weighting (red) used in Ali et al. ( 2015 ), which excises fringe rates at risk for contamination by crosstalk, and applies a Blackman–Harris window in the time domain to generate a compact time-domain convolution kernel with regions weighted below 5% of the peak response suppressed. Also illustrated are the weightings for matching the YY to the XX polarization beam (blue dashed) and for reducing polarization leakage (blue solid) described in Section 4.2 , as well as a weighting that balances the needs of sensitivity, polarization leakage, crosstalk removal, and off-axis foregrounds (green). Bottom: the time-domain convolution kernel corresponding to the red curve in the top panel. Real and imaginary components are illustrated in cyan and magenta, respectively, with the absolute amplitude illustrated in brown. The next step in implementing the fringe-rate filter is translating the analytic filter profile in fringe-rate space into a time-domain kernel that can be used to convolve the simulated time series of visibilities. In effect, we implement the fringe-rate filter as a finite impulse response (FIR) filter. The convolution kernel corresponding to this FIR filter is shown in the lower panel of Figure 3 . Applying the fringe-rate filter as an FIR filter in the time domain, as opposed to directly multiplying the desired filter to Fourier-transformed visibilities, has the advantage that flagged or missing data can be naturally excluded from the filter by neglecting FIR taps (coefficient multiplies) that target the missing data. The summed output of the FIR filter are then renormalized to account for the missing samples. Another advantage of the FIR implementation of the fringe-rate filter is the potential for windowing the time-domain filter profile. While time-domain windowing causes further deviations from the ideal fringe-rate filter profile, it can be used to produce a more compact time-domain kernel. Reducing the number of time-domain samples used in the FIR filter improves the computational efficiency of the filter, helps limit the number of samples potentially corrupted by spurious systematics such as radio frequency interference, and reduces boundary effects. In Ali et al. ( 2015 ), a 12 hr data set was filtered in this manner, with boundary effects limited to an hour on each end. The final analysis proceeded on 8.3 hr selected from within the region not affected by boundary effects. 4. APPLICATIONS In Section 3 , we discussed how a fringe-rate filter can be implemented in practice once a particular form for the filter is selected. In this section, we optimize the selection of filters (or equivalently, of fringe-rate weights) for various applications in low-frequency radio interferometry. The key to this optimization will be the insight from Section 2 , namely that the effect of fringe-rate filtering can be regarded as both a time integration and a modification of the spatial response of the primary beam on a per-baseline basis.


This work was supported under NASA contract NNG08FD60C and made use of data from the NuSTAR mission, a project led by the California Institute of Technology, managed by the Jet Propulsion Laboratory, and funded by NASA. Additional funding for this work was also provided under NASA grants NNX12AJ36G and NNX14AG07G. S.K. acknowledges funding from the Swiss National Science Foundation (200021-140308). A.J.M.’s participation was supported by NASA Earth and Space Science Fellowship award NNX13AM41H. Part of this work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. A.C. was supported by NASA grants NNX15AK26G and NNX14AN84G. I.G.H. is supported by a Royal Society University Research Fellowship. We thank the NuSTAR Operations, Software and Calibration teams for support with the execution and analysis of these observations. This research made use of the NuSTAR Data Analysis Software (NuSTARDAS), jointly developed by the ASI Science Data Center (ASDC, Italy) and the California Institute of Technology (USA). This research made extensive use of the IDL Astronomy Library ( http://idlastro.gsfc.nasa.gov/ ) and of the SolarSoft IDL distribution (SSW). Additional figures were produced using the Veusz plotting package (© 2003–2015 Jeremy Sanders). Facility: NuSTAR .


The research leading to these results received funding from the European Union Seventh Framework Program (FP7/2007-2013) under grant agreement n312789. This work has been financially supported by the Programme National Hautes Energies (PNHE). This work was supported in part by the Deutsche Forschungsgemeinschaft (DFG) via the Cologne Bonn Graduate School (BCGS), the Max Planck Society through the International Max Planck Research School (IMPRS) for Astronomy and Astrophysics, as well as special funds through the University of Cologne. M.Z., B.S., S.S., and A.B. are members of the IMPRS. Part of this work was supported by fruitful discussions with members of the European Union funded COST Action MP0905: Black Holes in a Violent Universe and the Czech Science Foundation—DFG collaboration (No. 13-00070J). This work was co-funded under the Marie Curie Actions of the European Commission (FP7-COFUND). M.G.-M. is supported by the German federal department for education and research (BMBF) under project number 50OS1101. We are grateful to all members of the ESO PARANAL team.


ACKNOWLEDGEMENTS We acknowledge the constructive criticisms of the reviewer.


triangles that connect to these points. 2.3.2 Identifying parent triangles Identifying the triangle which contains a given point can be done most easily by checking every triangle individually by brute force. Since the total cost for finding the triangles containing ALL points scales as , this method rapidly becomes too expensive even for a modest number of triangles and will dominate the CPU time for constructing the tessellation. A simple but effective speed-up is the so-called ‘jump and walk’ method. In this method, we select an initial triangle to start the search for a given point. This might be informed from the previous iteration of the triangulation or simply selected at random. The method then tests each face of the triangle to see if the point lies outside or inside the face. If the point is inside every face, then the triangle contains the point. If outside one or more faces, then the triangle is false. We would then ‘walk’ to the neighbouring triangle closest to the point. We then perform the tests again until the triangle has been correctly identified. 2.3.3 Degenerate triangles One common problem that is found in almost all Delaunay triangulation algorithms is that of degenerate triangles. Consider the simple 2D example where four points are exactly the vertices of a square, A, B, C and D. Due to the symmetry, then both of the triangle pairs ABC–CDA and ABD–BCD are possible triangulations. However, both fail the circumcircle test because the exterior fourth point lies exactly on the circle. There is algorithmically no way to distinguish the two cases. A similar related problem occurs when we compute which triangle contains a given point; if the point lies exactly (to floating point precision) on the line dividing two triangles, then there is no way to distinguish which triangle the point lies in. There are three common solutions to this problem: (i) add a small random perturbation to the positions of one of the points to break the degeneracy; (ii) add a virtual perturbation (without physically moving the particles) to each particle position to force the computation of the degenerate state to fall one side or the other (Edelsbrunner Mücke 1990 ), or (iii) use higher precision when computing the determinants, either using exact floating point arithmetic or long-integer arithmetic (Springel 2010 ). For our purposes, we chose the first solution, partly due to simplicity and secondly due to the fact that even though the Delaunay triangulation can be slightly altered, the Voronoi tessellation is (mainly) unaffected. 2.3.4 Creating the Voronoi tessellation To create the Voronoi tessellation, each face of the cell can be constructed by joining the circumcircle centres of Delaunay triangles that are common between two points. In 2D, this is trivial since each Voronoi cell face is a simple line represented by two points. In 3D, it is more complex since each Voronoi face is a complex polygon with an arbitrary number of vertices.


in concert. The quantification of the abundance uncertainties included S/N-dependent cross-validation and an error rescaling for some elements, exploiting the fact that abundance estimates for member stars of open clusters should on average not differ by less than their uncertainties. This provided a set of APOGEE-derived abundances that is unprecedented in its (pertinent) combination of quality, quantity, and homogeneity. We only considered stars with very similar stellar parameters, giants in a restricted T eff and log g range; we have 90 spectra across seven open clusters and thousands of “field stars” with the same data, S/N, and data analysis. For all of these stars, we have individual abundances for 20 elements (Fe, C, N, O, Na, Mg, Al, Si, S, K, Ca, Ti, V, Mn, Ni, P, Cr, Co, Cu, and Rb), with a median precision of 0.03 dex. We characterize these abundances by their values [X/Fe], except for iron, where we use [Fe/H]. On this basis, we undertook an extensive analysis of the chemical (in-)homogeneity of stars within an open cluster, testing the standard assumption that such stellar “birth siblings” were formed at the same time from chemically homogeneous material. This should result in identical element abundances, including those elements (e.g., C and N), whose photospheric abundance has been altered in giants by mass/age-dependent dredge-up. We confirm that the abundances of cluster member stars typically agree with each other within their small (0.03 dex) uncertainties, as had been found before (see Section 1 ). Moving beyond, we explicitly determined the intrinsic dispersion in these abundances, or derived upper limits for them. We found that (at least in the best sampled clusters), the abundance dispersions are essentially zero, with typical upper limits of ∼0.03 dex. However, there are exceptions: some elements in some clusters show small but significant dispersion, attributable to a subset of member stars. To quantify the abundance similarity among stars of known common birth origin (cluster members) to the (dis-)similarity among field stars, we compared the abundances among pairs of stars. It was tempting to define a distance measure in the high-dimensional space of element abundances, but the “curse of dimensionality” makes distance in a 20 dimensional space very dependent on prior assumptions about distance distributions once the distances become comparable to the measurement uncertainties. Therefore, we resorted to a simple statistic, , quantifying the likelihood of the 20 observed abundances (differences) for any pair of stars, assuming their intrinsic abundances were identical. When we construct for intracluster pairs of stars, we find that its median is similar to , again illustrating the level of chemical homogeneity within clusters. Yet, about 20% of intracluster star pairs have , indicating significant abundance differences in one or more elements. We find open clusters to be mostly, but not exclusively,


the molecular gas mass determined by Riechers ( 2013 ), and can be a result of the different resolution of the observations. Regardless of this difference, it is clear that the companion has a massive gas reservoir. The quasar was not detected by Sharon et al. ( 2016 ) but a 3σ upper limit is obtained, yielding a CO(1–0) line luminosity upper limit of , which converts to a molecular gas mass of . We also calculated the molecular gas mass from the CO(5–4) emission of the quasar, as this is the lowest J detection available for this source. We assume that the CO(5–4) transition is thermally excited, based on CO(4–3) observations of high- z type I QSOs, which found a unity ratio (e.g. Riechers et al. 2006 ; Weiß et al. 2007 ). With this assumption the molecular gas mass of the quasar is . These results suggest that there is a significant amount of warm gas in the quasar and it cannot be considered gas-poor. 3.5 <monospace>RADEX</monospace> modelling of the CO spectra To put constraints on the excitation properties of SMM J04135+10277, we modelled the SLED of both sources using our ALMA detections combined with CO(1–0) and CO(3–2) line observations from the literature (Riechers 2013 ; Sharon et al. 2016 ). We used the non-LTE molecular radiative transfer code radex (van der Tak et al. 2007 ) to calculate the line intensities of CO from transitions J up = 1 to J up = 8, within a wide range of physical parameters: kinetic temperature ( T kin ), number density of molecular hydrogen (), and column density of CO ( N CO ). During each run we set the background radiation temperature to the value of the cosmic microwave background at z = 2.84, adopted spherical geometry and assumed that the only collisional partner of CO is molecular hydrogen. As the linewidths of the low- and high- J CO lines are different, we use an average value during the radex modelling. The radex code only considers photodissociation regions and does not include mechanical and X-ray heating. We compared our observations with the models using χ 2 -analysis. In the first run we varied all three physical parameters in case of each source but as most of the models converged to the same CO column density, we fixed N CO and continued with fitting only T kin and . During the radex modelling of the quasar we set the line width of , fixed N CO to and run radex on a grid of and . It is important to note, that as we only have two detections for the quasar and two upper limits, we do not expect to arrive to a straightforward conclusion about the excitation properties of this source. However, by using the available data we can narrow down the possible temperature and density ranges. Fig. 6 shows how the χ 2 value of the models vary as a function of temperature and density. The upper J transitions of the quasar can be fitted by models with a continuous range of kinetic temperatures of and molecular hydrogen density between . Models with the lowest χ 2 values are outside of the typical temperature


as different catalogs cover different redshift ranges. We compile a set of small-scale rejection masks (bright stars, bad imaging tracks, and small regions without spectroscopic coverage) provided by these surveys and generate a joint rejection mask by taking the union. 8 8 The masks are available at 10.5281/zenodo.4012781 . Table 1 summarizes the basic parameters of the spectroscopic reference sources that we use after applying the joint SDSS rejection mask, the 60% Galactic mask, and the infrared point-source mask described in Section 3.1.1 . Table 1 Spectroscopic Redshift Reference Notes. a Effective unmasked sky area in deg 2 . b Number of sources in the effective area. c Fraction of the sources in the Northern Galactic Hemisphere. d Median and 68% CL range of the redshift distribution. References. (1) Strauss et al. ( 2002 ), (2) Blanton et al. ( 2005 ), (3) Reid et al. ( 2016 ), (4) Bautista et al. ( 2018 ), (5) Schneider et al. ( 2010 ), (6) Pâris et al. ( 2017 ), (7) Ata et al. ( 2018 ). 3.2. Clustering Redshifts We apply the clustering-based or cross-correlation-based redshift estimation following Ménard et al. ( 2013 ) for both the channel intensity and Planck's Compton y maps. The technique is based on the simple ansatz that all matter tracers appear spatially clustered on the sky if their redshift distributions overlap. One can thus take a “reference” sample of galaxies or quasars with known redshifts and propagate the redshift information into a “test” data set with an unknown redshift distribution. This is achieved by cross-correlating the reference and test samples as a function of redshift of the former. The first applications to large data sets are done in the regime of discrete objects as the test sample to estimate source redshift distributions in photometric surveys (e.g., Rahman et al. 2015 , 2016a , 2016b ; Scottez et al. 2016 ; Hildebrandt et al. 2017 ; Davis et al. 2018 ; Gatti et al. 2018 ; Kitanidis et al. 2020 ; Krolewski et al. 2019 ). It is straightforward to generalize the method and redshift inference to diffuse fields simply by replacing the notion of objects with pixels on a set of predetermined grids (Schmidt et al. 2015 ; Chiang Ménard 2019 ; Chiang et al. 2019 ). Our implementation in this work is largely based on that in Chiang et al. ( 2019 ); here we briefly describe the key steps and minor modifications made for the tSZ tomography. We denote the overdensity field of the 2D test intensity map as (where T = I ν i in the multichannel analysis and T = y for the direct y map tomography) and that for the 3D reference sources as . As both are, in general, biased tracers of the underlying matter density field with the angular correlation function at some effective scale, we can write down a linear expression for their cross-correlation amplitudes evaluated in bins of the reference redshift z i aswhere b T and b R are the effective linear-clustering bias for the test and reference data at the scales considered.


We gratefully acknowledge financial support from CONICYT-Chile through its FONDECYT postdoctoral grant number 3160747; CONICYT-PCHA through its national M.Sc. scholarship 2016 number 22162464; CONICYT through the Fondecyt Initiation into Research project No. 11130228; CONICYT-Chile through grant Fondecyt 1140816; CONICYT-Chile and NSF through the Programme of International Cooperation project DPI201400090; CONICYT through the infrastructure Quimal project No. 140003; Basal Project PFB–03; and the Ministry of Economy, Development, and Tourism’s Millennium Science Initiative through grant IC120009, awarded to The Millennium Institute of Astrophysics (MAS). Powered@NLHPC: this research was partially supported by the supercomputing infrastructure of the NLHPC (ECM-02). We acknowledge the usage of the Belka GPU cluster (Fondequip EQM 140101). This project used data obtained with the Dark Energy Camera (DECam), which was constructed by the Dark Energy Survey (DES) collaboration. Funding for the DES Projects has been provided by the U.S. Department of Energy, the U.S. National Science Foundation, the Ministry of Science and Education of Spain, the Science and Technology Facilities Council of the United Kingdom, the Higher Education Funding Council for England, the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign, the Kavli Institute of Cosmological Physics at the University of Chicago, Center for Cosmology and Astro-Particle Physics at the Ohio State University, the Mitchell Institute for Fundamental Physics and Astronomy at Texas AM University, Financiadora de Estudos e Projetos, Fundação Carlos Chagas Filho de Amparo, Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de Desenvolvimento Científico e Tecnológico, and the Ministério da Ciência, Tecnologia e Inovação, the Deutsche Forschungsgemeinschaft, and the Collaborating Institutions in the Dark Energy Survey. The Collaborating Institutions are Argonne National Laboratory, the University of California at Santa Cruz, the University of Cambridge, Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas-Madrid, the University of Chicago, University College London, the DES-Brazil Consortium, the University of Edinburgh, the Eidgenssische Technische Hochschule (ETH) Zürich, Fermi National Accelerator Laboratory, the University of Illinois at Urbana-Champaign, the Institut de Ciències de l’Espai (IEEC/CSIC), the Institut de Física d’Altes Energies, Lawrence Berkeley National Laboratory, the Ludwig-Maximilians Universität München and the associated Excellence Cluster Universe, the University of Michigan, the National Optical Astronomy Observatory, the University of Nottingham, the Ohio State University, the University of Pennsylvania, the University of Portsmouth, SLAC National Accelerator Laboratory, Stanford University, the University of Sussex, and Texas AM University. All plots were created using matplotlib (Hunter 2007 ). This work was performed in part at the La Serena School for Data Science, supported by the National Science Foundation grant AST-1354550, and at the Chile-Harvard Data Science School.


et al. ( 1989 ) code using a model of 14 configurations, our grasp 1 levels in the excited configurations lie closer to the NIST ones. In the case of four energy levels ( 2 D 5/2,3/2 , 4 P 5/2,3/2 ), our calculated energy levels are more closer to NIST than those of Aggarrwal et al. ( 2003 ). The average percentage difference of these grasp energies with NIST values is 2.2 per cent, and the maximum error of 6.3 per cent appears for the first excited state ( 2 D 3/2 ) of ground configuration. For more accurate target states we adopt a model of 13 electronic configurations which yields target-states energies as closer to NIST values as possible. For instance, our calculated energy levels 2 D 3/2,5/2 associated with the configuration 3s3p 4 lie more closer to the observed values as compared to existing calculations. The remaining set of energy levels are almost of the same accuracy as those of previous data when compared to experimental energies. From this comparison it is evident that present grasp 1 calculated N -electron target wavefunctions demonstrate good agreement with experimental values, which is necessary for more accurate PI cross-sections of Ni xiii . In order to further ascertain the accuracy of target wavefunctions, we have compared weighted oscillator strength ( gf -values) of electric dipole (E1) transitions of Ni xiv where available (Fritzsche et al. 1998 ; Landi Bhatia 2010 ) in the literature. In Table 2 , we present our calculated gf -values of E1 transitions in length form only from the ground state and first exited states to the 41 excited levels of Ni xiv ion. The online version of Table 2 contain the gf -values of all dipole transitions among the 41 fine-structure levels. The indices of lower and upper levels of a transition used in Table 2 are defined in Table 1 . The agreement between our calculated oscillator strengths and grasp 92 calculations (Fritzsche et al. 1998 ) is within 15 per cent for majority of the strong dipole transitions with gf -values ≥ 0.01, while fac oscillator strengths (Landi Bhatia 2010 ) lie within 25 per cent with the exception of few transitions for instance ( 2 D 3/2 – 2 P 3/2 ). We note some significant differences with those of Fritzsche et al. ( 1998 ) and Landi Bhatia 2010 within 70 per cent for weaker transitions like in the case of 4 S 3/2 – 4 F 5/2 and 2 D 3/2 – 2 S 1/2 transitions. Apart from these differences, the overall agreement between present MCDF and previous MCDF (Fritzsche et al. 1998 ) oscillator strengths is quite good. This gives confidence in the accuracy of target states to calculate PI cross-sections. Table 2. Comparison of present weighted oscillator strengths ( gf -values, dimensionless) for E1 transitions in Ni xiv with other theoretical calculations. The complete table is available online only. Notes. a fac : Oscillator strengths from fac code (Landi Bhatia 2010 ). b grasp 92: Oscillator strengths from grasp 92 code (Fritzsche et al. 1998 ). Figs 1 – 3 display our


ACKNOWLEDGEMENTS The author would like to thank the principle investigator of the CAMS project, Dr. Peter Jenniskens of the SETI Institute, for providing the CAMS California data set from the peak nights of the 2012 and 2015 Geminids that were used for this project. In addition, the FDL team members of Susana Zoghbi, Antonio Ordonez, Marcelo De Cicco, Andres Stapper, and Jack Collison, all deserve credit for their groundbreaking work in initially developing and applying deep learning techniques to the various components of meteor analysis in the CAMS pipeline. Finally, the author would like to thank the anonymous reviewers for their comments and suggestions, as well as Dr. Huzefa Rangwala of George Mason University for his instructional insights during his deep learning course presentations and careful review of this paper.


We thank the anonymous referee for the fruitful comments. We also would like to thank R. Yamazaki, Y. Ohira, and J. Shimoda for their fruitful discussion. This work is supported in part by Grant-in-Aid for Scientific Research of the Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan, No. 22684012 and 15K05107 (AB), 15K17657 (MS), and 16K17673 (SK). Facility: Suzaku .


This project is supported by the National Science Foundation of China under grant No. U1831205 and grant No. 11603058. S.W. acknowledges support from the Chinese Academy of Sciences President’s International Fellowship Initiative (grant No. 2017VMB0011). The authors wish to thank Caroline Bertemes for fruitful discussions. Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P. Sloan Foundation, the U.S. Department of Energy Office of Science, and the Participating Institutions. SDSS-IV acknowledges support and resources from the Center for High-Performance Computing at the University of Utah. The SDSS website is http://www.sdss.org . SDSS-IV is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration, including the Brazilian Participation Group, the Carnegie Institution for Science, Carnegie Mellon University, the Chilean Participation Group, the French Participation Group, Harvard-Smithsonian Center for Astrophysics, Instituto de Astrofísica de Canarias, Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe (IPMU)/University of Tokyo, Lawrence Berkeley National Laboratory, Leibniz Institut für Astrophysik Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für Astrophysik (MPA Garching), Max-Planck-Institut für Extraterrestrische Physik (MPE), National Astronomical Observatory of China, New Mexico State University, New York University, University of Notre Dame, Observatário Nacional/MCTI, The Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, Universidad Nacional Autónoma de México, University of Arizona, University of Colorado Boulder, University of Oxford, University of Portsmouth, University of Utah, University of Virginia, University of Washington, University of Wisconsin, Vanderbilt University, and Yale University.


of the DM from the detected giant micropulses. The red dashed curve stands for the constrained optimal Gaussian distribution with the best-fitting parameters shown in the text. As reported by Johnston et al. ( 2001 ), a threshold of R larger than 25 was taken to pick out the giant micropulses at 1413 MHz. The R parameter is defined as R i = (MAX i − m i )/ σ i , where MAX i is the maximum intensity, m i is the mean intensity and σ i is the rms in the i th bin. The phase-resolved R at 6800 MHz is shown in Figure 4 . Two peaks are clearly presented in the leading component and leading edge of the pulse, which implies the existence of giant micropulses with extremely high amplitude with respect to the mean intensity in these phase ranges. And the value of R decreases exponentially in the center and trailing of the pulse, which is inconsistent with the Gaussian statistics at 1413 MHz. As shown in Figure 1 , the giant micropulse emission in the center component has a higher occurrence rate and higher amplitude than that in the trailing component. Furthermore, no detection of giant micropulses with significant R -value occurs in the bump region. Figure 4. R -parameter as a function of pulse phase at 6800 MHz. The main panel of Figure 5 shows a scatter plot of peak flux density and the FWHM for detected giant micropulses. The pulse broadening caused by inner-channel dispersion (1.4 μ s) and scattering (1.0 ns) is negelected due to high observing frequency. To obtain the FWHM, a Gaussian function is adopted to fit each giant micropulse. The position of the center of the peak is kept fixed with the pulse phase of the maximum value. Then FWHM is given by , where σ is the determined parameter using the least-squares method. The giant micropulses have timescales (1.55 ms) much smaller than that of the average pulse profile (2.62 ms). As can be seen, the majority of giant micropulses tend to cluster in width of 50–500 μ s. In this interval, the width of a giant micropulse seems to be independent of its peak flux density, which is consistent with the result at 2.3 GHz (Kramer et al. 2002 ). The pulse-to-pulse energy distribution is served as one of the important differentiator between various emission processes (Burke-Spolaor et al. 2012 ). Probability density function (PDF) for the peak flux densities is shown in the upper panel, which is well described by a power law. The slope, obtained via least-square fitting, is give by α = −3.54 ± 0.04, which is the steepest distribution to our best knowledge. While a logarithmic normal distribution is presented for the PDF formed from the peak flux densities of normal pulses, as shown in Figure 6 . The distinctive distributions between giant micropulses and normal pulses may indicate their different emission mechanism. The pulse energies of the bursts from the Vela pulsar do not exceed 10 times the corresponding mean quantity. Nevertheless, the peak flux densities of the bursts are very large in absolute terms. For


ACKNOWLEDGEMENTS We thank Alexei Pevtsov for helpful discussions and suggestions. We also thank anonymous referee for his/her helpful comments. SDO is a mission for NASA’s Living With a Star (LWS) programme. The SDO/HMI data were provided by the Joint Science Operation Center (JSOC). Hinode is a Japanese mission developed and launched by ISAS/JAXA, with NAOJ as domestic partner and NASA and STFC (UK) as international partners. It is operated by these agencies in co-operation with ESA and NSC (Norway). This study was supported in part by the Russian Fund for Basic Research (RFBR) projects 17-52-53203 and 17-02-00049, by the National Natural Science Foundation of China projects 11673033, 11703042, 11427901, U1731241, by the cooperative NSFC-RFBR grant 11611530679 and by the Strategic Priority Research Program of the Chinese Academy of Sciences XDA15052200. AK and KK would like to thank the staff at HSOS of National Astronomical Observatories of China for warm hospitality and excellent working environment during their visit.


The research leading to these results has received funding from the European Commission’s Seventh Framework Programme (FP7/2007-2013) under the grant agreement eHeroes (project No. 284461, www.eheroes.eu ). We also acknowledge the financial support by the Academy of Finland to the ReSoLVE Centre of Excellence (project No. 272157).


such as the peculiar motion of the halo clouds, the nonuniform spectrum of the clouds due to the radiation balance and radiative transfer details, and so on. However, obviously, at this stage, those are lower-order effects with respect the global halo rotation. Moreover, since we consider M 104 as being foreground to the CMB, we note that for the maps we study (with monopole and dipole extracted) the foregrounds could also be negative due to physical processes, for example, in the case of clouds, the particular molecular energy level transitions, metastable states, two-photon emission or absorption, and so on. 3. Conclusions Similar to the case of other galaxies of the Local Group considered previously (in particular the galaxies M 31, M 82, M 81, M 33, and Cen A have been analyzed using Planck data and a temperature asymmetry Δ T about 60−80 μ K of one side with respect to the other about the rotation axis of the galactic disks has been detected in all cases), we found a consistent north–south temperature asymmetry toward the M 104 galaxy, that reaches values up to about 65 μ K within 0.6° (about 100 kpc) in all considered Planck bands 3 , and then starts to decrease. We mention that Chandra observations in the X-ray band of the M 104 galaxy show the presence of a diffuse X-ray emission extending at least up to 30 kpc from its center ( Li et al. 2011 ), together with hundreds of point sources which are a mixture of objects in the M 104 halo (mainly X-ray binaries) as well as background Quasars ( Li et al. 2010 ). However, the presence of this X-ray-emitting hot gas cannot explain the temperature asymmetry detected in Planck data. It is straightforward to show that if the cold-gas cloud model is at the origin of the detected temperature asymmetry (however, as anticipated in the previous section, other emission mechanisms may play a role in the detected signal), a lower limit to the M 104 galaxy dynamical mass is given by where R is the considered galaxy halo radius in units of 100 kpc, Δ T is the measured temperature asymmetry (in μ k ), and τ eff is the effective cloud optical depth (which depends on both the cloud filling factor and the averaged optical depth within a given Planck band. Expected values for τ eff are about a few 10 −3 ( Tahir et al. 2019 ), meaning that the M 104 dynamical mass out to ∼100 kpc is seen to be M dyn ≃ 3 × 10 12 M ⊙ , in agreement with other measurements (see, e.g., Tempel Tenjes 2006 ). It is interesting to mention in this respect that this galactocentric distance appears close to the transonic point (at ≃126 kpc), determined recently by Igarashi et al. (2014) within the framework of the transonic outflow model in a dark matter halo applied to the Sombrero galaxy 4 . The detected temperature asymmetry is, as discussed in the previous section, almost frequency-independent and indicates that the M 104 galaxy halo is rotating with respect to the major symmetry axis of the galaxy disk (Variant 1). However, the


ACKNOWLEDGEMENTS We used the nirvana code version 3.3, developed by Udo Ziegler at the Leibniz-Institut für Astrophysik Potsdam (AIP). For computations we used Leibniz Computer Cluster, also at AIP. We thank Dipankar Bhattacharya, Torsten Enßlin and Anvar Shukurov for very insightful discussions.


This work was supported under NASA Contract No. NNG08FD60C, and made use of data from the NuSTAR mission, a project led by the California Institute of Technology, managed by the Jet Propulsion Laboratory, and funded by the National Aeronautics and Space Administration. We thank the NuSTAR Operations, Software, and Calibration teams for support with the execution and analysis of these observations. This research has made use of the NuSTAR Data Analysis Software ( nustardas ) jointly developed by the ASI Science Data Center (ASDC, Italy) and the California Institute of Technology (USA). RK acknowledges support from Russian Science Foundation (grant 14-22-00271). GP acknowledges the Bundesministerium für Wirtschaft und Technologie/Deutsches Zentrum für Luftund Raumfahrt (BMWI/DLR, FKZ 50 OR 1408).


reveals a clear difference in the two moon orientations. Figure 6. Exoplanet orbit (blue) with two different exomoon orbits: the red solid line is prograde and coplanar to the planet, and the black dashed line is retrograde and misaligned to the planet. As seen by the observer (right) there is a degeneracy, as both moons has the same ( x , y ) position and ( v x , y y ) velocity, despite the side view (left) betraying a clear difference between the two orbits. L denotes the angular momentum vectors. This degeneracy may be broken by nodal precession, which would not occur for the coplanar orbit but would for the misaligned orbit. Fortunately, for a moon that orbits at a fair fraction of its planet’s Hill sphere, precession will be rapid, revealing the magnitude of the misalignment in just tens of orbits of the planet. Therefore, the dynamically evolving character of TDV will betray the prograde or retrograde character of the moon. If the planetary impact parameter is low then the “TIP–TDV” may be negligible and the magnitude of non-coplanarity may not be enough to break the degeneracy. In this case, higher-order dynamical effects that differ in sign between prograde and retrograde moons may need to be taken into account, as envisioned by Lewis Fujii ( 2014 ). Two alternative methods for breaking the degeneracy, practical only with Extremely Large Telescopes, were discussed by Heller Albrecht ( 2014 ). 5.2. The Prevalence of Large TTVs for Long-period Gas Giants According to the transit times of Table S3 of Teachey Kipping ( 2018 ), the planet Kepler-1625b has a mean absolute deviation from a constant-period model, normalized by the orbital period—a “scatter”—of s O − C / T P = 2.40 × 10 −5 . The timings have a median error bar normalized by the orbital period of σ / T P = 1.55 × 10 −5 . For the TTV measurements of Holczer et al. ( 2016 ), the data are more precise than that for 40 planets with T P > 100 days. Of those 40, 15 planets have larger TTV scatter, i.e., s O − C / T P > 2.40 × 10 −5 , and all of these are deemed significant at . The large amplitude and period of these signals makes them likely due to planet–planet perturbations. We conclude that Kepler-1625b may very likely have a TTV signal due to additional planets, which may be confused for exomoons, or at least contaminate the exomoon TTV signal. A repeated photometric transit signal of the exomoon, rather than the TTV induced on the planet, is likely a more reliable signature. 5.3. Overlapping Moon and Planet Transits There are two possible scenarios for overlapping moon and planet transits. First, the moon may be entirely in front of or behind the planet, in which case the photometric signal would be identical to that of an isolated planet transit and the moon would be hidden. Such an event is not explicitly considered in our equations. We estimate it to be rare though, with a likelihood on the order of ≈ R P / a M if I M = I P = 90°, and significantly less for inclinations that


also the channel maps by using the 13 CO data cube of the Galactic Ring Survey (GRS; Jackson et al. 2006 ). The RRLs corresponding to discrete regions are then used in the analysis of resolving the KDA. 3.1 Bubbles with detections of formaldehyde absorption The formaldehyde (H 2 CO) traces cold and dense ( n ∼ 10 4 cm −3 ) molecular gas (e.g. Young et al. 2004 ). By its absorption features of six fine structure transitions of (1 10 –1 11 ), H 2 CO has been widely detected in our Galaxy against radio continuum sources or even cosmic microwave background (CMB; Rodríguez et al. 2006 ). The transitions of H 2 CO (4829.6412–4829.6710 MHz) 5 close to the rest frequency of H110α (4874.157 MHz) have long been used to resolve the KDA for regions in the inner Galaxy (e.g. Downes et al. 1980 ; Watson et al. 2003 ; Sewilo et al. 2004 ; Du et al. 2011 ). Our observation covered the H 2 CO (1 10 –1 11 ) transition lines towards each of the targeted Spitzer infrared bubbles. The TianMa beam size for observing H 2 CO lines is about 3.9 arcmin. The typical on-source time is 2.5 min. Data processing is the same as for a single hydrogen RRL as described in Section 2 . H 2 CO absorptions along the line of sight of 27 out of the 75 infrared bubbles were detected. The absorption feature(s) is fitted by Gaussian(s) after removing a polynomial baseline (typically third order; Fig. 3 ). For the bubbles with H 2 CO detections, the spectra of RRL and H 2 CO are given in Appendix B (Supporting Information) . The fitted LSR velocity, the FWHM line width, the velocity-integrated line intensity, and their errors are listed in Table 3 . The rms noise for each spectrum estimated from the line-free channels is also incorporated. Figure 3. Examples of Spitzer infrared bubbles with detections of both RRLs ( lower panels , stacked spectrum) and formaldehyde lines near 4829.66 MHz ( upper panels ). From left to right, we show the KDA solutions of three bubbles assigned at near kinematic distance, far kinematic distance, and at the tangent point, respectively, according to the H 2 CO absorption method (see Section 3.2 ). The red vertical lines indicate the tangent point velocities derived by using the rotation curve of Russeil et al. ( 2017 ) with Galaxy fundamental parameters of R 0 = 8.34 kpc and (Reid et al. 2014 ). Table 3. Spitzer infrared bubbles with detections of H 2 CO (1 10 –1 11 ) transitions near 4829.66 MHz by the TianMa 65-m radio telescope. Column 1 is the source name; column 2 lists the measured LSR velocity from the H 2 CO spectrum, and its 1σ uncertainty is given in column 3; columns 4 and 5 are the measured FWHM line width and its 1σ uncertainty; columns 6 and 7 are the velocity-integrated intensity and its uncertainty, respectively; column 8 is the rms noise of the H 2 CO spectrum, estimated from the line-free channels. 3.2 Solution to the kinematic distance ambiguity Distance is a key parameter for Galactic sources. The trigonometric parallax (e.g. Reid et al.


We are grateful to the staff astronomers at Keck Observatory for their assistance with the observations, and to Jason X. Prochaska, Tom Barlow, and Michael T. Murphy for providing some of the software that was used to reduce the data. We also thank an anonymous referee who provided helpful suggestions that improved the presentation of this work, following a referee who was unable to respond in a timely manner. During this work, R.J.C. was supported by a Royal Society University Research Fellowship. R.J.C. acknowledges support from STFC (ST/L00075X/1, ST/P000541/1). C.C.S. has been supported by grant AST-1313472 from the U.S. NSF. This research was also supported by a NASA Keck PI Data Award, administered by the NASA Exoplanet Science Institute. Data presented herein were obtained at the W. M. Keck Observatory from telescope time partially allocated to the National Aeronautics and Space Administration through the agency’s scientific partnership with the California Institute of Technology and the University of California. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. We thank the Hawaiian people for the opportunity to observe from MaunaKea; without their hospitality, this work would not have been possible. This work used the DiRAC Data Centric system at Durham University, operated by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility ( http://www.dirac.ac.uk ). This equipment was funded by BIS National E-infrastructure capital grant ST/K00042X/1, STFC capital grant ST/H008519/1, and STFC DiRAC Operations grant ST/K003267/1 and Durham University. DiRAC is part of the National E-Infrastructure. This research has made use of NASA’s Astrophysics Data System. R.J.C. thanks S.O.C. for her impeccable timing and invaluable insight. Facility: Keck(HIRES) . Software: Astropy (Astropy Collaboration et al. 2013 ), Matplotlib (Hunter 2007 ), NumPy (van der Walt et al. 2011 ).


quantifies in Fourier space the sum of the square of the difference between the data and the restored object, degraded with the current estimated individual transfer functions . In the usual case that the image data has a good signal to noise ratio (S/N), the regularization constant may be set to zero. Equation ( 1 )makes use of the assumption of additive, Gaussian noise, in which case the common estimate of the Fourier transform of object , , for a given set of transfer functions is given by (see e.g., Paxman et al. 1996 ) in which the object is obtained by deconvolution of the average of a purposely degraded dataset, with the average over the autocorrelation function of the individual transfer functions. Since the data have already been degraded by the , the additional degradation of the data with the complex conjugate of the results in a dataset that has been degraded with a PSF that is centered on the origin, and which can therefore be added to other such data, without further degrading the result. We note that it is implicitly assumed that the transfer function is independent of the spatial coordinates, so that the convolution operator can be conveniently expressed as a multiplication in Fourier transformed space. While this is in reality not quite true, the assumption leads to a considerable reduction in computational effort, and for a 1 m-class solar telescope it is normally a good assumption over an area smaller than about 5 5. In practice, an image is therefore divided in tiles no larger than approximately 5 5, restored on a tile-by-tile basis, and then re-assembled to a single restored image, although this may become more problematic with the large 4 m-class solar telescopes currently planned or under construction (DKIST, EST), where this area is expected to reduce to only 2 2. The initial assumption made by the MFBD process, that the PSF is the result of a pure phase error of the wavefront entering the telescope pupil, is clearly only true if the image is recorded significantly faster than the time scale over which the wavefront changes. This so-called seeing freezing time scale is variable, dependent on the telescope diameter, and has been determined in the past to typically lie at or below 10 ms ( Tarbell Smithson 1981 ) for a 1 m-class telescope. If this time is exceeded significantly, the assumption of the PSF being the result of a pure phase error is no longer valid, and the fitted wavefront cannot be unambiguously interpreted as a wavefront anymore, as it describes a PSF that has been produced by integration over time of several wavefronts, which is inconsistent with the formation model. Due to the non-linearity of the mapping from wavefront to PSF, the correspondence of PSF to wavefront is generally non-linear and not unique. The latter, however, can be addressed by providing additional constraints, such as phase diversity, that are effortlessly included in the formalism used here, and have been used to reduce or even remove


Acknowledgments We thank to the anonymous reviewer for his/her careful reading of the manuscript and for critical and informative comments, which greatly improved and corrected this work. We are grateful to Polish National Science Centre for their support (grant no. 2011/01/D/ST9/00735). The European Very Long Base Interferomery Network (EVN) is a joint facility of European, Chinese, South African and other radio astronomy institutes funded by their national research councils. KG gratefully acknowledges the Poznan Supercomputing and Networking Centre (PCSS, Poland) for computing grant No. 195. This research has made use of the SIMBAD data base operated at Centre de Donnes astronomiques de Strasbourg (CDS), Strasbourg, France.


Acknowledgments The research leading to these results has received funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (grant agreement no. 670519: MAMSIE). The research presented here makes use of the MAST archive hosted by STScI in the USA and the Simbad astronomical database hosted in CDS, Stroudsbourg, France. This paper includes data collected by the Kepler mission. Funding for the Kepler mission is provided by the NASA Science Mission directorate.


The astronomical silicates and carbons are assumed from Draine ( 2003 ). The grain size distribution has a slope of −3.5 and goes from 0.03 μ m to 3 mm. To irradiate the disk the star is treated as an isotropic source with stellar spectral models obtained from the 5 Myr isochrones from Siess et al. ( 2000 ), with T eff ∼ 8000 K and a radius R ∼ 2.2 R ⊙ . The source is located at the distance of 117 pc, adopting the disk inclination and position angle of 13° and 5°. 3. Results Our reference profile for the gas and dust distributions is the DALI thermochemical model from FD17 , that models the dust surface density profile Σ dust with two dust rings (20–35 au and 56–83 au) and the gas density profiles Σ gas with an inner cavity (13–56 au) reduced by a factor 30–40. However, we considered an update of the published model of FD17 , limited by the spatial resolution of the available data at the time. Based on the 13 CO J = 3–2 ALMA archive data from Honda et al. ( 2012 ), the gas cavity appears to be located at ∼20–56 au. Figure 1 shows the temporal evolution of the dust and gas surface density profiles, Σ dust and Σ gas , in our simulation. Going from black to red, Σ dust and Σ gas are displayed as a function of time, that we recall is normalized to the orbital period of the outer planet at the initial position (55 au, T orb ∼ 320 yr). Figure 1. Σ dust (top panel) and Σ gas (bottom panel) as a function of the radius R for increasing time. The initial surface density profiles are in black. Our time unit is normalized with the initial orbital period of the outer planet (∼320 yr). The inner planet carves a cavity in the dust and in the gas, with a depletion factor of ∼10 −4 and ∼10 −1 , respectively, inward of its orbit. The outer planet first migrates (see Figure 2 ) while accreting the material, then opens a gap in dust and gas (with depletion factor ∼10 −4 and ∼10 −1 , respectively, in dust and gas) at his “equilibrium” location. The dust ring produced between the two planets is preserved for at least ∼500 orbits, i.e., for over ∼2 × 10 5 yr. At the same time, the gas is accreted on the star and the planets. The density profiles of the gas and dust in our simulation are due to a combination of factors. For the gas, the “cavity” is produced by the torques exerted by the outer planet onto the disk, which prevents the gas outside the outer planet to refill the inner regions that are emptied by viscous accretion. For the dust, the two prominent rings are created by the usual trapping at pressure maxima (indeed, we have verified that the ring location coincides exactly with pressure maxima). This generates a gas cavity with a width of ∼50 au, lowering the gas surface density and increasing the value of the Stokes number that quickly becomes larger than unity, helping the dust trapping due to the pressure gradient in preventing the dust migration and thus preserving the dust ring. Figure 2. Dynamics of the two planets. Top-right panel: the


from SIMBA are consistent at f gas 0.5, but significantly differ at f gas > 0.5 due to steeper decrease compared to our data. Such a sharp reduction in δ DGR translates to relatively low number of DSFGs with M dust / M ⋆ ≳ 0.01 produced in cosmological simulations. By investigating the connection between the δ DGR and Z gas in SIMBA, we find that very low δ DGR in galaxies from the highest-end of gas fraction is a result of their gas metallicities being lower by a factor of ∼4 relative to solar. The comprehensive treatment of different physical mechanisms that could be responsible for relative shortfall of model predictions, along with numerical limitations, is out of the scope of this paper. In the following we briefly emphasize their importance. The dust growth timescale is too long. One of the most critical parameters that describes the dust mass growth is the accretion timescale ( τ acc ). It is often modelled as: where a is a dust grain size which is usually assumed to be spherical with a typical size of ∼0.1 μ m ( Asano et al. 2013 ). The n H and T gas are the number density and temperature of the cold gas phase, and τ acc, 0 defines the timing of growth activation. The timescale for dust growth in the ISM changes as a function of gas surface density for different Z gas (see Popping et al. 2017 , their Fig. 1). If we apply M gas of our DSFGs, along with their compact ALMA continuum sizes (see the next section), we infer high median molecular gas surface density of ∼6.7 × 10 3 M ⊙ pc −2 . Such a high surface density implies short accretion timescales, on average τ acc ∼ 6 × 10 5 yr. These will be obtained if τ acc, 0 10 6 yr which is shorter than what has usually been adopted in cosmological simulations 6 . The short τ acc are proposed by Pantoni et al. (2019) , and are also reproduced in very recent semi-analytical models that claim fairly good overall match to the observations ( Triani et al. 2020 ). These are also in line with De Vis et al. (2017) , who found that variations in dust growth timescales might help to explain the M dust deficit at high gas-fractions in their large sample of nearby galaxies. Given the SIMBA’s ∼kpc resolution, a multiphase galaxy ISM cannot be resolved, which prevent us from knowing the exact dependence of the modelled dust content to the gas surface density. As a result, parameters such as the reference τ acc are tuned in order to boost the effective gas density. Thereby, it seems likely that use of shorter accretion timescales (equivalent to the increase in dust growth efficiency) in simulations could help partially overcome the shortfall to data. Dust destruction is too efficient. It is also possible that the dust destruction in simulations is too efficient. The total rate of dust mass destruction is given by Ṁ dest ∝ M dust / τ destr , where dust destruction timescale is usually approximated as ( Slavin et al. 2015 ): Here Σ M gas is the surface density of molecular gas mass, f ISM is the value


the same is not necessarily true for the standoff radius. In Fig. 3 we plot the standoff radius versus orbital radius. The standoff radius near the pericentre may not be resolvable, although at larger distances from Sgr A* the likelihood for resolving the source increases. It is also worth noting that we calculated the thermal free–free emission around Sgr A* and concluded that it is not detectable. Figure 3. Left: the standoff radius for S2 ( R o ) versus the orbital radius ( R ⋆ in units of 10 −3 pc). We see that the value is always less than unity, as expected. Right: angular diameter of the standoff radius (θ o ) versus the angular diameter of the orbital radius (θ ⋆ ). Around pericentre it may be difficult to resolve the finite size of the standoff radius. However, S2 should still be detectable via synchrotron emission. 4 CONCLUSIONS AND FUTURE OBSERVATIONS The innermost stars orbiting Sgr A* (such as the S-stars) produce a bow shock. Although this shock will likely not be detectable via thermal emission, we have shown that stars such as S2 may be detectable via synchrotron emission. Fig. 1 shows that the contrast of synchrotron flux relative to Sgr A* is maximized around the 1.4 GHz band. However, due to scattering we will need to use a higher frequency, around 10 GHz, if we are to resolve our star. If a star such as S2 emits strong synchrotron emission, the combined signal from the star and Sgr A* may exceed the quiescent radio emission from the black hole. As was the case with G2 (see next paragraph) it is not clear that any additional synchrotron emission will be observable. Arguably, it is best to resolve the synchrotron emission from any star orbiting Sgr A*, such as S2. At apoapse S2 is ∼0.23 arcsec from Sgr A* while at periapse it is only ∼0.015 arcsec away. Thus, to detect a star such as S2 requires both good sensitivity and resolution. VLBI can provide submilliarcsec observations of Sgr A* (e.g. Lu et al. 2011 ) and thus the required precision. S2 is an ideal test case since the star will reach periapse in 2017 or early 2018. Recently, gas cloud G2 was observed orbiting Sgr A*, and was approximately 3100 Schwarzschild radii from the black hole at pericentre. It was predicted that the bow shock from this encounter would displace the quiescent radio emission of Sgr A* by ∼33 mas (Narayan, Özel Sironi 2012 ; Sadowski et al. 2013 ). However, observations across the spectrum showed no apparent variability during the periastron passage of G2 (Bower et al. 2015 ; Valencia-S et al. 2015 ). It is unclear why a bow shock was not detected. One possibility is that at the centre of G2 is low-mass star with wind velocity ∼100 km s −1 (Crumley Kumar 2013 ; Scoville Burkert 2013 ). Synchrotron emission from such a small v w would be extremely difficult to detect. Star S2 is massive, and thus the winds are likely an order of magnitude larger. If synchrotron emission is not detected for S2 it may be that our value for ε nt is too large. It


The authors are grateful to the referee for comments which improved the manuscript. We thank Nikhil Mahajan for performing some of the early explorations. We are grateful to B.J. Fulton for permission to reproduce his figure and useful discussions. We acknowledge Tim Morton, Lauren Weiss, and Josh Winn for helpful insights. J.E.O. acknowledges support by NASA through Hubble Fellowship grant HST -HF2-51346.001-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555. Y.W. acknowledges support from NSERC.


reduced χ 2 values determined from GRB data alone are around unity for all models (being between 1.03 and 1.06), while those values determined from the H ( z ) + BAO data combination range from 0.48 to 0.53, with the lower reduced χ 2 here being due to the H ( z ) data (that probably have overestimated error bars). As discussed in Ryan et al. ( 2019 ) and Cao et al. ( 2020 ), the cases that involve H ii G and QSO-AS data have a larger reduced χ 2 (between 2.11 and 3.02), which is probably due to underestimated systematic uncertainties in both cases. Based on the AIC and the BIC (see Table 1 ), the flat ΛCDM model remains the most favoured model, across all data combinations, among the six models we study. 14 From ΔAIC and ΔBIC, we find mostly weak or positive evidence against the models we considered, and only in a few cases do we find strong evidence against them. According to ΔBIC, the evidence against non-flat XCDM is strong for the H ii G, QSO-AS, and GRB only cases, and very strong for the HQASG and HzBHQASG cases. Similarly, the evidence against flat φCDM is strong for the HQASG and HzBHQASG cases, and the evidence against non-flat φCDM is strong for the H ii G, QSO-AS, and GRB only cases, and very strong for the HQASG and HzBHQASG cases. Among these six models, a comparison of the ΔBIC values from Table 1 shows that the most disfavoured model is non-flat φCDM, and that the second most disfavoured model is non-flat XCDM. This is especially true when these models are fitted to the HQASG and HzBHQASG data combinations, in which cases non-flat φCDM and non-flat XCDM are very strongly disfavoured. These models are not as strongly disfavoured by the AIC, however; from a comparison of the ΔAIC values in Table 1 , we see that the evidence against the most disfavoured model (non-flat φCDM) is only positive. 6 CONCLUSION We find that cosmological constraints determined from higher z GRB, H ii G, and QSO-AS data are mutually consistent. It is both reassuring and noteworthy that these higher z data jointly favour currently accelerating cosmological expansion, and that their constraints are consistent with the constraints imposed by more widely used and more restrictive H ( z ) and BAO data. Using a data set consisting of 31 H ( z ), 11 BAO, 120 QSO-AS, 153 H ii G, and 119 GRB measurements, we jointly constrain the parameters of the GRB Amati relation and of six cosmological models. The GRB measurements are of special interest because they reach to z ∼ 8.2 (far beyond the highest z ∼ 2.3 reached by BAO data) and into a much less studied area of redshift space. Current GRB data do not provide very restrictive constraints on cosmological model parameters, but in the near future we expect there to be more GRB observations (Shirokov et al. 2020 ) that should improve the GRB data and provide more restrictive cosmological constraints. Some of our conclusions do not differ significantly between models and so are model independent. In particular, for the


ACKNOWLEDGEMENTS DT acknowledges support of a studentship funded by the Perren Fund of the University of London. This research was supported by the UK Science and Technology Facilities Council (STFC) grant ST/P000622/1. This research utilized Queen Mary’s Apocrita HPC facility, supported by QMUL Research-IT, http://doi.org/10.5281/zenodo.438045 .


we adopt the relation M star = M core /2, to ensure that the total mass of stars in our Class 0 binaries does not exceed that of their host cores. We may then rewrite equation ( 5 ) as After dividing equation ( 6 ) by equation ( 3 ), we find The numerical value for this ratio is actually an upper bound. First, Class 0 stars may have masses that are less than M core /2. Second, we have ignored the fact that the density distribution in the core is centrally peaked (see e.g. Jørgensen et al. 2007 ). Both corrections act to lower the ratio, but not by a lot. For example, if M star / M core is correct, but the interior density is 10 times the mean (an extreme assumption), then r star / r 0 falls to just 0.23. The lesson, in any case, is that the widest Class 0 binaries, which are presumably the youngest, are bound to their host core and not to each other. Nevertheless, the net force pulling on each star is inwards 4 towards the companion star, causing the two stars to drift together even as they are gathering mass from the core. The stars initially share the rotational motion of the core, but their transverse speed subsequently increases by conservation of angular momentum. Once their separation falls below the critical value, the stars attract each other and enter a true binary orbit. Inward drift continues and accelerates as angular momentum is transferred to the background gas via dynamical friction. Stahler ( 2010 ) has provided an analytic treatment for this orbital decay. Simulations of orbital shrinking indicate the process primarily occurs at early times. Offner et al. ( 2016 ) explored binary formation and evolution in magnetohydrodynamical simulations, and found that binaries with separations of few 10 3 au could shrink to separations of 100 au in only 0.1 Myr. Similarly, Bate, Bonnell Bromm ( 2002 ) found that wide binaries could produce very close binaries through accretion processes or via dynamical interactions while the stars are embedded in a gas-rich core. The optimal w_sb model gives a shrinking time-scale of t s / t 0 = 1.39, which becomes t s ≈ 0.28 Myr for t 0 = 0.2 Myr. (Note that the ejection models explored in Appendix A yield a similar shrinking rate for the optimal w_sb* model.) This shrinking rate is about three times longer than what was obtained by Offner et al. ( 2016 ) for a 4 M ⊙ core. Most of the cores in Perseus have masses of ∼1 M ⊙ (Sadavoy et al. 2010 ), so an average t s ≈ 0.3 Myr may still be in rough agreement with the simulations. Both the w_sb and w_sb* models predict that binary shrinking occurs primarily during the embedded phase, as is also found by simulations. Thus, our simple evolutionary models broadly agree with the theoretical studies currently available. Finally, our observations show that relatively tight binaries have random orientations with respect to their host cores, a situation that does not hold for the predominantly aligned wide binaries (recall Fig. 5 ). Thus, the processes


Acknowledgements We thank Thomas Tauris for his very useful comments. This work was supported in part by the National Science Foundation under Grant No. NSF PHY11-25915. This research has partially been funded by the Interuniversity Attraction Poles Programme initiated by the Belgian Science Policy Office (IAP P7/08 CHARM). It further was supported by the Netherlands Research Council NWO (NWO grant \#621.016.701 for LGM-II) and by the Netherlands Research School for Astronomy (NOVA). SdM acknowledges support by a Marie Sklodowska-Curie Action (H2020 MSCA-IF-2014, project id 661502). Part of the numerical computations were carried out on the Little Green Machine at Leiden University (612.071.305 and 621.016.701).


We are grateful to Dietrich Baade, Danny Lennon and Christophe Martayan for discussions and for pointing out the recent TESS result to us. We also thank our anonymous referee for useful comments on an earlier version of this manuscript.


We thank the European Research Council for funding support under Synergy Grant ERC-2013-SyG, G.A. 610256 (NANOCOSMOS). CB would like to thank the Ministerio de Ciencia, Innovación y Universidades for a Juan de la Cierva postdoctoral fellowship (FJCI-2016-27983). IT, VJH, and JLD acknowledge additional partial support from the Spanish State Research Agency (AEI) through grant FIS2016-77726-C3-1-P. We would also like to thank Rosa Lebrón, Jesús Quintanilla, and Cristina Soria for providing us with the sample of succinonitrile and Prof. Yasuki Endo for logistic support with the quantum chemical calculations. This work was also based on observations carried out with the IRAM 30-meter telescope. IRAM is supported by INSU/CNRS (France), MPG (Germany), and IGN (Spain).


ACKNOWLEDGEMENTS We thank the anonymous reviewer for the careful reading of our manuscript. The work was supported by the RFBR grant 18-32-00194. Funding for the SDSS has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the US 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 website is http://www.sdss.org/ . This research makes 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, and the LEDA data base ( http://leda.univ-lyon1.fr ). This research made use of Astropy, 10 a community-developed core python package for Astronomy (Astropy Collaboration 2013 ; Price-Whelan et al. 2018 ).


stripped from the progenitor within the last ∼5 Gyr (i.e., are part of the most recent leading debris tail). The model predicts that only the northeastern corner of the HiTS footprint should contain any Sgr debris. The mean distance of these model debris points is , with a spread of σ d ∼ 6 kpc. There are nine HiTS RRLs between 31 d H 49 kpc, of which four are in the region occupied by Sgr model debris (i.e., 170° 7R.A. 175°, −3° decl. 3°). Interestingly, these four stars are tightly clumped in distance, with a mean of and standard deviation of σ d ∼ 0.7 kpc. Nonetheless, given that these four stars are ∼165–20° from the center of the Sgr stream (using the Sgr-aligned coordinate system of Majewski et al. 2003 ), we consider their association with Sgr tentative at best. In conclusion, while there are likely stars from previously identified substructures in our sample of HiTS RRLs, it is unlikely that they have significantly biased our density profile fits, as each of the substructures would contribute only a small number of stars in our field of view. 7. Discussion and Summary We present the detection of 173 RRLs using observations from the 2014 campaign of the HiTS survey. The data cover ∼120 square degrees of the sky and include from 20 to 37 epochs in the g -band. The photometric depth of the HiTS data enables us to build a catalog that includes a significant number of stars that do not appear in previous public surveys overlapping the same sky region (such as the CRTS). Most of the additional RRLs we contribute have , corresponding to d H ≳ 60 kpc. The surveyed region overlaps with the position of currently known satellite galaxies of the Milky Way. We detect 65 RRLs members of the Sextans dSph, 46 of them being new discoveries. This number includes seven stars that were not classified as RRLs by other works, but were already considered as members of the dwarf. Two additional dwarf galaxies, Leo IV and Leo V, were found within our RRLs catalog. A more detailed analysis of the RRLs in Leo V has been presented in a companion paper (Medina et al. 2017 ). Regarding distant RRLs in our sample, we find 18 candidates with d H > 90 kpc, 11 of which are classified as ab -type, while seven are c -type. To understand the connection of this subsample with previously known/unknown systems, the period-amplitudes of the individual stars could play a major role. RRLs that are members of globular clusters are separated in the distincted Oosterhoff groups (Oo I and Oo II; Oosterhoff 1939 ). On the other hand, RRLs in ultra-faint dwarf galaxies are mostly Oo II (Clementini 2014 ), while the halo general population (within a radius of ∼80 kpc) presents stars in both locus, but the majority of them follow the locus of the Oo I group. This has been shown multiple times in the literature (e.g., Zinn et al. 2014 ; Catelan Smith 2015 ), and it is also clearly seen in Figure 4 . The distant sample of RRLs, however, does not follow the main trend of nearby field


ACKNOWLEDGEMENTS We appreciate the ATNF and CSIRO Data Access Portal for making such high-quality data publicly available. We thank the XMM–Newton help desk for important clarifications regarding the XMM–Newton data analysis. We also thank Bettina Posselt, Oleg Kargaltsev, George G. Pavlov, and Joanna Rankin for the useful discussions. We greatly appreciate Dr. Sebastien Guillot for carefully reviewing our manuscript and suggesting essential improvements. DM acknowledges funding from the grant ‘Indo-French Centre for the Promotion of Advanced Research – CEFIPRA’.


V.B.-R. acknowledges support by the Spanish Ministerio de Economía y Competitividad (MINECO) under grant AYA2013-47447-C3-1-P. This research has been supported by the Marie Curie Career Integration Grant 321520. V.B-R. also acknowledges financial support from MINECO and European Social Funds through a Ramón y Cajal fellowship.


order of 100,000 white dwarfs with stellar mass companions, meaning that such systems are far from extraordinary. Furthermore, many WDMS systems will be post-common-envelope systems (perhaps still even being surrounded by the remnant common envelope in the form of a planetary nebula; Jones Boffin 2017 ; Boffin Jones 2019 ), which may lead to increased local extinction as a result of dust formation in the ejected envelope (Lü et al. 2013 ). As such, they are rather appropriate systems to constrain the importance of extinction in deriving their stellar parameters. An important caveat that must be noted is that many of these WDMS systems could also exhibit significant levels of irradiation—a problematic effect when it comes to the treatment of extinction as irradiation alters the emergent stellar spectrum, while here we only consider non-irradiated atmosphere models (see the discussion of Horvat et al. 2019 for more details). 10 10 As the discussion here is considered only illustrative, we fix the bolometric albedos and bolometric limb-darkening coefficients of both components to standard values. As a starting point, let us take one of the best constrained eclipsing post-common-envelope binaries known: SDSS J235524.29+044855.7 (hereinafter referred to as SDSS J2355; Rebassa-Mansergas et al. 2019 ). SDSS J2355 is a short-period post-common-envelope binary comprising a relatively cool white dwarf ( K) and a low-mass, metal-poor, subdwarf star (spectral type ∼sdK7). As before, calculating synthetic light curves for the system with no extinction and then with extinction consistent with the Galactic bulge, we now see significant deviations between the two models in u , g, and r bands (See Figure 4 ). The u band shows the strongest difference at more than 0.25 mag during primary eclipse, closely followed by the g band (at 0.13 mag) and the r band (at 0.02 mag, approximately 4 σ ). Even in the i band, the deviation is almost 0.01 mag—representing a more than 1 σ difference. The deviation during secondary eclipse would not be detected in any band given that the eclipse is not complete and the primary is far more luminous. Figure 4. Synthetic LSST light curves of the white-dwarf–subdwarf binary SDSS J2355 (Rebassa-Mansergas et al. 2019 ), calculated without (dashed line) and with extinction (solid line) corresponding approximately to the average extinction of the Galactic bulge. The residuals between extincted and unextincted cases are shown below each light curve, highlighting that the difference would be detectable at several σ by LSST in u , g , and r bands and marginally detected in the i band (in each residual plot, the shaded region represents ). 4. PHOENIX Atmospheres To increase the fidelity of computed observables on the low-temperature end, PHOEBE 2.2 now incorporates PHOENIX model atmospheres (Hauschildt et al. 1997 ) as computed by Husser et al. ( 2013 ). PHOENIX is one of the leading alternatives to Castelli Kurucz that incorporates 3D


et al. 2011 ), was required to have an overall completeness (the fraction of spectroscopic targets that were observed) over 70 per cent and a redshift completeness (the fraction of observed galaxies with good spectra) over 80 per cent. We use these galaxies to construct an overdensity map , where i denotes the pixel on the sky. n i = ∑ j ∈ pixel i w j , where w j is the systematic weight (Anderson et al. 2014 ) of galaxy j . The map is given a healp ix pixelization with N side = 1024. Note that we do not weigh the pixels by their observed area because the healp ix pixels are much smaller than the observed sectors for which the completeness is computed, and we did not want to introduce extra power due to possible errors in the completeness on small scales. We also confirm (see Section 7 ) that including pixel weights have only a small effect on the final result. 4 ANGULAR POWER SPECTRA 4.1 Theory We model the theoretical galaxy-CMB lensing convergence angular cross-power spectrum and the galaxy clustering angular auto-power spectrum using standard methods. We assume ΛCDM with parameters consistent with Planck 2013 (Planck Collaboration XVI et al. 2014a ) and BOSS Data Release 11 (Anderson et al. 2014 ). We use these models to estimate statistical errors from mocks and systematic corrections to E G (see Section 5 ). However, our measurement of E G along with errors from jackknife resampling, which we use in our final result, does not use our power spectrum models and is independent of ΛCDM. In addition, the corrections we determine from these models are well within statistical error bars. Using the Limber approximation for small scales (l ≳ 10) and assuming the ΛCDM model, the galaxy-CMB lensing convergence angular cross-power spectrum can be written as where f g ( z ) is the galaxy redshift distribution, W ( z ) = χ(1 − χ( z )/χ CMB ) is the CMB lensing kernel, χ( z ) (χ CMB ) is the comoving distance out to redshift z (the CMB surface-of-last-scattering redshift z CMB = 1100), and P mg ( k, z ) is the matter–galaxy 3D cross-power spectrum as a function of z and wavenumber k (Hirata et al. 2004 ). The cosmological parameters present are the Hubble parameter today H 0 and the current matter density parameter Ω m, 0 . The galaxy redshift distribution for CMASS is shown in fig. 1 of Anderson et al. ( 2014 ). The galaxy clustering angular auto-power spectrum can be written as where H ( z ) is the Hubble parameter at redshift z and P gg ( k, z ) is the galaxy 3D auto-power spectrum. Figure 1. An equatorial map of the CMASS survey divided into 37 regions used for jackknife resampling. 4.2 Mock galaxy catalogues from <italic>N</italic>-body simulations We compute the power spectra P mg ( k, z ) and P gg ( k, z ) using N -body simulations in order to model both non-linearities and the occupation of haloes with galaxies. The N -body simulation runs using the TreePM method (Bagla 2002 ; White, Hernquist Springel 2002 ; Reid et al. 2014 ). We use 10


of the bolometric luminosity are presented in Fig. 10 . The bulk of the NIR emission is produced close to the inner edge of the thin disk, that is, the sublimation radius, consistent with observations (continuum reverberation mapping: e.g., Suganuma et al. 2006 ; interferometry: e.g., Kishimoto et al. 2011 ). Without a wind component, the model NIR luminosities are about 50% higher than those of the model with a wind component for type 1 objects, because the wind provides a nonnegligible NIR extinction. As expected, the NIR luminosities decrease significantly once the inner thin gas disk is hidden by the thick gas disk. We observe a less significant drop of the NIR luminosities for high inclination angles ( i >65°) in the presence of a wind. We interpret the additional NIR emission as the contribution of the unobscured basis of the wind to the NIR emission. Whereas the ratio between the NIR and bolometric luminosity is about 1∕10 for the basic wind model, it increases by a factor of ~1.5 and ~2 when the puff-up is located at a and 2 times smaller distance from the central black hole ( Fig. 11 ). The increase of the NIR luminosity due to higher dust temperatures is stronger than the decrease due to the smaller area where hot dust can be found. Fig. 10 Model NIR luminosities as a function of the bolometric luminosity. Blue represents type 1, red represents type 2. The Circinus model is shown with crosses and pluses; the NGC 1068 model with squares and triangles. The inclination angles of type 2 objects are indicated: i = 50° (green line), i = 70° (orange line), i = 90° (yellow line). Left panel : wind with 1∕ z density profile. Right panel : no wind component. The dotted lines correspond to L NIR = ξ L bol with ξ = 1, 1∕3, and 1∕10. Fig. 11 Model NIR luminosities as a function of the bolometric luminosity for the 1∕ z winds for a ( left panel ) and 2 ( right panel ) times smaller inner radius of the thin gas disk. The dotted lines correspond to L NIR = ξ L bol with ξ = 1, 1∕3, and 1∕10. The NIR luminosities as a function of the MIR luminosities are presented in Fig. 12 . As for the previous correlations, the differences between the 1∕ z and 1∕ z 2 models are minor. Whereas type 1 objects show NIR/MIR ratios between 0.5 and 1, the NIR luminosities of type 2 models are more than five times smaller than the MIR luminosities. For luminosities smaller than 10 44 erg s −1 and inclination angles between 50° and 60° the MIR/NIR luminosity ratio is about ten. The model with an inner radius located at 2 × r sub (right panel of Fig. 13 ) reproduces the observations of Burtscher et al. (2015) best. Fig. 12 Model NIR luminosities as a function of the MIR luminosity. Blue represents type 1, red represents type 2. The Circinus model is shown with crosses and pluses; the NGC 1068 model with squares and triangles. The inclination angles of type 2 objects are indicated: i = 50° (green line), i = 70°(orange line), i = 90° (yellow line). Left panel : wind with 1∕ z


however, the fraction of dust in the clumpy component ( F ) does evolve strongly with redshift, similar to the gas-mass fraction. Fig. 8 Evolution of massive galaxy properties from their local values out to z ~ 1. The evolution of the dust-mass fraction ( M d ∕ M * ) was determined from a power-law fit to data from Santini et al. (2014) , Béthermin et al. (2015) (for z ≤ 1), and Rémy-Ruyer et al. (2014) for z = 0. The upper bound to the M d ∕ M * evolution is given by assuming M d ~ 0.5 × Z × M g , and the evolution of gas and metallicity over this redshift and stellar mass range. The evolution of specific SFR is shaded purple between the relationship in Sargent et al. (2014) and . The evolution of the molecular gas fraction (blue) is from Tacconi et al. (2018) . We find that the fraction ( F ) of dust in clumps surrounding nascent star-forming regions has increased by a factor of ~5.5, and that the overall attenuation of UV (SFR MS /SFR UV ) has increased by a factor of ~2.5 (ranging from 3.4 to 1.9 for face-on to edge-on galaxies, respectively). da Cunha et al. (2010) , Smith et al. (2012) , Sandstrom et al. (2013) , and Rowlands et al. (2014) found that, in the local Universe, M d ∕ M * is proportional to sSFR. Studies such as Sargent et al. (2012) and Tasca et al. (2015) , that look at how sSFR changes with redshift, find that the sSFR varies as sSFR out to redshifts z 2. This would give a sSFR increase by a factor of ~3.6 between z = 0.07 and z = 0.7. We note, however, that this trend also is stellar mass dependent (e.g. Schreiber et al. 2015 ), and that lower-mass galaxies have a shallower evolution in sSFR than the most massive galaxies. Recent studies of molecular gas at high redshifts indicate that the cosmic density of molecular gas, similar to the cosmic density of star formation, peaks between redshifts 2 and 3 ( Decarli et al. 2016 ). Genzel et al. (2015) , Sargent et al. (2014) , and Tacconi et al. (2018) used compilations of studies that measure gas mass via CO line luminosities and found that M g ∕ M * varies like , which corresponds to an increase by a factor of ~3.5 between z = 0.07 and z = 0.7. On the other hand, Bauermeister et al. (2013) expect which would imply an increase in the gas mass fraction by a factor of ~4.4. In any case, the gas mass is expected to increase by a factor of ~4 between our two redshift slices. In Fig. 7 , we show with two solid lines the relations SFR UV /SFR and . The parameter that most strongly controls the dust-to-gas mass is the metallicity (e.g. Leroy et al. 2011 ; Accurso et al. 2017 ). According to the parametrization of Zahid et al. (2014) , a galaxy with log ( M * ∕ M ⊙ ) = 10.2 would have a metallicity of 0.069 dex less at z = 0.7 than at z = 0.07. A galaxy at M * ~ 10 10.5 M ⊙ , on the other hand, will have a change in metallicity of 0.035 dex between the same two redshifts. For our sample, the dust to gas ratio should not change significantly between z ~ 0 and z ~ 0.7, however, we


that we also tested the Cartesian grid initial distribution, similar to Hopkins ( 2015 ). The main mechanism for the decay of the disk is the same. In this paper, therefore, we do not show the results for the Cartesian grid case. In order to carry out a quantitative comparison of the results, we introduce a rough estimate of the disk lifetime. Let us consider the root mean square of the radius of the particles initially located at the inner edge of the disk. When this value exceeds 10% of the radius of the inner edge, we regard the disk as disrupted. Figures 1 and 2 show the lifetime and snapshots of the Keplerian disk for each AV implementation. The differences among the lifetimes of the disks obtained with different implementations are very large. In the case of vNRL-B95-CD10-G+12, the disk survived for a time more than 10 times longer than with the standard method used today (M97-B95-R+00-SPH). Note that the longest case, vNRL-B95-CD10-G+12′, indicates the results with the vNRL-B95-CD10-G+12 scheme, but with and . These parameters in the AV switch would also play important role for the long-time evolution of the disk. Figure 1. Lifetime of the disk for each AV implementation in units of Kepler time at r = 0.5 (inner edge of the disk). Note that the disk lifetime is shown in the log scale. Figure 2. Snapshots from the Keplerian disk test at ∼28 orbits at r = 0.5 (inner edge of the disk) with each AV implementation. The color-coding of the density is given at the bottom. Since no disk lifetime with M97 AV exceeds ∼28 orbits at r = 0.5, we only show the results of four cases. To clarify the effects of each option on the disk lifetime, we show the dependences of the disk lifetime for each option in Figure 3 . Here, we show how the lifetime of the disk changes when we change the method in one type, while keeping the methods for the other three types unchanged. We can clearly see the following tendencies. (i) The disk lifetime obtained with vNRL AV is much longer than that with M97 AV. (ii) Both of the two shear switches extend the disk lifetime. The CD10 switch works better than the B95 switch for M97 AV, while the B95 switch works better than the CD10 switch for the vNRL AV. (iii) Both shock indicators extend the disk lifetime. The CD10 shock indicator works better than R+00 does. (iv) The G+12 derivative operator works better than the SSPH derivative operator. This might be due to the fact that the SPH derivative operator omits the surface term (for details see Section 3.1 in Price 2008 ). Figure 3. The difference of the lifetime of the disk when (a) the AV scheme, (b) the shear switch, (c) the shock indicator, and (d) the derivative estimator are changed. Points connected by lines indicate the runs performed with the same method, except for that shown in panel. Figures 4 – 6 show the evolution of the inner part of the Keplerian disks for three representative runs (M97-No-No-SPH, M97-B95-R+00-SPH, and vNRL-B95-R+00-G+12). In Figures 7 – 9 ,


This research was enabled in part by support provided by WestGrid ( www.westgrid.ca ) and Compute Canada Calcul Canada ( www.computecanada.ca ), and by the National Science Foundation under Grant No. 1066293 to the Aspen Center for Physics. AB, FD and LL acknowledge support from NSERC (Canada) through the Discovery Grant program. RD acknowledges support from the South African Research Chairs Initiative and from NASA grant NNX12AH86G. NSK and MAF acknowledge support from NATA ATP grant NNX10AJ95G and NSF grant AST-1009652, respectively, to the University of Massachusetts. TQ was partially supported by NSF award AST-1311956. We would like to thank Shuiyao Huang and Jared Gabor for helpful discussions, and RD, AB and FD would like to acknowledge the simulating collaborative atmosphere of the Aspen Center for Physics, where this work was completed. Finally, we would like to thank the anonymous referee for valuable comments that improved the clarity of the paper, as well as M. L. Balogh, J. M. Gabor and A. H. Gonzalez for providing us with access to detailed observational and simulation results in advance of publication.


in the vicinity. Details of the array configurations are given in Table 2 . Observations were reduced following standard procedures in Miriad (Sault et al. 1995 ), with the flux density scale set by observations of calibrators PKS 1934−638 and/or PKS 0823−500. Initially, observations were made covering the nominal position of the 3FGL source, and the positions of radio sources cataloged by Schinzel et al. ( 2017 ) and candidate X-ray sources. Observations differed in length, hour-angle coverage, angular resolution, and sensitivity to extended radio emission in the vicinity, resulting in a heterogeneous data set. Schinzel et al. ( 2017 ), who observed with the ATCA in the relatively compact H168 and H214 array configurations, detected four sources within the 3 σ error region around 4FGL J1405.1−6119, all of which were brighter than 15 mJy, and are resolved out on longer ATCA baselines. Schinzel et al. ( 2017 ) also list a further 60 objects in the field detected outside the 3 σ region, which appear to be associated with the H ii region cataloged by Caswell Haynes ( 1987 ) at ( l , b ) = (311.627, +0.27). Observations of the candidate X-ray sources in more extended ATCA array configurations revealed the fainter (∼2 mJy), variable radio counterpart. The final observations of the series were conducted as targeted observations, with the phase calibrator PKS 1420−679 used throughout. 3.4. Near-infrared Observations and Analysis We observed the candidate near-IR counterpart to 4FGL J1405.1−6119 (2MASS J14051441−6118282, allWISE J140514.40−611827.7; Landi et al. 2017 ) with FLAMINGOS-2 (Eikenberry et al. 2004 ) on Gemini South on 2018 June 7 through Program ID GS-2018A-Q-412. We used the R3K grism and a 4 pixel slit, giving a resolution of R ∼ 1800 across the K -band. The target was observed with 10 separate 120 s exposures in a standard ABBA nod, giving 1200 s of exposure time total. We also observed the nearby A0V star HD 119942 as a telluric standard immediately before our science observations. The data were reduced using standard near-IR procedures, with optimal extraction of the spectra from subtracted, flat-fielded nodded pairs. The final combined spectrum has a signal-to-noise of about 140 per resolution element in the continuum. After interpolating over the intrinsic Br γ feature in the telluric standard, we corrected the 4FGL J1405.1−6119 spectrum for telluric absorption by scaling the telluric spectrum to minimize the residuals in the regions of strong telluric lines. 4. Results 4.1. Gamma-Ray Results The power spectra of the light curves of all 3033 3FGL and 5523 FL8Y sources were examined for indications of periodic modulation that could arise from previously unknown binary systems. For candidate new binaries our usual threshold for further investigation has been for a source to have a peak power ≥18× mean power level (FAP 5 × 10 −4 ) and for the period not to coincide with a known artifact. We also exclude very long periods that are


A.M. and G.L. warmly thank Matthieu Tristram for his invaluable help in the use of Xpol. We acknowledge financial support from the “Programme National de Cosmologie and Galaxies” (PNCG) funded by CNRS/INSU-IN2P3-INP, CEA and CNES, France, from the ANR under the contract ANR-15-CE31-0017 and from the OCEVU Labex (ANR-11-LABX-0060) and the A*MIDEX project (ANR-11-IDEX-0001-02) funded by the “Investissements d’Avenir” French government programme managed by the ANR. The research leading to these results has also received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant Agreement No. 617656 “Theories and Models of the Dark Sector: Dark Matter, Dark Energy and Gravity”.


the inverse time axis and divide the result by 2 to obtain an overall weighted summation versus time, . The maximum value of the obtained overall weighted summation yields the mirror time delay estimation , . Figure 2 plots 5, 8, and 11 illustrate the results from the mirror time delay estimator for , respectively. Among the three mirror time delay estimations, we choose (Figure 2 ; plot 5) since it follows the form of the basic definition in statistics and also shows high performance results (Section 3.5 ). We use the rest of the results for reliability testing of our time delay estimation, as we will describe later in this section. 5. Weighted average correlation, : To check the reliability of the estimated time delay, we will need a normalized maximum weighted summation (between −1 to +1). This can ensure that the best estimated time delay corresponds to a reasonable correlation between the two light curves. Dividing the maximum weighted summation of correlations by the sum of the corresponding weights yields weighted average correlations in the form ofand similarlyand also for the mirror estimator we havewhere the above equations are valid for , and the weighted average correlations have values in the range of . It is worth noting that using the weighted summation of correlations instead of the weighted average correlation enables us to consider the number of segments of data that contribute in the estimation of the best time delay. This gives more weights to time delays that are derived using more segments of the data, in comparison to time delays that are derived by considering only one or two segments of data. Therefore, we obtain the best time delay using the maximum weighted summation, while the weighted average correlation shows the reliability of the estimation. We see in our analysis that this approach can improve our analysis by minimizing the possibility of having any outliers in our results. 6. Reliability test: To check the reliability of the time delay estimation, we consider several criteria. First we follow Aghamousa Shafieloo ( 2015 ) in assigning and and () as an acceptance limit for correlation values. Next we check the consistency of each pair of , time delays by checking their sign. We expect the consistent pairs have opposite signs. In addition, we calculate the mean and standard deviations of the absolute values of three , time delay pairs and expect the reliable results to show a low discrepancy with days and . If any of the above conditions is not satisfied, we consider our method disqualified to attain a reliable time delay estimation for the case of study. Figure 2. Plots 1 and 2 show the weighted correlation coefficients and for seven data segments and smooth fit segments for the lensed quasar SDSS J1001+5027 light curve data, respectively. Plots 3, 6, and 9 represent the weighted summations, that is, , which are calculated from the weighted correlation coefficients shown in plot 1 using three different


length. N J can be written as where n 3 is the number density of the gas in units of 1000 cm −3 , 5, t is the turbulent velocity (approximated here as the velocity dispersion of the cloud) in km s −1 , and μ is the mean molecular weight that we will assume to be 2.3 for a gas composed of H 2 and He. The cloud is gravitationally unstable to collapse if N ≥ N J . The volume density can be obtained from Table 2 by taking the average column density, multiplying by the inverse of the OH/H 2 abundance, and dividing by the path length through the cloud. If we assume the cloud extends in the radial direction, the same amount as in the plane of the sky, the path length would be ≈1–4 pc for distances ranging from 400 to 100 pc. In the most extreme low column density case (), n has a value of 34–140 cm −3 . All other values of T ex lead to higher average densities. For these estimates of n, N J ranges from 3.7 to 7.5 × 10 21 cm −2 . The highest column density derivable from the OH data in Table 2 is based on . Using this value and the OH/H 2 abundance leads to an average N (H 2 ) of 1.1 × 10 21 . Even comparing the highest cloud column densities with the lowest values of N J leads to the conclusion that the cloud is not gravitationally collapsing. In this respect, G211+63 resembles the bulk of high-latitude molecular clouds that are not bound by gravity and likely breaking up on the sound crossing time (). If this analysis is confirmed for other IVMCs then these objects may be transient structures formed as thermal instabilities in large-scale atomic flows (e.g. Shore et al. 2003 ; Shore et al. 2007 ; Barriault et al. 2010b ). 5.2 Linewdiths compared to CO Désert et al. ( 1990 ) observed only one position in the cloud (which we refer to as the ‘CO peak’) in the CO(1–0) line. They noted one component with a velocity full width at half-maximum (FWHM) of . They also reported other CO observations but of the (2–1) line from the IRAM 30 m radio telescope that showed two distinct velocity components like the ones we observe for positions 1–3. They give no line parameters but comment that the strength of the two peaks was highly variable within two beams (about 30 arcsec) of the central observation at (l, b ) = (210.927°, 63.280°). They do show a spectrum for the central CO(2-1) position where the two components are each only two channels wide. Their IRAM observations were made at resolution so the individual components have to be less than wide (FWHM). Our OH linewidths are clearly larger than the CO lines in four out of seven instances. The reason for this behaviour is difficult to ascertain because the CO and OH observations are at significantly different sensitivities and resolutions. The behaviour of molecular gas at cloud edges is not often discussed and there is little consensus on even the phenomenology of spectral lines at cloud edges. If the OH main lines are tracing the diffuse outer regions of the molecular cloud, then the broader profiles could be


Acknowledgements We acknowledge the help of Roberto Menezes, Rogério Riffel, and Rogemar Riffel in reducing a Gemini spectrum of NGC 3115, the continuum of which unfortunately was dominated by stellar emission and contained no information on the LLAGN. We acknowledge useful discussions with João Steiner, Alexander Tchekhovskoy, and Massimo Gaspari. This work was supported by FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo) under grants 2015/26831-1 and 2016/24857-6.


prior. Since we benefitted from transit observations that span more than three years, we did not use a prior on the period and time of inferior conjunction of the transiting planet. 3.4. Results We present in Table 3 the median and 1 limits of the marginalised posterior distributions after running five chains of 100 000 accepted steps (considering a 20% burn-in phase). The acceptance rate is 25% (40% for the burn-in phase). The convergence of the chains is validated by the test of Gelman Rubin (1992) (PSFR better than 1.01), and the autocorrelations are shorter than 2000 steps. Including the second planet in the model undoubtedly improves the fit. The rms of the CORALIE data after the two-planet fit is ten times smaller than after a one-planet fit. The best fit solution is plotted in Fig. 8 for the transit light curves and in Fig. 9 for the radial velocities. Again, the values provided in Table 3 are not the ones used in Figs. 9 and 8 . We checked that they represent a self-consistent set of parameters by comparing the BIC using both sets of values (best fit and median of the posterior distribution) and get compatible results. Table 3 Median and 1 limits of the posterior marginalised PDFs obtained for the WASP-41 system derived from our global MCMC analysis. Notes. (*) Assuming zero albedo and efficient redistribution of energy. Fig. 8 WASP-41b transit data (blue: FTS ; green: TRAPPIST ; red: Danish ) and best fit model (black line). The TRAPPIST light curve was obtained by binning the data from five transit observations, and the Danish one from one full and one partial transit observations. Each point corresponds to a 7.2 min bin. Fig. 9 WASP-41 radial velocity data (blue: CORALIE, green: HARPS; red: HARPS RM sequence) and best fit model (black line). Top : phase-folded on the period of the inner planet (outer planet subtracted). Middle : zoom on the Rossiter-McLaughlin effect. Bottom : phase-folded on the period of the outer planet (inner planet subtracted). The best-fitting model suggests a misaligned planet with a projected orbital obliquity of . However, the uncertainties are large (see Fig. 10 ), and the data do not allow an aligned orbit to be excluded (). The rotation velocity expected from the photometric rotation period of the star (2.44 km s) is compatible within the error bars with the spectroscopic (2.64 0.25 km s), suggesting that the star is equator-on. That reinforces the possibility of an aligned planet. 4. Discussion We have shown that finding long-period planets with instruments such as CORALIE is still possible around active stars. Recognising the periodic structure of activity-related signals is essential to avoiding false detections. While spots or plages induce signals at the rotation period of the star, the evolution of their coverage of the stellar surface is correlated with the magnetic cycle of the star. Such cycles have periods of several years and must be distinguished from long-period companions. Lovis et al.