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time varies with rigidity E / Z , with Z the charge number, as t res ∝ ( E / Z ) s with s ≃ 0.4–0.6. There are a number of codes that model Galactic CR propagation and the CR interactions (losses, spallation, decay of unstable nuclei, and re-acceleration) in the Galaxy, such as galprop , see Strong et al. ( 2010 ), dragon , see Evoli et al. ( 2008 ), and crpropa , see Alves Batista et al. ( 2016 ). In this paper, we do not take into account the effects of CR advection by the Galactic winds, energy losses, and re-acceleration. We also do not consider the network of nuclear reactions that leads to the production of secondary CRs. These effects will be considered in future work. However, in these codes one usually limits the calculations to models with cylindrical symmetry models with an effective diffusion coefficient D , thereby neglecting the influence of the geometry and strength of the GMF on CR diffusion. Recently, some efforts has been taken to consider anisotropic diffusion models for Galactic CRs, see Evoli et al. ( 2017 ). We will consider anisotropic diffusion of CRs inside the Galaxy. We note that a similar calculation, again employing stochastic differential equations, has been applied to the interplanetary transport and acceleration of solar energetic particles in the solar wind see Dröge et al. ( 2010 ) and the references therein. The outline of this paper is as follows: in Section 2 , we discuss the GMF and introduce the main features of the Jansson–Farrar. In Section 3 , we present our numerical solution method to the CR diffusion, based on the Itô formulation of stochastic differential equations, using relevant input, like the diffusion tensor and its connection to the GMF in Section 3.1 . The grammage calculation is discussed in Section 3.3 . In Section 4 , we present the spatial distribution of the CRs from a single source the associated residence time distribution, as well as the grammage of CR particles. We do this for various combinations of parallel and perpendicular diffusion. Section 5 discusses the implications of the results presented in this paper and summarizes our conclusions. 2 MODEL FOR THE GMF The magnetic field in the diffuse interstellar medium (ISM) has two distinct components: a large-scale () regular field, as well as a small-scale turbulent component. The strength of the total magnetic field in the Galaxy has been estimated of about 6±2 μG, see Beck ( 2001 ) and Haverkorn ( 2015 ), with the amplitude of the random field comparable to that of the large-scale field. The large-scale GMF affects the propagation of CRs (Strong et al. 2007 ), the dynamics of molecular clouds and star formation, see Hennebelle Falgarone ( 2012 ). In this paper, we use the GMF model of Jansson Farrar ( 2012a ) and Jansson Farrar ( 2012b ) for this large-scale (regular) field. This model matches the WMAP 7 22 GHz synchrotron intensity map and the Galactic Faraday rotation data obtained from polarization measurements of background


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ACKNOWLEDGEMENTS We thank James Bolton, Tirthankar Roy Choudhury, Harley Katz, Laura Keating, and Ewald Puchwein for helpful discussions. This work was supported by the ERC Advanced Grant 320596 ‘The Emergence of Structure During the Epoch of Reionization’. The ramses simulations presented in this paper were performed on the COSMOS Shared Memory system at DAMTP, University of Cambridge, operated on behalf of the STFC DiRAC HPC Facility. This equipment is funded by BIS National E-infrastructure capital grant ST/J005673/1 and STFC grants ST/H008586/1 and ST/K00333X/1. The aton radiative transfer simulations in this work were performed using the Wilkes GPU cluster at the University of Cambridge High Performance Computing Service ( http://www.hpc.cam.ac.uk/ ), provided by Dell Inc., NVIDIA, and Mellanox, and part funded by STFC with industrial sponsorship from Rolls Royce and Mitsubishi HeavyIndustries.


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Acknowledgements Rosetta is an ESA mission with contributions from its member states and NASA. We are indebted to the whole Rosetta Mission Team, LCC, SONC, SGS, and RMOC, for their outstanding efforts to make this mission possible. The contributions of the ROMAP and RPC-MAG teams were financially supported by the German Ministerium für Wirtschaft und Energie and the Deutsches Zentrum für Luft- und Raumfahrt under contract 50QP1401. The SPICE kernels used for this work are available as ROS-E/M/A/C-SPICE-6-V1.0 through PSA and PDS.


O O O O O B-Wavelength O O O O B-Wavelength O O O O O O O O O O O O O O O B-Wavelength 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 O O O O O O O O O O O O B-Wavelength I-Wavelength O O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Telescope B-Instrument 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 B-Wavelength 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 B-Wavelength O O O O O O O O O O O O O B-Telescope B-Instrument O O O O O O O B-Model O O B-Wavelength O B-Wavelength 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 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 B-Wavelength O O O O O O B-Wavelength O O O O O O B-Dataset I-Dataset I-Dataset I-Dataset B-Dataset B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation O O O O O O O O O B-Survey O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O B-Wavelength I-Wavelength 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 B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O B-Formula I-Formula I-Formula I-Formula 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 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 B-Wavelength 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 B-Citation I-Citation I-Citation I-Citation 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 O B-Wavelength O O O O O B-CelestialObject B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-Wavelength 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 O O O O O B-Wavelength O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O

that all six galaxies are LyC leakers with f esc (LyC) ranging between 6 and 46 per cent. These values are much higher than f esc (LyC) of ∼0–4.5 per cent derived e.g. by Borthakur et al. ( 2014 ) and Chisholm et al. ( 2017 ) in SFGs with lower O 32 or with lower equivalent widths of the H β emission line (Hernandez et al. 2018 ). In this paper we present new HST /COS observations of the LyC in five compact SFGs with the highest O 32 ∼ 8–27 ever observed in order to detect ionizing radiation, and examine its behaviour over a wide range of O 32 . The properties of selected SFGs derived from observations in the optical range are presented in Section 2 . The HST observations and data reduction are described in Section 3 . The surface brightness (SB) profiles in the UV range are discussed in Section 4 . In Section 5 we compare the HST /COS spectra with the extrapolation of the modelled SEDs to the UV range. Lyα emission is considered in Section 6 . The escaping LyC emission is discussed in Section 7 together with the corresponding escape fractions. In Section 8 our results are compared with the LyC escape fractions for other galaxies obtained in some recent studies. We summarize our findings in Section 9 . 2 PROPERTIES OF SELECTED GALAXIES DERIVED FROM OBSERVATIONS IN THE OPTICAL RANGE 2.1 Emission-line diagnostic diagrams Our LyC leaker candidates were selected from the SDSS Data Release 12 (DR12) (Alam et al. 2015 ) by adopting the selection criteria described in Izotov et al. ( 2016a,c , 2018 ). All of them have a compact structure on SDSS images (Fig. 1 ) and high equivalent widths EW(H β) > 200 Å of the H β emission line in the SDSS spectra, indicating very recent star formation. These galaxies are located in the upper part of the SFG branch in the Baldwin–Phillips–Terlevich (BPT) diagram (filled stars in Fig. 2a ) implying the presence of high-excitation H ii regions. Izotov et al. ( 2016a,c ) discussed only galaxies with O 32 ∼ 5–7. In this paper and in Izotov et al. ( 2018 ) we report observations of galaxies with the considerably larger range of O 32 ∼ 8–27 (Table 1 ), aiming to study the applicability of the O 32 criterion to select galaxies with high escape fractions of ionizing radiation. It is seen in Fig. 2(b) that the selected galaxies have the highest O 32 ratios among all local LyC leaking galaxies observed so far. Figure 1. 25 arcsec × 25 arcsec SDSS composite images of selected galaxies. Figure 2. (a) The BPT diagram (Baldwin, Phillips Terlevich 1981 ) for SFGs. (b) The O 32 –R 23 diagram for SFGs where R 23 = ([O ii ]3727 + [O iii ]4959 + [O iii ]5007)/H β. The LyC leaking galaxies (this paper) and J1154+2443 (Izotov et al. 2018 ) are shown by filled stars in both panels. The location of LyC leaking galaxies by Borthakur et al. ( 2014 ) and Chisholm et al. ( 2017 ) are shown by open circles while LyC leaking galaxies by Izotov et al. ( 2016a,c ) are represented by open stars. The compact SFGs (Izotov et al. 2016b ) are


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We thank the Centre National d’Etudes Spatiales (CNES, France) and the French CNRS/INSU for continuous support for the preparation of the Gaia mission. This work benefited from travel support from the European Science Foundation through the GREAT Research Network Program. Some of the computations were done on the Mesocentre SIGAMM machine, hosted by the Observatoire de la Côte d’Azur. The first two authors would like to thank Naia for her numerous (and efficient) attempts to postpone the revision of this paper. We warmly thank C.A.L. Bailer-Jones for his constructive remarks, which helped to improve this article. We are also sincerely grateful to D. Katz for his help with regard to the in-flight RVS characteristics.


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This work received major support through an NSF grant NSF ANT-094513. We are thankful for the computing resources provided by the Minnesota Supercomputing Institute. EBEX is supported through NASA grants NNX08AG40G and NNX07AP36H. C. Bao acknowledges the support from the Doctoral Dissertation Fellowship from the University of Minnesota. C. Baccigalupi acknowledges the support from the INDARK INFN Grant.


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GA, RE, JMG, JFG, and JMT acknowledge support from MINECO (Spain) AYA2014-57369-C3 grant (co-funded with FEDER funds). JMG also acknowledges support from the MECD PRX15/00435 grant (Spain) and from the SI CGPS award, ‘Magnetic Fields and Massive Star Formation’. RE also acknowledges MDM-2014-0369 of ICCUB (Unidad de Excelencia ‘María de Maeztu’). SC acknowledges the support of DGAPA, UNAM, and CONACyT (Mexico).


O O O O O B-Person I-Person O O O O O O O B-Software I-Software I-Software I-Software I-Software O O O O O O O O O O O O O O O B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person O B-Person I-Person O O O O O O O O O O O O O B-Event I-Event I-Event I-Event O B-Location O O O B-Person O B-Person O O O O O O O O B-Organization O B-Location O O O O O O B-Person O O O O B-Organization B-Fellowship I-Fellowship I-Fellowship B-Person O B-Person O O O O B-Grant I-Grant I-Grant O O B-Organization I-Organization O O B-Organization O B-Grant B-Person O O O O O O O B-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization B-Person O O O B-Organization O B-Grant O B-Grant I-Grant I-Grant O O B-Organization O B-Grant O B-Grant B-Grant B-Grant B-Grant B-Grant B-Grant O B-Grant O B-Organization O O O O O O O O O O B-Software B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Software B-Citation I-Citation O O B-Software B-Citation I-Citation I-Citation O

ACKNOWLEDGEMENTS We are grateful to Yu Lu for making public his implementation of the Parkinson Cole merger tree algorithm. We thank the anonymous referee for constructive comments that improved the paper. We also thank Mike Grudic, Charlie Conroy, Chris McKee, Joss Bland-Hawthorn, Aldo Rodriguez-Puebla, and Rohan Naidu for helpful discussions. Ideas for this project were developed in part at the Near/Far Globular Cluster Workshop in Napa in 2017 December. KE and DRW are grateful for the hospitality provided by the MPIA in Heidelberg during the writing of this paper. KE acknowledges support from an NSF Graduate Research Fellowship. EQ and KE are supported by a Simons Investigator Award from the Simons Foundation and by NSF grant AST-1715070. DRW is supported by fellowships provided by the Alfred P. Sloan Foundation and the Alexander von Humboldt Foundation. MBK acknowledges support from NSF grant AST-1517226 and CAREER grant AST-1752913 and from NASA grants NNX17AG29G and HST-AR-13888, HST-AR-13896, HST-AR-14282, HST-AR-14554, HST-AR-15006, HST-GO-12914, and HST-GO-14191 from STScI. The analysis in this paper relied on the python packages NumPy (Van Der Walt, Colbert Varoquaux 2011 ), Matplotlib (Hunter 2007 ), and AstroPy (Astropy Collaboration 2013 ).


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ACKNOWLEDGEMENTS We thank the anonymous referee for helpful suggestions in improving the text. We thank O. Bromberg, A. Philippov, O. Porth, and E. Sobacchi for helpful discussions. KC thanks M. Lucchini, T. Beuchert, F. Krauß, and T.D. Russell for providing useful insights for the background study. This research was made possible by National Science Foundation (NSF) PRAC award no. 1615281, OAC-1811605, NSF AST-1911080, AST-1910248, and AST-1910451 at the Blue Waters sustained-petascale computing project and supported in part under grant no. NSF PHY-1125915. KC and SM are supported by the Netherlands Organization for Scientific Research (NWO) VICI grant (no. 639.043.513), ML is supported by the NWO Spinoza Prize and AT by Northwestern University, the TAC and NASA Einstein (grant no. PF3-140131) postdoctoral fellowships and the NSF grant 1815304 and NASA grant 80NSSC18K0565. KC thanks the Leids Kerkhoven-Bosscha Fonds (LKBF) subsidy no. 17.2.100 for travel funding. The simulation data presented in this work are available on request to AT at atchekho@northwestern.edu.


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

−12 with respect to H 2 (Quénard et al. 2017 ). The identification of this cation in various astrophysical environments may be attributed to its relatively large dipole moment (∼2.1 debye, Haese Woods 1980 , or ∼1.75 debye, Botschwina 1987 ). So far, protonated cyanoacetylene is the largest ion detected in space. For its formation in astrophysical media, Takagi et al. ( 1999 ) showed that the reaction of HCCH + with HNC followed by the protonation of HC 3 N leads to HC 3 NH + . They also established that the reaction between the N atom and cyclic C 3 H 3 + is not an efficient pathway for the production of HC 3 NH + in interstellar space (Takagi et al. 1999 ). HC 3 NH + may produce HCCCN and HNCCC species through a dissociative recombination reaction with electrons (Kawaguchi et al. 1994 ; Osamura et al. 1999 ). HC 3 NH + is suggested to play an important role in the production of cyanopolyynes (Turner, Amano Feldman 1990 ; Winstanley Nejad 1996 ; Quénard et al. 2017 ; Marcelino et al. 2020 ). Indeed, cyanopolyynes, HC 2 n +1 N, are widespread molecules in dark clouds. Molecular species up to HC 11 N have been identified in the ISM (Kawaguchi et al. 1994 ; Takagi et al. 1999 ; Sakai et al. 2008 ; Friesen et al. 2013 ; Loomis et al. 2016 ; Jaber Al-Edhari et al. 2017 ; Taniguchi et al. 2018 ). For their formation in astrophysical media, two pathways are proposed: (i) gas-phase neutral–neutral reactions between polyynes and CN or C 3 N radicals such as the reaction between C 2 H 2 and the CN radical, which leads to the formation of HCCCN molecules; and (ii) ion–molecule reactions involving HC 3 NH + , where the low temperature hinders the chemical reactions (e.g. at the so-called early times of less than 10 4 yr): In sum, the consideration of both neutral–neutral and ion–molecule reactions gives reasonable abundances of the cyanopolyyne species (Takagi et al. 1999 ; Wakelam et al. 2015 ; Agúndez et al. 2017 ; Yu et al. 2019 ). Moreover, the HC 3 NH + ion is involved in the chemistry of HCN and HNC, both of which are important species in the formation of larger and more complex nitrogen-containing molecules (Quénard et al. 2017 ) such as the building blocks of polycyclic aromatic nitrogen heterocycle molecules (PANHs) in protoplanetary disks (Mendoza et al. 2013 ). Collisional data represent an important input for the analysis of observed spectra emitted by molecular species in non-local thermodynamical equilibrium (non-LTE) interstellar medium and therefore for the derivation of more accurate molecular abundances (Sarrasin et al. 2010 ; Lique et al. 2015 ; Bop et al. 2019 ; Senent et al. 2019 ). These help astrochemists to propose new plausible routes and processes for the formation of complex molecular species. In particular, it is important to accurately estimate the abundances of HCCCNH + in astrophysical media to better understand the chemistry of complex nitrogen-bearing organic compounds such as cyanopolyynes. To the best of our knowledge,


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The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. Support for this work was provided by the NSF through the Grote Reber Fellowship Program administered by Associated Universities, Inc./National Radio Astronomy Observatory. This research was also supported by the NASA Ames Research Center via Cooperative Agreements NNA09DB30A, NNX15AD20A, and NNX16AF59G to J.O. Burns. The authors like to especially thank J. Aguirre for his constructive feedback on the formalism of our approach and discussions on other aspects related to the foreground polarization. The authors would also like to thank R. Monsalve for his comments on the instrumental aspects of the approach. The authors gratefully acknowledge J. Mirocha for providing the simulated global 21 cm data using ARES. B.D. Nhan is also grateful to K. Tauscher and R. Monsalve for their assistance in utilizing the sky map data.


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The authors thank Geza Kovacs and Lynne Hillenbrand for suggesting that we take a closer look at the Hyades and Praesepe, and for helpful comments on the manuscript. We also thank Scott Tremaine for suggestions that made the statistical discussion much clearer. This work was performed in part under contract with the Jet Propulsion Laboratory (JPL) funded by NASA through the Sagan Fellowship Program executed by the NASA Exoplanet Science Institute. This research has made use of the SIMBAD database and the VizieR catalog access tool, operated at CDS, Strasbourg, France.


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We acknowledge valuable contributions, useful discussions, and comments on the manuscript by Max-Niklas Newrzella, Martin Reinecke, Reimar Leike, Jakob Knollmüller, Björn Adebahr, Stefan Blex, and Alexander Becker. We also thank the anonymous referee for the insightful comments and suggestions. We thank Patricia Reich for providing the HEALPix map of the 1420 MHz radio continuum observations.


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of linking lengths is somewhat generous compared to previous studies. We use the FoF algorithm only as a basis for an X-ray-detected cluster catalog in the HectoMAP region. We would rather include false candidates than exclude real ones. We next show that this approach recovers the relevant set of X-ray clusters in a separate densely surveyed region with essentially full X-ray coverage (Starikova et al. 2014 ). We test the FoF on the SHELS survey (Geller et al. 2010 , 2012 , 2014 , 2016 ), a dense complete redshift survey with no color selection and covering two well-separated 4 deg 2 fields (F1 and F2) of the Deep Lens Survey (DLS, Wittman et al. 2002 ). We use the F2 survey alone for this investigation because it has essentially complete X-ray coverage of all of the possible massive systems in the appropriate redshift range. The F2 survey is ∼95% complete to R ≤ 20.6 with a number density of ∼3200 galaxies deg −2 . In total, there are 26 X-ray-extended sources detected based on Chandra and XMM X-ray data (Starikova et al. 2014 ); 18 of these X-ray sources are in the redshift range 0.2 z ≤ 0.6 of interest for testing our approach to HectoMAP X-ray clusters. Here, we select 12 X-ray sources within 0.2 z ≤ 0.5 for testing our cluster identification procedure because the F2 magnitude limit R ≤ 20.6 is ∼0.4 mag brighter than the HectoMAP limit. The brighter F2 limit precludes FoF cluster detection at z ≳ 0.5. The X-ray flux limit for the 12 X-ray-extended sources with z 0.5 is 4.3 × 10 −15 erg cm −2 s −1 within 0.5–2.0 keV energy band. This X-ray flux limit is nearly two orders of magnitude fainter than the one we reach for the HectoMAP systems. Starikova et al. ( 2014 ) showed that 10 of these sources have optical counterparts identified as clusters in the SHELS spectroscopic survey (Geller et al. 2010 ) or in the DLS weak lensing analysis (Wittman et al. 2006 ). Here, we examine the number of F2 X-ray extended sources recovered by the FoF algorithm with the HectoMAP choice of linking lengths. Figure 4 shows the cone diagram of the subset of F2 galaxies selected according to the HectoMAP red galaxy prescription within 0.2 z ≤ 0.5. In Figure 4 , the cyan circles display the locations of seven X-ray-extended sources with spectroscopically identified counterparts from Geller et al. ( 2010 ). We also show the X-ray extended sources (yellow circles in Figure 4 ) matched with weak lensing peaks (Wittman et al. 2006 ) or with optical concentrations on the sky in the DLS images (Starikova et al. 2014 ). The redshifts of these X-ray sources with photometrically identified counterparts may not be accurate because they are based on photometric redshifts. Figure 4. Cone diagram for the SHELS F2 survey subsample with R ≤ 20.6, ( g − r ) fiber,0 > 1.0, ( r − i ) fiber,0 > 0.5 projected in the R.A. direction. The cyan and yellow circles indicate extended X-ray sources in F2 with spectroscopic counterparts (Geller et al. 2010 ) and photometric counterparts


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of . The magnetic field strength B and fitted values translate to a radiative lifetime of ∼100 years, which is difficult to explain without distributed in situ acceleration—this requirement can be relaxed by using a lower value of B . Figure 9. Representative models for the SED of the high-energy synchrotron component along with our binned X-ray data for K61 (top) and the NHS (bottom). Dashed vertical lines represent the boundaries of the energy range that NuSTAR is capable of observing. Varying several of the input parameters can have a large effect on the shape of the curve above 7 keV for K61 and especially in the case of the NHS. The bottom of Figure 9 shows several representative models for the SED of the NHS near the NuSTAR energy band. Unlike K61, the low-energy tail of the second emission component of the NHS is not constrained by the radio or near-IR data. The models shown here vary wildly in emission above 7 keV, where the magnetic field strengths ranges over G, with , and , with a comoving luminosity of . Future observations using NuSTAR would allow us to constrain the SED up to ∼ 80 keV. If the X-ray emission is due only to EC/CMB, then an estimate of the magnetic field strength can be made using (Felten Morrison 1966 ), where is the apparent energy density of the CMB at redshift z , erg cm −3 is the local CMB energy density, the apparent temperature of the CMB is , and the temperature of the CMB is . This calculation gives a value of G. While this is comparable to that quoted for other jets where the EC/CMB model is used to model their X-ray emission, in this case a comoving luminosity of is required to fit the model to our X-ray data. We feel this is unrealistic, as it would violate the Eddington limit by many orders of magnitude. For that reason, we have not shown it in any figure. Additionally, assuming an equipartition magnetic field, a Doppler factor of is required for EC/CMB to explain the observed X-ray/radio NHS flux even for the case of using standard formulae (Harris Krawczynski 2002 ). The required beaming is highly unlikely given the observed properties of the 3C 111 jet, e.g., the observed brightness of the SHS and the lack of obvious blazar properties. We do not have many data points with which to constrain the model of the low-energy synchrotron component, especially in K30 and K61. We expect to be able model its SED well in a follow-up paper using JVLA observations of the jet. As well, additional HST and Chandra observations would help to better constrain the near-IR to optical and X-ray spectral indices of the components, and perhaps also constrain the X-ray emission mechanism of additional components. 5. CONCLUSIONS We have presented new Chandra and HST observations of 3C 111 that reveal that its jet has eight X-ray and near-IR/optical emitting components, which extend for 121 arcsec (355 kpc deprojected length) from its AGN nucleus in the approaching jet, and also reveal the hotspot emission on the


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β is examined. 3.1. Analysis of 100 minute Intervals Some examples of the spectra calculated with Blackman–Tukey and Morlet wavelet methods are shown in Figure 1 . The position of the peak in the signature toward higher frequencies is consistent with both methods. The Morlet method yields a smoother time-averaged spectrum than does the Blackman–Tukey method. Figure 1 (a) is a case where the two methods closely follow one another through the signature. About 30% of all cases have signature peaks within 20% of each other. More cases show a greater difference in magnitudes of the peak value such as those in Figures 1 (b) and (c). The rare case is shown in Figure 1 (d). Only about 4% of cases have a relative difference in peaks that are more than 80%. In no case did the sign of the signatures disagree. Figure 1. Sample magnetic helicity spectra σ m calculated with the Blackman–Tukey (black line) and Morlet wavelet (magenta, gray line) methods. Wind spacecraft data are employed in this figure and all subsequent figures. Intervals evaluated come from 2004 December 1 to 2005 December 31. In this figure, panel (a) shows an interval starting on 2005 January 10 17:47 UTC, (b) 2005 January 3 22:21, (c) 2004 December 29 17:25, and (d) 2005 January 16 18:25. The positions of the peaks in the signatures ν MW and ν BT are close for each interval. The corresponding scatter plot in Figure 2 shows that the data points cluster tightly along the line of equal values. In 3 of 289 intervals, the signature was absent from the Morlet wavelet spectrum (e.g., Figure 1 (d)), so the peak position could not be obtained. Markovskii et al. ( 2016 ) had established for the peak positions determined by the Blackman–Tukey method that the position in wavenumber based on the solar wind speed convecting the structure correlates with an inverse scale based on β 1/2 . Since the Blackman–Tukey method agrees with the Morlet wavelet method with respect to signature position, the correlation with this inverse scale is obtained with either method. Figure 2. Scatter plot of the magnetic helicity signature position calculated with the Blackman–Tukey ( ν BT ) and Morlet wavelet ( ν MW ) methods. The values of the signatures were not equal to each other in each interval. Figure 3 displays the scatter plot of the signature magnitude . The average absolute difference between σ BT and σ MW is 0.07, which can be regarded as an uncertainty in the measured peak value. Nevertheless, statistically, the results of the two methods are not much different. Figure 3. Scatter plot of the magnetic helicity signature magnitude calculated with the Blackman–Tukey ( σ BT ) and Morlet wavelet ( σ MW ) methods. Figure 4 plots the distribution functions of for each method. The distributions show comparable maxima and spreads. A student’s T-test (Trumpler Weaver 1953 ) calculation found that the means of each distribution are very likely the same (probability equals 0.82). The Blackman–Tukey distribution extends


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Comments of an anonymous referee on an earlier version of this paper are gratefully acknowledged. We are indebted to Rocío Márquez from the Scientific Instrumentation center of the University of Granada for providing the SEM images. This work been supported by the Plan Nacional de Astronomía y Astrofísica contracts AYA2015-67152-R and AYA2015-71975-REDT.


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L.S. is indebted to Jiang-Tao Li for the valuable advice and thanks Ning-Xiao Zhang for the technical help. This work is supported by the 973 Program under grants 2017YFA0402600 and 2015CB857100 and the NSFC under grants 11773014, 11633007, and 11851305. Facility: Chandra (ACIS-S). Software: CIAO (Fruscione et al. 2006 ), WVT binning (Cappellari Copin 2003 ; Diehl Statler 2006 ), Xspec (Arnaud 1996 ), SPEX (Kaastra et al. 1996 ), DS9. 12 12 http://ds9.si.edu/site/Home.html


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we note that the results for -ray spectra present a similar feature they are too soft as compared to observations. We compute the -ray spectral index in the energy range 0.87GeV at different Galactic coordinates ( l , b ) and, for each position in the sky, we estimated the difference between the spectral slope of simulated and observed -ray spectra (two examples of observed and simulated -ray spectra can be found in Fig. 7 , dashed and solid lines, respectively). For the observed spectra, the slope has been computed in the same energy range, from Selig etal. ( 2015 ). The results are shown in Fig. 2 , right-hand panel. The open histogram shows the distribution of the difference between the simulated and observed slopes. We limit this investigation to the region of the map at small latitudes, 5 b 5. The average value is around 0.08, indicating that the simulated -ray spectra are on average softer than what inferred from observations. To solve the inconsistency between observations and both the simulated CR spectrum at Earth and the -ray spectra, we consider a model with a harder injection spectrum . The shaded histograms in Fig. 2 show that in this case predictions of the CR slope around the location of the Earth (left-hand panel) and of the map of -ray radiation (right-hand panel) are in better agreement with observational constraints. For this reason, from now on we present and discuss in detail only the results obtained with 2.25. Fig. 2 (left-hand panel) also shows that the predicted CR spectrum at the location of the Earth (thick vertical line) is not representative of the average CR spectral slope (peak of the distribution). While in these examples the difference between the local and average spectral slopes is only 0.05, larger differences can be obtained by slightly changing the location of the arm as compared to the Earth. In this sense, the model is not predictive, and there is degeneracy among the simulation parameters. Although a complete study of the parameter space is beyond the scope of this paper, we outline that the proposed model gives a natural explanation for the increasing evidence that the local CR spectrum might not be representative of the average Galactic one (Ackermann etal. 2012 ; Neronov Malyshev 2015 ). Figure 2. Left-hand panel: the distribution of the simulated CR spectral index, estimated in the range 103000GeV, in the plane Z 0. The open histogram shows the results assuming an injection spectral index 2.3, while the shaded histogram is obtained for a harder injection index, 2.25. In both cases, the diffusion coefficient is proportional to E 0.4 . The vertical blue and grey lines depict the observed spectrum on the Earth, respectively. Right-hand panel: the distribution of the difference between the -ray spectral index in the plane of the sky obtained from simulations and from observations. A small latitude region has been selected: 5 b 5. The two different histograms respectively refer to the two different


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We thank the anonymous referee for helpful comments. We thank the staff of the Keck Observatory for their help in obtaining the observations presented herein. Support for this work at UCLA was provided by the Kaplan Family Student Support Fund and the W. M. Keck Foundation. The data presented herein were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. Facility: Keck:II (NIRC2). Software: NumPy (van der Walt et al. 2011 ), Astropy (Astropy Collaboration et al. 2013 ), emcee (Foreman-Mackey et al. 2013 ), SciPy (Jones et al. 2001 ), Matplotlib (Hunter 2007 ).


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 B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation O O O O O O O O O O O O O O O B-Organization B-Software I-Software I-Software O O O O O O O O O O B-Model O O O O O O O O O O O B-Organization O O O O B-Dataset B-URL 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 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 B-Model O O O B-Model O O O O O O O O O O O O O O O O O O O B-Dataset I-Dataset I-Dataset O O O O O B-Model O O O O O B-Model O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation B-Model I-Model I-Model 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 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 B-Model O O O B-Model B-Citation I-Citation I-Citation I-Citation O B-Model O O O O O O O O O B-Model I-Model I-Model I-Model I-Model B-Model O O O O O O B-Model O O B-Model I-Model I-Model B-Model B-Citation I-Citation I-Citation 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-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 B-Dataset I-Dataset I-Dataset 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 B-Model O O O O O O O O O O O O O


O O O O O O B-Organization O B-Grant O O O O O B-Organization O O B-Grant O O O O O O O B-Telescope O O O O O O B-Organization I-Organization I-Organization I-Organization O O O B-Organization I-Organization I-Organization O O O B-Organization O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization 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 B-Software I-Software I-Software I-Software B-Software O O O O B-Organization I-Organization I-Organization I-Organization B-Organization B-Location O O B-Organization I-Organization I-Organization I-Organization B-Organization B-Location O B-Collaboration I-Collaboration I-Collaboration 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 B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization O O B-Location I-Location O B-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Location O B-Organization I-Organization I-Organization O 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 I-Organization I-Organization I-Organization B-Organization B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O B-Organization I-Organization I-Organization I-Organization B-Organization O B-Location O O B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization O B-Location O O O O O O O O O O O O O O B-Organization I-Organization I-Organization I-Organization O B-Location O O B-Organization I-Organization I-Organization I-Organization O B-Location O O O O O O O O O O O O O O O O B-Organization I-Organization I-Organization B-Organization

We acknowledge financial support from the ASI-INAF grant I/037/12/0. 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 NASA. We thank the NuSTAR Operations, Software and Calibration teams for support with the execution and analysis of these observations. We also thank the Swift team for quickly approving and executing the requested ToO 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 (Caltech, USA). The Fermi -LAT Collaboration acknowledges generous ongoing support from a number of agencies and institutes that have supported both the development and the operation of the LAT, as well as scientific data analysis. These include the National Aeronautics and Space Administration and the Department of Energy in the United States; the Commissariat à l’Energie Atomique and the Centre National de la Recherche Scientifique/Institut National de Physique Nucléaire et de Physique des Particules in France; the Agenzia Spaziale Italiana and the Istituto Nazionale di Fisica Nucleare in Italy; the Ministry of Education, Culture, Sports, Science and Technology (MEXT), High Energy Accelerator Research Organization (KEK), and Japan Aerospace Exploration Agency (JAXA) in Japan; and the K. A. Wallenberg Foundation, the Swedish Research Council, and the Swedish National Space Board in Sweden. Additional support for science analysis during the operations phase is gratefully acknowledged from the Istituto Nazionale di Astrofisica in Italy and the Centre National d’Études Spatiales in France. Part of this work is based on archival data, software, or online services provided by the ASI Data Center (ASDC).


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

The authors acknowledge financial support from the Programme National de Physique Stellaire (PNPS) of CNRS/ INSU and from the Agence Nationale pour la Recherche (ANR) through the IMAGINE project. T.G. is supported by the Special Priority Program 1488 PlanetMag of the German Science Foundation. The authors wish to thank Sébastien Deheuvels for providing us with a density profile from a stellar evolutionary model.


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

CMB temperature maps for the low multipole l from other independent observations? If the answer is yes, then the reconstructed temperature map may be used to determine whether the anomalies are primordial or systematic. CMB polarization is one of the candidates. Due to the poor correlation coefficients (less than 0.5 for multipole l = 2 and l = 3), however, the reconstruction from only CMB polarization cannot achieve our goal. The scattering of CMB photons in clusters of galaxies may shed light on this attempt. The scattering of CMB photons in clusters of galaxies induces a polarization signal, which is determined by the quadrupole anisotropy in the photon distribution at the cluster location (Sazonov Sunyaev 1999 ). Therefore, the remote quadrupole in distant clusters, in principle, is investigable by the measurements of this induced polarization signal. The measurements of these signals were originally proposed to suppress the cosmic variance uncertainty (Kamionkowski Loeb 1997 ; Portsmouth 2004 ; Bunn 2006 ). Moreover, the magnitude of these signals gives some clues about the evolution of the CMB quadrupole to probe the dark energy. Of particular interest here is that it probes three-dimensional information of potential fluctuations around our last scattering surface (Seto Sasaki 2000 ). Even though this induced polarization in galaxy clusters has not been observed, its detection contains rich information for the study of cosmology. In this Letter, we propose an independent observation for the study of the CMB anomalies. We explore a practically useful cosmological probe from the measurements of remote quadrupole: the reconstruction of CMB temperature anisotropies for low multipole. Provided by the strong correlation of the remote quadrupole in low redshifts with the local CMB (Hall Challinor 2014 ), the reconstructed CMB temperature anisotropies are accurate enough for distinguishing the sources of low-quadrupole and axis-of-evil problems. 2 SIMULATIONS OF CMB SKY AND CMB INDUCED POLARIZATION IN DISTANT GALAXY CLUSTERS The CMB temperature anisotropies and E -mode polarization from a single plane wave can be written as (Ma Bertschinger 1995 ) where P l is Legendre polynomial, Δ Xl is the transfer function with X = T, E for temperature anisotropies and E -mode polarization, respectively. To compute the spherical harmonics coefficients of the temperature anisotropy and E -mode polarization a X,lm and some derivations later, we need the additional theorem of the spin-weighted spherical harmonics (Ng Liu 1999 ) where α, β and γ are the Euler angles as being composed of a rotation α around , followed by β around the new and finally γ around . Then, the spherical harmonics coefficients are On the other hand, the polarization effect in the distant clusters of galaxies arises from the presence of the quadrupole component of the CMB in the rest frame of a cluster. For a cluster located in the direction, the primordial CMB quadrupole induced


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This work has made use of data obtained at the Thai National Observatory on Doi Inthanon, operated by NARIT. We are grateful to Dr W.J. Tango for providing the data base of limb-darkening corrections and an anonymous referee for valuable comments and references. AR acknowledges support from the ESO Scientific Visitor Programme .


O O B-Person I-Person O O O O O O B-Software O O O O O O O O O B-Person I-Person O O O O O O O O O O B-Person I-Person O O 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 B-Observatory O O O B-Observatory I-Observatory I-Observatory I-Observatory O O O B-Grant B-Grant O B-Grant O O O O O O B-Organization B-Organization B-Organization O O B-Organization I-Organization I-Organization O O O O B-Collaboration I-Collaboration B-Organization O O B-Organization I-Organization I-Organization O O O B-Organization O B-Grant I-Grant O O B-Organization O B-Organization O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Location B-Survey O O O B-Location O O O O B-ObservationalTechniques O O O B-Telescope I-Telescope O B-Dataset I-Dataset 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I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O B-Organization I-Organization B-Person O O O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O O B-Grant O O O B-Organization I-Organization I-Organization I-Organization O O B-Grant B-Person O B-Person O O O O B-Organization I-Organization I-Organization B-Grant I-Grant I-Grant I-Grant B-Person O O O B-Grant I-Grant I-Grant O O O B-Organization B-Person O O O O O B-Organization I-Organization I-Organization O O O O O B-Fellowship I-Fellowship B-Person O O O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O B-Grant B-Person O O O O B-Grant I-Grant I-Grant B-Grant I-Grant I-Grant O O B-Organization I-Organization I-Organization B-Person O O O O O O B-Grant I-Grant B-Person O O O O B-Organization O O O B-Grant B-Person 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 O O O O O B-Fellowship I-Fellowship B-Person O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O B-Organization B-Organization I-Organization O O O B-Organization I-Organization I-Organization B-Grant I-Grant I-Grant I-Grant I-Grant B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O O B-Location O B-Location O O O O O O B-Software O B-Citation I-Citation O O B-Software O B-Citation I-Citation O O O O O O B-Software O B-URL O O O O B-Software I-Software I-Software O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O 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We thank Iftach Sadeh for the assistance in using the ANNz2 software, and for its continuous development, as well as Jonn Soo for very useful suggestions regarding the practicalities of the code. Ben Hoyle is acknowledged for enlightening discussions on machine-learning photo-z estima- tion. We also thank an anonymous referee for very useful comments and sugges- tions that allowed us to improve this paper. Based on data products from observations made with ESO Telescopes at the La Silla Paranal Observatory under programme IDs 177.A-3016, 177.A-3017 and 177.A-3018, and on data products produced by Target/OmegaCEN, INAF-OACN, INAF-OAPD and the KiDS production team, on behalf of the KiDS consortium. OmegaCEN and the KiDS production team acknowledge support by NOVA and NWO-M grants. Members of INAF-OAPD and INAF-OACN also acknowledge the support from the Department of Physics Astronomy of the University of Padova, and of the Department of Physics of Univ. Federico II (Naples). GAMA is a joint European-Australasian project based around a spectroscopic campaign using the Anglo-Australian Telescope. The GAMA input catalog is based on data taken from the Sloan Digital Sky Survey and the UKIRT Infrared Deep Sky Survey. Complementary imaging of the GAMA regions is being ob- tained by a number of independent survey programmes including GALEX MIS, VST KiDS, VISTA VIKING, WISE, Herschel-ATLAS, GMRT, and ASKAP providing UV to radio coverage. GAMA is funded by the STFC (UK), the ARC (Australia), the AAO, and the participating institutions. The GAMA website is http://www.gama-survey.org/ . 2dFLenS is based on data acquired through the Australian Astronomical Obser- vatory, under programme A/2014B/008. It would not have been possible without the dedicated work of the staff of the AAO in the development and support of the 2dF-AAOmega system, and the running of the AAT. Funding for SDSS-III was provided by the Alfred P. Sloan Foundation, the Partic- ipating Institutions, the National Science Foundation, and the U.S. Department of Energy Office of Science. The SDSS-III website is http://www.sdss3.org/ . SDSS-III is managed by the Astrophysical Research Consortium for the Par- ticipating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Labora- tory, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de As- trofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Van- derbilt University, University of Virginia, University of Washington, and Yale University. MBi is supported by the Netherlands Organization for Scientific Research, NWO, through grant number 614.001.451, and by the Polish National Science Center under contract UMO-2012/07/D/ST9/02785. MBi and HHo acknowledge support from the European Research Council FP7 grant number 279396. HHo acknowledges support from Vici grant 639.043.512, financed by the NWO. CB acknowledges the support of the Australian Research Council through the award of a Future Fellowship. JTAdJ is supported by the Netherlands Organisation for Scientific Research (NWO) through grant 621.016.402. HHi is supported by an Emmy Noether grant (No. Hi 1495/2-1) of the Deutsche Forschungs- gemeinschaft. MBr acknowledges financial contribution from the agreement ASI/INAF I/023/12/1. CH acknowledges support from the ERC under grant number 647112. KK acknowledges support by the Alexander von Humboldt Foundation. DP acknowledges the support of the Australian Research Council through the award of a Future Fellowship. GVK acknowledges financial support from the Netherlands Research School for Astronomy (NOVA) and Target. Tar- get is supported by Samenwerkingsverband Noord Nederland, European fund for regional development, Dutch Ministry of economic affairs, Pieken in de Delta, Provinces of Groningen and Drenthe. This work has made use of TOPCAT ( Taylor 2005 ) and STILTS ( Taylor 2006 ) software, as well as of PYTHON ( www.python.org ), including the packages N UM PY ( van der Walt et al. 2011 ), S CI PY ( Jones et al. 2001 ), and MATPLOTIB ( Hunter 2007 ).


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

We thank Flavien Kiefer, who worked with us at the beginning of the project. The invaluable advice of Shay Zucker about the analysis and the careful reading of the manuscript and very thoughtful comments of Arieh Konigl, Titos Matsakos, and Daniel C. Fabrycky are much appreciated. This research has received funding from the European Community’s Seventh Framework Programme (FP7/2007-2013) under grant-agreement numbers 291352 (ERC).


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

We thank the anonymous referee for useful comments that substantially improved this paper. Support for H.K., S.G.G., M.H., T.d.J., and C.P.G. is provided by the Ministry of Economy, Development, and Tourism’s Millennium Science Initiative through grant IC120009, awarded to The Millennium Institute of Astrophysics, MAS. H.K. and S.G.G. acknowledge support by CONICYT through FONDECYT grants 3140563 and 3130680, respectively. H.K. also acknowledges helpful support from the staffs of Cerro Pachón and NOAO South during the observing run. K.M. acknowledges financial support by Grant-in-Aid for Scientific Research (No. 23740141 and 26800100) from the Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT). The work by K.M. is partly supported by WPI Initiative, MEXT, Japan. E.Y.H. acknowledges the generous support provided by the Danish Agency for Science and Technology and Innovation through a Sapere Aude Level 2 grant. 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.


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We are grateful to the anonymous referee for his/her careful reading and helpful and constructive comments that improved the paper. N.M. thanks the École Normale Supérieure de Cachan and the Laboratoire AstroParticle et Cosmologie for financial support in the early stage of this work. B.S. acknowledges financial support from MIUR PRIN2010-2011 (J91J12000450001), from the PRIN-MIUR 201278X4FL grant, from a PRIN-INAF/2012 Grant, from the inDark INFN Grant and from the Consorzio per la Fisica di Trieste. A portion of the research described in this paper was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.


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

and FRI classes. However, it performs worse overall for the FRIIs, as shown in Table 9 . This may be due to the more complex decoder confusing radio emission from the FRIIs with noise. Table 9. The average metrics (in percentages) across each of the classes in the original LOFAR data set, for the inc. decoder CapsNet model. Five runs were done in total, using 600 samples in the test set. As the default CapsNet model performs better overall compared to the other two CapsNet models, it is chosen as the basis of comparison against the two ConvNet models across the original fits and masked 4rms sigma-clipped data sets. The default CapsNet model still performs significantly worse compared to the two ConvNets, as it is beyond both their 95 per cent confidence intervals, across all metrics. The variability in metrics is higher for the original data set compared to that of the two ConvNets, as is evident in the generally increased confidence intervals of the CapsNet model, in Table 7 , particularly for the FRIIs. Fig. 8 shows the Receiver Operating Characteristic (ROC) curves across the default capsule network and ConvNet-4. ROC curves plot the true positive rate (recall) against the false positive rate. Figure 8. ROC curves for both a single run with the default CapsNet model and the ConvNet-4 model. The curves show that ConvNet-4 outperforms the default CapsNet across all the classes. In a first attempt to use the default CapsNet model (containing 58M free parameters), we observed a clear overfitting, owing to the large number of free parameters compared to the number of training images. Despite this, the model still achieved very similar results to the models using many fewer parameters quoted in this work. Table 10 shows the labels and prediction vector for some sources that the Capsule network could not reliably classify , as probabilities higher than 0.5 across two classes were attained. Table 10. The labels and corresponding probability vector of the default CapsNet network predictions, using four examples of sources shown in Fig. 10 , having probabilities greater than 0.5 across two classes. 5.2 LOFAR original and augmented images We augmented the images with translation, rotation, and flipping as outlined in Section 3.2 , keeping the distribution of FRI and FRII sources the same as in the original data set. Table 1 gives the number of original and augmented images. There are again 79 per cent and 21 per cent of the original samples used in training and testing, respectively. 5.2.1 ConvNet-4 and ConvNet-8 We applied both ConvNet-4 and ConvNet-8 models to the original and augmented data set, with the results shown in Tables 5 and 6 . The overall metrics are significantly better (Avg. Recall = 93.4 and 94.3) than was observed when the same model was used on the original images (Avg. Recall = 88.7 and 91.2 for ConvNet-4 and ConvNet-8, respectively), therefore both models benefit from data augmentation. The confidence intervals are also


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O O O B-Software O O O O O O O O O O B-Software I-Software B-Software I-Software I-Software I-Software I-Software 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 B-ObservationalTechniques I-ObservationalTechniques I-ObservationalTechniques B-ObservationalTechniques O O O O O O O O O O O O O O O B-ObservationalTechniques 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-ObservationalTechniques O O O 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 B-ObservationalTechniques O O O O O O O O O O O O B-CelestialObject 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 B-ObservationalTechniques O O O O O O O B-ObservationalTechniques O 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O 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 B-ObservationalTechniques O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O B-ObservationalTechniques O B-Formula I-Formula I-Formula 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 O O O O B-ObservationalTechniques O O O O O O O O O O O B-ObservationalTechniques B-Formula I-Formula I-Formula O O O B-Formula I-Formula I-Formula O B-Citation I-Citation I-Citation I-Citation O 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 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 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-ObservationalTechniques I-ObservationalTechniques O O O O O O O O B-ObservationalTechniques 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

standard packages in iraf . 1 Aperture photometry was carried out using the task daophot ii (Dominion Astrophysical Observatory Photometry software, Stetson 1987 ). Signal-to-noise ratio was found to peak for a photometric aperture radius nearly two times the seeing disc whose FWHM was determined by averaging the profiles of five fairly bright, unsaturated stars recorded in the same CCD frame. The measured instrumental magnitudes were then used to derive the ‘differential light curves’ (DLCs) of the target AGN relative to two (steady) comparison stars, as well as the star−star DLC for the session (see Goyal et al. 2013 , for details of the procedure). In Fig. 1 , we show the DLCs obtained from one of the 30 sessions; the DLCs for all 30 monitoring sessions are presented in the online Fig. 1. Figure 1. An example of the DLCs obtained in the present study. The target AGN is the BAL quasar J090552.41+025931.5. DLCs for all the 30 sessions are presented in online Fig. 1. The date and duration of monitoring and the telescope used are mentioned at the top. The profile in the upper panel presents the DLC of the chosen two comparison stars (‘star–star’ DLC). The two middle profiles display the DLCs of the BAL quasar relative to the two comparison stars, as mentioned in the labels on the right side. The profile in the bottom panel shows the variation of the seeing disc (full width at half-maximum, FWHM) through the monitoring session. 4 STATISTICAL ANALYSIS AND RESULTS Following Goyal et al. ( 2013 ), we applied the widely used F η test to the DLCs of the target AGN relative to the two comparison stars (s1, s2). The parameter F η computed for the two AGN DLCs is defined as Here Var( q − s j ) is the variance of the ‘AGN− j th comparison star’ DLC, where j = 1,2 and σ i ,err ( q − s j ) are the photometric error of the N individual data points in the DLC (as returned by the daophot routine). For each of the two DLCs, i = 1 to N and η = 1.5 (see Goyal et al. 2012 ). For each of the two DLCs of the target AGN, online Table 2 (Column 7) compares the computed values of F η with the critical value of F (=). The values of α are set at 0.05 and 0.01, corresponding to 95 per cent and 99 per cent confidence levels for INOV detection. If the computed F η for a DLC exceeds , the null hypothesis (i.e. no variability) is rejected at the corresponding confidence level. We thus classify a DLC as variable (‘V’) if its computed F η > F c (0.99); probably variable (‘PV’) if the F η lies between F c (0.95) and F c (0.99), and non-variable (‘NV’) in case F η F c (0.95) (Goyal et al. 2013 ). Column 10 in the online Table 2 lists the session averaged photometric accuracy of the measured differential magnitudes . It is estimated using the two AGN-star DLCs and is nearly always better than 3 per cent (median = 2.0 per cent). 5 DISCUSSION AND CONCLUSION The main result from this study (online Table 2) is the non-detection of INOV in any of the 30 sessions devoted to the


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the r- process event would overpower signatures left over from any neutron-capture processes that may occur before or after. But to make matters more complication, at least two stars in Ret II display rather low Sr and Ba values (not shown in the figure but see fig. 3 in Ji et al. 2016c ), and the UFDs without clear r -process enrichment do contain a lot of stars with significant amount of s -process material. Nevertheless, our results clearly show that for stars with measurable neutron-capture element abundances, AGB stars alone are not sufficient source to explain the origin of Ba and Sr for these stars. However, we also note that likely more stars exist in these systems that have lower Sr and Ba measurements than what is represented with the current observed sample. 2 Those stars (1) might not yet have such measurements due to being faint and corresponding poor data quality especially in the blue spectral regime preventing even meaningful upper limits, (2) or these stars simply have not even been observed yet at all. Such a putative low Sr-Ba-population may well be explained solely with an AGB origin scenario. Future observations can hopefully shed further light on this issue so that our predictions could be further put to the test. In fact, there are hints of this being the case. Metal-poor halo stars have [Ba/Fe] going down to about [Ba/Fe] ∼ −2.0 which is roughly at the level of the simulated stars formed last in our simulation (light green circles in the figure). Furthermore, all stars with red symbols with [Ba/Fe] > −2.0 form a branch not unlike that of MW stars albeit offset to lower [Ba/Fe] values. The lower of these stars overlap with the top end of the simulated later-time stars – clearly more overlap would be achieved with improved spectral line detections should additional data become available (e.g. with the Giant Magellan Telescope ). Figure 3. Observed abundances in UFDs overlaid with our RMS model results for [Ba/Fe] (top panels) and [Sr/Fe] (bottom panels). Symbols and colours are the same as in Fig. 2 . The simulated abundances agree well with the observed abundances, including the largely flat trend with [Fe/H]. The scatter of [Ba/Fe] and [Sr/Fe] in each galaxy is also an interesting piece of information. Observationally, Bootes I (Boo I), Carina II (Car II), and Coma Berenices (ComBer) show significant scatter while most other UFDs do not. We also note that the number of observations is limited due to observational difficulties such as stars being too faint to obtain higher signal-to-noise observations while also requiring high spectral resolution. Therefore, even for UFDs with little apparent scatter, significant scatter in [Ba/Fe] and [Sr/Fe] may still be present within. In our simulation, large scatter is observed both in the L- and M-UFDs. The Ba content of S-UFD is too little, and therefore we cannot discuss the scatter. There are two kinds of inhomogeneities to diversify the abundances of the neutron-capture


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ACKNOWLEDGEMENTS We want to thank all people in social networks that shared their pictures and data and that finally allowed professional and amateur astronomers to work on this. We are particularly grateful to the MIDAS survey for discovering the impact and announcing early without any embargo. This generosity allowed all of us to discover the data hidden in pictures and videos. We especially want to thank the careful review of the first versions of the manuscript made by Dr. Rodrigo Leiva from Southwest Research Institute, his suggestions and comments were very important for our work. We would also like to thank all the amateur astronomers that contributed the images necessary for this work: Petr Horálek from Cape Verde, Gregory Hogan from USA, Fritz Helmut Hemmerich from Canary Islands, Libor Haspl from Czech Republic, Robert Eder Artis from Austria, Dr. Sighard Schräbler and Dr. Ulrike Löffler from Germany, and a couple more amateur astronomers who provided their images, but were unable to meet the scientific precision required. Last, but not least, we greatly appreciate the insightful comments of Maria Gritsevich, Janne Sievinen, and an anonymous colleague. Their skepticism, criticism, and key suggestions shaped this work to its final form.


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Section 3.3 ). A two-sided KolmogorovSmirnov (KS) test on the redshift and i -band magnitude distributions of the matched samples return probabilities of 0.999863 and 0.984483, respectively, thus there is no evidence for rejecting the null hypothesis that the two histograms are drawn from the same underlying distributions of these two observables. Figure 1. The i -band luminosity and redshift ranges for the quasars detected in the FIR at 2 (red points), and the matched sample of quasars undetected at 1 (blue points). The histograms on the bottom and side show the normalized distributions of the respective populations in redshift and L i . Fig. 2 shows the cumulative distributions of C iv blueshift for the FIR-detected and FIR-undetected matched samples. The FIR-detected quasars show larger blueshifts than is expected from their FIR-undetected counterparts, with a two-sided KS test returning a probability that the two distributions are drawn from the same underlying sample of 10 12 . Using 3 and 4 FIR detections instead of the 2 detections, the KS test returns probabilities of 10 8 and 0.0001 that the FIR-detected and FIR-undetected distributions are from the same underlying samples. The 4 sample contains only 140 FIR-detected objects, and thus suffers from the small sample size. Recall that BALQSOs have been removed from the sample, so the difference cannot be attributed to absorbed flux in the blue wing of the emission line. While a nuclear outflow is not always accompanied by a FIR excess, for the sample as a whole, at a given optical luminosity, FIR-bright quasars have larger C iv blueshifts than FIR-undetected quasars. Figure 2. Cumulative distribution of the blueshift of the C iv emission line for the quasars detected in the FIR at 2 (red solid line), and those undetected at 1 (blue dashed line). The FIR-detected quasars have larger C iv blueshifts, indicating more prominent nuclear-driven outflows. The bottom panel shows normalized histograms of the FIR-detected and FIR-undetected C iv blueshifts, in red and blue, respectively. 3.3 Red or reddened quasars Vigorous SF is known to be a dusty process, so if the FIR flux is at least partly from SF, we may expect the FIR-detected quasars to be reddened by dust in the host galaxies, as evidenced by redder optical colours with respect to the general quasar population. Using the same FIR-detected and FIR-undetected matched samples as before, we compare the SDSS g r colours of the two samples. For these luminous quasars, the optical photometry is entirely dominated by emission from the quasar, even if accompanied by a starburst in the host galaxy. To remove the redshift dependence of quasar colours, the colour of an unreddened model quasar similar to that from Maddox etal. ( 2008 ) is subtracted from each object to create a normalized colour. Using the normalized colour, with the redshift dependence removed, creates a distribution that better illustrates departures from the median colour of a