ShantanuT01/DACTYL-Pretraining huggingface dataset:
We consider the area functional defined by the integral of an Ornstein-Uhlenbeck process which starts from a given value and ends at the time it first reaches zero (its equilibrium level). Exact results are presented for the mean, variance, skewness and kurtosis of the underlying area probability distribution, together with the covariance and correlation between the area and the first passage time. Amongst other things, the analysis demonstrates that the area distribution is asymptotically normal in the weak noise limit, which stands in contrast to the first passage time distribution. Various applications are indicated.
The coronal magnetic field cannot be directly observed, but in principle it can be reconstructed from the comparatively well observed photospheric magnetic field. A popular approach uses a nonlinear force-free model. Non-magnetic forces at the photosphere are significant meaning the photospheric data are inconsistent with the force-free model, and this causes problems with the modeling (De Rosa et al., Astrophys. J. 696, 1780, 2009). In this paper we present a numerical implementation of the Grad-Rubin method for reconstructing the coronal magnetic field using a magnetostatic model. This model includes a pressure force and a non-zero magnetic Lorentz force. We demonstrate our implementation on a simple analytic test case and obtain the speed and numerical error scaling as a function of the grid size.
One of the cornerstones of modern physics is Einstein's special relativity, with its constant speed of light and zero photon mass assumptions. Constraint on the rest mass m_{\gamma} of photons is a fundamental way to test Einstein's theory, as well as other essential electromagnetic and particle theories. Since non-zero photon mass can give rise to frequency-(or energy-) dependent dispersions, measuring the time delay of photons with different frequencies emitted from explosive astrophysical events is an important and model-independent method to put such a constraint. The cosmological gamma-ray bursts (GRBs), with short time scales, high redshifts as well as broadband prompt and afterglow emissions, provide an ideal testbed for m_{\gamma} constraints. In this paper we calculate the upper limits of the photon mass with GRB early time radio afterglow observations as well as multi-band radio peaks, thus improve the results of Schaefer (1999) by nearly half an order of magnitude.
We present the first determination of the radial velocities and metallicities of 78 red giant stars in the isolated dwarf irregular galaxy WLM. Observations of the calcium II triplet in these stars were made with FORS2 at the VLT-UT2 in two separated fields of view in WLM, and the [Fe/H] values were conformed to the Carretta & Gratton (1997) metallicity scale. The mean metallicity is <[Fe/H]> = -1.27 +/- 0.04 dex, with a standard deviation of 0.37. We find that the stars in the inner field are more metal rich by [Fe/H] =0.30 +/- 0.06 dex. These results are in agreement with previous photometric studies that found a radial population gradient, as well as the expectation of higher metallicities in the central star forming regions. Age estimates using Victoria-Regina stellar models show that the youngest stars in the sample (< 6 Gyr) are more metal rich by [Fe/H] = 0.32 +/- 0.08 dex. These stars also show a lower velocity dispersion at all elliptical radii compared to the metal-poor stars. Kinematics for the whole red giant sample suggest a velocity gradient approximately half that of the gas rotation curve, with the stellar component occupying a thicker disk decoupled from the HI rotation plane. Taken together, the kinematics, metallicities, and ages in our sample suggest a young metal-rich, and kinematically cold stellar population in the central gas-rich regions of WLM, surrounded by a separate dynamically hot halo of older, metal poor stars.
3C186, a radio-loud quasar at $z=1.0685$, was previously reported to have both velocity and spatial offsets from its host galaxy, and has been considered as a promising candidate for a gravitational wave recoiling black hole triggered by a black hole merger. Another possible scenario is that 3C186 is in an on-going galaxy merger, exhibiting a temporary displacement. In this study, we present analyses of new deep HST/WFC3-IR and ACS images, aiming to characterize the host galaxy and test this alternative scenario. We carefully measure the light-weighted center of the host and reveal a significant spatial offset from the quasar core ($11.1\pm0.1$kpc). The direction of the confirmed offset aligns almost perpendicularly to the radio jet. We do not find evidence of a recent merger, such as a young starburst in disturbed outskirts, but only marginal light concentration in F160W at $\sim30$kpc. The host consists of matured ($>200$Myr) stellar populations and one compact star-forming region. We compare with hydro-dynamical simulations and find that those observed features are consistently seen in late-stage merger remnants. Taken together, those pieces of evidence indicate that the system is not an on-going/young merger remnant, suggesting that the recoiling black hole scenario is still a plausible explanation for the puzzling nature of 3C186.
Equal-arm interferometric detectors of gravitational radiation allow phase measurements many orders of magnitude below the intrinsic phase stability of the laser injecting light into their arms. This is because the noise in the laser light is common to both arms, experiencing exactly the same delay, and thus cancels when it is differenced at the photo detector. In this situation, much lower level secondary noises then set overall performance. If, however, the two arms have different lengths (as will necessarily be the case with space-borne interferometers), the laser noise experiences different delays in the two arms and will hence not directly cancel at the detector. In order to solve this problem, a technique involving heterodyne interferometry with unequal arm lengths and independent phase-difference readouts has been proposed. It relies on properly time-shifting and linearly combining independent Doppler measurements, and for this reason it has been called Time-Delay Interferometry (or TDI). This article provides an overview of the theory and mathematical foundations of TDI as it will be implemented by the forthcoming space-based interferometers such as the Laser Interferometer Space Antenna (LISA) mission. We have purposely left out from this first version of our ``Living Review'' article on TDI all the results of more practical and experimental nature, as well as all the aspects of TDI that the data analysts will need to account for when analyzing the LISA TDI data combinations. Our forthcoming ``second edition'' of this review paper will include these topics.
A new derivation of the classic asymptotic expansion of the n-th prime is presented. A fast algorithm for the computation of its terms is also given, which will be an improvement of that by Salvy (1994).   Realistic bounds for the error with $\li^{-1}(n)$, after having retained the first m terms, for $1\le m\le 11$, are given. Finally, assuming the Riemann Hypothesis, we give estimations of the best possible $r_3$ such that, for $n\ge r_3$, we have $p_n> s_3(n)$ where $s_3(n)$ is the sum of the first four terms of the asymptotic expansion.
Local solvability is analyzed for natural families of partial differential operators having double characteristics. In some families the set of all operators that are not locally solvable is shown to have both infinite dimension and infinite codimension.
Kilonovae represent an important electromagnetic counterpart for compact binary mergers, which could become the most commonly detected gravitational wave (GW) source. Follow-up observations, triggered by GW events, of kilonovae are nevertheless difficult due to poor localization by GW detectors and due to their faint near-infrared peak emission that has limited observational capability. We show that the Near-Infrared Camera (NIRCam) on the James Webb Space Telescope (JWST) will be able to detect kilonovae within the relevant GW-detection range of $\sim$ 200 Mpc in short ($\lesssim$ 12-second) exposure times for a week following the merger. Despite this sensitivity, a kilonova search fully covering a fiducial localized area of $10$ $\mbox{deg}^2$ will not be viable with NIRCam due to its limited field of view. However, targeted surveys may be developed to optimize the likelihood of discovering kilonovae efficiently within limited observing time. We estimate that a survey of $10$ $\mbox{deg}^2$ focused on galaxies within 200 Mpc would require about 13 hours, dominated by overhead times; a survey further focused on galaxies exhibiting high star-formation rates would require $\sim$ 5 hours. The characteristic time may be reduced to as little as $\sim$4 hours, without compromising the likelihood of detecting kilonovae, by surveying sky areas associated with 50%, rather than 90%, confidence regions of 3 GW events, rather than a single event. On detection and identification of a kilonova, a limited number of NIRCam follow-up observations could constrain the properties of matter ejected by the binary and the equation of state of dense nuclear matter.
The analysis of high spectral resolution spectroscopic and spectropolarimetric observations constitute a very powerful way of inferring the dynamical, thermodynamical, and magnetic properties of distant objects. However, these techniques are photon-starving, making it difficult to use them for all purposes. One of the problems commonly found is just detecting the presence of a signal that is buried on the noise at the wavelength of some interesting spectral feature. This is specially relevant for spectropolarimetric observations because typically, only a small fraction of the received light is polarized. We present in this note a Bayesian technique for the detection of spectropolarimetric signals. The technique is based on the application of the non-parametric relevance vector machine to the observations, which allows us to compute the evidence for the presence of the signal and compute the more probable signal. The method would be suited for analyzing data from experimental instruments onboard space missions and rockets aiming at detecting spectropolarimetric signals in unexplored regions of the spectrum such as the Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP) sounding rocket experiment.
The profile of the fluorescent iron line from black hole accretion disks is a powerful diagnostic of black hole properties, such as spin and inclination. The state-of-the-art, however, considers an accretion disk whose angular momentum is aligned with that of the black hole; this is a very constraining assumption which is unlikely to apply to many or even most astrophysical systems. Here, we present the first simulation of the reflection spectrum from warped accretion disks using a realistic model of the reflected emission based on the xillver code. We present the effects that the radial location of the warp and the tilt angle have on the line profile, and highlight that the results are highly dependent on the azimuth position of the observer relative to the tilt angle. We fit these profiles in XSpec with the standard relxill lamppost model to quantify the effect that neglecting the disk warps has on the inferred black hole spins and inclinations. We show that fits with two-component relxill can be used to derive more accurate spin and inclination estimates.
This paper provides an alternate proof to parts of the Goulden-Slofstra formula for enumerating two vertex maps by genus, which is an extension of the famous Harer-Zagier formula that computes the Euler characteristic of the moduli space of curves. This paper also shows a further simplification to the Goulden-Slofstra formula. Portions of this alternate proof will be used in a subsequent paper, where it forms a basis for a more general result that applies for a certain class of maps with an arbitrary number of vertices.
A novel laser molecular beam epitaxy (LMBE) system for the fabrication of atomically controlled oxides superlattices and an x-ray diffractometer that measures spatially-resolved x-ray diffraction spectra have been developed based on the concept of combinatorial methodology. The LMBE chamber has two moving masks, an automated target stage, a substrate heating laser, and an in-situ scanning reflection high-energy electron diffraction system. The x-ray diffractometer with a curved monochromator and two-dimensional detector is used for rapid concurrent x-ray diffraction intensity mapping with the two axes of the detector corresponding to the diffraction angle and a position in the sample.
We first consider interval partitions whose complements are Lebesgue-null and introduce a complete metric that induces the same topology as the Hausdorff distance (between complements). This is done using correspondences between intervals. Further restricting to interval partitions with alpha-diversity, we then adjust the metric to incorporate diversities. We show that this second metric space is Lusin. An important feature of this topology is that path-continuity in this topology implies the continuous evolution of diversities. This is important in related work on tree-valued stochastic processes where diversities are branch lengths.
It is now well established that many young brown dwarfs exhibit characteristics similar to classical T Tauri stars, including infrared excess from disks and emission lines related to accretion. Whether the same holds true for even lower mass objects, namely those near and below the Deuterium-burning limit, is an important question. Here we present optical spectra of six isolated planetary mass candidates in Chamaeleon II, Lupus I and Ophiuchus star-forming regions, recently identified by Allers and collaborators to harbor substantial mid-infrared excesses. Our spectra, from ESO's Very Large Telescope and New Technology Telescope, show that four of the targets have spectral types in the ~M9-L1 range, and three of those also exhibit H_alpha. Their luminosities are consistent with masses of ~5-15 M_{Jupiter} according to models of Chabrier, Baraffe and co-workers, thus placing these four objects among the lowest mass brown dwarfs known to be surrounded by circum-sub-stellar disks. Our findings bolster the idea that free-floating planetary mass objects could have infancies remarkably similar to those of Sun-like stars and suggest the intriguing possibility of planet formation around primaries whose masses are comparable to those of extra-solar giant planets. Another target appears to be a brown dwarf (~M8) with prominent H_alpha emission, possibly arising from accretion. The sixth candidate is likely a background source, underlining the need for spectroscopic confirmation.
The continuum-discretized coupled-channels method (CDCC) for exclusive reactions and the eikonal reaction theory (ERT) as an extension of CDCC to inclusive reactions are applied to deuteron induced reactions. The CDCC result reproduces experimental data on the reaction cross section for $d+^{58}$Ni scattering at 200 MeV/nucleon and ERT does data on the neutron-stripping cross section for inclusive $^7$Li$(d,n)$ reaction at 40 MeV. For deuteron induced reactions at 200 MeV/nucleon, target-dependence of the reaction, elastic-breakup, nucleon-stripping, nucleon-removal, complete- and incomplete-fusion cross sections is clearly explained by simple formulae. Accuracy of the Glauber model is also investigated.
Honeycomb structure has a natural extension to the three dimensions. Simple examples are hyperhoneycomb and stripy-honeycomb lattices, which are realized in $\beta $-Li$_{2}$IrO$_{3}$ and $\gamma $-Li$_{2}$IrO$_{3}$, respectively. We propose a wide class of three-dimensional (3D) honeycomb lattices which are loop-nodal semimetals. Their edge states have intriguing properties similar to the two-dimensional honeycomb lattice in spite of dimensional difference. Partial flat bands emerge at the zigzag or beard edge of the 3D honeycomb lattice, whose boundary is given by the Fermi loop in the bulk spectrum. Analytic solutions are explicitly constructed for them. On the other hand, perfect flat bands emerge in the zigzag-beard edge or when the anisotropy is large. All these 3D honeycomb lattices become strong topological insulators with the inclusion of the spin-orbit interaction. Furthermore, point-nodal semimetals may be realized in the presence of both the antiferromagnetic order and the spin-orbit interaction.
Based on N different coherent states with equal weights and phase-space rotation symmetry, we introduce N-headed incoherent superposition states (NHICSSs) and N-headed coherent superposition states (NHCSSs). These N coherent states are associated with N-order roots of the same complex number. We study and compare properties of NHICSSs and NHCSSs, including average photon number, Mandel Q parameter, quadrature squeezing, Fock matrix elements and Wigner function. Among all these states, only 2HCSS (i.e., Schrodinger cat state) presents quadrature-squeezing effect. Our theoretical results can be used as a reference for researchers in this field.
We present CCD BVRI photometry for PSN J07285387+3349106 in NGC 2388 collected from 2015 February 17 until March 17. Decaying by 3.6 mag in the R band in the first 20 days post-maximum, this object is among the fastest supernovae observed to date. The peak absolute R magnitude exceeds -18.7 and may be as high as -20.1.
A quantum gravity-gradiometer consists of two spatially separated ensembles of atoms interrogated by pulses of a common laser beam. Laser pulses cause the probability amplitudes of atomic ground-state hyperfine levels to interfere, producing two motion-sensitive phase shifts which allow the measurement of the average acceleration of each ensemble, and, via simple differencing, of the acceleration gradient. Here I propose entangling the quantum states of the two ensembles prior to the pulse sequence, and show that entanglement encodes their relative acceleration in a single interference phase which can be measured directly, with no need for differencing.
We analyse in detail the X-ray data of the microquasar Cygnus X-3 obtained during major radio flaring episodes in 2006 with multiple observatories. The analysis consists of two parts: probing the fast (~ 1 minute) X-ray spectral evolution with Principal Component Analysis followed by subsequent spectral fits to the time-averaged spectra (~ 3 ks). Based on the analysis we find that the overall X-ray variability during major flaring episodes can be attributed to two principal components whose evolution based on spectral fits is best reproduced by a hybrid Comptonization component and a bremsstrahlung or saturated thermal Comptonization component. The variability of the thermal component is found to be linked to the change in the X-ray/radio spectral state. In addition, we find that the seed photons for the Comptonization originate in two seed photon populations that include the additional thermal emission and emission from the accretion disc. The Comptonization of the photons from the thermal component dominates, at least during the major radio flare episode in question, and the Comptonization of disc photons is intermittent and can be attributed to the phase interval 0.2-0.4. The most likely location for Comptonization is in the shocks in the jet.
We analyze the stability of stationary solutions of a singular Vlasov type hydrodynamic equation (HE). This equation was derived (under suitable assumptions) as the hydrodynamical scaling limit of the Hamiltonian evolution of a system consisting of a massive piston immersed in an ideal gas of point particles in a box. We find explicit criteria for global stability as well as a class of solutions which are linearly unstable for a dense set of parameter values. We present evidence (but no proof) that when the mechanical system has initial conditions ``close'' to stationary stable solutions of the HE then it stays close to these solutions for a time which is long compared to that for which the equations have been derived. On the other hand if the initial state of the particle system is close to an unstable stationary solutions of the HE the mechanical motion follows for an extended time a perturbed solution of that equation: we find such approximate periodic solutions that are linearly stable.
We present a statistical analysis of the X-ray luminosity of rotation powered pulsars and their surrounding nebulae using the sample of Kargaltsev & Pavlov (2008) and we complement this with an analysis of the gamma-ray-emission of Fermi detected pulsars. We report a strong trend in the efficiency with which spin-down power is converted to X-ray and gamma-ray emission with characteristic age: young pulsars and their surrounding nebulae are efficient X-ray emitters, whereas in contrast old pulsars are efficient gamma-ray emitters. We divided the X-ray sample in a young (Tau < 1.7x10^4 yr) and old sample and used linear regression to search for correlations between the logarithm of the X-ray and gamma-ray luminosities and the logarithms of the periods and period derivatives. The X-ray emission from young pulsars and their nebulae are both consistent with L_X ~ Pdot^3/P^6. For old pulsars and their nebulae the X-ray luminosity is consistent with a more or less constant efficiency eta = L_X/Edot = ~ 8x10^-5. For the gamma-ray luminosity we confirm that L_gamma ~ Edot^(1/2).   We discuss these findings in the context of pair production inside pulsar magnetospheres and the striped wind model. We suggest that the striped wind model may explain the similarity between the X-ray properties of the pulsar wind nebulae and the pulsars themselves, which according to the striped wind model may both find their origin outside the light cylinder, in the pulsar wind zone.
The circumstellar disk density distributions for a sample of 63 Be southern stars from the BeSOS survey were found by modelling their H$\alpha$ emission line profiles. These disk densities were used to compute disk masses and disk angular momenta for the sample. Average values for the disk mass are 3.4$\times$10$^{-9}$ and 9.5$\times$10$^{-10}$ $M_{\star}$ for early (B0-B3) and late (B4-B9) spectral types, respectively. We also find that the range of disk angular momentum relative to the star are between 150-200 and 100-150 $J_{\star}/M_{\star}$, again for early and late-type Be stars respectively. The distributions of the disk mass and disk angular momentum are different between early and late-type Be stars at a 1\% level of significance. Finally, we construct the disk mass distribution for the BeSOS sample as a function of spectral type and compare it to the predictions of stellar evolutionary models with rapid rotation. The observed disk masses are typically larger than the theoretical predictions, although the observed spread in disk masses is typically large.
An entanglement measure for pure-state continuous-variable bi-partite problem, the Schmidt number, is analytically calculated for one simple model of atom-field scattering.