nonlinear differential and integral equations. After introducing a general formalism for the derivation of the equations of motion in arbitrary spherically symmetric static geometries, and of the general mathematical formalism of the Laplace-Adomian Decomposition Method, we obtain the series solution of the geodesics equation in the Schwarzschild geometry. The truncated series solution, containing only five terms, can reproduce the exact numerical solution with a high precision. In the first order of approximation we reobtain the standard expression for the perihelion precession. We study in detail the bending angle of light by compact objects in several orders of approximation. The extension of this approach to more general geometries than the Schwarzschild one is also briefly discussed., Comment: 33 pages, 4 figures, accepted for publication in Advances in High Energy Physics

If dark matter is composed of massive bosons, a Bose-Einstein Condensation process must have occurred during the cosmological evolution. Therefore galactic dark matter may be in a form of a condensate, characterized by a strong self-interaction. We consider the effects of rotation on the Bose-Einstein Condensate dark matter halos, and we investigate how rotation might influence their astrophysical properties. In order to describe the condensate we use the Gross-Pitaevskii equation, and the Thomas-Fermi approximation, which predicts a polytropic equation of state with polytropic index $n=1$. By assuming a rigid body rotation for the halo, with the use of the hydrodynamic representation of the Gross-Pitaevskii equation we obtain the basic equation describing the density distribution of the rotating condensate. We obtain the general solutions for the condensed dark matter density, and we derive the general representations for the mass distribution, boundary (radius), potential energy, velocity dispersion, tangential velocity and for the logarithmic density and velocity slopes, respectively. Explicit expressions for the radius, mass, and tangential velocity are obtained in the first order of approximation, under the assumption of slow rotation. In order to compare our results with the observations we fit the theoretical expressions of the tangential velocity of massive test particles moving in rotating Bose-Einstein Condensate dark halos with the data of 12 dwarf galaxies, and the Milky Way, respectively., Comment: 22 pages, 7 figures, accepted for publication in EPJC

We perform the study of the stability of the Lorenz system by using the Jacobi stability analysis, or the Kosambi-Cartan-Chern (KCC) theory. The Lorenz model plays an important role for understanding hydrodynamic instabilities and the nature of the turbulence, also representing a non-trivial testing object for studying non-linear effects. The KCC theory represents a powerful mathematical method for the analysis of dynamical systems. In this approach we describe the evolution of the Lorenz system in geometric terms, by considering it as a geodesic in a Finsler space. By associating a non-linear connection and a Berwald type connection, five geometrical invariants are obtained, with the second invariant giving the Jacobi stability of the system. The Jacobi (in)stability is a natural generalization of the (in)stability of the geodesic flow on a differentiable manifold endowed with a metric (Riemannian or Finslerian) to the non-metric setting. In order to apply the KCC theory we reformulate the Lorenz system as a set of two second order non-linear differential equations. The geometric invariants associated to this system (nonlinear and Berwald connections), and the deviation curvature tensor, as well as its eigenvalues, are explicitly obtained. The Jacobi stability of the equilibrium points of the Lorenz system is studied, and the condition of the stability of the equilibrium points is obtained. Finally, we consider the time evolution of the components of the deviation vector near the equilibrium points., Comment: 17 pages, 9 figures, accepted for publication in Int. J. of Geometric Methods in Modern Physics

We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects interacting with their external medium based on a generalized Langevin equation with colored noise, which accounts for the general memory and retarded effects of the frictional force, and on the fluctuation-dissipation theorem. The presence of the memory effects influences the response of the disk to external random interactions, and modifies the dynamical behavior of the disk, as well as the energy dissipation processes. The generalized Langevin equation of the motion of the disk in the vertical direction is studied numerically, and the vertical displacements, velocities and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and the Kerr cases. The Power Spectral Distribution (PSD) of the disk luminosity is also obtained. As a possible astrophysical application of the formalism we investigate the possibility that the Intra Day Variability (IDV) of the Active Galactic Nuclei (AGN) may be due to the stochastic disk instabilities. The perturbations due to colored/nontrivially correlated noise induce a complicated disk dynamics, which could explain some astrophysical observational features related to disk variability., Comment: 17 pages, 10 figures, accepted for publication in EPJC

We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects based on the generalized Langevin equation, which accounts for the general retarded effects of the frictional force, and on the fluctuation-dissipation theorems. The vertical displacements, velocities and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and the Kerr cases. The Power Spectral Distribution of the luminosity it is also obtained, and it is shown that it has non-standard values. The theoretical predictions of the model are compared with the observational data for the luminosity time variation of the BL Lac S5 0716+714 object., Comment: 4 pages, two figures, accepted for publication in Journal of Astrophysics and Astronomy