adsabs/WIESP2022-NER huggingface dataset:
Paper: 2020MNRAS.494.4950P (fulltext)
must come from combinations of the harmonics contained in . Recall that we defined containing both synodic terms with harmonics λ 1 − λ 2 and λ 2 − λ 3 , which we wrote in equation ( 16 ) in terms of the new variables . Therefore, the harmonics that are included in are combinations of these synodic harmonics; more specifically, they come from the products of their cosines. 6 Using the standard trigonometric identity , the resulting harmonics are so the harmonic with the lowest fraction of is . Specializing now to the case of a chain with the same resonance index k (1) = k (2) = k , this simply gives With the aid of an algebraic manipulator, one can compute the full expression of and select the desired harmonic term (we used the software package wolfram mathematica ), thus obtaining its coefficient (actually, one can see that this term emerges solely from the term ). We avoid writing here the full expression, which is rather cumbersome; moreover, as in ( 35 ), we evaluate it at the reference values of the actions so the term multiplying the cosine becomes a numerical coefficient, and we write this term as Since we want to compare the frequency of to that of , we need to consider the resonant Hamiltonian in the variables, expand the ‘barred’ variables around the equilibrium point characterized by the equilibrium actions and the equilibrium angles (equation 20 ) as in Section 4.3 , and then introduce the transformation to the action-angle variables , which transforms into the sum of decoupled harmonic oscillators plus higher order terms (equation 22 ). It is also useful to translate the value of around its initial reference value introducing . Therefore, we write in terms of the variables . The Hamiltonian will now contain harmonic terms of type where is an integer combination with coefficients of the angles φ 1 , ..., φ 4 , which we can calculate explicitly. Therefore, whenever , a secondary resonance is crossed. We can rewrite this expression as . Since the Hamiltonian has d’Alembert characteristics in each pair ( I l , φ l ), and the values of the actions are initially (that is, before their excitation) small, the strongest secondary resonances will come from lowest integer combinations , that is, where most h l are zero. We also note that since and the frequencies ω l are all negative, a secondary resonance term can only appear when , which, together with the requirement that be small, is tantamount to requiring that all non-zero integers h l are positive. Since we calculated ω ( m pl ) in Section 4.3 , we can calculate for each the relative frequency as a function of m pl , and check if any of these vanish for some value of m pl , which corresponds to crossing a secondary resonance. We carried out the calculation with the aid of the mathematica software in the reference case k = 3 and a 1 ≃ 0.1, which corresponds to the evolution shown in Fig. 1(b) (and also Figs 2 and 3 ). We found that contains, among many others, the following
Paper: 2017ApJ...836....9C (fulltext)
PO light cone output (Evrard et al. 2002 ), extracted from the DES_v1.02 mock galaxy catalog. 5 5 http://www.slac.stanford.edu/mbusha/mocks/catalogs.html ; provided by M. Busha R. Wechsler. The halos were identified directly on the dark matter light cone using a spherical overdensity halo finder. The algorithm defines spherical regions that are overdense with respect to the critical density . The halos mass M 200 is defined as the mass enclosed in a sphere of radius whose mean density is times the threshold density. Hence, the M 200 mass is given by 4.1. Mass Function Definition and Results in Simulations Since the theoretical models for the halo bias have been derived from the mass function (e.g., Mo White 1996 ; Sheth Tormen 1999 ), we first study the theoretical models of the halo abundance. The comoving number density of halos with mass between M and M + dM or the unconditional mass function can be written aswhere is the multiplicity function (the fraction of mass in collapsed objects) and is the mean comoving mass density. The height of the density peaks is defined aswhere is the critical density for spherical collapse and is the variance of matter density fluctuations on mass scale M . Sheth Tormen ( 1999 ) generalized the expression of the Press–Schechter mass function (Press Schechter 1974 ) and calibrated the free parameters using numerical simulations. It can be written as with p = 0.3, q = 0.707, and . Later, Tinker et al. ( 2008 ) also calibrate fitting functions for the mass function and bias using high-resolution simulations. They choose the formwhere , and d are the free parameters for each overdensity Δ value with respect to the mean density of the universe, . These parameters were calibrated in simulations at z = 0. They also provide redshift correction to match the mass function to simulations. In the DES light cone, the halo finder defines overdense regions with respect to the critical density instead of . So If we define an overdensity contrast as , we can use this functional form for any value of . The values of the parameters at z = 0 are calculated by spline interpolation as a function of , and then we calculate their redshift evolution. We compare the mass function measured in redshift bins of width using the dark matter halo simulation with a DES volume with the Sheth Tormen ( 1999 ) model with p and q fiducial values evaluated at the mean redshift. Since there is a high disagreement in all the mass ranges, we fit the parametric model to the halo catalog measurement. Our fitting method is a simple of the difference between the theoretical model and the measured counts in bins (e.g., Jenkins et al. 2001 ; Manera et al. 2010 and Manera Gaztañaga 2011 ). We also studied the accuracy of the fitting function for Δ overdensities of Tinker et al. ( 2008 ). Figure 1 shows the comparison of the systematic error with the statistical error σ for the two models. In all the redshift bins we found that the deviations, , increase
Paper: 2019A&A...621A.114Z (fulltext)
which could make the analyses more complicated. We analyzed the PILS data for lines of CH3SD similarly to what Drozdovskaya et al. (2018) did for CH3SH. We adopted an excitation temperature T ex = 125 K, a source size of 0.5′′, and a full line width at half maximum (FWHM) of 1 km s −1 . We did not detect CH3SD, but we derived an upper limit on its column density of 8.8 × 10 14 cm −2 (±0.88). The 12 most constraining lines are shown in Fig. 3 . Drozdovskaya et al. (2018) determined a column density of 4.8 × 10 15 cm −2 (±0.48) for CH3SH 2 . Our upper limit corresponds thus to a D/H ratio of less than 0.18 ± 0.025; the uncertainty was estimated as previously ( Drozdovskaya et al. 2018 ). This value is probably not particularly constraining compared with the deuteration of H2CS per H atom of ∼0.05 ± 0.007 ( Drozdovskaya et al. 2018 ). Deeper interferometric observations are required in order to conclusively verify whether the level of deuteration of H2CS is lower, higher, or preserved at the next level of chemical complexity into CH3SH. Fig. 3. Sections of the Protostellar Interferometric Line Survey (PILS) toward a position slightly off-set from source B displaying the 12 most constraining lines of CH3SD. 5. Conclusion and outlook In the present work, the rotational spectrum of CH3SD has been investigated in the frequency range 150−510 GHz in order to provide accurate predictions for astronomical searches. Extensive assignments have been made for the ground, first, and second excited torsional states up to high J and K a quantum numbers (see Table 1 ). The detailed modeling of the absorption spectra of the CH3SD has been performed in a global fit of a dataset of 4905 rotational transitions to the RAM Hamiltonian containing 78 parameters. The overall weighted standard deviation of the global fit is 0.9 in the range 150–510 GHz, indicating that our set of parameters reproduces the assigned lines within experimental uncertainties. Transition frequencies calculated from these parameters should be reliable for astronomical observations. A first attempt to search for CH3SD in the PILS data turned out to be negative. The upper limit, though not unreasonable, is not very constraining either. Future, even more sensitive observations may provide insight into the deuteration of CH3SH. A search for the potentially more abundant CH2DSH was hampered by insufficient laboratory data reported for this isotopolog. Calculations of the rotational spectrum of CH3SD will be available in the catalog section of the Cologne Database for Molecular Spectroscopy, CDMS, ( Endres et al. 2016 ). The input and output files of the fit as well as auxiliary files are available in the data section of the CDMS 3 . Appendix A: Additional tables Table A.1. Spectroscopic parameters of CH3SD (cm −1 ). Notes. (a) n = t + r , where n is the total order of the operator, t is the order of the torsional part and r is the order of the rotational part, respectively. The ordering scheme of
Paper: 2017ApJ...851..144L (fulltext)
not trivial, the main obstacle being the lack of robust estimates for key parameters (e.g., distance, Doppler factor), as well as the lack of contemporaneous multi-wavelength radio observations. In most cases, the range of available frequencies was confined in the lower frequency range (43 GHz). The observed flux density at higher frequencies was the result of extrapolation by assuming that the spectral index derived from the highest available frequencies of each microquasar remains constant up to 142.33 GHz (which is the highest available frequency for the supermassive BH sample). To estimate the relativistic boosting and revert to the rest frame, we gathered for each source all available estimates in the literature for the velocity of the jet, distance, and viewing angle (Table 1 ). For each source, we created a parameter space set by the extrema of the aforementioned quantities. We then uniformly drew a random value for each of these parameters and calculated . We repeated this process 10 4 times and calculated the mean and spread (minimum, maximum) of for each source. The y -values for the microquasars in Figure 3 are the mean, and the y -axis errorbars the spread for each of the sources that resulted from the random sampling. We follow a similar procedure for the , by gathering all the available estimates in the literature and calculating the mean and spread. The x -values for the microquasars in Figure 3 are the mean, and the x -axis errorbars are the spread for each of the sources. The microquasars, parameter ranges, and the references to them are the following. For SS 433. we used radio data from Trushkin et al. ( 2003 ), and parameter values from Seward et al. ( 1980 ), Fender ( 2001 ), Trushkin et al. ( 2003 ), Bowler ( 2010 ), Panferov ( 2010 ), Cherepashchuk et al. ( 2013 ), and references therein. For GRS 1915+105, we used radio data from Rodriguez et al. ( 1995 ), and parameter values from Mirabel Rodríguez ( 1994 ), Fender ( 2001 , 2003 ), Fender Belloni ( 2004 ), Miller-Jones et al. ( 2005 ), Punsly ( 2011 ), Reid et al. ( 2014 ), Zdziarski ( 2014 ), Punsly Rodriguez ( 2016 ), and references therein. For Cyg X-3, we used radio data from Koljonen et al. ( 2010 ), and parameter values from Fender et al. ( 1997 ), Ling et al. ( 2009 ), Hjalmarsdotter et al. ( 2009 ), Vilhu et al. ( 2009 ), Dubus et al. ( 2010 ), Vilhu Hannikainen ( 2013 ), Zdziarski et al. ( 2012 , 2013 , 2016 ), and references therein. For GRO J1655-40, we used radio data from Hannikainen et al. ( 2000 ), and parameter values from Hannikainen et al. ( 2000 ), Trushkin ( 2000 ), Mirabel et al. ( 2002 ), Fender ( 2003 ), Fender et al. ( 2004 , 2010 ), Narayan McClintock ( 2005 ), Motta et al. ( 2014 ), Stuchlík Kološ ( 2016 ), and references therein. For V* V404 Cyg, we used radio data from Gallo et al. ( 2005 ), and parameter values from Cherepashchuk et al. 2004 , Heinz Merloni ( 2004 ), Miller-Jones et al. ( 2009 ), Khargharia et al. ( 2010 ), Xie et al. ( 2014
Paper: 2020A&A...640A..39C (fulltext)
for small values of the BH spin and θ v , those effects should have a minor weight on the results. For the fitting procedure, we used the sources NGC 5548 and MRK 509 (see Appendix C for details) also studied by KD 18. We found that, as for KERRBB, the modeling with AGNSED of the optical-UV-X SED is degenerate: by changing the model parameters (i.e., BH mass, spin, Eddington ratio, corona size) appropriately, it is possible to reproduce the same set of data (for some reference values, see Fig. C.1 ). For NGC 5548, results from both models are compatible while for MRK 509, KERRBB BH masses are larger than the AGNSED ones by a factor ≲0.2 dex (Fig. C.2 , right panel). We argue that for NGC 5548, the absence of relativistic effects in AGNSED is balanced out by modeling a large corona above the disk, leading to the same BH mass. Instead, for MRK 509, the smaller X-ray corona leads to different results because it does not compensate the differences between the two models. In general, KERRBB observed disk luminosity is dimmer than the intrinsic one because of a compact corona located in the inner region of the disk, the presence of which modifies the AD emission and leads to an overestimated BH mass. By correcting the KERRBB disk lumminosity by a factor ≲0.2 dex, results from the two models related to MRK 509 show better compatibility (see Appendix C for more details about this correction). The partial compatibility between KERRBB and AGNSED shows that BH masses estimated though the SED fitting procedure clearly depend on the adopted model and their physical background. Despite these findings, KERRBB results for both sources are still compatible with SE and RM ones within uncertainties (Fig. 4 ). Moreover, results presented by KD 18 are compatible with ours for what concerns the BH spin: taking their finding for the BH masses as reference values, both their results and ours favor low values of a . 6. Discussion and conclusions We used the relativistic thin AD model KERRBB ( Li et al. 2005 ) to infer the BH masses of 28 sources from the AGN Black Hole Mass Database ( Bentz Katz 2015 ). These sources have a BH mass estimate from the RM studies and show clear evidence in the UV band of the so-called Big Blue Bump produced by the radiation coming from an AD around a SMBH. Since we did not have information about the viewing angle for the majority of them, we assumed that the Type 1 QSOs were observed with θ v ≤ 45° in order to avoid the absorption from the dusty torus (assumed to have an average opening angle of ∼45°). Our results can be summarized as follows: The majority of the sources of our sample show a good match between data and the modeling with KERRBB. The modeling led to a relatively good estimate of the spectrum peak position (i.e., peak frequency and luminosity; see Appendix B ) with a small uncertainty (∼0.05 dex on average). The total uncertainty related to the AD BH mass estimates is ∼0.45 dex, which is connected to the unknown BH spin
Paper: 2017ApJ...835..101H (fulltext)
9799, the total population of GCs out to (the limit of the ACS field of view, as well as the limit of the halo-light photometry) is brighter than I = 27.0 from integration of the radial profile. This limit is 0.12 mag fainter than the GCLF peak (Paper I) and thus should include 54% of the total over all luminosities assuming the GCLF is Gaussian in number per unit magnitude, and using the parameters from Paper I. We therefore obtain for (110 kpc). Integrating the light profile (Seigar et al. 2007 ) to the same radius gives a total integrated magnitude , which corresponds to assuming a mean color for giant early-type galaxies. The specific frequency of the GC system is then . If we were to choose to integrate the entire GC system profile all the way to the WFC3 field at R = 300 kpc, the result would be clusters, but this estimate is much more uncertain. For UGC 10143, if again we restrict the calculation conservatively to the ACS field of view (), the total number of GCs with is , which translates into over all magnitudes. Integration of the halo light (Donzelli et al. 2011 ) into the same radius gives , . Finally then, to that radius. The more risky extrapolation of the GC profile out to the WFC3 field limit at (270 kpc) would give . The UGC 9799 GC system is therefore relatively richer than for UGC 10143, but the specific frequencies of both are in the range observed for other BCGs (e.g., Harris et al. 2013 ). For NGC 4889, the profile integration gives clusters brighter than (); this limiting magnitude is very near the GCLF peak point. We therefore double that number to , which when combined with gives a specific frequency of . This galaxy is very luminous, but relative to its size, it does not have an exceptionally populous cluster system in the more typical BCG range. The story is somewhat different and more complex for the central Coma cD NGC 4874: Peng et al. ( 2011 ) estimate GCs excluding the more extended IGC population. When we use , as did Harris et al. ( 2009 ), we obtain . If instead N tot is normalized to the entire luminosity profile out to a much larger radius of 520 kpc, then S N decreases markedly to 3.7 ± 0.1 (Peng et al. 2011 ); but since the IGC clusters outnumber the “intrinsic” GCs that are more clearly associated with the galaxy itself, this lower specific frequency is perhaps more of a statement about S N (IGC). In this respect, it is worth noting that Durrell et al. ( 2014 ) find for the Virgo cluster GCs in their entirety, of which a large fraction are IGCs, and less than a quarter are from M87 itself. 8. DISCUSSION For extremely broad and nearly featureless MDFs such as we find in NGC 6166 (Paper II), UGC 9799, and UGC 10143, the imposition of a bimodal Gaussian numerical model, or any simplistic multimodal fitting process, begins to look increasingly arbitrary. Transformation of their CDFs back into the underlying metallicity distribution by way of Equation ( 1 ) yields a similarly broad unimodal MDF. We stress
Paper: 2016A&A...591A.128L (fulltext)
C.1 shows the losses at these three wavelengths, and for the weak sources with fluxes 400 mJy these losses clearly become more significant at the short wavelength range (closer to m), while the losses are moderate above the m. We used this information to correct the average correlated fluxes of the sources for this work. For the source with high correlation losses we took the average correlated flux obtained after the data reduction and multiplied it by the decorrelation correction factor obtained from our dilution experiment. Appendix D: Dust sublimation Fig. D.1 Temperatures for the three smallest grain sizes of each species in a shell with a radial optical thickness of ( top ) and ( bottom ). The colors indicate the different species of grains: blue – graphites , green – graphites , and red – silicates. Fig. D.2 Convergence of the temperature for the three smallest grains. Each line indicate the relative difference after each iteration. The darker the color, the higher the number of iterations. The radiative transfer code RADMC-3D does not include an internal computation to account for dust sublimation. To include dust sublimation in our models, we slightly modified the code. Each time a photon package enters a cell, it increases the energy of the cell and thus increases the temperature of the dust of this cell. When the dust in the cells exceeds the dust sublimation temperature, the dust inside the cell is completely removed. To accurately estimate the temperature of the system using dust sublimation, we performed an iterative process for which the code several times computed the temperatures and removed the corresponding cells. When the differences between different iterations were below a certain tolerance (we took a value of 5%), we performed a last computation without removing any dust in the cells to ensure the conservation of energy in the system. To show how our implementation of the dust sublimation works in different situations we show examples of an optically thick and optically thin case. In Fig. D.1 we show the temperature of the three smallest grains of each species for a spherical shell with and , respectively. Both shells have an initial inner radius of 0.3 pc and an outer radius of 5 pc. We can observe clearly that in the optically thick case, the temperature rises more quickly and the sublimation radius for the three species are closer than in the optically thin case. We made sure that we had enough cells close to the inner radius to obtain an accurate solution. In Fig. D.2 , we show for the optically thick case, the relative differences between each iteration and our final computation. After a few iterations, the temperature in every cell reaches a relative difference below our tolerance value. Appendix E: Acceptance levels For our method we used linear transformations computed for each model to remove the mean values, normalize the variance, and remove correlations. We expect that if our models agree with the
Paper: 2019MNRAS.486..885S (fulltext)
μ) and Q 0 (0, μ) in the case of ( 1 7 ) are simple: In Table 1 we give the angular distribution J (μ) = I 0 (0, μ)/ I 0 (0, 0) and the degree of polarization p (μ) = − Q 0 (0, μ)/ I 0 (0, μ) per cent at and 1 for the incident non-polarized radiation perpendicular to the surface. Note that negative Q 0 (0, μ) corresponds to the wave electric-field oscillations perpendicular to the plane ( nN ). This holds in our case. Table 1 shows that the chaotic Faraday rotations strongly decrease the polarization and weakly affect the angular distribution. Table 1. The angular distribution J (μ) = I 0 (0, μ)/ I 0 (0, 0) and the degree of polarization p (μ) = − Q 0 (0, μ)/ I 0 (0, μ) per cent at and 1 for the incident non-polarized radiation normal to the surface. Recall that we consider the atmosphere without pure absorption (a conservative atmosphere). It follows from equation ( 13 ) that the zero moments of functions β(μ) and γ(μ) are equal to and , respectively. These moments are μ-integrals over the interval (0,1) (see Silant’ev et al. 2019 ). Taking the integral μ I 0 (0, μ) dμ over the same interval and using equation ( 13 ), we obtain that the flux of outgoing radiation is equal to the flux F I of the incident radiation. For a conservative atmosphere this is the evident result. In Fig. 1 the polarization degree p (μ) of the reflected radiation for different parameters h is given. The angular dependence J (μ) practically does not depend on h . Therefore, we give J (μ) for and 30. The numbers over the curves denote the values of h . Figure 1. The angular distribution J (μ) = I 0 (0, μ)/ I 0 (0, 0) and polarization degree p (μ) = − Q 0 (0, μ)/ I 0 (0, μ) per cent of reflected radiation. The incident radiation is perpendicular to the surface. The numbers denote the values of parameter h . It is of interest to compare the multiple scattered outgoing intensity I 0 and parameter Q 0 to the results for single scattered radiation: The flux of outgoing single scattered radiation is equal to F single = 0.168 F I , i.e. only ≃ 17 per cent of the total flux. The other 83 per cent of the emerging radiation is concerned with two and more scatterings in the semi-infinite atmosphere. In our case, the considered normal incident radiation penetrates deeper into the atmosphere than in other inclinations. It means that F single = 0.168 F I is the minimum value of the single scattered radiation fluxes. The corresponding angular distribution and the degree of polarization have the form The polarization p single (μ) at μ = 0 is equal to 100/(1 + h ) per cent. This result clearly demonstrates the decrease of polarization with increasing parameter h . This decrease holds along the outflow of single scattered non-polarized radiation. Recall that single scattering of non-polarized radiation gives rise to 100 per cent polarization of the scattered one if the scattering angle (the angle between the incident radiation and the scattered one) is equal to 90° (see, for example,