O O O O B-Person I-Person O O O O O O O O O B-Organization I-Organization O O O O O B-Proposal I-Proposal O O O O O O B-Organization I-Organization I-Organization B-Grant I-Grant B-Person B-Person B-Person B-Person O B-Organization I-Organization I-Organization B-Grant I-Grant O O B-Organization I-Organization I-Organization B-Grant I-Grant B-Person B-Person O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O B-Organization O O O B-Grant I-Grant I-Grant I-Grant I-Grant O O O O O O B-Grant I-Grant I-Grant

We are grateful to Ilia Potravnov for a number of useful comments and to the Swift team for the execution of our ToO request. This work was supported by the Russian Science Foundation grant 14-12-01287 (S.S.T., A.A.M., A.A.L., V.S.), the Academy of Finland grant 268740, and the National Science Foundation grant PHY-1125915 (J.P.). V.D. thanks the Deutsches Zentrums for Luft- und Raumfahrt (DLR) and the DFG for financial support (grant DLR 50 OR 0702). We also acknowledge the support of COST Action MP1304.


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ACKNOWLEDGEMENTS Our anonymous referee provided valuable feedback that helped improve this manuscript. We thank Hiroyuki Hirashita for providing us with the tabulated form of grain velocities calculated over an extended grain-size range and used in Hirashita Yan ( 2009 ). We also thank Takaya Nozawa for making available the tabulated versions of the SN grain-size distributions presented in Nozawa et al. ( 2007 ) and the SN dust destruction efficiencies used in Asano et al. ( 2013b ). Finally, we are grateful to Volker Springel for sharing access to arepo . The simulations were performed on the joint MIT-Harvard computing cluster supported by MKI and FAS. RM acknowledges support from the DOE CSGF under grant number DE-FG02-97ER25308. MV acknowledges support through an MIT RSC award and the support of the Alfred P. Sloan Foundation. PT acknowledges support from NASA through Hubble Fellowship grant HST -HF2-51341.001-A awarded by STScI, which is operated under contract NAS5-26555. RK acknowledges support from NASA through Einstein Postdoctoral Fellowship grant number PF7-180163 awarded by the Chandra X-ray Center, which is operated by the Smithsonian Astrophysical Observatory for NASA under contract NAS8-03060.


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ACKNOWLEDGEMENTS We thank the referee for his/her constructive reports and very helpful suggestions regarding the presentation of this paper and the interpretation of our results, S. J. Aarseth for providing the code used in this research, O. Vaduvescu, F. Roig, M. N. De Prá, and S. Deen for comments, and A. I. Gómez de Castro for providing access to computing facilities. This work was partially supported by the Spanish ‘Ministerio de Economía y Competitividad’ (MINECO) under grants ESP2015-68908-R and ESP2017-87813-R. In preparation of this paper, we made use of the NASA Astrophysics Data System and the Minor Planets Center (MPC) data server.


O O B-CelestialObjectRegion I-CelestialObjectRegion B-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 O B-Citation I-Citation I-Citation I-Citation O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O B-Citation I-Citation I-Citation O O O O O B-CelestialObject 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-CelestialObjectRegion I-CelestialObjectRegion 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 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 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 O O O O O O O O O O O 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 B-CelestialObjectRegion O B-CelestialObjectRegion I-CelestialObjectRegion O B-CelestialObjectRegion I-CelestialObjectRegion 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 O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion 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 B-Citation I-Citation I-Citation

for the Galactic bar (Dehnen 2000 ). For all of the following calculations, we assumed a rotation velocity of 220 km s −1 (Kerr Lynden-Bell 1986 ; Bovy et al. 2012 ), a distance to the Galactic centre of 8.2 kpc (Bland-Hawthorn Gerhard 2016 ), and the same peculiar solar motion as in Section 3 , and we integrated forward in time up to 1 Gyr. The galpy software allows one to calculate parameters of individual orbits, including e.g. eccentricity e , maximum height above or below the Galactic plane z max , and peri and apocenter of the orbit, r peri and r apo , respectively. For each star, we ran a Monte Carlo simulation. We calculated 200 orbital solutions in which we varied the initial conditions (proper motions, radial velocities, and distances) within their uncertainties assuming that their distribution is Gaussian. From the resulting distribution, we calculated the median orbital parameters for both Oosterhoff groups. The results are listed in Table 2 . In order to test the differences between the two Oosterhoff groups we used the CM test (see Section 3 ). For the entire distribution of orbital parameters z max , e, r peri , and r apo , the CM test yields p CM = 0.68, there is no statistical evidence that the two distributions are not identical. Table 2. Median values of calculated parameter orbits for the individual Oosterhoff groups. Column 1 lists the studied components, columns 2 and 3 list values for each Oosterhoff group. Fig. 5 depicts the distribution of apocentric distances for the studied RR Lyrae stars. In this diagram, we see that both Oosterhoff groups have very similar apocentric distance distributions. We also noticed a sudden decrease at ≈ 3 kpc (log( r apo ≈ 0.5 kpc), which is roughly in agreement with the overlap between bulge, metal-weak thick disc, and inner halo (3.5 kpc; Ness et al. 2013b ). In fact, the majority of the RR Lyrae stars in our sample stay inside the bulge volume during their full orbits. Figure 5. The distribution of apocentric distances for the studied variables. The blue and red histograms represent the Oo I and Oo II groups, respectively. Based on the negligible difference in the median value of z max between the two Oosterhoff groups, we explored whether the Oo II variables could follow higher orbits from the Galactic plane and thus possibly come from the halo. Based on the distribution of apocentric distances (Fig. 5 ), as a nominal boundary for the Galactic bulge we chose z max > 3 kpc (roughly above ± 20 deg at the distance of the Galactic bulge) and calculated the number of stars that fulfil this condition in at least 50 per cent of the iterations of the Monte Carlo simulation. In total, only 34 RR Lyrae stars fulfil the aforementioned condition. Among these 34 variables, 35 per cent belong to the Oo II population. This is a significant increase in comparison with the overall bulge and halo Oosterhoff population where the fraction of Oo II pulsators is around 25 per cent (Drake et al.


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

to a symmetry property of the solution to the transfer equation. To solve this problem, some specific ‘disambiguation’ techniques have been developed. The authors point to one special case where the ambiguity is resolved by the data when combined with knowledge of the state of excitation of the radiating atoms. A purely spectroscopic disambiguation method has also been devised (Landi Degl’innocenti Bommier 1993 ) based on the observation of the Stokes parameter profiles in resonance lines originating from transitions between polarized atomic levels . In this case, the radially streaming radiation from the solar atmosphere introduces a ‘symmetry breaking’ in the physical conditions that allows one, in some cases, to recover the magnetic field vector without ambiguity. The problem remains, even here, that one must know the state of atomic populations of the Zeeman-split M states within the atomic levels. Such conditions exist only for particular radiative transitions. Most polarimetry is performed on photospheric lines formed where collisions tend to enforce equality of M-state populations within local thermodynamic equilibrium (LTE) levels, negating the possibility of any atomic polarization and of symmetry breaking through the radiation field. More worrying, the ‘disambiguation’ methods inflict prior assumptions on solutions to produce ‘inverted’ data compatible with both the assumptions and the data themselves. Especially worrisome are studies seeking to minimize part of the energy of a system, and/or those seeking some kind of minimal discontinuity in the magnetic structure sampled at the photosphere. Such constraints cannot be theoretically supported, the latter, for example, explicitly reject classes of solutions available to magnetohydrodynamics (MHD). ‘Weak’ MHD solutions (e.g. Courant Hilbert 1962 ) exist under conditions encountered on the Sun. Weak solutions solve integral forms of the governing equations in which discontinuities are permitted. Such phenomena not only are expected to pervade the Sun’s atmosphere, but they are expected to harbor much of the free energy in the form of current sheets (e.g. Parker 1972 ; Parker 1994 ). It is precisely this free energy that is so important to the dynamic changes in radiation, particles, and magnetic fields ejected from the Sun. Rapid reconnection associated with current sheets are important for the operation of the large-scale solar dynamo. Recent work has re-assessed the disambiguation problem using ‘realistic’ MHD model calculations of the solar atmosphere, in a hare-and-hound exercise (Fleishman et al. 2017 ). Both successes and failures were found by the authors, conditions within strongly magnetized regions being more reliable than weaker regions. But such methods can never replace more observationally constrained methods, such as those proposed here. They remain dependent on the reality of models, and upon the essential assumptions of the ‘disambiguation’ methods used. The ambiguities


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We thank the anonymous referee for useful suggestions that helped to improve the paper. This work was supported under NASA Contract NNG08FD60C, and it 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 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). A.M., A.C., and S.P. acknowledge support from the ASI/INAF grant I/037/12/0-011/13. M.B. acknowledges support from NASA Headquarters under the NASA Earth and Space Science Fellowship Program, grant NNX14AQ07H. We acknowledge support from CONICYT-Chile grants Basal-CATA PFB-06/2007 (F.E.B., C.R.), FONDECYT 1141218 (F.E.B., C.R.), “EMBIGGEN” Anillo ACT1101 (F.E.B., C.R.), and the Ministry of Economy, Development, and Tourism’s Millennium Science Initiative through grant IC120009, awarded to The Millennium Institute of Astrophysics, MAS (F. E. B.). W. N. B. acknowledges support from NuSTAR subcontract 44A-1092750.


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Acknowledgments We thank the anonymous referee for his/her very helpful suggestions on the manuscript. This work is supported by the Natural Science Foundation of China (Nos 11422324, 11521303, 11390374), by Yunnan province (Nos 2012HB037, 2013HA005) and by the Chinese Academy of Sciences (No. KJZD-EW-M06-01).


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

to better than 1/ ω for values of ω with a significant spectral component. If Δ l is by hypothesis less than the duration of the undispersed pulse, τ , which is of the order of 1 ms, then the spread in the lensing delays is only of the order of ( R s / R E ) 2 Δ l ( R s / R E ) 2 τ , where R s and R E are respectively the apparent source radius and the Einstein radius of the lens. (That the delay is only second-order in ( R s / R E ) follows from Fermat’s principle, namely that the propagation time is a local minimum relative to all other neighboring trajectories, e.g., Narayan Bartleman 1996 ). If FRBs are at cosmological distances, then, as the apparent source size R S is limited to the FRB pulse width (∼10 −3 c s), and R E 2 is of the order of , it follows that the spread in delays, which is of the order of , is indeed much less than 1 ns. Similarly, the difference in the dispersion time t d ∼ 1 along the two light paths, if the intergalactic medium is smooth, of the order of δθt d , where δθ , the angular separation of the images, obeys δθ 2 / H ∼ 2 Δ l . If Δ l ≪ 1 ms, then δθ ≲ 10 −11 . Conceivably, the intervening medium is clumpy on a much smaller scale than c / H , so the difference in dispersions—in this case governed by the sharp density gradients of the clumps—is larger. This would not destroy the effect; the delay is nonetheless well-defined. It would be due to dispersion differences rather than the lens, but the existence of the multiple paths—and hence the existence of the lens—would be demonstrated. A related question is whether the delay is constant over the course of the FRB. While the apparent source size of an FRB is only about 1 milli-lightsecond, the bulk Lorentz factor Γ of the emitting region must be at least of the order of 10 3.5 (Lyubarsky 2014 ), so the emitting region may move relative to the observer with an apparent velocity of ≳10 3.5 c . Now, for a source at a cosmological distance c / H , the Einstein radius of a lens of mass m is [( c / H )(2 Gm / c 2 )] 1/2 ≃ [10 16 ( m / M ⊙ )] 1/2 cm. So the apparent time to cross the Einstein radius is ∼10 2 [10 3.5 /Γ] [ m / M ⊙ ] 1/2 s, and over the 1 ms duration the change in the source position could be at most 10 −5 [10 3.5 /Γ] [ m / M ⊙ ] −1/2 R E . The change in the delay Δ l due to the motion of the emitting region would then be less than 10 −10 [10 3.5 /Γ] −2 [[ m / M ⊙ ] −1 Δ l ≃ 10 −15 [Γ/10 3.5 ] 2 s, which, for imaginable values of Γ, is much less than the baseband period. The importance of condition ( 3 ) over the full frequency range of significant G ( ω ), together with the broadband requirement ( 7 ) on G , is emphasized. The effect suggested here is not apparent in any formalism that assumes a monochromatic wave because adding a monochromatic wave to a delayed version of itself merely shifts the phase, and changes the amplitude by a modest factor (e.g., Deguchi Watson 1986 , Stanek et al. 2016 ). This is insufficient to reveal to the observer


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We thank A. Heger, M. Limongi, and K. Nomoto for providing progenitor models, M. Tanaka for fruitful discussions, and S. Veith for proofreading. The numerical computations in this study were partly carried out on XT4 and XC30 at CfCA in NAOJ and SR16000 at YITP in Kyoto University. This study was supported in part by the Grant-in-Aid for Scientific Research (Nos. 25103511, 26870823, 23540323, 23340069, 24103006, 26707013, and 24244036), JSPS postdoctoral fellowships for research abroad, MEXT SPIRE, and JICFuS.


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SH acknowledges support from an STFC-funded studentship. CD acknowledges support from an STFC consolidated grant (ST/L000768/1), an STFC Advanced Fellowship, an EU Marie-Curie IRG grant under the FP7 and an ERC Starting (Consolidator) Grant (no. 307209). The authors would like to thank Roberta Paladini, Simon Casassus and Tim Pearson for helpful discussion and comments. The authors would also like to thank Yvette Perrott and the MRAO AMI group for providing the AMI SA observation of LDN 1622.


O O O B-Person I-Person O B-Person I-Person O O O O O O O O O O O O O O B-Person O O O B-Organization I-Organization O B-Instrument O B-Grant B-Person O O O O B-Organization I-Organization I-Organization O B-Grant O O O O O O B-Database I-Database I-Database B-Database O O O O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization

The authors thank Michael Dopita and Stephanie Juneau for very useful discussions, and the anonymous referee for in-depth reading and helpful comments. P.M.W. received funding through BMBF Verbundforschung (project MUSE-AO, grant 05A14BAC). E.Z. acknowledges funding from the Swedish Research Council (project 2011-5349). This research made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.


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

respect to the location of the analogous peak observed for S Mon. Sung Bessell (2010) examined the median ages and cumulative age distributions of PMS stars in the various NGC 2264 subregions, to derive some information on the star formation processes within the region. The picture they deduced from their analysis is overall consistent with the scenario we outlined here: a picture of sequential star formation, where objects that populate the Halo and Field regions were formed first, followed by stars in S Mon and Cone (H), then sources in Cone (C) and, finally, those in the Spokes subcluster. The separate analysis we conducted here for disked vs. non-disked (and accreting vs. non-accreting) objects as a function of age allowed us to: i) confirm the model-based indication of an age spread by the association with measurable quantities, such as the presence of disks or accretion; ii) obtain a more detailed overview of the dynamical evolution of the cluster; iii) explore the mechanisms and characteristic timescales of evolution of PMS objects across the region (see Sects. 5.1 and 5.3 ). 5.3. Impact of environmental conditions on disk evolution In their investigation of the star formation history of NGC 2264, Sung Bessell (2010) showed that, while the age distribution of the S Mon population exhibits a significantly different behavior from those of the Spokes or Cone (C) populations (in the sense that the probability that they are drawn from the same parent distribution is very low), the populations of S Mon and of Cone (H) exhibit very similar distributions in age. However, some differences between the two regions appear when we restrict our analysis to disk-bearing or accreting objects (see Table 2 ). Namely, while the median ages associated with Class III objects in S Mon and in Cone (H) are similar to each other, the median age of disk-bearing objects in S Mon is noticeably lower than that of disk-bearing objects projected onto Cone (H). The difference is more marked when only CTTS are considered: a K-S test applied to the age distributions of accreting objects in S Mon and in Cone (H) returns a probability of 0.03 that they are drawn from the same population. This difference in median age between the two populations might be understood if objects in S Mon were formed at a later time than objects in Cone (H). However, the fact that S Mon hosts a significant fraction of Class III objects at any given age, and the fact that the number of Class II objects located in S Mon decreases sharply after 2.5 Myr (lower right panel of Fig. 11 ), would rather suggest that the characteristic timescales associated with disk accretion and disk evolution are shorter in the northern half of NGC 2264 than elsewhere within the region. This may result from non-uniform environmental conditions across the cluster. The S Mon region shown in Fig. 10 is distinguished by the presence of the massive binary S Mon (the primary component is an O7 V star and the secondary


O O O O O O O B-Archive I-Archive I-Archive I-Archive I-Archive I-Archive O O O B-Observatory I-Observatory I-Observatory O O B-Observatory O O O O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Fellowship I-Fellowship B-Fellowship B-Grant I-Grant B-Grant O B-Organization I-Organization I-Organization B-Grant I-Grant O O O B-Grant

Acknowledgements This research has made use of NASA's Astrophysics Data System Bibliographic Services. We thank the European Southern Observatory staff at Paranal for their support during the observations. We acknowledge support from a Science and Technology Facilities Council Rutherford Fellowship (ST/J004030/1), Rutherford Grant (ST/K003445/1) and European Research Council Starting Grant (Grant Agreement No. 639889).


O O O O O O O O O O O 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-Mission I-Mission I-Mission I-Mission O B-Mission I-Mission O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization 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 B-Location I-Location I-Location I-Location O O O O O O O O O O O O O O O O O O O O O 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 O B-Wavelength O O O O B-CelestialObject I-CelestialObject O O O O B-Instrument I-Instrument I-Instrument I-Instrument B-Instrument 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 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-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 I-Software I-Software O B-Mission O B-Wavelength O O O O O B-Software I-Software I-Software I-Software B-Software B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O B-Software I-Software I-Software I-Software O B-Citation I-Citation I-Citation I-Citation O O O B-Software O O B-Mission I-Mission 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 B-Wavelength 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 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 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 B-CelestialObject I-CelestialObject 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 O O O O O O O O O O O O O

is as follows. The observations and data are described in Section 2 , the methods of analysis are described in Section 3 , and the results are discussed in Section 4 . 2. Observations The X-Ray Pulsar Navigation -I ( XPNAV -1) satellite is the first mission operated by the China Academy of Space Technology to demonstrate navigation using X-ray pulsars. This small (270 kg) satellite was launched on 2016 November 10, by the Long March 11 rocket at the Jiuquan satellite launch centre to the 500 km LEO orbit. It operates in the three-axis stabilization mode with the ability to quickly point to any inertial position with an accuracy within 2 arcmin according to demand, and to provide up to 90 minutes sustained observation on any target (see Zhang et al. 2017 ; Huang et al. 2018a ). The X-ray instrument used for this Crab pulsar glitch observation is the time-resolved soft X-ray spectrometer (TSXS). This instrument uses a grazing incidence focusing lens composed of four nested mirror shells with a collecting area of 30 cm 2 to focus X-ray photons within a 15 arcmin field-of-view onto a silicon drift detector. The effective detecting area of the instrument is 2.4 cm 2 at 1.5 keV. A GPS-calibrated Rb clock is included to provide accurate timing and a quasi-parallel optical star is used to assist the inertial pointing. The TSXS has the ability to provide 1.5 μ s time resolution. The observations used in this work were obtained from the period between UTC 2017 October 10 and 2018 April 28. A total of 627 observations of duration more than 1500 s were selected. Of these observations, 71 were collected pre-glitch, and 556 post-glitch. 3. Data Processing 3.1. Data Analysis Software System for XPNAV-1 The X-ray data are processed by the Data Analysis Software System (DASS; Zhang et al. 2017 ), which is illustrated in Figure 1 . Figure 1. Data flow of the Data Analysis Software System (see Zhang et al. 2017 ). In the DASS, data from XPNAV -1 are first unpacked to extract the GPS data, the satellite attitude data, the satellite status flag data, and the X-ray photon data. Then the X-ray photons are selected as described by Huang et al. ( 2018a ). The top-level timing formula is based on Edwards et al. ( 2006 , Equation (7)). The timescale transformation from the local time to the barycentric coordinate time and the time delays associated with the Earth’s and satellite’s orbital motion are considered, so that the Roemer delay, the Shapiro delay, the parallax delay, the Einstein delay, and the vacuum propagation delay are calculated to correct the photon arrival time at the satellite to that at the solar system barycenter (SSB) (see Edwards et al. 2006 ; Hobbs et al. 2006 ). The satellite position at each single photon’s arrival time is propagated from the on-board GPS data. With the photon arrival time at the SSB, we fold the pulse profiles into 256 bins per period. Pulse times of arrival (TOAs) are calculated by cross-correlation between the folded profile


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

, which were obtained using a density functional theory level of theory (M05/6-31G(d)). An analysis of the observed intensities through a rotational diagram provides a rotational temperature of 9 ± 1 K. We performed a model fitting directly to the observed line profiles as described by Cernicharo et al. (2021a) , with the result that the best match between the computed synthetic spectrum and the observations was obtained for T r = 7 K and N(H 2 CCCHCCH) = (1.2 ± 0.2) × 10 13 cm −2 . Figure 1 shows the synthetic spectrum. Only the transition 9 19 − 8 1, 8 required a correction intensity by a factor of 0.8, while for all the other lines the model matches the observations perfectly. Using the H 2 column density derived by Cernicharo et al. (1987) , the abundance of H 2 CCCHCCH relative to H 2 towards TMC-1 is 1.2 × 10 −9 . This abundance is similar to that of vinyl acetylene ( Cernicharo et al. 2021a ), about ∼3 below that of propylene (CH 3 CHCH 2 ; Marcelino et al. 2007 ), and a factor of ten below that of methyl acetylene (CH 3 CCH; Cabezas et al. 2021 ). Hence, allenyl acetylene is one of the most abundant hydrocarbons in TMC-1, and probably, together with CH 3 C 4 H (see Sect. 3.2 ), the most abundant compound containing five carbon atoms. It is interesting to compare the abundance of allenyl acetylene with that of cyano allene (H 2 CCCHCN). This species has been recently analysed by Marcelino et al. (2021) , resulting in a rotational temperature of 5.5 ± 0.3 K and a column density of (2.7 ± 0.2) × 10 12 cm −2 . Consequently, the abundance ratio of H 2 CCCHCCH over H 2 CCCHCN is ∼4.5, that is to say the acetylenic derivative of allene is slightly more abundant than the cyanide one. A similar value (∼1.8) was obtained for the abundance ratio between CH 2 CHCCH and CH 2 CHCN ( Cernicharo et al. 2021a ). The measured frequencies of the lines observed in TMC-1 can be used to improve the rotational and distortion constants of H 2 CCCHCCH. We used the fitting code FITWAT described in Cernicharo et al. (2018) . Table 1 provides the results obtained by fitting the laboratory data of McCarthy et al. (2020) alone, and those obtained from a fit to the merged laboratory plus the TMC-1 frequencies. A significant improvement in the uncertainty in the rotational and distortion constants was obtained. The fit to the laboratory data alone results in exactly the same constants as those obtained by McCarthy et al. (2020) . The merged fit is recommended to predict the frequency of the rotational transitions of this species above 50 GHz. Predictions could be accurate enough up to 150 GHz to allow for a search of this species in the 3 mm domain. Table B.1 provides the observed and calculated frequencies and their differences. Table 1. Rotational and distortion constants of H 2 CCCHCCH. Notes. (a) Laboratory frequencies from McCarthy et al. (2020) . 3.2. Methyl diacetylene, CH3C4H This C 5 H 4 isomer was found in TMC-1 by MacLeod et al.


O B-Person O O O O B-Organization O O O O O O O B-Organization B-Grant O O O B-Grant O O O O O O O O B-Archive I-Archive I-Archive I-Archive I-Archive I-Archive O O O O O O O O O O O O O O

Acknowledgements MAV acknowledges support from a CONACYT scholarship. Both authors appreciate the support of UNAM-DGAPA, PAPIIT through the grant IN110316. This work has made extensive use of the NASA's Astrophysics Data System Abstract Service. We also thank the anonymous referee for the suggestions that helped improve our work.


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

by l b = ( π b + M b ) modulus 360deg. For CARMENES and the HARPS data sets, the total RV jitter is comparable at ≲ 2 m s −1 , while it is 5.62 m s −1 for the HIRES data. With 1.77 m s −1 , the root mean square of the residuals of the model fits is lowest for the HARPS post-upgrade data, followed by the HARPS pre-upgrade (2.15 m s −1 ) and the CARMENES (2.66 m s −1 ) data. Again, HIRES shows the highest value, with 6.02 m s −1 . Compared to the formal uncertainties of the measurements (see Sect. 3 ), this means a factor of around three for HIRES and the HARPS pre-upgrade, and a factor of two for the HARPS post-upgrade and the CARMENES data. The GLS periodogram of the residuals does not show any significant signals (lower panel Fig. 1 ). However, there is some power at periods around 45 days and its overtones. This can be attributed to the rotation period P rot = 46.04 d of the host star. Moreover, the strongest peak at around P ≈ 190 d nearly reaches the 1% FAP level. The source of this signal is currently unknown, although the activity indicators hint at stellar activity. We also analyzed the residuals for possible long-term structures, but found the results inconclusive. While the entire data set shows only a negligible drift term of 0.03 ms −1 yr −1 , it is more significant for the residuals of the most recent RV measurements. A linear fit to the combined residuals from the HARPS post-upgrade epoch together with the CARMENES data gives a slope of around 0.5 ms −1 yr −1 . This could be an indication for an additional long-term signal, which in the HIRES data might be obscured by the comparably high scatter. In order to investigate the robustness of our fit results against possible contributions from correlated noise and additional RV or activity signals, we studied five additional models, using the concepts of moving averages (MA) and Gaussian process (GP) regression. The results from this analysis and their discussion can be found in Appendix. B . They agree with the orbital parameters reported here. Fig. 2 Unfolded ( left ) and phase-folded ( right ) RV measurements of the individual instruments for HD 180617, together with the best fit overplotted. 4.3 Activity analysis Periodic variability in RV measurements can also be introduced by stellar activity. Chromospheric emission, chromatic dependence of the RVs, and changes in line profiles are indicative of stellar activity. In Fig. 4 we provide GLS periodograms for some of these quantities, derived from the available CARMENES spectra. The H α index, the chromatic index (CRX), and the differential line width (dLW), shown in the three uppermost panels, are derived from the time series of activity indicators directly provided by SERVAL ( Zechmeister et al. 2018 ). While the chromatic index reflects wavelength dependencies of the measured RVs in the different échelle orders, which can result from the temperature surface structure onthe star (spots or faculae), the differential line width


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wind. Thus, we simulate the transonic hydrodynamic planetary winds. At the Roche lobe height, all simulated atmospheres reach velocities between 10 and 20 km s. 4.2.1. Atmosphere of HD 209458 b First, we focus on the atmosphere of HD 209458 b, which is depicted by the green solid lines in Fig. 5 . Panel a shows how the density decreases from the boundary density of to cm. The extent of the Roche lobe for HD 209458 b is 4.2 above the substellar point and the sonic point is reached at 3.5. The optical depth for EUV photons (60 eV) reaches one at a height of 1.03. This height corresponds well with the atmospheric layer that experiences the maximum volume heating rate. Panel b in Fig. 5 shows that the absorption of XUV emission around the height of 1.03 increases the temperature. This raises the atmospheric scale height and the density gradient becomes more shallow above this height. The temperature reaches a maximum of 9100 K. The bulk velocity strongly increases along with the temperature in the lower atmosphere (see panel c). Panel d shows the net specific radiative heating rate throughout the atmosphere. We plot the specific heating rate, which is the heating rate per gram of material, because it clearly shows where the atmospheric material gains most of the energy for the escape. The net heating rate has a maximum close to the temperature maximum, but declines above 1.6 where the atmosphere is more strongly ionized. There is a distinct dip in the net heating rate at 1.15, which is caused by hydrogen line cooling. This can be seen in panel e, where we show the radiative heating and cooling rates separately as thin, solid lines. Subtracting the radiative cooling rate from the heating rate gives the net radiative-heating rate (solid thick line), which is displayed in panels d and e. Between 1.05 and 1.8 about 45% of the radiative heating produced by the absorption of XUV radiation is counterbalanced by hydrogen line emission, which is mainly Ly cooling. In panel e we further compare the radiative heating rate to the hydrodynamic sources and sinks of internal energy. In the atmosphere of HD 209458 b the advection of internal energy is a heat sink below 1.7, but acts as a heat source above this level, providing 50% of the energy in the upper thermosphere. The adiabatic expansion of the gas is a heat sink throughout the atmosphere. This term stands for the energy, which is converted into gravitational potential and kinetic energy. It now becomes clear why the temperature decreases in the upper thermosphere: Radiative heating becomes inefficient due to a high degree of ionization, but the adiabatic cooling term remains large. Therefore, the advected thermal energy is used to drive the expansion of the gas. Panel e also shows cooling due to thermal conduction, which is largest where the temperature increases most strongly, but it is not relevant in any of the simulations. In Fig. 6 the H+He atmosphere of HD 209458 b is depicted in the middle


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moderately warm ( T dust ≈ 50 K). With these conditions, the low-lying H 2 O lines at submm wavelengths (240 − 400 μ m) are efficiently pumped, but little absorption is produced in the far-IR with only significant absorption in the H 2 O lines at 75 and 108 μ m. Nevertheless, the inferred colums are more than enough to extinguish any line emission at short wavelengths, and indeed the Pa- α emission within r = 0.5 kpc primarily probes the western (near) side of the nuclear bar, with a morphology different from that of the continuum submm emission (Fig. 17 b). It is within the envelope region where the CO 2–1 line becomes very broad (Fig. 15 c), which is probably a direct consequence of the shocks produced by the inflowing gas and may be evidence of disordered motions that would eventually lead to a pseudobulge. High-lying molecular absorption lines in the far-IR are produced when the columns are so high that the far-IR continuum becomes optically thick ( González-Alfonso et al. 2015 ), and these conditions are also linked to the emission in the H 2 O448 line. In ESO 320-G030, a nuclear disk with projected radius of ≈40 pc attains these conditions, though still with moderately warm dust ( T dust ≈ 55 K). The disk is distorted, elongated in the direction of the bar, and highly turbulent (Δ V / V rot ≈ 1); it is thus expected to be geometrically thick (e.g., Cazzoli et al. 2020 ). At the center of the disk, an unresolved, extremely buried ( τ 100 ≫ 1) and very warm ( T dust ∼ 100 K for the far-IR photosphere; see González-Alfonso Sakamoto 2019 ) core component is identified from the absorption detected in very high-lying lines of H 2 O, of which the H 2 O 7 07 − 6 16 line at 71.95 μ m ( E lower = 640 K) is an excellent tracer. We estimate a core radius of R = 9 − 16 pc, but higher angular resolution observations are required to better determine its size. HCN vibrational emission has been recently detected in ESO 320-G030 (Falstad et al., in prep.), additionally indicating the presence of a very warm optically thick region. In such environments, trapping of IR radiation raises T dust and the mid-IR radiation density within the cocoon of dust, but the resulting SED does not show any enhanced mid-IR emission as only the photosphere is probed at mid- and even far-IR wavelengths ( González-Alfonso Sakamoto 2019 ). Because of their extreme extinction, the nature of these very compact nuclear components has been long debated; even X-rays and mid-IR high ionization tracers from a putative AGN are expected to be severely attenuated. ESO 320-G030 is undetected with the Swift /BAT all-sky survey observations 1 in the 14 − 195 keV band with a sensitivity of 8.4 × 10 −12 erg s −1 cm −2 , which translates into a luminosity of 6 × 10 8 L ⊙ . Assuming a ∼5% contribution to the bolometric AGN luminosity in the quoted band, the upper limit for L AGN is ≲10 10 L ⊙ ; however, absorption at 30 keV is still relevant for N H ∼ 10 25 cm −2 , and an AGN with ∼10% of the


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This work has been partially supported by the Italian Ministry of the University under grant RBFR082838 and “LNS-Astrofisica Nucleare (fondi premiali)” by PRIN-MIUR 2010-2011 ( Chemical and dynamical evolution of the Milky Way and Local Group galaxies , PI F. Matteucci), by PRIN-INAF 2012 ( The M4 Core Project with Hubble Space Telescope , PI L. Bedin), and by INFN ( Iniziativa specifica TAsP ).


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; Ghosh Chakrabarti 2018 ). So, Θ itself indicates (see Fig. 5 ), from its day-to-day time evolution, the arrival time lag, i.e. the size of the disc. It is shown recently by Ghosh et al. ( 2019 ) that the temporal evolution of RXTE /ASM soft and hard photon fluxes is, respectively, similar to that of disc and halo mass rates obtained from the TCAF-extracted RXTE /Proportional Counter Array (PCA) (2.5–25 keV) spectra. Also, during an outburst, the Comptonizing efficiency (CE) computed from ASM data behaves in a similar manner with the accretion rate ratio obtained from PCA data. According to TCAF, the Keplerian disc component is mainly responsible for the soft photon counts, whereas the halo component controls the hard photon counts. It is customary to assume soft and hard photons to represent multicolour blackbody distribution and power law, respectively (see Ghosh Chakrabarti 2018 ; Ghosh et al. 2019 ). Since TCAF is a general paradigm, it can be always utilized whether phenomenological descriptions such as power law plus blackbody fits the data already or not. Even if we have only ASM data, the knowledge of behaviour of the flows from TCAF enable us to choose Θ as the unique variable to classify the outbursts. Therefore, Θ is used for cross-correlation (CC) with individual fluxes, as the former represents relative change of one flux with respect to the other. So, the relative time lag between the hard flux and the soft flux of either photons or energy would be defined as (Ghosh Chakrabarti 2018 ), τ r > 0 implies that the disc radiation flux lags behind the halo radiation flux. Both evolve simultaneously if τ r = 0. Typical behaviour of Θ during a normal outburst is schematically shown in Fig. 4 . We wish to mention that while taking CCs, the direct hard flux versus soft flux correlation is not the proper quantity to discuss (see Fig. 6), because the hard flux does not depend on the soft flux alone. It also depends on the properties of the Compton cloud such as its size (CENBOL) and its optical depth. Furthermore, in an outburst, hard flux will always be seen increasing with the soft flux. So the lag between hard and soft, in general, would be seen to be zero. What is important is the rate at which two accreting masses change since these are guided by the viscosity in the halo and disc components. Since RXTE /ASM did not record X-ray data continuously from any particular source, there are gaps in the data, in particular, due to the annual solar constraints. We smoothed out the unevenness of the data interval by using a fortran code for interpolation. The fits files obtained from these daily light curves are used to produce CCs between Θ and two fluxes using crosscor task of heasoft/xronos package in order to obtain the time lags estimated from Θ. 3 RESULTS We present the photon energy fluxes, Θ-behaviour, their CCs, and most importantly, the hysteresis property of the standard Keplerian disc for showing difference in temporal and spectral


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scale of PSF, which causes correlation of the fluctuations in adjacent pixels; (e) estimating the “residual variance” from contaminating sources remaining in the masked image and subtracting this variance from the power spectrum amplitude to obtain the corrected SBF magnitude ; (f) adopting a value for from either an empirical or theoretical SBF calibration (generally based on galaxy color) to obtain the distance modulus, . For this NGVS SBF analysis, we adopted the sky background estimates and galaxy isophotal models described by Ferrarese et al. ( 2012 ). The large-scale residuals, still present in the frame after subtracting the galaxy model, were removed using the background map obtained with SExtractor (Bertin Arnouts 1996 ) adopting a mesh size ≈10 times the FWHM (Tonry et al. 1990 ; Cantiello et al. 2005 ). We refer to the image with the sky, galaxy model, and large-scale residuals all subtracted as the residual frame. The photometry of the external sources (stars, background galaxies, and GCs) was done by running SExtractor on the residual frame after masking saturated stars, very extended galaxies, and other large features that could be problematic for SExtractor. We used an input weight image that included the galaxy photometric noise as well as additional variance caused by the SBF (for details, see Jordán et al. 2004 ; Cantiello et al. 2005 ) to avoid detecting the fluctuations as objects themselves. The SExtractor MAG_AUTO measurements include roughly 90% of the light from faint sources; the aperture corrections for these magnitudes were obtained from a number of isolated sources in each frame using a curve-of-growth analysis out to large radii (Cantiello et al. 2009 , 2011b ). The cutouts of the NGVS images used for the analysis are wide on each side; on such scales the PSF variation is small enough that the typical rms scatter is ∼0.01 mag for the aperture corrections. 9 9 For galaxies close to MegaPrime image tile edges, where the PSF or the image quality might be rapidly changing on spatially small scales, we limited our aperture corrections, PSF selection, and SBF analysis to the regions with the best image quality. Once the catalog of sources had been derived, the next step was to fit the luminosity function of the sources, which was necessary in order to estimate the amount of contamination from unmasked faint sources in the residual frame. We fitted a source magnitude distribution to a model, including a combination of the GCLF and a power-law background galaxy luminosity function (examples are shown in Figure 1 , discussed below). As noted above, bright stars and the most extended sources had been masked and were therefore not present in the catalog. At these high Galactic latitudes, the surface density of fainter stars is small compared the GCs in the vicinity of bright galaxies. The best fit to the combined GCLF and galaxy luminosity function was used to derive the background fluctuation correction term, P r , as


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The authors would like to thank Marco Castellano, Dijana Vrbanec, Benedetta Ciardi, Darren Croton, and Manodeep Sinha for useful discussions and comments. The authors acknowledge Peter Creasey for permission to use his Python library as a basis for the computation of the power spectra, and Benedetta Ciardi for a collaboration in developing pCRASH. A.H. is supported under the Australian Research Council’s Discovery Project funding scheme (project number DP150102987). P.D. acknowledges support from the European Commission’s CO-FUND Rosalind Franklin program. C.M.T. is supported under the Australian Research Council’s Discovery Early Career Researcher funding scheme (project number DE140100316) and the Centre for All-sky Astrophysics (an Australian Research Council Centre of Excellence funded by grant CE110001020). Finally, this research was supported by the Munich Institute for Astro- and Particle Physics (MIAPP) of the DFG cluster of excellence “Origin and Structure of the Universe.”


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Acknowledgments The authors thank D. Giannios for use of the numerical code. AP acknowledges support from an NWO Vidi Fellowship. The authors also thank the referee, Rosario Iaria, for useful comments.


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ACKNOWLEDGEMENTS We thank Srikara S (IISER Pune) for taking part in discussions during initial part of the work. PD thanks Nagendra Kumar for helpful discussions on QPOs. We thank the anonymous reviewer for thoughtful suggestions. This work is partly supported by an India–Israel joint research grant (6-10/2014[IC]) and by the ISRO project with research Grant No. ISTC/PPH/BMP/0362. PS and PD thank KITP for their participation in the program ‘Confronting MHD Theories of Accretion Disks with Observations’. This research was supported in part by the National Science Foundation under Grant No. NSF PHY-1125915. Some of the simulations were carried out on Cray XC40-SahasraT cluster at Supercomputing Education and Research Centre (SERC), IISc.


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ACKNOWLEDGEMENTS SS and AI acknowledge support from the Royal Society. We acknowledge useful comments from the referee Javier Garcia that improved the paper. This research has made use of data and/or software provided by the High Energy Astrophysics Science Archive Research Center (HEASARC), which is a service of the Astrophysics Science Division at NASA/GSFC and the High Energy Astrophysics Division of the Smithsonian Astrophysical Observatory.


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one-to-one correspondence of the brightest H II regions and the brightest LOFAR emission neither spatially nor in flux/intensity. This may be an effect of the dust absorption, which affects the H α line flux in the disc. The number of H II regions that coincide with LOFAR emission are therefore at the front side of the galaxy. The H α bright central region is also the brightest region in radio continuum, implying efficient dust removal, probably due to a wind from this central region. There are several kiloparsec-sized radial filaments visible in the LoTSS image extending into the halo; see arrow marks in Fig. 12 . In most cases (#2, 3, 4, and 7) these filaments connect back to large H II regions in the disc of NGC 3556, or broader filaments (#1, 5, 6, and 8) connect to a large, bright region containing DIG. It is tempting to identify these filaments as magnetised chimneys from giant H II regions and more evolved, bright regions of DIG with still significant SNe activity. Despite the lower resolution and smaller signal-to-noise ratio, the overall morphology of the radial filaments extending into the halo resembles that of the starburst galaxy M82, see for example the unpublished 5 GHz map (NRAO News Release, 2014 February 3). The non-detection of a diffuse large-scale outflow in our H α data is most probably due to the relatively low sensitivity of our optical data. Still, the clear connection of non-thermal radio continuum filaments to large star-forming regions and regions of large diffuse H α emission implies an outflow/wind driven by the combined pressure from cosmic rays and hot thermal gas as result of SNe activity. Fig. 12. Sub-image measuring 9′ × 6′ of the high-resolution LoTSS tile containing NGC 3556 plotted as greyscale image; our continuum-subtracted H α image is overlaid as a pseudo-colour image (intensity scale rainbow: from low intensity = violet and blue to high intensity = red). North is up, east is left in the image. Several radio structures are marked and numbered. 4. Discussion As shown in Sect. 3 , the extent of the faint halo increases from high to low frequency. The radial extent, however, does not increase. This has been observed in many spiral edge-on galaxies (e.g. in the CHANG-ES sample) and can be interpreted as a cosmic-ray driven galactic wind ( Butsky Quinn 2018 ). Furthermore, the extent in the CHANG-ES maps is generally smaller than in the LOFAR map. This can be a result of the missing-spacing problem, where an interferometer does not “see” emission on angular scales above a certain size. For the D-array/ C -band combination, however, the largest angular scale is about 4′ in size 7 . This is comparable to the extent seen in the LOFAR map, so it is reasonable to assume that the halo would be seen in its entirety. Hence, we conclude that since the observed halo extent is smaller than in the 144 MHz map, the CRe did not propagate any further as a result of spectral ageing. As the top panel of Fig. 5 shows, the


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We are grateful to the referee for valuable comments. This work was supported by the NSFC under grants 11303016 and 11373023, and by the NKBRSF under grants 2011CB811402 and 2014CB744203.


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ACKNOWLEDGEMENTS The authors thank Dr M. Mollá for a scrupulous reading of the manuscript and many important remarks and suggestions which improved our paper.


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We appreciate the anonymous referee’s valuable comments. This work was supported by JSPS KAKENHI grant No. 18K18774. The authors thank Akio Inoue and Tohru Nagao for suggestions on metallicity and the dust-to-gas ratio in AGNs.


O O O O O O O O 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 O O 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 B-Software I-Software 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 B-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 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 B-Software B-Citation I-Citation I-Citation I-Citation O B-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 B-Software 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 B-CelestialObject I-CelestialObject 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-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 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

population thought to result from satellite galaxy accretion (e.g. Forbes Bridges 2010 ; Leaman, VandenBerg Mendel 2013 ). These results suggest that the detailed age–metallicity distribution of GCs may be used to infer the accretion history of the host galaxy. The key ingredient enabling us to extract the wide range of information encoded in the Galactic GC population is the E-MOSAICS 1 project (Pfeffer et al. 2018 ; Kruijssen et al. 2019 ). Cluster formation and disruption are well known to depend on the local environmental conditions within galaxies (see recent reviews by Kruijssen 2014 ; Forbes et al. 2018 ). Modelling the co-formation and co-evolution of GC populations and their host galaxies thus requires following the spatial and kinematic phase-space distributions of the cluster populations self-consistently in their cosmological context. This prohibits the use of models based on semi-analytic or particle tagging techniques. Instead, E-MOSAICS self-consistently couples environmentally dependent sub-grid models for the formation, evolution, and tidal disruption of stellar clusters (MOSAICS, Kruijssen et al. 2011 , 2012 ; Pfeffer et al. 2018 ) to the locally resolved baryonic conditions obtained with the state-of-the-art cosmological galaxy formation model EAGLE (Schaye et al. 2015 ; Crain et al. 2015 ). The initial set of 25 hydrodynamical cosmological zoom-in simulations of Milky Way-mass galaxies allows us to follow the co-formation and co-evolution of galaxies and their GC populations. Specifically, we show in Kruijssen et al. ( 2019 ) that the distribution of GCs in age–metallicity space is a sensitive probe of the host galaxy’s formation and assembly history. The GC age–metallicity distributions obtained in E-MOSAICS exhibit strong galaxy-to-galaxy variations, resulting from differences in their evolutionary histories. By correlating several metrics describing the GC age–metallicity distributions of the 25 simulated galaxies with quantities describing their formation and assembly histories (such as halo properties, formation and assembly redshifts, stellar mass assembly time-scales, numbers of major and minor mergers, redshift distribution of mergers), we identify a set of 20 correlations with high statistical significance. These correlations show that the GC age–metallicity distribution is a sensitive probe of the host galaxy’s stellar mass growth, metal enrichment, and minor merger history. Moreover, it is shown that the mass dependence of galaxy evolution in age–metallicity space enables the use of individual GCs to infer the masses and metallicities of their natal galaxies as a function of redshift. We demonstrate that this can be used to reconstruct the merger tree of the host galaxy. Applying any of these individual results to the GC population of the Milky Way may already significantly increase our understanding of its formation and assembly history. In this paper, we take the comprehensive approach of employing the full


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The authors thank the anonymous referee for the thorough review and constructive suggestions that lead to an improvement of the paper. S.E.H. was supported by the National Research Foundation of Korea through grant 2007-0093860. H.K. was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education (2014R1A1A2057940). The work of D.R. was supported by the year of 2014 Research Fund of UNIST (1.140035.01).


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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-Event I-Event I-Event B-Event O O O O O O O O O B-Survey I-Survey 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 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 B-Telescope 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 B-Event I-Event I-Event I-Event O O O O O O O O O O O O O B-Software O B-Citation I-Citation I-Citation I-Citation O O O B-Telescope 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

that the main limitation of this approach is the fact that simulations may not fully reproduce all the cluster properties, and the absolute performance derived may therefore be taken with caution. However, we found it the most operational way to compare the relative performance of the different algorithms on a common ground. The full methodology currently developed to determine the selection function and the related mass proxy will be addressed in future work. The performance of the cluster finder algorithms has been tested and compared in a series of four Cluster Finder Challenges (CFC) between 2013 and 2017. The codes were tested on Euclid survey-like mock catalogs based on semianalytic models ( Merson et al. 2013 ; Gonzalez-Perez et al. 2014 ) and halo occupation modeling ( Carretero et al. 2015 ). The positions of the mock clusters were unknown to the participants of the challenges. Through the years, the mock catalogs were refined to better represent the properties of galaxies within clusters. In particular, photometric redshifts were assigned to galaxies in order to run the codes as they would be run in the Euclid context. In the first challenges, photometric redshifts were assigned following a simplistic Gaussian distribution, while in the later ones, photometric redshift codes were used. At the end of the third cluster finder challenge, the methodology and analysis pipeline were sufficiently mature for a first assessment of the relative performance of the different codes. While eight cluster finder codes in total were tested in the three preliminary challenges, only six of them took part in the final challenge described in this paper. In this article, we present the methodology used to assess the performance of the codes and the results obtained from the final cluster finder challenge. The detection codes were applied blindly to a realistic galaxy mock, built using PhotReal ( Ascaso et al. 2015 ) on the Euclid wide light-cone ( Merson et al. 2013 ), which was considered to be the best compromise available in terms of angular size (300 deg 2 ), depth ( z > 2.5), and realistic modeling of galaxy properties. We present the main assumptions and methodology of each of the competing codes and discuss the main properties of the simulated mock in the context of cluster detection. The code detections were matched to the true mock clusters and this information was used to evaluate the performance of the algorithms. Special care was given to the matching procedure by using several methods, allowing us to estimate the associated systematic uncertainties. In light of the mock properties, the performance comparison of the different algorithms participating in the challenge guided our selection of those now being validated and implemented in the Euclid pipeline. At this stage, we stress that the goal of this paper is not yet to compute a robust selection function and robust mass proxies, but instead, to compare the relative performance of different


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We thank an anonymous referee for her/his useful comments and suggestions. S.-P.M. and O.C. were supported by NASA Living with a Star grant no. NNX16AC11G. J.J.D. was supported by NASA contract NAS8-03060 to the Chandra X-ray Center. J.D.A.-G. was supported by Chandra grants AR4-15000X and GO5-16021X. C.G. was supported by Chandra grants GO7-18017X and GO5-16021X. Simulation results were obtained using the Space Weather Modeling Framework, developed by the Center for Space Environment Modeling, at the University of Michigan with funding support from NASA ESS, NASA ESTO-CT, NSF KDI, and DoD MURI. Simulations were performed on NASA’s PLEIADES supercomputer under award HEC-SMD-17-1190.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Citation I-Citation I-Citation 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 limit of weak viscosity and/or magnetic diffusivity is accessible. 5. Naturally all the renormalized coefficients are proportional to D 1 , which is the magnitude of the nonreflectionally symmetric component of the stirring force. It follows that the α -effect is impossible if the turbulence is not helical: . 6. Finally, an interesting observation was made, that in the strong MHD turbulence the energy spectra are substantially influenced by the helical component of the stirring force, whereas the helicity spectrum is determined by both the helical and nonhelical components of the forcing. All the nonlinear corrections to turbulent energy and helicity spectra are at leading order proportional to the energy of the mean magnetic field, which emphasizes its role in the MHD turbulence. A significant limitation of the presented analysis is that the turbulence, i.e., the stirring force, was assumed isotropic. This is a great simplification; however, the natural astrophysical and geophysical flows, in the majority of cases, possess at least one distinguished axis associated with the background rotation, which introduces anisotropy. Application of the renormalization group technique to rapidly rotating MHD flows, in order to obtain a more astrophysically realistic form of the mean EMF (the -tensor), is a subject of current research (see Mizerski 2020 ). Appendix The details of the renormalization procedure applied in order to obtain the mean field equations are given here. First of all, we clarify how the ensemble averaging should be understood and explain the concept of a conditional average over a statistical subensemble for short-wavelength modes. We adopt the approach of McComb et al. ( 1992 ; see also McComb Watt 1990 , 1992 ). The essential idea of this approach is the introduction of a subensemble of flow realizations including near-chaotic statistical properties for the short-wavelength shell , but remaining quasi-deterministic for . The subensemble average can be precisely defined and then, utilizing the assumption that in the turbulent cascade the energy transfer in the Fourier space is local, the following crucial properties can be proved: For details see particularly Section IV and the beginning of Section V in McComb et al. ( 1992 ). We now substitute the expressions for short-wavelength modes from Equations ( 65a ) and ( 65b ) into the conditional averages in the equations for long-wavelength modes in Equations ( 64a ) and ( 64b ). Neglecting higher-order correlations of the type , etc. (which eliminates the rests in Equations ( 65a ) and ( 65b )), and using , , and , one obtains The order of accuracy kept above, i.e., up to terms of the order with neglect of terms 7 7 Recall that this allows for neglect of the terms proportional to and in the rest ( 67b ). in particular, allows us to keep in the two last terms in the Lorentz force ( 127b ); anticipating the results, we may say that these terms account for the Lorentz force effect


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 O O O O O O O O O O O O O O O O O O O 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 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 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 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 B-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 B-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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Model O B-Model O O O O O O O O O O O B-Telescope 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 B-Citation I-Citation I-Citation O B-Citation 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 O O O O O O O O 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 B-Formula I-Formula I-Formula I-Formula O O

to match the observed LFs at redshifts z = 6 − 10. Although not shown in the present paper, we find that a roughly constant (; best-fitting value) ε * is needed for all the flat and non-flat models considered here (see fig. 2 of Paper I ). We can then get limits for f esc at different redshifts from equation ( 12 ) using the MCMC constraints already obtained on the evolution of N ion ( z ). Note that we take the value of N γ as ≈3200 which is appropriate for the PopII Salpeter IMF assumed here. The redshift evolution of f esc for different models is shown in Fig. 4 . The corresponding 2-σ uncertainties, indicated by shaded regions in the plot, have been computed using the quadrature method (Mitra et al. 2013 ). We find that the best-fitting f esc remains almost constant at for the whole redshift range in all the flat models ( l eft panel). On the other hand, a strong redshift evolution of this quantity is required for the non-flat models (right panel) – it can increase by a factor of ∼7 from redshift 6 to 10. Moreover, if we consider their 2-σ ranges, these non-flat models can lead to an impractically high f esc (≳1) at redshifts z ≳ 8. The sole reason behind such trends is that the values of N ion for non-flat models can become as high as ∼1000 around z ≈ 8 − 9, considering their 2-σ limits (see panel (a) of Fig. 3 ), in order to produce very high optical depths required for those models. On the other hand, the upper limits (2-σ) of escape fraction for the flat models having relatively lower τ el can become at most for all the redshift ranges considered here. Such one-to-one correspondence between strong redshift evolution of f esc ( z ) and higher reionization optical depths has also been reported earlier in many studies (see e.g. Haardt Madau 2012 ; Kuhlen Faucher-Giguère 2012 ; Mitra et al. 2013 ). Figure 4. Redshift evolution of the escape fraction f esc ( z ) along with its 2-σ errors for all the flat (left panel) and non-flat (right panel) models considered in this work. The red solid lines in both panels correspond to an escape fraction of unity. 4 CONCLUDING REMARKS We have presented detailed statistical analysis of reionization in tilted flat and untilted non-flat ΛCDM, XCDM and φCDM inflation models. The cosmological parameters for these models are constrained by Planck 2015 TT + lowP + lensing CMB anisotropy and SNIa, BAO, H ( z ), and growth rate data, using physically motivated inflation power spectra for energy density inhomogeneities (Park Ratra 2018a , c ). For the non-flat models, these data prefer mildly closed models with Ω k ∼ −0.006 to −0.008. Although such models provide better fits to the observed low-l temperature anisotropy C l ’s and weak-lensing σ 8 estimates, they provide worse fits to the observed higher-l temperature anisotropy C l ’s and primordial deuterium abundances (Penton et al. 2018 ). These closed models also predict relatively higher reionization optical depth values (τ el ≈ 0.11–0.12) compared to


O O O O O O O O O O O O O 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 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 O O O O O O B-CelestialRegion I-CelestialRegion O O O B-CelestialRegion I-CelestialRegion O O O O O O O O O O O O O O O O O O B-Observatory B-Telescope O O O O O O O B-Instrument O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-Telescope I-Telescope I-Telescope I-Telescope O O B-Observatory I-Observatory I-Observatory I-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 B-Wavelength I-Wavelength O O O O O B-CelestialRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 B-Telescope O O O O O O O O O O B-Instrument I-Instrument I-Instrument B-Instrument B-Citation I-Citation I-Citation I-Citation O O O B-Telescope I-Telescope I-Telescope B-Telescope O B-Location I-Location O B-Location B-Instrument O O O O O O O O O O O O O O O O O O O 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 B-Wavelength O B-Wavelength O O B-Wavelength 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 B-Formula I-Formula I-Formula O O O O B-Formula I-Formula I-Formula O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-Telescope O O O O O O O O O O B-Instrument O O O O O O B-Instrument O O O O O O O B-Wavelength I-Wavelength 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 B-Wavelength O O O O B-Wavelength 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

contain groups of background QSOs. The narrowband filter has an FWHM of 40 Å, corresponding to the radial separation of 42 cMpc. The survey volume of the 2622 groups is cMpc cMpc cMpc cMpc 3 . Thus, BOSS1441 can be regarded as the most extreme system selected from a ≈1.0 × 10 8 cMpc 3 survey volume using our selection technique. 3. Deep Imaging and Spectroscopy in the BOSS1441 Field After selecting the BOSS1441 field, we conducted deep narrowband and broadband imaging and multiple-slit spectroscopy to search for LAEs in this field. 3.1. KPNO-4 m/MOSAIC Narrowband + Broadband Imaging We used the MOSAIC1.1 camera (Sawyer et al. 2010 ) at the f /3.1 prime focus of the 4 m Mayall Telescope at the Kitt Peak National Observatory to conduct deep narrowband and broadband imaging. We obtained deep narrowband images with the NB403 narrowband filter. As shown in Section 2.2 , NB403 is used for probing the Ly α -emitting galaxies at . The BOSS1441 overdensity was observed on 2013 March, and 2014 April and June. The total exposure time is 17.9 hr, which consists of individual 15 or 20 minute exposures with a standard dither pattern to fill in the gaps between the eight chips. The seeing ranges from 11 to 17, with a median combined seeing of 132. We observed with the broadband filter (Bw) for 3 hr to match our selection criteria. These observing conditions enable us to achieve a narrowband magnitude at 5 σ using a circle aperture of 25 and a Bw -band magnitude m B = 25.9 at 5 σ using the same aperture. The narrowband sensitivity limit corresponds to a Ly α surface brightness of erg s −1 cm −2 arcsec −2 . 3.2. LBT Multiple-wavelength Broadband Imaging Our multiband imaging was conducted with the Large Binocular Cameras (LBC; Giallongo et al. 2008 ) at the Large Binocular Telescope (LBT) on Mount Graham in Arizona. LBC is characterized by a unique optical system. Each of the two mirrors has a collecting area of 8.4 × 8.4 m 2 and a field of view of 23′ × 23′. For a complete selection of star-forming galaxies at , we used the LBT to conduct deep multiple broadband observations in the U , V , and i filters (Steidel et al. 2005 ). Multiple broadband imaging can also eliminate the low-redshift [O ii ] interlopers that are the main contaminants of LAEs at z = 2.3. We use the standard z = 2 star-forming galaxy selection (BX selection) technique (Adelberger et al. 2005 ) to eliminate the low- z interlopers. The one-night LBT/LBC deep multicolor imaging was carried out in 2014 March. The LBC binocular mode was used, and the LBC blue channel was used solely for deep U -band observations. On the red side, we observed the same field in the V and i filters. We conducted 6 hr deep imaging in U , 2.5 hr in V , and 3.5 hr in i . The individual exposure was six minutes with a standard five-point dither pattern to fill in the CCD gaps. The conditions were partially cloudy, with a median seeing of 06. Our observations reached at 5 σ , at 5 σ , and at 5 σ . These depths are