Fast radio bursts (FRBs) are millisecond-duration radio waves from the Universe. Even though more than 50 physical models have been proposed, the origin and physical mechanism of FRB emissions are still unknown. The classification of FRBs is one of the primary approaches to understanding their mechanisms, but previous studies classified conventionally using only a few observational parameters, such as fluence and duration, which might be incomplete. To overcome this problem, we use an unsupervised machine-learning model, the Uniform Manifold Approximation and Projection to handle seven parameters simultaneously, including amplitude, linear temporal drift, time duration, central frequency, bandwidth, scaled energy, and fluence. We test the method for homogeneous 977 sub-bursts of FRB 20121102A detected by the Arecibo telescope. Our machine-learning analysis identified five distinct clusters, suggesting the possible existence of multiple different physical mechanisms responsible for the observed FRBs from the FRB 20121102A source. The geometry of the emission region and the propagation effect of FRB signals could also make such distinct clusters. This research will be a benchmark for future FRB classifications when dedicated radio telescopes such as the square kilometer array or Bustling Universe Radio Survey Telescope in Taiwan discover more FRBs than before.

We investigate the relationship between a galaxy cluster’s hydrostatic equilibrium state, the entropy profile, K, of the intracluster gas, and the system’s non-thermal pressure (NTP), within an analytic model of cluster structures. When NTP is neglected from the cluster’s hydrostatic state, we find that the gas’ logarithmic entropy slope, $k\equiv \mathrm{d}\ln K/\mathrm{d}\ln r$, converges at large halocentric radius, r, to a value that is systematically higher than the value $k\simeq1.1$ that is found in observations and simulations. By applying a constraint on these ‘pristine equilibrium’ slopes, $k_\mathrm{eq}$, we are able to predict the required NTP that must be introduced into the hydrostatic state of the cluster. We solve for the fraction, $\mathcal{F}\equiv p_\mathrm{nt}/p$, of NTP, $p_\mathrm{nt}$, to total pressure, p, of the cluster, and we find $\mathcal{F}(r)$ to be an increasing function of halocentric radius, r, that can be parameterised by its value in the cluster’s core, $\mathcal{F}_0$, with this prediction able to be fit to the functional form proposed in numerical simulations. The minimum NTP fraction, as the solution with zero NTP in the core, $\mathcal{F}_0=0$, we find to be in excellent agreement with the mean NTP predicted in non-radiative simulations, beyond halocentric radii of $r\gtrsim0.7r_{500}$, and in tension with observational constraints derived at similar radii. For this minimum NTP profile, we predict $\mathcal{F}\simeq0.20$ at $r_{500}$, and $\mathcal{F}\simeq0.34$ at $2r_{500}$; this amount of NTP leads to a hydrostatic bias of $b\simeq0.12$ in the cluster mass $M_{500}$ when measured within $r_{500}$. Our results suggest that the NTP of galaxy clusters contributes a significant amount to their hydrostatic state near the virial radius and must be accounted for when estimating the cluster’s halo mass using hydrostatic equilibrium approaches.

We investigate the connection between a cluster’s structural configuration and observable measures of its gas emission that can be obtained in X-ray and Sunyaev–Zeldovich (SZ) surveys. We present an analytic model for the intracluster gas density profile: parameterised by the dark matter halo’s inner logarithmic density slope, $\alpha$, the concentration, c, the gas profile’s inner logarithmic density slope, $\varepsilon$, the dilution, d, and the gas fraction, $\eta$, normalised to cosmological content. We predict four probes of the gas emission: the emission-weighted, $T_\mathrm{X}$, and mean gas mass-weighted, $T_\mathrm{m_g}$, temperatures, and the spherically, $Y_\mathrm{sph}$, and cylindrically, $Y_\mathrm{cyl}$, integrated Compton parameters. Over a parameter space of clusters, we constrain the X-ray temperature scaling relations, $M_{200} - T_\mathrm{X}$ and $M_{500} - T_\mathrm{X}$, within $57.3\%$ and $41.6\%$, and $M_{200} - T_\mathrm{m_g}$ and $M_{500} - T_\mathrm{m_g}$, within $25.7\%$ and $7.0\%$, all respectively. When excising the cluster’s core, the $M_{200} - T_\mathrm{X}$ and $M_{500} - T_\mathrm{X}$ relations are further constrained, to within $31.3\%$ and $17.1\%$, respectively. Similarly, we constrain the SZ scaling relations, $M_{200} - Y_\mathrm{sph}$ and $M_{500} - Y_\mathrm{sph}$, within $31.1\%$ and $17.7\%$, and $M_{200} - Y_\mathrm{cyl}$ and $M_{500} - Y_\mathrm{cyl}$, within $25.2\%$ and $22.0\%$, all respectively. The temperature observable $T_\mathrm{m_g}$ places the strongest constraint on the halo mass, whilst $T_\mathrm{X}$ is more sensitive to the parameter space. The SZ constraints are sensitive to the gas fraction, whilst insensitive to the form of the gas profile itself. In all cases, the halo mass is recovered with an uncertainty that suggests the cluster’s structural profiles only contribute a minor uncertainty in its scaling relations.

We investigate the relationship between a dark matter halo’s mass profile and measures of the velocity dispersion of kinematic tracers within its gravitational potential. By predicting the scaling relation of the halo mass with the aperture velocity dispersion, $M_\mathrm{vir} - \unicode{x03C3}_\mathrm{ap}$, we present the expected form and dependence of this halo mass tracer on physical parameters within our analytic halo model: parameterised by the halo’s negative inner logarithmic density slope, $\unicode{x03B1}$, its concentration parameter, c, and its velocity anisotropy parameter, $\unicode{x03B2}$. For these idealised halos, we obtain a general solution to the Jeans equation, which is projected over the line of sight and averaged within an aperture to form the corresponding aperture velocity dispersion profile. Through dimensional analysis, the $M_\mathrm{vir} - \unicode{x03C3}_\mathrm{ap}$ scaling relation is devised explicitly in terms of analytical bounds for these aperture velocity dispersion profiles: allowing constraints to be placed on this relation for motivated parameter choices. We predict the $M_{200} - \unicode{x03C3}_\mathrm{ap}$ and $M_{500} - \unicode{x03C3}_\mathrm{ap}$ scaling relations, each with an uncertainty of $60.5\%$ and $56.2\%$, respectively. These halo mass estimates are found to be weakly sensitive to the halo’s concentration and mass scale, and most sensitive to the size of the aperture radius in which the aperture velocity dispersion is measured, the maximum value for the halo’s inner slope, and the minimum and maximum values of the velocity anisotropy. Our results show that a halo’s structural and kinematic profiles impose only a minor uncertainty in estimating its mass. Consequently, spectroscopic surveys aimed at constraining the halo mass using kinematic tracers can focus on characterising other, more complex sources of uncertainty and observational systematics.

Mercury is locked in an unusual 3:2 spin-orbit resonance and as such is expected to be in a state of equilibrium called Cassini state. In that state, the angle between the spin axis and orbit normal, called obliquity, remains almost constant while the spin axis remains almost in the plane, also called Cassini plane, defined by the normal to the Laplace plane and the normal to the orbital plane. The spin axis and the orbit normal precess together with a period of about 300 kyr. The orientation of the spin axis of Mercury has been estimated using different approaches: (i) Earth-based radar observations, (ii) Messenger images and altimeter data, and (iii) Messenger radio tracking data. The different estimates all tend to confirm that Mercury occupies the Cassini state. The observed obliquity is small and close to 2 arcmin. It indicates a normalized polar moment of inertia of about 0.34. This information, combined with the existence of a liquid iron core, as evidenced by the librations, allows to constrain the interior structure of Mercury. However, the different estimates of the orientation of the spin axis locate the spin axis somewhat behind or ahead of the Cassini plane, and it is difficult to reconcile and interpret them coherently in terms of detailed interior properties. We review recent models for the obliquity and spin orientation of Mercury, which include the effects of complex orbital dynamics, tidal deformations and associated dissipation, and internal couplings related to the presence of fluid and solid cores. We discuss some implications regarding the interpretations of the orientation estimates in term of interior properties.

We studied the probability distribution function of the column density (N-PDF) of molecular clouds based on a fit with a multi-log-normal function using the Nobeyama 45-m Cygnus X CO survey data. We identified 124 molecular clouds in 13CO data using the DENDROGRAM and SCIMES algorithms. The N-PDF was constructed for 11 extended (≥ 0.4 deg2) molecular clouds of these identified clouds. We found that every N-PDF is well-fitted with one or two log-normal (LN) distributions. We investigated the distributions of the column density, C18O dense cores, and radio continuum source in each cloud and found that the N-PDF was less correlated with the star-forming activity. The LN N-PDF parameters showed two impressive features. First, the LN distribution at the low-density part had the same mean column density (∼1021.5 cm−2 ) for almost all the molecular clouds. Second, the wider LN distribution tended to show the lower mean density of the structures.

During the late stages of a neutron star binary inspiral finite-size effects come into play, with the tidal deformability of the supranuclear density matter leaving an imprint on the gravitational-wave signal. As demonstrated in the case of GW170817—the first direct detection of gravitational waves from a neutron star binary—this can lead to strong constraints on the neutron star equation of state. As detectors become more sensitive, effects which may have a smaller influence on the neutron star tidal deformability need to be taken into consideration. Dynamical effects, such as oscillation mode resonances triggered by the orbital motion, have been shown to contribute to the tidal deformability, especially close to the neutron star coalesence. We calculate the contribution of the various stellar oscillation modes to the tidal deformability and demonstrate the (anticipated) dominance of the fundamental mode, showing what the impact of the matter composition is on the tidal deformability.

The averaged four-planetary motion theory is constructed up to the third order in planetary masses. The equations of motion in averaged elements are numerically integrated for the Solar system’s giant planets for different initial conditions. The comparison of obtained results with the direct numerical integration of Newtonian equations of motion shows an excellent agreement with them. It suggests that this motion theory is constructed correctly. So, we can use this theory to investigate the dynamical evolution of various extrasolar planetary systems with moderate orbital eccentricities and inclinations.

We present a closed-form normalization method suitable for the study of the secular dynamics of small bodies inside the trajectory of Jupiter. The method is based on a convenient use of a book-keeping parameter introduced not only in the Lie series organization but also in the Poisson bracket structure employed in all perturbative steps. In particular, we show how the above scheme leads to a redefinition of the remainder of the normal form at every step of the formal solution of the homological equation. An application is given for the semi-analytical representation of the orbits of main belt asteroids.

Tidal evolution of low-eccentric circumbinary planets is expected to drive the rotational evolution toward a pseudo-synchronous solution. In this work, we present a study of the oscillation amplitudes around this state by considering that the two central stars exert creep tides on the planet. These amplitudes are computed by direct numerical integrations of the creep equations and also by means of the calculation of the coefficients of the periodic terms in this stationary solution. As in the two-body-problem, the planetary spin and lag-angle are observed to have maximum oscillation amplitudes for stiff bodies and almost null oscillation for the gaseous regime, while the opposite behaviour is observed in the equatorial and polar flattenings. Our analytical approximation shows to be very accurate and specially necessary for very-low eccentric planets. However, the magnitudes of the oscillation amplitudes around the pseudo-synchronous solution in the circumbinary problem appears to be very small respect to the mean value. Thus, considering these oscillation in the computation of the tidal energy dissipation may not have a substantial contribution in the results, at least compared to the case in which only the mean values are taken into account.

Recent observations of globular clusters encourage to revise some aspects of the traditional paradigm, in which they were considered to be isotropic in velocity space and non-rotating. However, the theory of collisionless spheroids with some kinematic richness has seldom been studied. We present here a further step in this direction, owing to new results regarding the linear stability of rotating Plummer spheres, with varying anisotropy in velocity space and total amount of angular momentum. We extend the well-known radial orbit instability to rotating systems, and discover a new regime of instability in fast rotating, tangentially anisotropic systems.

Recent observations of globular clusters imposed major revisions to the previous paradigm, in which they were considered to be isotropic in velocity space and non-rotating. However, the theory of collisionless spheroids with some kinematic richness has seldom been studied. We present here a first step in this direction, owing to new results regarding the linear stability of rotating Plummer spheres, with varying anisotropy in velocity space and total amount of angular momentum. We extend the well-known radial orbit instability to rotating systems, and discover a new regime of instability in fast rotating, tangentially anisotropic systems.

. We present a significantly improved version of our numerical code JASMINE, that can now solve the Jeans equations for axisymmetric models of stellar systems, composed of an arbitrary number of stellar populations, a Dark Matter halo, and a central Black Hole. The stellar components can have different structural (density profile, flattening, mass, scale length), dynamical (rotational support, velocity dispersion anisotropy), and population (age, metallicity, Initial Mass Function, mass-to-light ratio) properties. These models, when combined with observations, will allow to investigate important issues, such as quantifying the systematic effects of IMF variations, of mass-to-light ratio gradients, and of different stellar kinematic components (e.g. counter rotating disks, kinematically decoupled cores) on luminosity-weighted properties. The developed analytical and numerical framework aims at modeling Early-Type Galaxies, but it can also be applied to dwarf Spheroidal galaxies and Globular Clusters.

We present a new experimental setup called AROMA (The Aromatic Research of Organics with Molecular Analyzer) based on the use of laser mass spectrometry techniques. We demonstrate the potential of AROMA for the analysis of meteoritic samples and cosmic dust analogues. Tens of peaks are identified in the mass spectra with notable discrepancies across the different samples. These discrepancies provide clues on the chemical history of each sample and are not a bias of our analysis. A double bound-equivalent (DBE) method is applied to sort the detected carbonaceous molecules into families of compounds. It reveals in addition of polycyclic aromatic hydrocarbons, the presence of other populations such as mixed aromatic-aliphatic species and carbon clusters.

Obliquity (axial tilt) and its variability could play an important role in the climate and habitability of a planet. We explore the spin-axis dynamics of two specific habitable zone exoplanets, Kepler-62f and Kepler-186f, using numerical and analytical techniques. Based on our current understanding of their orbital architecture, we find that, in contrast with the typical conditions in the Solar System, Kepler-62f and 186f should have low obliquity variations except in fine-tuned conditions. Extra undetected planetary companions and/or the existence of a satellite could either stabilize or destabilize obliquities at a variety of values.

A constraint on Solar System formation is the high 26Al/27Al abundance ratio, 17 times higher than the average Galactic ratio, while the 60Fe/56Fe value was lower than the Galactic value. This challenges the assumption that a nearby supernova was responsible for the injection of these short-lived radionuclides into the early Solar System. We suggest that the Solar System was formed by triggered star formation at the edge of a Wolf-Rayet (W-R) bubble. We discuss the details of various processes within the model using numerical simulations, and analytic and semi-analytic calculations, and conclude that it is a viable model that can explain the initial abundances of 26Al and 60Fe. We estimate that 1%-16% of all Sun-like stars could have formed in such a setting.

While the observed polarization maps of spatially resolved post-AGB objects usually require numerical modelling of radiative transfer, it is useful to have known analytical solutions of the polarized radiative transfer equation (PRTE) as benchmarks of computer codes in the simplest model cases. We consider two such solutions: cylindrically symmetric Green’s function for an infinite medium and cylindrically symmetric inner eigenfunctions of PRTE.

Photometric passbands are usually characterised through laboratory measurements and once in operations they are refined with true observations of reference sources with known spectral energy distribution. This paper revises the methods to determine those passbands and discusses the limitations encountered. The passbands are not fully constrained by the reference sources used and the method presented here allows to evaluate which is the constrained and the unconstrained component of the passband.

There seems to be magnetic fields at all scales and epochs in our Universe, but their origin at large scales remains an important open question of cosmology. In this work we focus on the generation of magnetic fields in the intergalactic medium due to the photoionizations by the first galaxies, all along the Epoch of Reionization. Based on previous studies which considered only isolated sources, we develop an analytical model to estimate the mean magnetic energy density accumulated in the Universe by this process. In our model, without considering any amplification process, the Universe is globally magnetized by this mechanism to the order of, at least, several 10−18 G during the Epoch of Reionization (i.e. a few 10−20 G comoving).

In this article we described CoLiTec software for full automated frames processing. CoLiTec software allows processing the Big Data of observation results as well as processing of data that is continuously formed during observation. The scope of solving tasks includes frames brightness equalization, moving objects detection, astrometry, photometry, etc. Along with the high efficiency of Big Data processing CoLiTec software also ensures high accuracy of data measurements. A comparative analysis of the functional characteristics and positional accuracy was performed between CoLiTec and Astrometrica software. The benefits of CoLiTec used with wide field and low quality frames were observed. The efficiency of the CoLiTec software was proved by about 700.000 observations and over 1.500 preliminary discoveries.