ShantanuT01/DACTYL-Pretraining huggingface dataset:
Time-distance helioseismology is a set of powerful tools to study features below the Sun's surface. Inverse methods are needed to interpret time-distance measurements, with many examples in the literature. However, techniques that utilize a more statistical approach to inferences, and broadly used in the astronomical community, are less-commonly found in helioseismology. This article aims to introduce a potentially powerful inversion scheme based on Bayesian probability theory and Monte Carlo sampling that is suitable for local helioseismology. We describe the probabilistic method and how it is conceptually different from standard inversions used in local helioseismology. Several example calculations are carried out to compare and contrast the setup of the problems and the results that are obtained. The examples focus on two important phenomena studied with helioseismology: meridional circulation and supergranulation. Numerical models are used to compute synthetic observations, providing the added benefit of knowing the solution against which the results can be tested. For demonstration purposes, the problems are formulated in two and three dimensions, using both ray- and Born-theoretical approaches. The results seem to indicate that the probabilistic inversions not only find a better solution with much more realistic estimation of the uncertainties, but they also provide a broader view of the range of solutions possible for any given model, making the interpretation of the inversion more quantitative in nature. Unlike the progress being made in fundamental measurement schemes in local helioseismology that image the far side of the Sun, or have detected signatures of global Rossby waves, among many others, inversions of those measurements have had significantly less success. Such statistical methods may help overcome some of these barriers to move the field forward.
The Galactic globular cluster 47 Tucanae (47 Tuc) shows a rare increase in its velocity dispersion profile at large radii, indicative of energetic, yet bound, stars at large radii dominating the velocity dispersion and, potentially, of ongoing evaporation. Escaping stars will form tidal tails, as seen with several Galactic globular clusters, however, the tidal tails of 47 Tuc are yet to be uncovered. We model these tails of 47 Tuc using the most accurate input data available, with the specific aim of determining their locations, as well as the densities of the epicyclic overdensities within the tails. The overdensities from our models show an increase of 3-4% above the Galactic background and, therefore, should be easily detectable using matched filtering techniques. We find that the most influential parameter with regard to both the locations and densities of the epicyclic overdensities is the Heliocentric distance to the cluster. Hence, uncovering these tidal features observationally will contribute greatly to the ongoing problem of determining the distance to 47 Tuc, tightly constraining the distance of the cluster independent of other methods. Using our streakline method for determining the locations of the tidal tails and their overdensities, we show how, in principle, the shape and extent of the tidal tails of any Galactic globular cluster can be determined without resorting to computationally expensive N-body simulations.
We study the matter bispectrum of large structure by comparing theoretical models (perturbation theories and halo models) to numerical simulations using shape and amplitude correlators. We show that among the perturbation theories at one loop the effective field theory of large scale structure extends the furthest into the non-linear regime. We analyse the one and two-loop bispectra in the renormalised perturbation theory and we show that there is a significant extension in the range where results are accurate when going to two loops. In the case of the halo model, we show that there are deficiencies in the modelling of the two-halo term at redshifts z>0 that worsen in the past. Based on this observation and on the shapes identified in the halo model, we build a simple `three-shape model' that provides a good fit to N-body simulations on all scales, at both low and high redshifts. We show that this model can be easily extended to local and equilateral primordial non-Gaussianity using the same shapes.
We report the first observations of Type III-like bursts at frequencies 10 30 MHz. More than 1000 such bursts during 2002 2004 have been analyzed. The frequency drift of these bursts is several times that of decameter Type III bursts. A typical duration of the Type III-like bursts is 1 2 s. These bursts are mainly observed when the source active region is located within a few days from the central meridian. The drift rate of the Type III-like bursts can take a large value by considering the velocity of Type III electrons and the group velocity of generated electromagnetic waves.
Given an $n$-connected binary matroid, we obtain a necessary and sufficient condition for its single-element coextensions to be $n$-connected.
The eclipsing binary DI Herculis garnered interest for several decades because of an apparent disagreement between the observed and calculated values of the apsidal precession rate. The problem was resolved when both stars were found to have high obliquities, but the reason for the high obliquities is unknown. Here we investigate the possibility that the obliquities are (or were) excited by an unseen tertiary star. Obliquity excitation in the current orbital configuration can be ruled out with existing data; any tertiary star that is sufficiently close or massive to overcome the strong spin-orbit coupling of the binary would have been detected through various dynamical effects. It remains possible that the orbit of DI Herculis was initially wider and the obliquity was excited during high-eccentricity tidal migration driven by a tertiary companion, but in this scenario it would be difficult to explain why the observed spin rates are much faster than the pseudo-synchronous rate. In addition, inward migration is most likely to arise when the mass of the perturbing star is comparable to the binary mass, and such a bright tertiary would have been detected in imaging or spectroscopic data. Alternative explanations that do not invoke a tertiary star should be sought for the large obliquities in DI Herculis.
Multi-frequency radio observations of the radio bridge of a powerful classical double radio source can be used to determine: the beam power of the jets emanating from the AGN; the total time the source will actively produce jets that power large-scale radio emission; the thermal pressure of the medium in the vicinity of the radio source; and the total mass, including dark matter, of the galaxy or cluster of galaxies traced by the ambient gas that surrounds the radio source. Empirical determinations of each of these quantities are obtained and analyzed for 22 radio sources. Typical beam powers are about $10^{45} {erg s}^{-1}$. The characteristic or total time the AGN will actively produce a collimated outflow is estimated. Typical total lifetimes are $\sim (10^7$ to $10^8$) years. Total masses, and mass-density profiles, similar to those of low-redshift clusters of galaxies are obtained. Thus, some clusters of galaxies, or cores of clusters, exist at redshifts of one to two.   A new method of estimating the thermal pressure of the ambient gas in the vicinity of a powerful classical double radio source is presented. This new estimate is independent of synchrotron and inverse Compton aging arguments, and depends only upon the properties of the radio lobe and the shape of the radio bridge. Thermal pressures on the order of $10^{-10} {dyne cm}^{-2}$, typical of gas in low-redshift clusters of galaxies, are found for the environments of the sources studied here. It is shown that appreciable amounts of cosmic microwave background diminution (the Sunyaev-Zel'dovich effect) are expected from many of these clusters. This could be detected at high frequency where the emission from the radio sources is weak.
In this paper we investigate an optimal dividend problem with transaction costs, where the surplus process is modelled by a refracted L\'evy process and the ruin time is considered with Parisian delay. Presence of the transaction costs implies that one need to consider the impulse control problem as a control strategy in such model. An impulse policy $(c_1,c_2)$, which is to reduce the reserves to some fixed level $c_1$ whenever they are above another level $c_2$ is an important strategy for the impulse control problem. Therefore, we give sufficient conditions under which the above described impulse policy is optimal. Further, we give the new analytical formulas for the Parisian refracted $q$-scale functions in the case of the linear Brownian motion and the Cr\'amer-Lundberg process with exponential claims. Using these formulas we show that for these models there exists a unique $(c_1, c_2)$ policy which is optimal for the impulse control problem. Numerical examples are also provided.
Twisted sectors --solutions to the equations of motion with non-trivial monodromies-- of three dimensional Euclidean gravity are studied. We argue that upon quantization this new sector of the theory provides the necessary (and no more) degrees of freedom to account for the Bekenstein-Hawking entropy.
Let $G$ be a finite group, $\Lambda$ an absolutely irreducible $\Z[G]$-module and $w$ a weight of $\Lambda$.   To any Galois covering with group $G$ we associate two correspondences, the Schur and the Kanev correspondence.   We work out their relation and compute their invariants.   Using this, we give some new examples of Prym-Tyurin varieties.
Wythoff's Game is a game for two players playing alternately on two stacks of tiles. On her turn, a player can either remove a positive number of tiles from one stack, or remove an equal positive number of tiles from both stacks. The last player to move legally wins the game. We propose and study a new extension of this game to more than two stacks, which we call Twyst-off, inspired by the Reidemeister moves of knot theory. From an ordered sequence of stacks of tiles, a player may either remove a positive number of tiles from one of the two end stacks, or remove the same positive number of tiles from two consecutive stacks. Whenever an interior stack is reduced to 0, the two neighboring stacks are combined. In this paper, we prove several results about those Twyst-off positions that can be won by the second player (these are called P-positions). We prove an existence and uniqueness result that makes the visualization of data on three-stack P-positions possible. This shows that many such positions are symmetric, like the easy general examples (a,a,a) and (a,a+1,a). The main result establishes tight bounds on those three-stack P-positions that are not symmetric. We go on to prove one general structural result for positions with an arbitrary number of stacks. We also prove facts about the game when allowing stacks of infinite size, including classifying all positions with only infinite stacks in sequences of up to six stacks.
We simulate entanglement sharing between two end-nodes of a quantum network using SeQUeNCe, an open-source simulation package for quantum networks. Our focus is on the rate of entanglement generation between the end-nodes with many repeaters with a finite quantum memory lifetime. Our findings demonstrate that the performance of quantum connection depends highly on the entanglement management protocol scheduling entanglement generation and swapping, resulting in the final end-to-end entanglement. Numerical and analytical simulations show limits of connection performance for a given number of repeaters involved, memory lifetimes for a given distance between the end nodes, and an entanglement management protocol.
We explore how the co-evolution of massive black holes (MBHs) and galaxies is affected by environmental effects, addressing in particular MBHs hosted in the central galaxies of clusters (we will refer to these galaxies in general as 'CGs'). Recently the sample of MBHs in CGs with dynamically measured masses has increased, and it has been suggested that these MBH masses (M_BH) deviate from the expected correlations with velocity dispersion (sigma) and mass of the bulge (M_bulge) of the host galaxy: MBHs in CGs appear to be `over-massive'. This discrepancy is more pronounced when considering the M_BH-sigma relation than the M_BH-M_bulge one. We show that this behavior stems from a combination of two natural factors, (i) that CGs experience more mergers involving spheroidal galaxies and their MBHs, and (ii) that such mergers are preferentially gas-poor. We use a combination of analytical and semi-analytical models to investigate the MBH-galaxy co-evolution in different environments and find that the combination of these two factors explains the trends observed in current data-sets.
Inspired by a Zudilin-Zhao's supercongruences pattern related to Ramanujan-like series for $1/\pi^k$, we conjecture a kind of $p$-adic expansions.
Here we report on new, multi-wavelength radio observations of the unusual point source "N3" that appears to be located in the vicinity of the Galactic Center. VLA observations between 2 and 50 GHz reveal that N3 is a compact and bright source (56 mJy at 10 GHz) with a non-thermal spectrum superimposed upon the non-thermal radio filaments (NTFs) of the Radio Arc. Our highest frequency observations place a strict upper limit of 65 x 28 mas on the size of N3. We compare our observations to those of Yusef-Zadeh & Morris (1987) and Lang et al. (1997) and conclude that N3 is variable over long time scales. Additionally, we present the detection of a compact molecular cloud located adjacent to N3 in projection. CH3CN, CH3OH, CS, HC3N, HNCO, SiO, SO, and NH3 are detected in the cloud and most transitions have FWHM line widths of ~20 km/s. The rotational temperature determined from the metastable NH3 transitions ranges from 79 K to 183 K depending on the transitions used. We present evidence that this molecular cloud is interacting with N3. After exploring the relationship between the NTFs, molecular cloud, and N3, we conclude that N3 likely lies within the Galactic Center. We are able to rule out the HII region, young supernova, active star, AGN, and micro-quasar hypotheses for N3. While a micro-blazar may provide a viable explanation for N3, additional observations are needed to determine the physical counterpart of this mysterious source.
In the articles [1] and [2] of D. Finch, M. Haltmeier, S. Patch and D. Rakesh inversion formulas were found in any dimension $n\geq2$ for recovering a smooth function with compact support in the unit ball from spherical means centered on the unit sphere. The aim of this article is to show that the methods used in [1], [2] can be modified in order to get similar inversion formulas from spherical means centered on an ellipsoid in two and three dimensional spaces.
We investigate the phenomenon of producing vibration-induced rotational motion in a cylinder filled with achiral rods and being vibrated by an external drive. The arrangement of the rods develops chirality as a result of the interaction of gravity and steric hindrance, which is responsible for the induced motion. A two-rod arrangement is sufficient to generate a persistent motion. The average angular velocity $\langle \omega \rangle$ of the rods at long times varies non-monotonically with the packing fraction $\phi$ for a given drive strength $\Gamma$. Though the precise nature of the variation of $\langle \omega \rangle$ with $\phi$ depends on the details of the interaction between individual rods, its general characteristics hold true for rods of various materials and geometries. A stochastic model based on the asymmetric simple exclusion process helps in understanding the key features of our experiments.
We studied the temperature and metal abundance distributions of the intra-cluster medium (ICM) in a group of galaxies NGC 1550 observed with Suzaku. The NGC 1550 is classified as a fossil group, which have few bright member galaxies except for the central galaxy. Thus, such a type of galaxy is important to investigate how the metals are enriched to the ICM. With the Suzaku XIS instruments, we directly measured not only Si, S, and Fe lines but also O and Mg lines and obtained those abundances to an outer region of ~0.5 r_180 for the first time, and confirmed that the metals in the ICM of such a fossil group are indeed extending to a large radius. We found steeper gradients for Mg, Si, S, and Fe abundances, while O showed almost flat abundance distribution. Abundance ratios of alpha-elements to Fe were similar to those of the other groups and poor clusters. We calculated the number ratio of type II to type Ia supernovae for the ICM enrichment to be 2.9 +- 0.5 within 0.1 r_180, and the value was consistent with those for the other groups and poor clusters observed with Suzaku. We also calculated metal mass-to-light ratios (MLRs) for Fe, O and Mg with B-band and K-band luminosities of the member galaxies of NGC 1550. The derived MLRs were comparable to those of NGC 5044 group in the r<0.1 r_180 region, while those of NGC 1550 are slightly higher than those of NGC 5044 in the outer region.
We study structure functions of rotation measures in the Canadian Galactic Plane Survey (CGPS) region and the North Galactic Pole (NGP) to extract the interstellar medium (ISM) fluctuation information. The CGPS data are divided into three longitude intervals: $82^\circ<l<96^\circ$ (CGPS1), $115^\circ<l<130^\circ$ (CGPS2) and $130^\circ<l<146^\circ$ (CGPS3). The structure functions of all three regions have large uncertainties when the angular separation is smaller than $\delta\theta\approx 1^\circ$. A power law can fit the structure function well for $\delta\theta>1^\circ$. The power law indices get smaller from CGPS1 to CGPS3 and the amplitudes decrease. The variations of the large-scale field and the electron density have only negligible effects on the structure function and thus cannot account for the changes, indicating that the turbulent properties of the Galactic ISM are intrinsically longitude-dependent. The Kolmogorov-like fluctuation spectrum of the electron density or the magnetic field should produce a power law structure function with an index of 5/3 or 2/3, neither of which is consistent with our results of small indices in the three sub-CGPS regions. For the NGP region, the structure function is flat, showing that the rotation measures are mostly intrinsic to the extragalactic sources, and the ISM is very random in that part of our Galaxy. It is obvious that the ISM fluctuation is latitude-dependent when comparing the results in the NGP region and the CGPS regions.
Systematic surveys of astronomical objects often lead to discoveries, but always provide invaluable information for statistical studies of well-defined samples. They also promote follow-up investigations of individual objects or classes. Surveys using a yet unexplored observing wavelength, a novel technique or a new instrument are of special importance. Significantly improved observing parameters (e.g. sensitivity, angular resolution, monitoring capability) provide new insight into the morphological and physical properties of the objects studied. I give a brief overview of the important Very Long Baseline Interferometry (VLBI) imaging surveys conducted in the past. A list of surveys guides us through the developments up until the present days. I also attempt to show directions for the near future.
We study the effect of spin-phonon coupling in small magnetic clusters, concentrating on a S=1/2 ring of 4 spins coupled antiferromagnetically. If the phonons are treated as classical variables, there is a critical value of the spin-phonon coupling above which a static distortion occurs. This is a good approximation if the zero point energy is small compared to the energy gain due to the distortion, which is true for large exchange interactions compared to the phonons energy ($J\gg\hbar\omega$). In the opposite limit, one can integrate out the phonon degrees of freedom and get an effective spin hamiltonian. Using exact diagonalizations to include the quantum nature of both spins and phonons, we obtain the spectrum in the whole range of parameters and explicit the crossover between the classical and quantum regimes. We then establish quantitatively the limits of validity of two widely used approaches (one in the quantum and one in the classical limits) and show that they are quite poor for small magnetic clusters. We also show that upon reducing $\hbar\omega/J$ the first excitation of a 4-site cluster becomes a singlet, a result that could be relevant for Cu$_2$Te$_2$O$_5$Br$_2$.
This was an expository lecture for the graduate student colloquium at the University of Arizona on the topic of numbers.
We study the short- and long-term effects of an intermediate mass black hole (IMBH) on the orbits of stars bound to the supermassive black hole (SMBH) at the center of the Milky Way. A regularized N-body code including post-Newtonian terms is used to carry out direct integrations of 19 stars in the S-star cluster for 10 Myr. The mass of the IMBH is assigned one of four values from 400 Msun to 4000 Msun, and its initial semi-major axis with respect to the SMBH is varied from 0.3-30 mpc, bracketing the radii at which inspiral of the IMBH is expected to stall. We consider two values for the eccentricity of the IMBH/SMBH binary, e=(0,0.7), and 12 values for the orientation of the binary's plane. Changes at the level of 1% in the orbital elements of the S-stars could occur in just a few years if the IMBH is sufficiently massive. On time scales of 1 Myr or longer, the IMBH efficiently randomizes the eccentricities and orbital inclinations of the S-stars. Kozai oscillations are observed when the IMBH lies well outside the orbits of the stars. Perturbations from the IMBH can eject stars from the cluster, producing hypervelocity stars, and can also scatter stars into the SMBH; stars with high initial eccentricities are most likely to be affected in both cases. The distribution of S-star orbital elements is significantly altered from its currently-observed form by IMBHs with masses greater than 1000 Msun if the IMBH/SMBH semi-major axis lies in the range 3-10 mpc. We use these results to further constrain the allowed parameters of an IMBH/SMBH binary at the Galactic center.
Hecke expected that an explicit set of theta series obtained from maximal orders of the definite quaternion algebra over Q which is ramified at a prime N will be a basis of the space of holomorphic modular forms of weight 2 and level N. However, later Eichler noticed that Hecke's conjecture does not hold in general. It is natural to ask for the dimension of the subspace of the modular forms spanned by the theta series. This question is called Hecke's basis problem. Boecherer and Schulze-Pillot have given an answer using the theory of theta liftings. In this paper we will give another proof of their results using arithmetic and geometric properties of the modular curve.
In any dimension $n \geq 3$, we show that spherically symmetric bounded energy solutions of the defocusing energy-critical non-linear Schr\"odinger equation $i u_t + \Delta u = |u|^{\frac{4}{n-2}} u$ in $\R \times \R^n$ exist globally and scatter to free solutions; this generalizes the three and four dimensional results of Bourgain and Grillakis. Furthermore we have bounds on various spacetime norms of the solution which are of exponential type in the energy, which improves on the tower-type bounds of Bourgain. In higher dimensions $n \geq 6$ some new technical difficulties arise because of the very low power of the non-linearity.