adsabs/WIESP2022-NER huggingface dataset:
Paper: 2017MNRAS.470.1073K (fulltext)
the zero-order solution: The last system of equations can be rewritten in the following form: Then, the solution of the last system has the form To obtain the first and next amendments, we use a form such as N i = C η −α Φ i ( x ), and when we insert N 0 into ( 11 ), we will obtain an equation for N 1 : If we expand the exponent in the last equation in a Taylor series, we obtain Here, the first condition ( 12 ) was applied, i.e. the integration was carried out from 0 to x . We will seek a solution of the last equation in the following form: After an expansion of the exponent in a series followed by integration, we obtain The last condition ( 12 ) for finding B was used, i.e. Φ 1 ( x 0 ) = 0, and then B has the following form: And, as a result, the first amendment is When we perform similar actions in order to find the second amendment, we will obtain An exact solution for this problem was initially obtained by Dolginov Toptygin ( 1967 ). In our notation, it has the following form: where F ( a, b ; x ) is the confluent hypergeometrical function (Bateman Erdelyi 1953 ). In particular, from the property of the confluent hypergeometrical function, it follows that for the simpler case when α = 3, the exact solution ( A11 ) has the form APPENDIX B: κ = <italic>k</italic><sub>0</sub>η To obtain a solution for the problem, we introduce the following dimensionless variables: and . Then, taking into account ( 6 ) and ( 9 ), we obtain a system of questions for finding the zero-order solution: The last system can be rewritten in the following form: Then, the solution of the last system has the form After inserting N 0 into ( 11 ), we will obtain an equation for N 1 : After differentiating the left-hand side of the last equation, we obtain where Here, the limits of integration were selected as being from 0 to x in consequence of applying the first condition ( 12 ). Now, we consider the integral I separately. If we define , then the expression for I can be rewritten in the following form: Whereas N 0 has the form ( B3 ), then, taking into account the second condition ( 12 ), it is necessary to search for an N 1 of the following form: And, as a result, the first amendment takes the following form: It should be noted that N 1 is not defined for α = 0, 12. APPENDIX C: κ = <italic>k</italic><sub>0</sub>βη To obtain a solution for the problem, we introduce the following dimensionless variables: and . Note that for such a problem, the diffusion coefficient κ can be rewritten in the following form: . This follows from the fact that and . Taking into account ( 6 ) and ( 9 ), we obtain a system of equations for finding the zero-order solution: The last system can be rewritten in the form Then, the solution of the last system has the form After inserting N 0 into ( 11 ), we will obtain an equation for N 1 : After introducing the variable: and simplifying the last equation, we obtain where . Note that the limits of integration in K, L, M were selected as being from 0
Paper: 2015MNRAS.453..469T (acknowledgments)
We thank the anonymous referee for useful comments on the paper. AT and RM acknowledge the support of NASA ROSES 12-EUCLID12-0004. We thank Rachel Bean, Jonathan Blazek, Nick Gnedin, Katrin Heitmann, Michael Schneider, and other member of the LSST-DESC collaboration for providing helpful feedback on this work. TDM has been funded by the National Science Foundation (NSF) PetaApps, OCI-0749212 and by NSF AST-1009781 and ACI-1036211. AK was supported in part by JPL, run under a contract by Caltech for NASA. AK was also supported in part by NASA ROSES 13-ATP13-0019. This research used resources of the National Energy Research Scientific Computing Center (NERSC), a DOE Office of Science User Facility supported by the Office of Science of the US Department of Energy under Contract No. DE-AC02-05CH11231.
Paper: 2015MNRAS.449.3927F (acknowledgments)
We acknowledge partial financial support by contract PRIN/MIUR 2009: ‘Dynamics and Stellar Populations of Superdense Galaxies’ (Code: 2009L2J4MN) and by INAF/PRIN 2011: ‘Galaxy Evolution with the VLT Survey Telescope (VST)’. BV was supported by the World Premier International Research Center Initiative (WPI), MEXT, Japan, and by the Kakenhi Grant-in-Aid for Young Scientists (B)(26870140) from the Japan Society for the Promotion of Science (JSPS).
Paper: 2019ApJ...871..197D (acknowledgments)
The optical observations were done at the Indian Optical Observatory (IAO) at Hanle. We thank the staff of IAO, Hanle, and CREST, Hosakote, that made these observations possible. The facilities at IAO and CREST are operated by the Indian Institute of Astrophysics, Bangalore. The H i observations were done using the GMRT. We thank the staff of the GMRT that made these observations possible. GMRT is run by the National Centre for Radio Astrophysics of the Tata Institute of Fundamental Research. This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the higher Education Funding Council for England. The SDSS web site is http://www.sdss.org/ . The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of CH i cago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the CH i nese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, OH i o State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington. Facilities: GMRT , HCT , GALEX , SDSS. Software: AIPS, IRAF, NEMO, MIRIAD, KARMA, PYTHON, SAOIMAGE.
Paper: 2019A&A...621A..47K (acknowledgments)
Acknowledgements This work is based on observations obtained at the Bernard Lyot Telescope (TBL, Pic du Midi, France) of the Midi-Pyrénées Observatory, which is operated by the Institut National des Sciences de l’Univers of the Centre National de la Recherche Scientifique of France. Also based on observations obtained at the Canada-France-Hawaii Telescope (CFHT), which is operated by the National Research Council of Canada, the Institut National des Sciences de l’Univers of the Centre National de la Recherche Scientifique of France, and the University of Hawaii. O.K. acknowledges support by the Swedish Research Council (project 621-2014-5720), and the Swedish National Space Board (projects 185/14, 137/17). M.S. is supported by Natural Sciences and Engineering Research Council (NSERC) of Canada Postdoctoral Fellowship program.
Paper: 2016MNRAS.460.2015S (fulltext)
bars stand for standard deviations of the mean correlation functions. As expected, dark matter particles within the closely bound regions of the haloes do not present any particular arrangement (red dashed line), they are homogeneously distributed around the centre of masses. When considering all the particles within a 6 h −1 Mpc radius sphere, the layout is not that much different, although the trend of a preferential direction begins to appear more clearly (black dotted line). Finally, selecting only infalling particles outside the closely bound regions but within 6 h −1 Mpc the signal (blue solid line) is quite strong: there are 5 ± 2 times more particles forming a small angle between themselves than when considering a random distribution and the particles, i.e. infalling particles are non uniformly distributed around the haloes. Knowing that particles falling on to the inner part of dark matter haloes are arranged along a preferred direction, the mean positions of the infalling particles in the different simulations can be derived. We find that the mean coordinates obtained for the different simulations are very similar in all the realizations. The resulting direction of ‘close’ (in the sense that only particles within 6 h −1 Mpc are considered) infall is, on average, along the axis formed between the mean position of Virgo haloes (−4.5 ± 0.6; 8.3 ± 0.4; 0.99 ± 0.8) h −1 Mpc in supergalactic coordinates and the point of supergalactic Cartesian coordinates (−4.8 ± 0.6; 9.3 ± 0.5; 0.26 ± 0.8) h −1 Mpc. To compare with the observed infall, it seems reasonable to look at farther particles. The resulting ‘far’ infall is illustrated by Aitoff projections in Fig. 6 where particles (yellow dots) are shown to fall along the filament linked to the observed Virgo cluster (thick red cross)/ simulated Virgo halo (orange cross). The particles come on average from the supergalactic Cartesian coordinates (−1.5,7.5,−0.05) h −1 Mpc, the supergalactic longitude and latitude (101.45,−0.337) in degrees and the galactic longitude and latitude (287.57,76.77) in degrees. The top projection is centred on the observer (blue cross) while the bottom projection is centred on the observed Virgo cluster. This is in agreement with West Blakeslee ( 2000 ) who suggest that infall of material along the Virgo-Abell 1367 filament has driven the formation of the Virgo cluster. The observational latitude and longitude coordinates, (235.08,73.02) in degrees, of the Abell 1367 cluster (violet triangle) are indeed very close to the direction of infall in the simulations. Figure 6. Aitoff projection in supergalactic (top) and galactic (bottom) coordinates of galaxies from the V8k redshift catalogue (black dots), of the observer (thick blue cross), of the observed Virgo cluster (thick red cross), of one Virgo halo (orange cross) and of the particles infalling on to this halo at redshift zero (yellow dots) The size of the dots in this latter case is proportional to the infall
Paper: 2020ApJ...896...74L (fulltext)
in the selection of the most basic data sets, namely, the HJD dates of the midpoints of the X-ray flares and of the peak points of the IR flares that were taken as the events to be analyzed. This is why additional observations and analysis by different people are required in order to strengthen the evidence for the operation of the two pacemakers, or to refute this claim. The numbers S X = 0.1976 (Section 4.1 ) and (Section 6.2.3 ) should be compared with 0.2887, the StD of a rectangular distribution over the [−0.5, 0.5] interval. It seems that the grouping of the X-ray flares, and even more so of the NIR ones, around tick marks of the corresponding pacemakers is not very tight. The model presented in Section 8 suggests that the dispersion of the flare times around the pacemaker tick marks is inherent to the flare phenomenon itself. Rather than being well concentrated around some fixed phase of the pacemaker cycle, the flare events occur within a wide section of it. Therefore, if future observations are to strengthen the evidence for pacemakers in the Sgr A* system, it will not come in the form of diminishing the value of the S parameter as longer series of detected flare times are considered. Further evidence could come from finding in future new independent sets of observations the effect of two pacemakers of the same frequencies F X and F IR , but not necessarily with smaller dispersions. On the theoretical side, the model suggested here relies on post-Newtonian equations applied on a highly relativistic system. Such an approach could be too simplistic. For one thing, there is, so far, no observational hint regarding the rate of rotation of the BH at the center. If it is a fast rotator, the Schwarzschild metric itself is not an appropriate description of spacetime in its vicinity. But even within the context of the Schwarzschild metric it is yet to be proven that the Paczynsky–Witta potential function is an adequate approximation in the extreme conditions of existence of the alleged star. Furthermore, the equations in Table 4 are strictly consistent only for e ≈ 0, implying, according to Table 5 , that M ≅ 4.4. This value lies at the extreme end of the uncertainty in the value of M as estimated by other, more direct measurements. Also, as noted in Section 8.3.2 , P orb must be understood as referring to a mean value of the sidereal orbital cycle of the star, and the NIR pacemaker frequency F IR uncovered in the data is the mark of this mean value. In Equations (5) and (6), the relevant parameter x should represent an instantaneous distance r of the star from the BH that is varying between the extreme values and at the apicyclic frequency. For e > 0, the use of the constant a value in these equations may therefore be a poor approximation. Also for e > 0.02 the orbit leads the star to within the ISCO circle around the BH where the post-Newtonian approximation may break down. It may therefore be that in order to place the model on firmer
Paper: 2016ApJ...833...95D (fulltext)
are required to find the true convergence time. Figure 6. Simulation of a theoretical 10 Myr old TWA-like association with four different initial velocity dispersions, σ init . The curves show the traceback age that is derived after randomly adding noise that simulates measurement uncertainties. The derived traceback age drops steeply with increasing measured uncertainties. The total measurement uncertainty in our data is dominated by uncertainties in the RV and parallax measurements. See Section 4.1 for more details. Typical expected velocity dispersions for open clusters are around 1–2 km s −1 (Adams 2000 ). Assuming an initial velocity dispersion for TWA of σ init = 2 km s −1 , we would need to measure the UVW velocities with a precision of 0.25 km s −1 to accurately measure the traceback time to within 1 Myr. Given our current mean measurement uncertainties of σ meas = 1.3 km s −1 , the initial velocity dispersion of TWA would have to be greater than 11 km s −1 for us to accurately measure the traceback age to within 1 Myr. The GAIA spacecraft will soon obtain parallaxes to a billion stars with unprecedented precision. Given the low uncertainties in GAIA parallaxes and proper motions, the RVs will become the dominate source of noise. From the calculations above, the RVs will need to have a precision of 0.25 km s −1 for a proper traceback analysis, a quarter of our current average RV uncertainty. We ran another traceback analysis, this time with only stars with RV uncertainties below 0.5 km s −1 (17 stars). This produces a traceback age of 2.9 ± 0.5 Myr. This is a slightly higher value than most of the subsamples tested, but still falls quite short of the expected value. Given the low traceback ages that we obtain for TWA, it is likely that its initial velocity dispersion is too low for an accurate determination of its age using a traceback analysis. 5. PRE-MAIN-SEQUENCE TRACK AGE 5.1. Calculating the Ages of Individual Stars To determine the ages of individual TWA stars, we compare the stars to the pre-main-sequence tracks of Baraffe et al. ( 2015 ). We use our parallax values to convert 2MASS apparent magnitudes to absolute magnitudes. We took optical spectral types from the literature and converted them to effective temperature using Table 6 of Pecaut Mamajek ( 2013 ). For stars M5–M7, we use the main-sequence values in Table 5 of Pecaut Mamajek ( 2013 ). It is interesting to note the disagreement between Pecaut Mamajek ( 2013 ) and Luhman ( 1999 ), which was used in Weinberger et al. ( 2013 ) to convert to effective temperature. The disagreement is typically about 100 K cooler for Pecaut Mamajek ( 2013 ) than for Luhman ( 1999 ), with particular disagreement around M5 with a difference of about 250 K. For stars with spectral type greater than M7, we used the polynomial relation in Table 19 of Faherty et al. ( 2016 ) for moving group members. Spectral types and temperatures for the entire sample are listed in Table 4 . Table 4
Paper: 2016A&A...592L...6S (fulltext)
redshifts that is insensitive to assumptions about the cosmological parameters. In the next section, we derive relations between cosmological distances that are independent of cosmological parameters and allow us to construct combinations of that no longer carry a dependence on cosmology. 3. Distance relation in isotropic universes The two-dimensional separation vector between two infinitesimally close light rays follows the geodesic deviation equation where is the affine parameter along the light rays, and is the optical tidal matrix, which is determined by the Ricci and Weyl tensors of the spacetime metric (see, e.g., Chap.3 of Schneider et al. 1992 ; Seitz et al. 1994 ). In an isotropic universe, the tidal part of vanishes, so that , where is the two-dimensional unit matrix and is a scalar function, proportional to the local density. If the two light rays intersect at a vertex at under an angle , we can write , where satisfies the differential equation with initial conditions , , where the latter value depends on the choice of the affine parameter. By definition, is the angular-diameter distance of a source at , seen from an observer at . The second-order differential Eq. ( 7 ) has two independent solutions; we chose them to be and , that is, the angular-diameter distances as measured from observers located at and , respectively. A third solution, , must necessarily be a linear combination of the other two. If we write it in the form where is a constant, then we see that the first initial condition is satisfied, . For the second initial condition, we have where is the Wronskian From Eq.( 7 ), we directly see that , i.e., is constant. We can calculate this constant considering at , which yields yielding . Therefore, Thus, we have expressed the angular-diameter distance as seen from an observer at affine parameter by the corresponding expression for the angular-diameter distance for observers at and . The resulting expression contains the initial conditions at and . If we now specialize Eq.( 9 ) to the case of , with the corresponding angular-diameter distance denoted as , we obtain Combining Eqs.( 9 ) and ( 10 ), we then find The final equality no longer contains the initial conditions. It is valid for any spacetime that is isotropic around the observer through which the radial light bundle passes. Furthermore, this equation does not refer to the Einstein field equation and is therefore independent of the validity of General Relativity, as long a spacetime is characterized by a metric. A more graphical derivation of the result ( 11 ) is given in Schneider (2016) . If, in addition to isotropy, we assume a spatially homogeneous spacetime, which can then be expressed in the form of the Robertson–Walker metric, the initial conditions are , where is the redshift with which sources at are seen by the observer at (or redshift zero). For this, we chose a parametrization of the affine parameter such that it locally coincides with the comoving
Paper: 2015MNRAS.449.3537B (acknowledgments)
This work is funded by the UK Science and Technology Facilities Council, grant ST/I002871/1. The author thanks the CANARY team for allowing on-sky testing.
Paper: 2021A&A...650A.124W (fulltext)
for extracting information from the phase-space spiral. For example, Li Widrow (2021) infer the gravitational potential of the disk using the bulk stellar density in the ( z , w )-plane and then fit the spiral to the residual of the inferred steady state distribution. The fitted spiral constitutes a consistency check of the inferred potential and is seen as a straight line in the plane of angle and frequency. While our method is accurate in terms of one-dimensional simulations, the actual Milky Way is significantly more complex. To begin with, stars in the Galactic disk do not only oscillate in the vertical direction, but also move in the radial direction as they orbit the Galactic centre. Indeed, the phase-space spiral of the Milky Way has a different form depending on cuts in angular momentum or the galactocentric radius (see for example Fig. 14 in Laporte et al. 2019 , as well as Khanna et al. 2019 ). When applying our method to Gaia data for the first time, we plan to select stars of the solar neighbourhood that have approximately circular orbits, for which the assumptions of our model are most likely to be valid. It would be interesting, although probably quite complicated, to see what kind of information about the global structure of the Milky Way could be extracted from the shape of the spiral in different bins of Galactic angular momentum. Ultimately, we would want to test and refine our method using a high-resolution simulation of a galaxy in three spatial dimensions. Up until now, simulations of Milky Way-like systems (such as Laporte et al. 2018 and Bland-Hawthorn Tepper-García 2021 ) have not had sufficient resolution to produce well-resolved phase-space spirals in stellar density in the ( z , w )-plane. To do so requires billion-particle simulations, which have only recently become feasible ( Asano et al. 2020 , Hunt et al. in prep.). Furthermore, our modelling of the gravitational potential needs to be expanded somewhat; the Poisson equation is no longer one-dimensional but also has a smaller contribution from the radial direction (the so-called rotation curve term). A useful test in terms of systematic uncertainties would be to perform separate analyses of different segments of the phase-space spiral. The assumptions of our analytical model are probably only valid over a certain range in vertical energy; fitting the spiral over a large area in the z , w -plane would give a small statistical uncertainty, but potentially at the price of large systematic errors. It would be possible, at least to some extent, to quantify systematic errors by comparing the results of the smaller, separate spiral segments. Another test in a similar vein would be to abandon the form of the function as defined in Eq. ( 9 ), which might not be completely accurate due to effects of, for example, self-gravity; instead, we could simply assume that the spiral angle is a smooth function with respect to E z and model it as a Gaussian process. Observational