ShantanuT01/DACTYL-Pretraining huggingface dataset:
We theoretically quantify the impact of observational errors on the recovered age for stars in MS and RGB phases. We adopted Teff, [Fe/H], Delta_nu and nu_max as observational constraints. Artificial stars were sampled from a reference isochrone and subjected to random perturbation to simulate observational errors. Their ages were then recovered by means of a MCMC approach. The differences between the recovered and true ages were modelled against the errors in the observables by means of linear models and projection pursuit regression models. From linear models we find that no age error source dominates. For MS the most important error source is Teff. An offset of 75 K accounts for an underestimation of the stellar age from 0.4 to 0.6 Gyr for initial and terminal MS. An error of 2.5% in nu_max accounted for about -0.3 Gyr. A 0.1 dex error in [Fe/H] resulted particularly important only at the end of the MS, with an age error of -0.4 Gyr. For the RGB phase the dominant source of uncertainty is nu_max, causing an underestimation of about 0.6 Gyr; the offset in the effective temperature and Delta_nu caused respectively an underestimation and overestimation of 0.3 Gyr. We find that the inference from the linear model is a good proxy for that from projection pursuit regression models, so that linear models can be safely used thanks to its broader generalizability. Finally, we explored the impact on age estimates of adding the luminosity to the other observational constraints. We assumed - for computational reasons - a 2.5% error in luminosity, much lower than the average error in the Gaia DR2 catalogue. Even in this optimistic case, the luminosity does not increase precision of age estimates. Moreover, the luminosity resulted as a major contributor to the variability in the estimated ages, accounting for an error of about -0.3 Gyr in the explored evolutionary phases.
Many galaxy clusters host Megaparsec-scale radio halos, generated by ultrarelativistic electrons in the magnetized intracluster medium. Correlations between the power of radio halos and the thermal properties of the hosting clusters were established in the last decade, including the connection between the presence of a halo and cluster mergers. The X-ray luminosity and redshift limited Extended GMRT Radio Halo Survey provides a rich and unique dataset for statistical studies of the halos. We uniformly analyze the radio and X-ray data for the GMRT cluster sample, and use the new Planck SZ catalog, to revisit the correlations between the power of halos and the thermal properties of galaxy clusters. We find that the radio power of halos at 1.4 GHz scales with the cluster X-ray (0.1--2.4 keV) luminosity computed within R_500 as P_1.4 L_500^2.0. Our bigger and more homogenous sample confirms that the X-ray luminous (L_500 > 5x10^44 erg/s) clusters branch into two populations --- radio halos lie on the correlation, while clusters with upper limits to radio-halo emission are well below that correlation. This bimodality remains if we excise cool cores from the X-ray luminosities. Correlating with Planck data, we find that P_1.4 scales with the cluster integrated SZ signal within R_500 as P_1.4 Y_500^2.1, in line with previous findings. However, contrary to previous studies that were limited by incompleteness and small sample size, we find that the "SZ-luminous" Y_500 > 6x10^-5 Mpc^2 clusters show a bimodal behavior similar to that in the radio-X-ray diagram. Bimodality of both correlations can be traced to clusters dynamics, with radio halos found exclusively in merging clusters. These results confirm the key role of mergers for the origin of giant radio halos, suggesting that they trigger the relativistic particle acceleration.
Tiwari {\it et al.}\ have identified an annual modulation of the $\gamma$-ray flux at the Soudan Underground Laboratory which is strongly correlated to the radon concentration. The $\gamma$-ray flux results from ($\alpha$,$\gamma$) reactions which are induced by the $\alpha$ activity of radon and its daughters. Unfortunately, the quantitative analysis of the $\gamma$-ray flux is based on unrealistic ($\alpha$,$\gamma$) cross sections, and thus the calculated $\gamma$-ray fluxes are not reliable.
We establish a variety of properties of the discrete time simple random walk on a Galton-Watson tree conditioned to survive when the offspring distribution, $Z$ say, is in the domain of attraction of a stable law with index $\alpha\in(1,2]$. In particular, we are able to prove a quenched version of the result that the spectral dimension of the random walk is $2\alpha/(2\alpha-1)$. Furthermore, we demonstrate that when $\alpha\in(1,2)$ there are logarithmic fluctuations in the quenched transition density of the simple random walk, which contrasts with the log-logarithmic fluctuations seen when $\alpha=2$. In the course of our arguments, we obtain tail bounds for the distribution of the $n$th generation size of a Galton-Watson branching process with offspring distribution $Z$ conditioned to survive, as well as tail bounds for the distribution of the total number of individuals born up to the $n$th generation, that are uniform in $n$.
Plaskett's "star" appears to be one of a small number of short-period binary systems known to contain a hot, massive, magnetic star. Building on the 2013 discovery investigation, we combine an extensive spectropolarimetric (Stokes $V$) dataset with archival photometry and spectropolarimetry to establish the essential characteristics of the magnetic field and magnetosphere of the rapidly rotating, broad-line component of the system. We apply Least-Squares Deconvolution (LSD) to infer the longitudinal magnetic field from each Stokes $V$ spectrum. Using the timeseries of longitudinal field measurements, in combination with CoRoT photometry and equivalent width measurements of magnetospheric spectral lines, we infer the rotation period of the magnetic star to be equal to $1.21551^{+0.00028}_{-0.00034}$ d. Modeling the Stokes $V$ LSD profiles with Zeeman Doppler Imaging, we produce the first {reliable} magnetic map of an O-type star. We find a magnetic field that is predominantly dipolar, but with an important quadrupolar component, and weak higher order components. The dipolar component has an obliquity near 90 deg and a polar strength of about 850 G, while the average field strength over the entire surface is 520 G. We update the calculations of the theoretical magnetospheric parameters, and in agreement with their predictions we identify clear variability signatures of the H$\alpha$, H$\beta$, and He II $\lambda 4686$ lines confirming the presence of a dense centrifugal magnetosphere surrounding the star. Finally, we report a lack of detection of radial velocity (RV) variations of the observed Stokes $V$ profiles, suggesting that historical reports of the large RV variations of the broad-line star's spectral lines may be spurious. This discovery may motivate a fundamental revision of the historical model of the Plaskett's star as a near-equal mass O+O binary system.
Yes, for a wide range of cosmological models ($\Lambda$CDM, non-interacting $w_z$CDM or models with possible interactions between dark energy and dark matter, in either phantom or non-phantom regimes). In the recent past there have been many attempts to solve the tension between direct measurements of $H_0$ and $\sigma_8 \sqrt{\Omega_{0 {\rm m}}}$ from the respective low redshift observables and indirect measurements of these quantities from the cosmic microwave background (CMB). In this work we reconstruct a model independent approach that boils down to different classes of cosmological models under suitable parameters choices. We test this parameterization against the latest Planck CMB data combined with recent BAO, SNeIa datasets and the R16 direct $H_0$ measurements, and compare among different cosmological models. Our analysis reveals that a strong positive correlation between $H_0$ and $\sigma_8$ is more or less generic, irrespective of the choice of cosmological models. We also find that present data slightly prefers a phantom equation of state for dark energy and a slight negative value for effective equation of state for dark matter (which is a direct signature of interacting models) with a relatively high value for $H_0$ consistent with R16 and simultaneously, a consistent value for $\Omega_{0 {\rm m}}$. Thus, even though the tensions cannot be fully resolved, interacting models with phantom equation of state get a slight edge over the others for currently available data. We also see that allowing interaction between dark energy and dark matter may resolve the tension between the high redshift CMB data and individual low redshift datasets, but the low redshift datasets have inconsistencies between them (e.g. between BAO and $H_0$, SNeIa and BAO, and cluster counts and $H_0$) that are practically independent of the cosmological model.
The basic workings of inflationary models are summarized, along with the arguments that strongly suggest that our universe is the product of inflation. I describe the quantum origin of density perturbations, giving a heuristic derivation of the scale invariance of the spectrum and the leading corrections to scale invariance. The mechanisms that lead to eternal inflation in both new and chaotic models are described. Although the infinity of pocket universes produced by eternal inflation are unobservable, it is argued that eternal inflation has real consequences in terms of the way that predictions are extracted from theoretical models. Although inflation is generically eternal into the future, it is not eternal into the past: it can be proven under reasonable assumptions that the inflating region must be incomplete in past directions, so some physics other than inflation is needed to describe the past boundary of the inflating region. The ambiguities in defining probabilities in eternally inflating spacetimes are reviewed, with emphasis on the youngness paradox that results from a synchronous gauge regularization technique.
Specific features of orbital and spin structure of transition metal compounds in the case of the face-sharing MO$_6$ octahedra are analyzed. In this geometry, we consider the form of the spin--orbital Hamiltonian for transition metal ions with double ($e_g^{\sigma}$) or triple ($t_{2g}$) orbital degeneracy. Trigonal distortions typical of the structures with face-sharing octahedra lead to splitting of $t_{2g}$ orbitals into an $a_{1g}$ singlet and $e_g^{\pi}$ doublet. For both doublets ($e_g^{\sigma}$ and $e_g^{\pi}$), in the case of one electron or hole per site, we arrive at a symmetric model with the orbital and spin interaction of the Heisenberg type and the Hamiltonian of unexpectedly high symmetry: SU(4). Thus, many real materials with this geometry can serve as a testing ground for checking the prediction of this interesting theoretical model. We also compare general trends in spin--orbital ("Kugel--Khomskii") exchange interaction for three typical situations: those of MO$_6$ octahedra with common corner, common edge, and the present case of common face, which has not been considered yet.
In this paper, the concept of the classical $f$-divergence for a pair of measures is extended to the mixed $f$-divergence for multiple pairs of measures. The mixed $f$-divergence provides a way to measure the difference between multiple pairs of (probability) measures. Properties for the mixed $f$-divergence are established, such as permutation invariance and symmetry in distributions. An Alexandrov-Fenchel type inequality and an isoperimetric inequality for the mixed $f$-divergence are proved.
We search for the maximum oxygen abundance in spiral galaxies. Because this maximum value is expected to occur in the centers of the most luminous galaxies, we have constructed the luminosity - central metallicity diagram for spiral galaxies, based on a large compilation of existing data on oxygen abundances of HII regions in spiral galaxies. We found that this diagram shows a plateau at high luminosities (-22.3 < M_B < -20.3), with a constant maximum value of the gas-phase oxygen abundance 12+log(O/H) ~ 8.87. This provides strong evidence that the oxygen abundance in the centers of the most luminous metal-rich galaxies reaches the maximum attainable value of oxygen abundance. Since some fraction of the oxygen (about 0.08 dex) is expected to be locked into dust grains, the maximum value of the true gas+dust oxygen abundance in spiral galaxies is 12+log(O/H) ~ 8.95. This value is a factor of ~ 2 higher than the recently estimated solar value. Based on the derived maximum oxygen abundance in galaxies, we found the oxygen yield to be about 0.0035, depending on the fraction of oxygen incorporated into dust grains.
The aim of this note is twofold. The first one is to find conditions on the asymptotic sequence which ensures differentiation of a general asymptotic expansion with respect to it. Our method results from the classical one but generalizes it. As an application, our second aim is to give sharp asymptotic estimates at infinity of the heat kernel on H-type groups by the method of differentiation provided we have the result of the isotropic Heisenberg groups.
Let $X$ be an algebraic variety and let $S$ be a tropical variety associated to $X$. We study the tropicalization map from the moduli space of stable maps into $X$ to the moduli space of tropical curves in $S$. We prove that it is a continuous map and that its image is compact and polyhedral. Loosely speaking, when we deform algebraic curves in $X$, the associated tropical curves in $S$ deform continuously; moreover, the locus of realizable tropical curves inside the space of all tropical curves is compact and polyhedral. Our main tools are Berkovich spaces, formal models, balancing conditions, vanishing cycles and quantifier elimination for rigid subanalytic sets.
When matter undergoes a phase transition from one state to another, usually a change in symmetry is observed, as some of the symmetries exhibited are said to be spontaneously broken. The superconducting phase transition in the underdoped high-Tc superconductors is rather unusual, in that it is not a mean-field transition as other superconducting transitions are. Instead, it is observed that a pseudo-gap in the electronic excitation spectrum appears at temperatures T* higher than Tc, while phase coherence, and superconductivity, are established at Tc (Refs. 1, 2). One would then wish to understand if T* is just a crossover, controlled by fluctuations in order which will set in at the lower Tc (Refs. 3, 4), or whether some symmetry is spontaneously broken at T* (Refs. 5-10). Here, using angle-resolved photoemission with circularly polarized light, we find that, in the pseudogap state, left-circularly polarized photons give a different photocurrent than right-circularly polarized photons, and therefore the state below T* is rather unusual, in that it breaks time reversal symmetry11. This observation of a phase transition at T* provides the answer to a major mystery of the phase diagram of the cuprates. The appearance of the anomalies below T* must be related to the order parameter that sets in at this characteristic temperature .
We present an analysis of the galaxy environment and physical properties of a partial Lyman limit system at z = 0.83718 with HI and metal line components closely separated in redshift space ($|\Delta v| \approx 400$ km/s) towards the background quasar HE1003+0149. The HST/COS far-ultraviolet spectrum provides coverage of lines of oxygen ions from OI to OV. Comparison of observed spectral lines with synthetic profiles generated from Bayesian ionization modeling reveals the presence of two distinct gas phases in the absorbing medium. The low-ionization phase of the absorber has sub-solar metallicities (1/10-th solar) with indications of [C/O] < 0 in each of the components. The OIV and OV trace a more diffuse higher-ionization medium with predicted HI column densities that are $\approx 2$ dex lower. The quasar field observed with VLT/MUSE reveals three dwarf galaxies with stellar masses of $M^* \sim 10^{8} - 10^{9}$ M$_\odot$, and with star formation rates of $\approx 0.5 - 1$ M$_\odot$ yr$^{-1}$, at projected separations of $\rho/R_{\mathrm{vir}} \approx 1.8 - 3.0$ from the absorber. Over a wider field with projected proper separation of $\leq 5$ Mpc and radial velocity offset of $|\Delta v| \leq 1000$ km/s from the absorber, 21 more galaxies are identified in the $VLT$/VIMOS and Magellan deep galaxy redshift surveys, with 8 of them within $1$ Mpc and $500$ km/s, consistent with the line of sight penetrating a group of galaxies. The absorber presumably traces multiple phases of cool ($T \sim 10^4$ K) photoionized intragroup medium. The inferred [C/O] < 0 hints at preferential enrichment from core-collapse supernovae, with such gas displaced from one or more of the nearby galaxies, and confined to the group medium.
In this paper, we introduce an extension of the Dirac equation, very similar to Dirac oscillator, that gives stationary localized wave packets as eigenstates of the equation. The extension to the Dirac equation is achieved through the replacement of the momentum operator by a PT-symmetric generalized momentum operator. In the 1D case, the solutions represent bound particles carrying spin having continuous energy spectrum, where the envelope parameter defines the width of the packet without affecting the dispersion relation of the original Dirac equation. In the 2D case, the solutions are localized wave packets and are eigenstates of the third component of total angular momentum and involve Bessel functions of integral order. In the 3D case, the solutions are localized spherical wave packets with definite total angular momentum.
The role of the equivalence principle in the context of non-relativistic quantum mechanics and matter wave interferometry, especially atom beam interferometry, will be discussed. A generalised form of the weak equivalence principle which is capable of covering quantum phenomena too, will be proposed. It is shown that this generalised equivalence principle is valid for matter wave interferometry and for the dynamics of expectation values. In addition, the use of this equivalence principle makes it possible to determine the structure of the interaction of quantum systems with gravitational and inertial fields. It is also shown that the path of the mean value of the position operator in the case of gravitational interaction does fulfill this generalised equivalence principle.
We improve the theorem of Beck giving a lower bound on the number of $k$-flats spanned by a set of points in real space, and improve the bound of Elekes and T\'oth on the number of incidences between points and $k$-flats in real space.
We present a formalism that enables the study of the non-Markovian dynamics of a three-level ladder system in a single structured reservoir. The three-level system is strongly coupled to a bath of reservoir modes and two quantum excitations of the reservoir are expected. We show that the dynamics only depends on reservoir structure functions, which are products of the mode density with the coupling constant squared. This result may enable pseudomode theory to treat multiple excitations of a structured reservoir. The treatment uses Laplace transforms and an elimination of variables to obtain a formal solution. This can be evaluated numerically (with the help of a numerical inverse Laplace transform) and an example is given. We also compare this result with the case where the two transitions are coupled to two separate structured reservoirs (where the example case is also analytically solvable).
The concept of a L\'evy subordinator is generalized to a family of non-decreasing stochastic processes, which are parameterized in terms of two Bernstein functions. Whereas the independent increments property is only maintained in the L\'evy subordinator special case, the considered family is always strongly infinitely divisible with respect to time, meaning that a path can be represented in distribution as a finite sum with arbitrarily many summands of independent and identically distributed paths of another process. Besides distributional properties of the process, we present two applications to the design of accurate and efficient simulation algorithms. First, each member of the considered family corresponds uniquely to an exchangeable max-stable sequence of random variables, and we demonstrate how the associated extreme-value copula can be simulated exactly and efficiently from its Pickands dependence measure. Second, we show how one obtains different series and integral representations for infinitely divisible probability laws by varying the parameterizing pair of Bernstein functions, without changing the law of one-dimensional margins of the process. As a particular example, we present an exact simulation algorithm for compound Poisson distributions from the Bondesson class, for which the generalized inverse of the distribution function of the associated Stieltjes measure can be evaluated accurately.
Quantum point contact (QPC), one of the typical mesoscopic transport devices, has been suggested to be an efficient detector for quantum measurement. In the context of two-state charge qubit, our previous studies showed that the QPC's measurement back-action cannot be described by the conventional Lindblad quantum master equation.   In this work, we study the measurement problem of a multi-state system, say, an electron in disordered potential, subject to the quantum measurement of the mesoscopic detector QPC. The effect of measurement back-action and the detector's readout current are analyzed, where particular attention is focused on some new features and the underlying physics associated with the measurement-induced delocalization versus the measurement voltages.
The maximum entropy approach operating with quite general entropy measure and constraint is considered. It is demonstrated that for a conditional or parametrized probability distribution $f(x|\mu)$ there is a "universal" relation among the entropy rate and the functions appearing in the constraint. It is shown that the recently proposed variational formulation of the entropic functional can be obtained as a consequence of this relation, that is from the maximum entropy principle. This resolves certain puzzling points appeared in the variational approach.
In spite of large overabundances of Xe II observed in numerous mercury-manganese (HgMn) stars, Xe II oscillator strengths are only available for a very limited number of transitions. As a consequence, several unidentified lines in the spectra of HgMn stars could be due to Xe II. In addition, some predicted Xe II lines are redshifted by about 0.1 A from stellar unidentified lines, raising the question about the wavelength accuracy of the Xe II line data available in the literature. For these reasons we investigated the Xe II lines lying in the 3900-4521 A, 4769-7542 A, and 7660-8000 A spectral ranges of four well-studied HgMn stars. We compared the Xe II wavelengths listed in the NIST database with the position of the lines observed in the high-resolution UVES spectrum of the xenon-overabundant, slowly rotating HgMn stars HR 6000, and we modified them when needed. We derived astrophysical oscillator strengths for all the Xe II observed lines and compared them with the literature values, when available. In this framework, we performed a complete abundance analysis of HD 71066, while we relied on our previous works for the other stars. We find that all the lines with wavelengths related to the 6d and 7s energy levels have a corresponding unidentified spectral line, blueshifted by the same quantity of about 0.1 A in all the four stars, so that we identified these lines as coming from Xe II and modified their NIST wavelength value according to the observed stellar value. We find that the Xe II stellar oscillator strengths may differ from one star to another from 0.0 dex to 0.3 dex. We adopted the average of the oscillator strengths derived from the four stars as final astrophysical oscillator strength.