O O O O O O B-Person I-Person O O B-Organization O B-Location O O O O O O O O B-Telescope O O O O O O O O O O B-Person I-Person O B-Organization O B-Person I-Person I-Person O B-Organization O B-Location O O O O O B-Telescope O B-Person O O O O O B-Organization B-Location I-Location I-Location I-Location I-Location B-Location O O O B-Grant O O O O O B-Organization I-Organization I-Organization O O O O O O O O O O O O O O O O O O O O O O O O B-Observatory I-Observatory B-Person O B-Person O O O O O B-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O O O O O B-Organization I-Organization I-Organization B-Organization O O O O B-Grant I-Grant I-Grant I-Grant O O B-Organization I-Organization O O B-Grant I-Grant I-Grant I-Grant O B-Organization O O B-Grant B-Person O O O B-Grant B-Person O O B-Grant B-Organization O B-Grant B-Organization O O O O O O O O O O

We give a special thank to Sambit Roychowdhary, then at NCRA in Pune, for helping us carry out some of the GMRT observations. We are grateful for the tips we got from Jayaram Chengalur at NCRA and K. S. Dwarakanath at RRI in Bangalore regarding the reduction of the GMRT data. T.P.K.M. acknowledges financial support from the Spanish Ministry of Economy and Competitiveness (MINECO) under grant number AYA2013-41243-P. He is grateful to the Kapteyn Astronomical Institute for their hospitality as a long-term guest during the time much of this paper was being written. Part of this work was done at Leiden Observatory. M.A.W.V. and T.P.K.M. acknowledge financial support provided by NOVA, the Netherlands Research School for Astronomy, and travel support from the Leids Kerkhoven-Bosscha Fonds. M.A.W.V. acknowledges support from the FP7 Marie Curie Actions of the European Commission, via the Initial Training Network DAGAL under REA grant agreement 289313. M.A.B. acknowledges support from NSF/AST-1009471. K.B.W. acknowledges grants OISE-754437 (NSF) and 614.000.807 (NWO). We finally thank the referee for constructive comments and suggestions.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength O O O O O O B-Wavelength O O O O O O O B-Wavelength O B-Wavelength O O O O O O B-Wavelength O O O O O O O O B-Model I-Model I-Model I-Model O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model I-Model B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O

determine whether the remnant continues to migrate in the HR diagram towards the hotter S Dor instability strip occupied by quiescent LBVs, or if increasing extinction from ongoing dust condensation in the ejecta pushes it redwards again. Figure 10. Modification of the HR diagram for LBVs and their kin from Mauerhan et al. ( 2015 , see their fig. 8). The magenta coloured square is the previous estimate for the precursor star from Mauerhan et al. ( 2015 ), uncorrected for possible circumstellar extinction. The red square represents the revised best-matching model of the precursor SED, corrected for grey circumstellar extinction (see the text). The blue square indicates the aftermath of the eruption, a hot B4–B5 supergiant, also corrected for grey circumstellar extinction. The luminosities of the remnant and the revised precursor were calculated by integrating the UV–IR SEDs of the best-matching models shown in Figs 8 and 9 . The revised parameters of the stellar precursor warrant re-analysis of the star's initial mass as well, which was previously estimated at ∼30 M ⊙ (Mauerhan et al. 2015 ). Fig. 11 shows the data, after correcting for the purported grey circumstellar extinction parameters discussed above (for the remnant, E ( B − V ) = 0.48 mag and R V = 5.4; for the precursor, E ( B − V ) = 0.16 mag and R V = 5.4), along with evolutionary tracks from the Geneva rotating stellar models for 50 and 60 M ⊙ (Ekström et al. 2012 ); the data appear to most closely match (but are slightly below) the 60 M ⊙ model, which at the locations of both the remnant and precursor is undergoing core-He burning (Ekström et al. 2012 ). This revised initial mass is approximately twice as high as the circumstellar extinction-free estimate by Mauerhan et al. ( 2015 ). Interestingly, the photometry of the remnant and precursor, which was corrected for different values of circumstellar extinction and based on the best SED matches, is consistent with no significant change in stellar luminosity between before and after the 2014 eruption. Figure 11. The precursor (open black square) and remnant (filled black square) photometry of SN Hunt 248 on the HR diagram, after correcting for our estimated circumstellar extinction parameters (see the text, Section 4.1.2 ). The evolutionary tracks are from Geneva rotating stellar models (Ekström et al. 2012 ) at solar metallicity for initial masses of 50 M ⊙ (green curve) and 60 M ⊙ (magenta curve). 4.2 The 2014 outburst, revisited 4.2.1 Massive binary merger-burst? The energy source of the 2014 eruption is uncertain. The structure of the outburst light curve, the outflow velocity and the large-amplitude pre-outburst variability detected over prior decades might provide clues. We can speculate that the cool-hypergiant precursor was a massive interacting binary, perhaps similar to HR 5171 (Chesneau et al. 2014a ), and that its large pseudophotosphere was the signature of a common envelope. If this is the case, it is plausible that SN


O O O O O O O O O O O O O O O O O B-Person I-Person I-Person I-Person I-Person O B-Person I-Person I-Person O O O O O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O B-Grant B-Grant B-Grant B-Grant O B-Grant B-Grant O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O O B-Grant B-Person O O O O B-Fellowship I-Fellowship B-Person O O O O B-Grant O O B-Organization B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant

We are grateful to the anonymous referee for the constructive comments that helped us improve this paper. Prof. Neal J. Evans II and Dr. Kee-Tae Kim are also acknowledged for useful discussions. This work is supported by the National Natural Science Foundation of China through grants 11503035, 11573036, 11373009, 11433008 and 11403040, 11403041, the International ST Cooperation Program of China through the grant of 2010DFA02710. T.L. is supported by the EACOA fellowship. K.W. is supported by grant WA3628-1/1 through the DFG priority program 1573 “Physics of the Interstellar Medium.”


O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-Survey O B-TextGarbage I-TextGarbage B-URL O O O O O O O B-Survey O O O O O B-Survey O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O B-Telescope O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

instead. In addition, some R 50 of SLSN hosts are provided in Lunnan et al. ( 2015 ). Otherwise, we use the the half-light radius within the SDSS catalog 13 13 http://www.sdss3.org/ by matching the SN host galaxies with SDSS galaxies within 3′′. In the SDSS catalog, the half-light radius is estimated from the r -band Petrosian half-light radius R 50,petro and the Petrosian 90% radius R 50,petro following R 50 = R 50,petro /(1 – 8 × 10 −6 ( R 90,petro / R 50,petro ) 8.47 ) (Graham et al. 2005 ). We also update the offset parameters from the literatures. Lunnan et al. ( 2015 ) calculated the projected R off from HST images for SLSNe. Anderson et al. ( 2016 ) reported the projected R off from SNe II to the nearest H ii regions. Kelly Kirshner ( 2012 ) provided the deprojected r off = R off / R 50 for SNe II and SNe Ibc. Although projected offsets and deprojected offsets are statistically consistent, they are different for specific objects. Since most offsets in the literature and catalogs are projected, we use these deprojected offsets only when projected offsets are not available. We also convert them to r off when R 50 is available in our catalog. The sample sizes for SLSNe, SNe Ibc, SNe II, and SNe Ia with host galaxy properties are 107, 900, 4251, and 7221, respectively. To have a consistent z range as the FRB sample, we screen the samples with z 1. This gives sample sizes of 95, 874, 2829, and 7003 for the four types, respectively. Most SNe Ibc, SNe II, and SNe Ia have z 1. The excluded objects are mostly those without redshift information. The sample size for each parameter for each type of stellar transient is presented in Table 2 . 3. Multivariate Comparison We would like to perform a comparative study of the host galaxy properties between FRBs and other stellar transients. Since multiple parameters are involved, multivariate analysis methods are needed. We perform two tests. First, taking all the FRBs as a whole sample, we compare it with other samples using the multivariate Kolmogorov–Smirnov (KS) test. Second, we also compare each individual FRB with other samples to see which type it most likely belongs to. For easy understanding, we use the naive Bayes method to test individual FRBs in the FRB sample to see how they may be consistent with various types of stellar transients. We try to classify LGRBs, SLSNe, SNe Ib/Ic, SNe II, SNe Ia, and SGRBs with their host galaxy properties using the naive Bayes method and then apply the same method to each FRB. Galaxies evolve with redshift, and the FRBs in our sample all have redshift z 1, so to enable a direct comparison, in the following we compare the FRBs with the transients with redshifts z 1 only. 3.1. Multivariate KS Test 3.1.1. Method The classical KS test compares the cumulative distribution function (CDF) of two distributions P ( x ) and P ( x ′), which could be one data sample and one model sample, or two data samples. The largest distance between the two CDFs is defined as D


O O O B-Person I-Person O O O O B-Survey O O O O O O B-Person O B-Person O O O O B-Organization B-Person O B-Person O O O B-Organization B-Grant I-Grant I-Grant B-Person O O O O B-Fellowship I-Fellowship I-Fellowship B-Person O O O O B-Organization I-Organization B-Person B-Person B-Person B-Person O B-Telescope O O O O B-Organization O B-Grant B-Person O O O B-Grant I-Grant I-Grant O O O O O O O O B-Person I-Person I-Person

ACKNOWLEDGEMENTS We thank Arif Babul and members of the LoCuSS collaboration for their support and assistance. SLM and GPS acknowledge support from the STFC. AF and AEE acknowledge support from NASA Chandra Grant G06-17116B. AF acknowledges support from a McWilliams Postdoctoral Fellowship. GPS acknowledges support from the Royal Society. CO, DPM, ZA, JEC, and CARMA operations were supported by NSF grant AST-1140019. CPH acknowledges support from PRIN INAF 2014. This paper is dedicated to the memory of Dr. Yu-Ying Zhang.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O B-CelestialObject O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject B-CelestialObject O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

order of Type 2, 3, and 4 successively. The Type 1 clumps are puzzling, because we would expect that they are the clumps just before the onset of cluster formation in a stage prior to the Type 2 clumps, but their chemical compositions indicate that they are older than the Type 2 clumps. We will discuss the nature and origin of the Type 1 clumps in Section 4.3 . 4.2. Velocity Structures of the Clumps The results shown in Figures 11 – 12 suggest that there are interesting systematic differences among the types of clumps. In the following, we further investigate the velocity structures of the Types 1–3 clumps. Figure 15 shows the distribution of the velocity dispersion σ obs measured with the 13 CO and C 18 O emission lines for the 24 clumps as a function of the projected distance from the cluster center (for Type 2 and Type 3 clumps) or from the clump peak (for Type 1 clumps). Values of σ obs measured with the two emission lines are shown by dots with different colors—gray and pink for the 13 CO and C 18 O emission lines. We found that σ obs at the center of the clumps differs depending on the types of the clumps; the σ obs values of Type 1 (except for clumps 3890a and 3890b), Type 2 (except for 4417b), and Type 3 are mostly ≲0.5 km s −1 , ≳1.0 km s −1 , and ≳0.5 km s −1 , respectively. This suggests that the large velocity dispersion at the clump center is a typical feature of cluster-forming Type 2 and Type 3 clumps. The velocity dispersion is particularly large in the Type 2 clumps, indicating that there must be a lot of motions around the clump center in the beginning of cluster formation. Figure 15. Variation of velocity dispersion ( σ obs ) for each clump as a function of the distance from the cluster center (for the Types 2 and 3 clumps) or the C 18 O emission peak position (for the Type 1 clumps). The different color dots represent the velocity dispersion values measured from the 13 CO (gray) and C 18 O (pink) data. Blue and red squares represent the median values of σ obs in the 0.2 pc bin for the 13 CO and the C 18 O data, respectively. The error bars show the standard deviation of each piece of data in the bins. We also investigated the C 18 O distributions based on the position–velocity (PV) diagrams for all of the clumps. In Figure 16 , we show examples of the PV diagrams measured along the major and minor axes of the clumps, which are displayed in panels (b) and (c) of the figure. As denoted by the white broken circles in panels (b), we found that the PV diagrams of some Type 2 clumps measured along the major axis show double peaks separated by ∼1 km s −1 , and they are symmetrically located with respect to the clump centers. This feature is seen only in three of the seven Type 2 clumps (4417c, 4423a, and 4753b), but not in Type 1 or Type 3 clumps. Figure 16. Distributions of the H 2 column density derived from the C 18 O integrated intensity, observed position–velocity diagram measured along the major axis (cut 1–1′) , and that


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O B-Wavelength O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Observatory O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O O O O O O O O O O O O B-Observatory O O O O O O O O O O O O O O O O O O O O B-Observatory O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O B-Wavelength O B-Wavelength I-Wavelength O O O O O O O O O B-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

indices in the respective bands (see equation 2 ), for a large control sample of aperiodic quasars. This requires the availability of spectra in both bands, as well as optical and UV time-domain data (ideally sampled in both bands at the same time). Unfortunately, the number of quasars with such data are limited; Charisi et al. ( 2018 ) analysed a small sample of 42 quasars and found that the Doppler signature can arise by chance in (40 per cent) of the cases for the near-UV (far-UV) band. This probability reflects the limited data quality of the control sample (as is also demonstrated from the increase of chance coincidence in the lower quality far-UV data), and represents only an upper limit on how frequently quasars mimic the Doppler colour variations. A larger sample of quasars with better UV + optical is needed to assess this caveat more accurately. 4.6 Constraints from future observations An interesting question to ask is how much the evidence for or against the Doppler model may tighten with continued multiband monitoring of PG1302-102. To address this question, we generated hypothetical data representing future observations over ∼10 yr, covering two additional cycles of periodicity, and computed the p -values of the Doppler model with the extended data. For simplicity, we focused on the V and M 2 bands only. In particular, we assumed that the follow-up monitoring will continue with observations similar to those in Cycles 13 and 14. We mimicked the cadence of the existing Swift observations, by picking consecutive epochs of future observed dates that are 122 d apart (i.e. three epochs per year), and generated a total of 33 new mock observations to cover a baseline of 10 yr. We also approximated the photometric errors for the mock V - and M 2-band data by taking the average of the errors over the last seven Swift observations, which yields ∼0.03 and ∼0.01 mag, respectively. 14 Finally, we combined the additional hypothetical data with the original nine Swift points to construct the full new light curves. First, we assumed that the Doppler boost model is, in fact, correct. We simulated 50 random realizations of mock V -and M 2-band data, using the fiducial DB and DRW parameters from DHS15 . We generated continuous DB and DRW light curves for a time period of 10 yr, downsampled these at the forecast future MJDs and added photometric uncertainty. We show an example of a hypothetical light curve in the left most panel of Fig. 11 . The other two panels in Fig. 11 represent different models from the fiducial, which will be explained later in this section. We then computed the corresponding p -values of the mock data, following the method described in Section 2.2 . We generated 1000 mock light curves to assemble the reference CDF, corresponding to the ‘theoretical prediction’ for the new data in the Doppler model (see Fig. 2 ). In this analysis, we added the new mock data points one-by-one, and re-computed the p -values as each of the 1, 2,


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software I-Software B-Citation I-Citation I-Citation O O O O O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

magnitude smaller than the size of the thermal disturbance. In all cases, the back torque exerted on the planet by the perturbed disc was evaluated using the softening length ε 2 . We have found that thermal torques thus evaluated do not depend on the softening length, and that there are only minute differences in the perturbation of the density field arising from heat release. All runs with larger mass planets as well as those focused on the study of the cold torque were performed using a softening length ε 2 . 2.3 Code and mesh domain To numerically solve equations ( 1 )–( 5 ), we use the hydrodynamic public code fargo3d 1 (Benítez-Llambay Masset 2016 ) with orbital advection enabled (Masset 2000 ). We have implemented the energy diffusion equation as an additional source step corresponding to the following differential equation: where is given by equation ( 4 ). In our simulations we adopt parameters for the pressure length-scale and for the thermal diffusivity that are typical of those found at a few astronomical units in protoplanetary discs (e.g. Benítez-Llambay et al. 2015 ; Bitsch et al. 2015 ; Lega et al. 2015 ). As a consequence the size of the thermal disturbance λ c is significantly smaller than the pressure length-scale H (Masset 2017 ). This is in contrast with the work of Hankla et al. ( 2020 ), who considered a thermal disturbance comparable in size to the pressure length-scale, which allowed them to satisfy largely the scale separation between the distance x p of the planet to corotation, and λ c , i.e. they have x p ≪ λ c ≲ H , whereas in our case we have x p ≲ λ c ≪ H . Namely, we take the following values in all our runs: where Ω p is the planet’s frequency. At the planet’s location we have Resolving this length-scale over a few zones while simulating a full disc would have a prohibitive computational cost, especially for parameter space explorations such as those presented here. For this reason we restrict our computational domain in the three coordinates. In the r -direction we cover the interval [ r min , r max ] = [0.9 r p , 1.1 r p ], in the θ-direction we use (hence we simulate only one hemisphere of the disc and use reflecting boundary conditions at the mid-plane). Finally our azimuthal extent is . The cell numbers in each direction are ( N r , N θ , N φ ) = (880, 64, 1536). Recast in pressure length-scale our box size is (4 H, H , 7 H ), while its resolution is (2.3 × 10 −4 r p , 7.8 × 10 −4 r p , 2.3 × 10 −4 r p ). To avoid reflections on the radial boundaries of our computational box, we use damping boundary conditions as in de Val-Borro et al. ( 2006 ), the width of the inner damping ring being 3 × 10 −2 r p and that of the outer ring being 3.5 × 10 −2 r p , the damping time-scale at the edge of each damping ring being 1/20th of the local orbital period. The size of the box considered is too small to properly capture the Lindblad and corotation torques. However, when our focus is on the heating torque, we


O O O O O O O O B-Organization O O O O O B-Person I-Person O B-Person I-Person I-Person O O O O B-Person I-Person I-Person O B-Person I-Person O O O O O O O O O O O O O O O O O B-Organization I-Organization I-Organization I-Organization O B-Grant B-Person I-Person O O O O O B-Organization I-Organization I-Organization B-Location B-Grant O O O O O B-Organization I-Organization I-Organization I-Organization B-Person O O O O O B-Organization I-Organization I-Organization I-Organization O B-Grant B-Person O B-Person O O O O O B-Grant I-Grant I-Grant I-Grant O B-Survey I-Survey I-Survey I-Survey O O O O O B-Organization I-Organization I-Organization I-Organization B-Organization O B-Organization I-Organization I-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization O B-Observatory I-Observatory I-Observatory I-Observatory O O B-Organization I-Organization I-Organization O O O O O O O O O B-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization O O B-Organization I-Organization I-Organization

The authors thank the anonymous referee and the AAS Journal statistician for useful comments, Łukasz Stawarz and Fabio R. Herpich for fruitful discussions, and Rafael Pacheco Cardoso and Graciana Brum for their help in the morphological classification. This work was carried out within the framework of the Polish National Science Centre grant UMO-2013/09/B/ST9/00026. Grażyna Stasińska was partially supported by the National Research Centre, Poland, DEC-2013/08/M/ST9/00664, within the framework of the HECOLS International Associated Laboratory. D.K.W. was partly supported by the Polish National Science Centre grant UMO-2013/09/B/ST9/00599. G.S. and N.V.A. acknowledge the support from the CAPES CSF–PVE project 88881.068116/2014-01. The Sloan Digital Sky Survey is a joint project of The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, the Johns Hopkins University, the Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy, the Max-Planck-Institute for Astrophysics, New Mexico State University, Princeton University, the United States Naval Observatory, and the University of Washington. Funding for the project has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Administration, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society.


O O O O O O O O O O B-Survey O O O B-Observatory B-Observatory I-Observatory I-Observatory I-Observatory O B-Survey O O O O O O O O O O O B-Location B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O B-Grant O O O O O O O B-Observatory I-Observatory I-Observatory I-Observatory B-Observatory O O O O B-Organization I-Organization I-Organization O B-Person B-Person B-Person B-Person B-Person O B-Person O O O O B-Organization O O O B-Grant O B-Grant O O O B-Organization I-Organization I-Organization O B-Person B-Person B-Person B-Person O B-Person O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O B-Organization I-Organization I-Organization I-Organization B-Organization O O O O B-Organization I-Organization I-Organization O B-Person O B-Person O O O O B-Organization O O O B-Grant B-Person O O O O B-Organization O B-Grant B-Person O O O O B-Organization I-Organization O O O O O B-Fellowship I-Fellowship I-Fellowship B-Person O O O O B-Organization O O B-Grant O O O O B-Fellowship I-Fellowship I-Fellowship B-Person O O O B-Organization O B-Grant O O O O B-Grant I-Grant B-Organization B-Person O O O O O B-Organization O O B-Fellowship I-Fellowship I-Fellowship B-Fellowship B-Person B-Person O B-Person O O O O O B-Organization O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant B-Grant I-Grant B-Person O O O O B-Fellowship I-Fellowship I-Fellowship O O O O O O O O O O O B-Organization I-Organization I-Organization O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O O B-Organization I-Organization O O O O O O O O O O O B-Organization I-Organization O B-Person B-Grant I-Grant O O O O O O O O O B-Organization I-Organization I-Organization B-Organization O B-Telescope O B-URL O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-URL O O O O B-Organization O O O O O O O O O O O O O B-Collaboration I-Collaboration I-Collaboration B-Software O O O O O B-Organization I-Organization I-Organization I-Organization O O O O B-Organization O B-Organization O O O O O O O B-Archive I-Archive I-Archive O O O O O B-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Grant I-Grant I-Grant


O O O O B-Software I-Software O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O O O O B-Software O O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O B-Software O O O O O O O O O O O O O O O O O O B-Software I-Software I-Software O O O O O O O O O O O O O O B-Software I-Software O O O O O O O O O O O O O O B-Software I-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

We see that the Strang CTU algorithm achieves second order for most variables (as expected), with some quantities converging to almost third order (for smooth flows, the PPM algorithm approaches third-order accuracy in space), while having difficulty with . For SDC-2, we see second-order convergence in all the variables, including . Finally, for SDC-4, all of the variables converge at rates of ∼3.8–3.9, demonstrating the fourth-order accuracy expected for the method. This test shows that the SDC algorithm can achieve fourth-order convergence for reactive hydrodynamics problems with astrophysical networks. Figure 7. Thermodynamic, dynamic, and nuclear state at t = 0.06 s for the reacting hydrodynamics test run with SDC-4 using 128 2 cells. Table 6 Convergence ( L 1 Norm) for the Reacting Convergence Problem with the Strang CTU Solver Table 7 Convergence ( L 1 Norm) for the Reacting Convergence Problem with the SDC-2 Solver Table 8 Convergence ( L 1 Norm) for the Reacting Convergence Problem with the SDC-4 Solver 5.6. Burning Buoyant Bubble Our final convergence test problem considers a hydrostatic atmosphere with a temperature perturbuation. 11 11 This problem setup is available in Castro as Exec/reacting _ tests/bubble _ convergence . Buoyancy causes the perturbation to rise (and eventually roll up in the nonlinear phase). The presence of reactions prevents the bubble from fizzling out, keeping it buoyant via the heat deposition. In addition to looking at the convergence rate of the numerical solutions, we also consider how well we maintain hydrostatic equilibrium in an undisturbed hydrostatic atmosphere. We create an initial atmospheric model that is isentropic and in hydrostatic equilibrium by integrating the system where the relation ρ ( p , s ) is provided by our equation of state. We take gravity, g , to be constant and the composition to be uniform throughout the atmosphere (pure helium, with the other nuclei mass fractions set to the small value 10 −8 ). To integrate this system, we specify the conditions at the base of the atmosphere, which we take to be the lower domain boundary (not the center of the bottom-most cell). We specify and , and get and through the general stellar equation of state. We integrate this system using fourth-order Runge–Kutta, using a step size of Δ x /2 to get from the bottom of the domain to the first cell center, and then a step size of Δ x to integrate to each of the remaining cell centers vertically in the domain. The initial conditions are then converted to cell averages using the same transformation discussed earlier in the paper. Note that the hydrostatic model is generated specifically for the resolution of the problem, and as such, the initial atmosphere converges with fourth-order accuracy. For the boundary conditions, we use periodic conditions on the sides and reflecting boundary conditions at the top and bottom. Table 9 lists the problem setup parameters. Table 9 Hydrostatic Atmosphere


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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.


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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 .


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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.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O B-Model I-Model O O O O O O B-Model I-Model O O O B-Model I-Model O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O

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.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

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,


O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O B-Wavelength O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Tag O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O B-Observatory O O O B-Wavelength O B-Wavelength O O O O O B-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O B-Model O O O O B-Software B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O B-Software I-Software O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

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


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-URL O O O O O O O O O O O O O O O O O O O B-Survey O O O O B-CelestialObject O O O B-Wavelength O O O O O O O O O B-ObservationalTechniques I-ObservationalTechniques O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialRegion I-CelestialRegion I-CelestialRegion O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O B-Dataset I-Dataset I-Dataset I-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation O B-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O B-ObservationalTechniques I-ObservationalTechniques O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O B-Formula I-Formula I-Formula O O O O O B-ObservationalTechniques O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

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.


O O O O O O B-Organization O O B-Grant I-Grant I-Grant I-Grant I-Grant B-Organization O O O B-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship B-Organization O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant B-Organization O O B-Grant I-Grant B-Organization O B-Organization O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant B-Organization O O B-Grant I-Grant I-Grant I-Grant I-Grant B-Grant I-Grant I-Grant O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Grant I-Grant I-Grant O B-Grant I-Grant O O O B-Organization I-Organization I-Organization I-Organization B-Organization B-ComputingFacility O O O O O O O O O O O B-ComputingFacility B-ComputingFacility O O O O O O B-ComputingFacility I-ComputingFacility O B-Grant I-Grant I-Grant O O O O O O O B-Instrument I-Instrument I-Instrument B-Instrument O O O O O B-Survey I-Survey I-Survey B-Survey O O O O B-Survey O O O O O O B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Location O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Location I-Location O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility O O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O B-Location I-Location I-Location B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization O O B-Collaboration I-Collaboration I-Collaboration I-Collaboration I-Collaboration I-Collaboration I-Collaboration O B-Collaboration I-Collaboration O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O B-Collaboration I-Collaboration O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization B-Location B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O O O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O B-Observatory I-Observatory I-Observatory I-Observatory O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O O O O O B-Software B-Citation I-Citation O O O O O O O O O B-Event I-Event I-Event I-Event I-Event I-Event O O O B-Organization I-Organization I-Organization O B-Grant O O O B-Organization I-Organization I-Organization I-Organization

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.


O O O O O O O O O O O O O O O O O O O O O O O O B-Database O O O O O O O O O O O O O O O O O O O O O O O O O B-Database O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-Database O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Database O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O B-Model O O B-Model B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O

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


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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.


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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 .


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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.


O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O

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


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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.


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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).


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O B-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O B-Wavelength O O O B-CelestialObject I-CelestialObject O O O O O O O B-Wavelength O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O B-Wavelength O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O B-Wavelength O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O

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


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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.


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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).