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 O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation 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 B-Person I-Person O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation B-Person O O O B-Organization I-Organization O O B-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship O O O B-Organization I-Organization I-Organization I-Organization O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization O O B-Grant B-Person O O O B-Fellowship I-Fellowship O B-Fellowship I-Fellowship O O B-Organization I-Organization B-Person O O O O B-Observatory I-Observatory I-Observatory O O B-Fellowship I-Fellowship B-Person O O O O B-Person B-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship O O B-Fellowship O O B-Software B-Citation I-Citation I-Citation O B-Software B-Citation I-Citation O B-Software B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Software B-Citation I-Citation O B-Software B-Citation I-Citation I-Citation I-Citation O B-Software B-Citation I-Citation O

ACKNOWLEDGEMENTS The authors thank Charlie Conroy for useful discussions and for providing comments on a draft of this paper. We thank Steve Finkelstein, Fred Davies, and Brad Greig for useful discussions and for providing: the model from Finkelstein et al. ( 2019 ), and posteriors from Davies et al. ( 2018 ) and Greig et al. ( 2019 ), respectively. We thank Austin Hoag for sharing the posterior from Hoag et al. ( 2019 ). CAM acknowledges support by NASA Headquarters through the NASA Hubble Fellowship grant HST-HF2-51413.001-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555. RPN gratefully acknowledges an Ashford Fellowship and Peirce Fellowship granted by Harvard University. ST is supported by the Smithsonian Astrophysical Observatory through the CfA Fellowship. JL is supported by an NSF Astronomy and Astrophysics Postdoctoral Fellowship under award AST-1701487. Software : ipython (Pérez Granger 2007 ), matplotlib (Hunter 2007 ), numpy (Van Der Walt, Colbert Varoquaux 2011 ), scipy (Oliphant 2007 ), astropy (Robitaille et al. 2013 ), dynesty (Speagle 2019 ).


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u g as well, the sample increases to 114. We also see that as we impose even stricter cuts, we can decrease the number of SDSS objects by an order of magnitude, while keeping nearly all of the known lenses. We do not use the stricter cuts in this implementation, but they could be used in the future with larger data sets to keep things more tractable. 3.2.4 Choosing features We build our features from combinations of magnitudes in different bands. Fig. 1 shows the distribution of our training set data in various colour and magnitude spaces. As can be seen, different kinds of objects occupy specific locations in feature space. By choosing features that best distinguish between types of objects and combining them into one high-dimensional space, our model can more easily separate the different populations of objects. Figure 1. Colourcolour plots showing the locations of our training sets in feature space. The red, green, blue and orange points represent the point-like QSOs, extended QSOs, simulated lensed quasars and blue cloud galaxies, respectively. The black stars are known lensed quasars that lie in the SDSS footprint. The dashed lines show the colour cuts listed in equation ( 6 ). Dotted lines represent either cuts that are within or statements or other cuts often used to eliminate contaminants. The black stars represent 128 known lenses that lie in SDSS, found by various selection techniques. Many have similar colours to point-like quasars, indicative of the colour selection step described by Oguri etal. ( 2006 ). Others have redder colours, corresponding to either Type-II AGN sources or bright lensing galaxies. We are mainly concerned with finding blended, small-separation lenses, since the large separation counterparts are more likely to have been found already. Therefore, we are less interested in the objects that fall on the point-like QSO locus. The dashed lines in the plot show the typical cuts that we use when selecting objects. In order to include lenses that have larger contributions from the lensing galaxy, we use relatively loose cuts in u g and W 1 W 2. However, known lenses do not lie predominantly at low W 1 W 2 or high u g . Additional metrics, such as those using the K band, can be useful for trimming contaminants in these regimes, as is done by Ostrovski etal. ( 2017 ), but this introduces two issues for our purposes. First, many of the simulated lenses are particularly bright in K . This is because the lenses are constructed via sparse interpolation over 2MASS magnitudes that suffer from Malmquist bias. Secondly, we are introduced with a depth-versus-footprint trade-off that must be addressed. Surveys such as the Two Micron All-Sky Survey (2MASS) cover the whole sky, but are not always deep enough for our purposes. In fact, only 16percent of our SDSS training set objects have valid K magnitudes in 2MASS. Deeper surveys such as the UKIRT Infrared Deep Sky Survey (UKIDSS) and the VISTA Hemisphere Survey (VHS), on the other


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

the strongest deviations growing at the particle Nyquist wavenumber k Ny (indicated by a dotted vertical line) – and linear perturbation theory is not recovered even on the largest scales. While we show results only for 1LPT and at starting time z start = 49, this result is almost independent of the used LPT order. Since the error is driven by a spurious growing mode, its amplitude is to first order simply determined by the starting time – with earlier starts leading to a larger error. It is also insensitive to the specific choice of softening length, as long as it is appreciably smaller than the mean particle separations. Once the small scales have shell-crossed and collapsed, at z ≲ 2.5, the spurious growth is slowed. Figure 6. Evolution of the baryon–CDM density difference power spectrum P bc in a gravity-only N -body simulations, where both baryon and CDM are simulated with N -body particles with small softening. Simulation results in solid lines (faint dashed lines) with 2 × 512 3 (2 × 1024 3 ) particles initialized at z start = 49 ( z start = 24) using 1LPT (3LPT) ICs, by suitably backscaling the amplitudes from Class at the reference redshift z ref = 2.125. Those backscaled power spectra are shown as black dashed lines, before applying the particle realization. The vertical dotted line indicates the particle Nyquist wavenumber. Top panel: Simulation results where is absorbed into particle displacements (using equation 14 ). We observe the well-known spurious growing mode due to discreteness errors in the particle discretization of the fluids (the discrete δ bc is not compensated at the discretization scale, if not sufficiently smoothed by gravitational softening, and therefore grows). Bottom panel: Same as above but now is absorbed into perturbed particle masses (using equation 15 ). Here, discretization errors are strongly suppressed, and the late-time power asymptotes to a constant noise spectrum beyond k Ny . These errors are furthermore vastly reduced when 2 × 1024 3 particles and 3LPT ICs are used. In stark contrast, the situation improves dramatically when the initial density perturbation is incorporated by perturbing the initial particle masses (using equation 15 ), instead of adding initial displacements. This result is shown in the lower panel of Fig. 6 in solid lines with the same particle load and resolution as above, while the results from the higher resolution simulation (2 × 1024 3 particles, 3LPT with z start = 24) are shown as faint dashed lines. In this case, P bc is exactly constant on large scales and exhibits non-linear growth at intermediate scales, as expected. On the smallest scales, we observe that in all cases the solution asymptotes to a constant power spectrum for k ≳ k Ny with a scaling inversely proportional to the particle number (as is expected for shot noise in the power spectrum, e.g. Colombi et al. 2009 ). We expect that this behaviour close to the particle Nyquist wavenumber is thus a combination of


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comprehensive data on jet motions come from studies of the nearest sources, particularly the Fanaroff–Riley type-I (FR I; Fanaroff Riley 1974 ) radio galaxies M87 (Reid et al. 1989 ; Biretta et al. 1995 ; Cheung et al. 2007 ; Kovalev et al. 2007 ) and Centaurus A (Goodger et al. 2010 ; Müller et al. 2014 ). M87 is a nearby source, at a distance of only 16.7 Mpc (Blakeslee et al. 2009 ), that hosts a bright jet spanning 20′′, ∼1.6 kpc projected, from the central AGN of the system. Kiloparsec-scale, knotted structure has been directly observed within the jet using radio, optical, and X-ray observations (e.g., Owen et al. 1989 ; Sparks et al. 1996 ; Harris et al. 1997 ; Perlman et al. 2001 ; Marshall et al. 2002 ; Perlman Wilson 2005 ; Meyer et al. 2013 ). Previous measurements of proper motions in M87 have detected sub-relativistic speeds within a parsec of the AGN using the Very Long Baseline Interferometry (VLBI; Reid et al. 1989 ; Kovalev et al. 2007 ; Mertens et al. 2016 ; Walker et al. 2018 ). Superluminal motions on larger-scales were detected from the VLBI (Cheung et al. 2007 ; Giroletti et al. 2012 ), the Very Large Array (VLA; Biretta et al. 1995 ), and the Hubble Space Telescope ( HST ; Biretta et al. 1999 ; Meyer et al. 2013 ). While proper motions have yet to be detected at higher energies, measuring the kinematics of X-ray-emitting regions potentially provides the best probe for sites of particle acceleration because high energy radiation is produced by more energetic particles. Recent work from Snios et al. ( 2019 ) measured X-ray proper motions for the first time in the jet of Centaurus A, at a distance of 3.8 Mpc (Harris et al. 2010 ), by applying new methods to analyze Chandra observations. We may apply those techniques to measure proper motions in the X-ray jet of M87. In this work, we investigate proper motions and brightness variations within the X-ray jet of M87 using two Chandra observations separated by 5 yr. The remainder of the paper is structured as follows. Section 2 discusses the details of the Chandra observations and the corresponding data reduction. In Section 3 , difference maps are generated from the coaligned observations and statistical uncertainties are quantified. Evidence of proper motion for the innermost knots of the X-ray jet are presented in Section 4 . In Section 5 , the proper motion results are compared with measurements from other wavelengths. Lastly, brightness changes of the knots are utilized to investigate both the primary mechanism for fading and the magnetic field strengths of the knots. 2. Data Acquisition and Reduction The jet of M87 is known to be a bright X-ray source. In existing Chandra observations with the Advanced CCD Imaging Spectrometer (ACIS), several features of the jet, including the AGN and HST-1, are significantly affected by pile-up (>0.25 counts frame −1 ; Marshall et al. 2002 ; Wilson Yang 2002 ; Harris et al. 2003 ). ACIS observations were initially considered for our


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r in = 0.1, and magnetic dipole moment μ 26 = 0.5. It is seen that the model can produce the values measured in the RMSP and LMXB states, consistently with the observed X-ray luminosities. The in the LMXB state is about six times greater than that in the RMSP state. This changes r in only by a small factor of ∼1.09 due to very weak dependence of r in on . The resultant increase in the spin-down torque is also small (∼27 per cent) in good agreement with the observations. Since the accretion and dipole torques are only a few per cent of the torque produced by the disc–field interaction, the onset of accretion with the transition to the weak-propeller phase does not affect significantly. With μ 26 = 4.7, estimated in our model, the dipole torque is found to be about five and seven times smaller than the observed torques in the RMSP and LMXB states, respectively. We note that for r in scaling with r A in the propeller phase, the magnetic torque would be proportional to , implying changes by a factor of ∼5, not in agreement with the measured torques. Table 1. The model parameters and results for J1023. These results are obtained with η = 0.78, Δ r / r in = 0.1, and magnetic dipole moment μ 26 = 0.5. The L x, model values for the high mode and the low mode correspond to L * and L d , respectively. In the last column, Γ acc and Γ tot are the magnitudes of the accretion (spin-up) and the spin-down torques, respectively. For the RMSP state, the observed L x ∼ 10 32 erg s −1 given in Table 1 is the 0.5–10 keV luminosity estimated by Archibald et al. ( 2010 ). From the spectral fits, Li et al. ( 2014 ) estimated that the 3–79 keV luminosity is 5 × 10 32 erg s −1 . In both observations, the X-ray flux was found to be modulated with the orbital motion, which is likely to be due to an intra-binary shock produced by the interaction of pulsar wind with the matter outflowing from the companion. A shock region close to the inner Lagrangian point that is eclipsed when the companion star is between the Earth and the neutron star could explain the observed modulations (Archibald et al. 2010 ; Bogdanov et al. 2011 ; see also Li et al. 2014 for a different interpretation). From the orbital modulations, it is expected that at least half of the X-rays are produced at the shock region in the RMSP state. These observations do not exclude a continuous emission from the disc with r in close to r co characterized by the conditions around the inner disc in the RMSP state. A large fraction of the total L x is emitted by the intra-binary shock modulated by the orbital motion, while the remaining smaller fraction could be produced by the inner disc. The X-ray luminosity estimated in our model is compatible with (smaller than) the continuous portion of the total X-ray luminosity in the RMSP state. We note that the disc emission spectrum could significantly change in the RMSP state due to strong propeller mechanism which can produce not only mass outflow but also hot matter


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ACKNOWLEDGEMENTS Development of the robotic SL-SLODAR was funded by the European Southern Observatory (ESO). The authors would like to thank the staff at Paranal Observatory for their assistance with the robotic SL-SLODAR project. TB, JO, and RWW are grateful to the Science and Technology Facilities Committee (STFC) for financial support (grant reference ST/P000541/1). The authors would like to thank the anonymous reviewer for their constructive comments that helped to improve the paper. This research made use of python including numpy, scipy , (van der Walt, Colbert Varoquaux 2011 ) and matplotlib (Hunter 2007 ).


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ACKNOWLEDGEMENTS We thank the anonymous referee for comments on the manuscript. GL acknowledges support from the European Union’s Horizon 2020 Sundial Innovative Training Network, grant no. 721463. This work has made use of the HyperLeda data base (Paturel et al. 2003 ).


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binaries, CVs, and qLMXBs in the comparison samples. The RS stars also fall in the same region as the SSGs. This overlap with the active binaries hints that heightened chromospheric activity may be responsible for the X-ray activity observed for at least some, and perhaps many, SSG and RS stars. The diminished overlap between the SSG and BY Dra stars (which are also chromospherically active) is due to the generally lower optical luminosities of most BY Dra stars in the comparison samples relative to the SSGs. The X-ray luminosities of the SSGs agree well with both the BY Dra and RS CVn active binary samples. 5.3. Frequency of SSGs across Different Star Clusters Figure 7 shows the number (top panel) and specific frequency (bottom panel) of SSGs as a function of the cluster mass for all clusters with SSGs in our sample. The black symbols in this figure show only the SSGs that are the most probable cluster members and are within our minimum radius completeness limit, and the gray symbols show all SSGs. The Pearson’s correlation coefficient, relating cluster mass and number of SSGs, for the full sample of highly likely cluster members is 0.925. However, this value is large because of ω Cen and 47 Tuc. Excluding these two clusters (the only ones in our sample with masses above 10 6 ) results in a Pearson’s correlation coefficient of −0.278. Furthermore, a test indicates that this limited sample of clusters (still excluding ω Cen and 47 Tuc) is consistent with a flat line at the mean value of SSGs. This result holds even if we include ω Cen and 47 Tuc in this test (using ), with a reduced value of . We conclude that, for this sample, there is no significant correlation between the number of SSGs and the cluster mass. This lack of a correlation in versus results in a clearly visible trend in the bottom panel of Figure 7 : the number of SSGs per unit mass increases toward lower-mass clusters. A test shows that the full sample of SSGs is inconsistent with a flat line at the mean value at very high significance (). The same result holds true for the open and globular clusters individually. The open clusters have a significantly higher specific frequency of SSGs than do the globular clusters. If we take the mean specific SSG frequency for the open clusters of ∼10 −3 −1 and extrapolate that to the globular cluster regime, this would predict about 100 SSGs in a globular cluster with a total mass of 10 5 . The maximum number of SSGs known in any cluster is 19 in ω Cen, followed by eight in 47 Tuc (both of which have masses ). A hint of this trend was also noted by Cool et al. ( 2013 ) in comparing their ω Cen SSG sample to those in M67 and NGC 6791. This is now verified with the larger sample of SSGs studied here, and we discuss the implications of this result in Section 6 . 5.4. Summary of Demographics We conclude that the SSG region has an elevated frequency of variable stars and X-ray sources relative to stars of similar luminosities in the normal


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We acknowledge valuable comments from an anonymous referee. L.C. and R.C. are supported by YDUN grant DFF 4090-00079. S.D.V. is supported by the French National Research Agency (ANR) under contract ANR-16-CE31-0003 BEaPro. S.L. has been supported by FONDECYT grant number 1140838 and partially by PFB-06 CATA. A.d.U.P. and C.T. acknowledge support from Ramón y Cajal fellowships, and with RSR a BBVA Foundation Grant for Researchers and Cultural Creators, and the Spanish Ministry of Economy and Competitiveness through project AYA2014-58381-P. G.B. acknowledges support from the National Science Foundation through grant AST-1615814. Z.C. acknowledges support from the Juan de la Cierva Incorporación fellowship IJCI-2014-21669 and from the Spanish research project AYA 2014-58381-P. P.J. and K.E.H. acknowledge support by a Project Grant (162948–051) from The Icelandic Research Fund. J.J. acknowledges support from NOVA and NWO-FAPESP grant for advanced instrumentation in astronomy. R.S.R. acknowledges support from ASI (Italian Space Agency) through the Contract No. 2015-046-R.0 and from European Union Horizon 2020 Programme under the AHEAD project (grant agreement No. 654215). M.V. gratefully acknowledges financial support from the Danish Council for Independent Research via grant no. DFF 4002-00275.


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We acknowledge L. Fuhrmann for careful reading and for useful comments and suggestions to the manuscript. We thank the anonymous referee for comments and criticism that helped to improve this manuscript. C.M.F. was supported for this research through a stipend from the International Max Planck Research School (IMPRS) for Astronomy and Astrophysics at the Universities of Bonn and Cologne. Part of this work was supported by the COST Action MP0905 “Black Holes in a violent Universe”. E.R. acknowledges partial support from MINECO grants AYA2009-13036-C02-02 and AYA2012-38491-C02-01 as well as Generalitat Valenciana grant PROMETEO/2009/104. M.P. acknowledges financial support from MINECO grants AYA2010-21322-C03-01, AYA2010-21097-C03-01, and CONSOLIDER2007-00050. This work is based on observations with the VLBA, which is operated by the NRAO, a facility of the NSF under cooperative agreement by Associated Universities Inc. This research made use of data from the MOJAVE database that is maintained by the MOJAVE team ( Lister et al. 2009 ).


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We thank Andy Strong, Regina Caputo, and an anonymous referee for a detailed reading of this paper and for several valuable suggestions. This work was supported by NSF grant AST-1263034, “REU Site: Astronomical Research and Instrumentation at Texas AM University.” We acknowledge support from NASA Astrophysics Theory grant NNX12AC71G. Work at NRL is supported by NASA. 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. This work performed in part under DOE Contract DE-AC02-76SF00515. Software: Astropy (Astropy Collaboration et al. 2013 , 2018 ), Jupyter (Kluyver et al. 2016 ), Matplotlib (Hunter 2007 ), NumPy (van der Walt et al. 2011 ), Pandas (McKinney 2010 ), SciPy (Jones et al. 2001 ).


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We acknowledge the support of the U.S. National Science Foundation (NSF) for WHAM development, operations, and science activities. The survey observations and work presented here were funded by NSF awards AST-0607512 and AST-1108911. R.A.B. acknowledges support from the NASA grants NNX10AI70G and HST -GO-13721.001-A. A.S.H. acknowledges support from NASA grant HST -AR-14297.001-A. We would also like to acknowledge the support of NSF REU Site grant AST-1004881 and the contributions of undergraduate researchers Peter Doze (Texas Southern University), Andrew Eagon (University of Wisconsin-Whitewater), and Alex Orchard (University of Wisconsin-Madison) to the initial analysis of the WHAM all-sky survey results.


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E.N. thanks the staff of the Department of Astronomy of the University of Guanajuato for the continuous support during the development of this work.


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We thank the referee for very useful comments. We are grateful for support from the National Natural Science Foundation of China through grants 11373010 and 11473037.


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Acknowledgments This work is based on observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the Science and Technology Facilities Council (United Kingdom), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia), Ministério da Ciência e Tecnologia (Brazil) and south-eastCYT (Argentina). CB thanks to CNPq for financial support. RAR. acknowledges support from FAPERGS (project N0. 2366-2551/14-0) and CNPq (project N0. 470090/2013-8 and 302683/2013-5). This research has 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. We acknowledge the usage of the HyperLeda database ( http://leda.univ-lyon1.fr ).


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Wavelength 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 B-Wavelength I-Wavelength O O O B-Wavelength O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey O O O O O O O O O O O O O O O B-Telescope O B-Telescope O O B-Telescope O O O B-Telescope O O O O O O O O O O O O B-Telescope O B-Telescope O O O O O O O O O O O B-Telescope O O O O O O O O O B-Telescope B-Instrument O O O O B-Instrument B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O B-Instrument B-Wavelength I-Wavelength I-Wavelength O O O B-Instrument O O O B-Wavelength I-Wavelength I-Wavelength O O O O O O O O B-Telescope B-Instrument O O O O

and, instead, seem to confirm the action of a predominantly “high-soft” radiation field. 9. Dust and molecular gas-to-stellar mass ratios that are typically much higher than can be explained by stellar recycling from the aging burst population. This indicates that the dust and gas reservoirs were not entirely expelled during burst truncation. 10. Negative trends of PAH/TIR and dust-to-stellar mass ratio as a function of post-burst age, consistent with observations of dusty ETGs, indicating the effect of accumulating grain destruction and an incipient transition to virialized early-type gas conditions. 11. Little evidence for significant AGN activity beyond potential low-level activity associated with their existing LINER classifications. The high-ionization emission line [O iv ] is only detected in one source (weakly), and PAH band ratios show no evidence of small-grain depletion. One galaxy (2360_167_53728) displays extreme AGN colors in the near-IR WISE bands, with evidence for a very hot dust component to its SED. The presumed AGN is likely deeply embedded. Three sources appear to display an excess at 1.4 GHz, relative to the radio–infrared correlation, potentially indicating the presence of radio AGN activity. One source, in particular, is clearly a radio galaxy—the same source that is detected in [O iv ]. 12. Low star formation rates and efficiencies. Offsets from the star-forming main sequence are typically >10 and reach factors of >100 in some cases, for a variety of tracers, characterizing these galaxies as truly quiescent. Offsets from the KS relation exist for most sources and range from ∼3 to >10 for reliable tracers, depending on the comparison sample considered. These results paint a compelling picture: one of galaxies whose star formation was, indeed, rapidly truncated, and which are transitioning away from compact starbursting systems, but in which the gas and dust have not been completely expelled and instead are supported against further star formation by turbulent or mechanical heating. The resulting dense, modestly aged burst stellar populations appear to provide a “high-soft” radiation field, which dominates the unusual ISM energetics of galaxies seen after the fall from a prior star-forming peak. Appendix A Photometric Tables and SDSS Spectra In Tables 5 – 7 we present the photometry for the sample from the Spitzer , Herschel , and WISE space observatories, respectively. Spitzer photometric data only exist for the original sample of 15 sources, while Herschel and WISE data are shown for the full sample of 33. Table 5 Spitzer Photometric Data Note. Column (1): galaxy ID. Columns (2)–(5): Spitzer IRAC flux densities. Column (6): IRAC 8 μ m FWHM. Computed as the geometric mean of the major and minor axes of 2D elliptical Gaussian. Column (7): ratio of synthetic IRAC 8 μ m, computed from the IRS spectrum, to global 8 μ m; used for spectral scaling of SL. Columns (8)–(10): Spitzer MIPS flux densities. Column (11):


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ACKNOWLEDGEMENTS We thank Chris Thompson and the anonymous referee for comments that helped to clarify the presentation of this work. SKL acknowledges support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 665778, via fellowship UMO-2016/21/P/ST9/03689 of the National Science Centre, Poland. Both authors thank the PHAROS COST Action (CA16214) for partial support. This work used the DiRAC@Durham facility managed by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility ( www.dirac.ac.uk ). The equipment was funded by BEIS capital funding via STFC capital grants ST/P002293/1, ST/R002371/1, and ST/S002502/1, Durham University and STFC operations grant ST/R000832/1. DiRAC is part of the National e-Infrastructure.


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-CelestialObjectRegion I-CelestialObjectRegion O O O B-Mission O O O O O O O O O O O O O B-CelestialObject O O O O O O O B-CelestialObject 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 B-CelestialObjectRegion 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-Mission O O O O O O O O O O O O O O O O O O O O O O O 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 B-Mission O O O O O O O O O B-CelestialObject O O O O O O O O O O B-CelestialObject O O O O O O O O B-Instrument O O B-Model 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 B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O B-CelestialObject O O O O O O O O B-Mission O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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-CelestialObjectRegion I-CelestialObjectRegion I-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-CelestialObject 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 B-CelestialObject 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 B-CelestialObject O O O O O O O O O O

human beings in near-Earth space, and provides a certain reference value in designing spacecraft materials in future deep-space exploration missions. Figure 8. GCR radiation dose rates on the lunar surface measured by the LRO/CRaTER. The horizontal dashed–dotted line marks the peak value of does rate in the solar minimum P 24/25 . 4. Conclusions The Sun was extraordinarily quiet during the recently complete solar cycle 24, with very low sunspot numbers, an extremely flat HCS, a reduced CME eruption rate, and a weak interplanetary magnetic field and turbulence level. The observed GCR intensities (both in interplanetary space and at the ground level) are sensitive to the heliospheric conditions, the so-called solar modulation. In this work, we focus on the variations of the GCR intensities for the period from 1997 through 2020 with measurements from the ACE/CRIS instrument, and investigate the influence of inner heliospheric environments on the GCR intensities. In addition, the long-term variations of the ground-based NM count rates are also studied. The conclusions are summarized as follows. 1. The GCR intensities observed at 1 au reach the highest levels in the solar minimum P 24/25 since the launch of the ACE spacecraft, which is ∼25% higher than that in the solar minimum P 22/23 and ∼6% higher than that in the solar minimum P 23/24 . With the extension of IMP-8 measurements and BON2020 numerical simulation results, we find that the GCR intensities during the recent solar minimum are at the highest levels since the start of the space age, having particle energies from tens to several hundred MeV nuc −1 . The record-breaking GCR intensities at 1 au increase the radiation dose rates near the lunar surface by ∼5% in comparison to those of the solar minimum P 23/24 , from the measurements of LRO/CRaTER instrument. 2. The peak value of NM count rates in the solar minimum P 24/25 is lower than that in late 2009. The difference between GCR intensities in interplanetary space and NM count rates seems to be relevant to the different modulation processes of the high- and low-energy particles. We think that the high-energy GCR particles are not as heavily modulated as the low-energy ones, which means the low-energy GCR particles are more likely to be influenced by varying solar modulation. An alternate or additional possibility is that the NM count rates are sensitive to the conditions of the Earth’s magnetosphere and atmosphere. It remains to be further studied in a future work. 3. We find that during the solar minimum P 24/25 , the mean solar polar field strength remains weak and is close to the value in the 2009 solar minimum; the HCS tilt angle reaches a minimum value of ∼2.1° in 2020 April, which is ∼22% lower than that in the solar minimum P 22/23 and ∼53% lower than that in the solar minimum P 23/24 ; the CME eruption rate is very small, and is less than half of the CME rate during the solar minima P 22/23 and P 23/24 ; the strength and


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the WISE images, which are likely the shock fronts. At the angular resolution of the H i data, this appears to be the case. Figure 5. Position–velocity slice for clouds G228 and G230. The left panel is the unWISE mid-infrared image, with a dashed green line illustrating the path along which the slice was made. The right panel shows the brightness temperature of the 21 cm line, with the horizontal axis being position along the slice (starting from 0 at the top of the green line in the left panel), and the vertical axis being the velocity (0.8 km s −1 pixels, spanning 50 km s −1 ). 4.2. Atomic and Molecular Content Comparing the Planck and GASS surveys highlights further the drastic differences between the G228 and G230. Figure 6 shows that G230 has a far higher amount of dust per unit atomic gas than G228. We showed earlier that both G228 and G230 contain CO in their cores, with central velocity and width similar to those of the narrow H i component, and CO core brightness comparable between the two clouds (Reach et al. 1994 ). Figure 6. Comparison of dust optical depth and H i column density for G228 and G230. The purple scale bar is 1° long (1.75 pc if the cloud is at a distance of 100 pc). The left panel shows the dust image, and the right panel shows the scatter-plot. Subsets of the data are shaded in color on the left image and have colored symbols on the right. In red are the points with the highest excess of dust optical depth compared to H i column density; these locations are concentrated in cloud G230, where CO was also detected. In green are the points selected to have the highest H i column density. The H i peak is in G228, and not coincident with the dust peak, which is in G230. In blue are the points selected in the southern “tail” of the image, south of G228 and G230. This region has roughly the same dust-versus-gas trend as the rest of the image and is normal, diffuse atomic gas. This figure, and similar ones in this paper, was made using the package glue (Beaumont et al. 2015 ). The Planck and GASS surveys show that the amount of dust per unit atomic gas is radically different between G228 and G230. If we use the gas column density from the H i 21 cm line and the dust optical depth from far-infrared emission (see Equation (4) of Reach et al. 2015 ), the atomic gas-to-dust ratio is [G/D] = 84 in the regions surrounding the clouds, [G/D] = 55 in G228, and [G/D] = 12 in G230. If the total gas-to-dust ratio is 84 everywhere, then there is significant non-atomic gas in both clouds. The amount of this “dark” gas per unit atomic gas (Equation (7) of Reach et al. 2015 ) is f dark = 1.5 in G228 and f dark = 7 in G230. There is no large-scale CO emission from the main bodies of the clouds in the Planck CO survey, which sets a limit W (CO) 7 K km s −1 on widespread CO. But we did detect CO from the cloud cores using ground-based telescopes (Reach et al. 1994 ); the CO brightness was W (CO) = 2.1 K km s −1 . Mapping observations showed


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ACKNOWLEDGEMENTS This work was supported by the Russian Foundation of Basic Research (grant 17-52-80139 BRICS-a). SST acknowledges the support of the Academy of Finland grants 309228, 316932 and 317552. VD thanks the Deutsches Zentrum for Luft- und Raumfahrt (DLR) and Deutsche Forschungsgemeinschaft (DFG) for the support. Authors thank to Prof. Frederick Walter for comments and suggestions that allowed to improve the manuscript. The research has made use of Chandra data and software provided by the Chandra X-ray Centre. We used also data supplied by the UK Swift Science Data Centre at the University of Leicester. Results are also based on data products from VVV Survey observations made with the VISTA telescope at the ESO Paranal Observatory.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 B-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula 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 B-CelestialObject I-CelestialObject 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 B-Instrument 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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

exploration of the entire multidimensional space of atmospheric parameters. We thereby assume no a priori values for the H 2 O abundances and cloud/haze properties. There are also several differences between our study and that of Barstow et al. ( 2017 ). The differences are of three kinds: model parametrizations, statistical sampling algorithms, and reported estimates. We here discuss each of these in turn. There are several important differences in the model parametrizations. The main aspect of the Barstow et al. ( 2017 ) study is that it is effectively a grid-based retrieval, in the sense that a separate retrieval is conducted for each assumption of a cloud prescription. Importantly, the study treats two kinds of cloud models separately: a model with Rayleigh-like slopes (i.e. our hazes) and one with grey opacity (i.e. our clouds). On the other hand, our cloud/haze model simultaneously accounts for small and large particle sizes (see equation 4 ). An important distinction also lies in the aerosol parametrization. Our study includes a grey cloud overlain by a haze such that both types of aerosols are retrieved for a planet, although the retrieved parameters could indicate no hazes (i.e. a = 1 and γ = −4) and/or no grey clouds (i.e. P cloud ≳ 10 bar). On the other hand, Barstow et al. ( 2017 ) allows for the presence of a vertically finite cloud or haze deck at variable locations in the atmosphere. In some cases (e.g. HD 189733b) where our study retrieves a deep cloud layer with an extensive overlying haze layer, Barstow et al. ( 2017 ) retrieve a decade-confined haze layer confined to low pressures. These two different interpretations, however, produce similar fits to the spectrum. An additional crucial difference in the aerosol models is that this study accounts for inhomogeneous clouds and hazes along the planetary limb. The inclusion of patchy clouds is important since the shape of the H 2 O feature in the WFC3 bandpass is sensitive to the degree of cloud contribution (e.g. see Line Parmentier 2016 ). These differences in modelling are likely another principal element responsible for discrepancies in the cloud and haze properties between this work and that of Barstow et al. ( 2017 ). Secondly, Barstow et al. ( 2017 ) assumes an isotherm for the observable region of the atmosphere (pressures below 0.1 bar) whereas we allow a fully general temperature profile that allows for any temperature gradient. Thirdly, there is a significant difference in the treatment of opacity in the radiative transfer. Whereas the previous study assumes the correlated- k distribution for opacities, our study uses opacity sampling from very high-resolution cross-sections for the different molecules. This difference in opacity treatments could potentially influence the retrievals. However, generally similar water abundance estimates between the two methods is encouraging. Fourthly, the cloud properties and temperature profiles in Barstow et al. ( 2017 ) were


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Telescope B-Wavelength 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 O O O O O O O O O B-Telescope O O O B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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-Instrument O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

cool prominence plasma being ejected away from the reconnection region. The bulk of the ejected material consists of two main components denoted as S1 and S2 in Fig. 2 . Component S1 moves upwards freely and undergoes helical motion believed to be the result of the reconnection of a twisted bundle of prominence threads with overlying field lines. Helical motion of the ejected surge material suggests that the reconnection lead to the release of the magnetic twist accumulated in the flux rope supporting the prominence. The ejection of component S2 is triggered by the reconnection of a prominence thread with a closed coronal loop. The confined material then moves along a closed loop-like trajectory and subsequently falls towards the solar surface. Fig. 2. Evolution of the rotating flux tube. Top : superimposed snapshots in IRIS FUV SJI data during three different phases of the torsional oscillation of the surge material. White dotted lines outline the helical trajectories of the plasma threads. The arrow shows the direction of the rotation. The white vertical line corresponds to the fraction of the slit intersecting the surge plasma. The freely moving and confined component of the ejected surge material are denoted S1 and S2, respectively. Bottom : IRIS Si IV and Mg II K spectra of the surge material corresponding to the fraction of the slit marked by the white line. We show spectral snapshots from three different phases of the motion of the plasma at the slit position. In each panel, the vertical dashed line indicates the mean Doppler velocity of the plasma. The alternating tilt of the emission in the different phases, denoted in each panel by the tilted dashed line (obtained by visual examination) corresponds to the torsional motion of the surge material. Animation of this figure is available online . The direction of the helical motion of the surge material alternates, suggesting a large-scale torsional wave is set up in the flux tube following the reconnection. The helical motion of the individual threads is observable both in the imaging and spectral data. Rotation in a clockwise direction viewed edge-on is revealed in spectral data as opposite red and blue-shifted emission on the top and bottom edges of the flux tube, relative to the mean line-of-sight velocity. The reverse is true for a counter-clockwise rotation. The IRIS SG slit is in sit-and-stare mode and crosses the surge material at an angle. As a result, it is possible to determine the presence and direction of rotation from variations of the Doppler shift as a function of distance along the slit. Figure 2 shows SJI snapshots at various phases of the torsional motion of the flux tube as well as the Si IV and Mg II K line profiles along the slit between y = −254′′ and y = −244′′, where the slit intersects with the surge material. We note that the imaging and spectral snapshots are not concurrent because by the time the third phase of the propagating oscillation is visible in the


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S.G. and P.H. acknowledge the support from grant 16-17586S of the Czech Science Foundation (GAČR). S.G. and P.H. acknowledge the support from project RVO:67985815 of the Astronomical Institute of the Czech Academy of Sciences. S.G. and P.H. thank for the support from the MPA Garching. U.A. thanks for the support from the Astronomical Institute of the Czech Academy of Sciences. D.H.M. acknowledges financial support from the STFC, the Leverhulme Trust, and NASA. ALMA is an international partnership of the European Southern Observatory (ESO) representing its member states, the U.S. National Science Foundation (NSF) and the National Institutes of Natural Sciences (NINS) of Japan, together with NRC (Canada), NSC and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO, and NAOJ. S.G. is an expert member of the Solar Simulations for the Atacama Large Millimeter Observatory (SSALMON) network.


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

We acknowledge the support from: the US National Science Foundation (NSF); the US Department of Energy Office of High-Energy Physics; the Laboratory Directed Research and Development (LDRD) program of Los Alamos National Laboratory; Consejo Nacional de Ciencia y Tecnología (CONACyT), México (grants 271051, 232656, 260378, 179588, 239762, 254964, 271737, 258865, 243290, 132197), Laboratorio Nacional HAWC de rayos gamma; L’OREAL Fellowship for Women in Science 2014; Red HAWC, México; DGAPA-UNAM (grants IG100317, IN111315, IN111716-3, IA102715, 109916, IA102917); VIEP-BUAP; PIFI 2012, 2013, PROFOCIE 2014, 2015; the University of Wisconsin Alumni Research Foundation; the Institute of Geophysics, Planetary Physics, and Signatures at Los Alamos National Laboratory; Polish Science Centre grant DEC-2014/13/B/ST9/945; Coordinación de la Investigación Científica de la Universidad Michoacana. Thanks to Luciano Díaz and Eduardo Murrieta for technical support.


O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula O B-Dataset I-Dataset O O O O B-Formula I-Formula I-Formula O O O O O O B-Formula I-Formula I-Formula O B-Dataset I-Dataset O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O B-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula O B-Dataset I-Dataset O O O O B-Formula I-Formula I-Formula O O O O O O B-Formula I-Formula I-Formula O B-Dataset I-Dataset 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Formula I-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula O B-Dataset I-Dataset O O O O B-Formula I-Formula I-Formula O O O O O O B-Formula I-Formula I-Formula O B-Dataset I-Dataset O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O B-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula O B-Dataset I-Dataset O O O O B-Formula I-Formula I-Formula O O O O O O B-Formula I-Formula I-Formula 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 B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O B-Model O O O O O O O O B-Model O B-Model O O O O O O O O O O O O O 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 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 O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O 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 O O O O O O O O B-Model 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 O O B-Model 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O 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 O O O O O O

between the data and the model. The four panels correspond to the four respective sub-samples: N = 6 BAO data, N = 30 DA data, the N = 35 combined BAO+DA sample with the H ( z = 2.34) data point excluded, and the full N = 36 combined BAO+DA data. Figure 8. Histograms of the Om ( z i , z j ) two-point diagnostic residuals R Om ( z i , z j ) calculated with different samples: N = 6 BAO data, N = 30 DA data, the N = 35 combined BAO+DA sample with the H ( z = 2.34) data point excluded, and the full N = 36 combined BAO+DA data. In each panel the results for three different cosmological models are shown. Figure 9. The Omh 2 ( z i , z j ) two-point diagnostic residuals displayed as the weighted mean (left panels) and as the median value (right panels) indicated by dashed lines surrounded by color bands denoting 68% confidence regions. In each panel the results for three different cosmological models are shown. The long solid line shows the level expected for perfect agreement between the data and the model. The four figures correspond to the four respective sub-samples: N = 6 BAO data, N = 30 DA data, the N = 35 combined BAO+DA sample with the H ( z = 2.34) data point excluded, and the full N = 36 combined BAO+DA data. Figure 10. Histograms of the Omh 2 ( z i , z j ) two-point diagnostic residuals calculated with different samples: N = 6 BAO data, N = 30 DA data, the N = 35 combined BAO+DA sample with the H ( z = 2.34) data point excluded, and the full N = 36 combined BAO+DA data. In each panel the results for three different cosmological models are shown. One can see from Figure 7 that the residuals R Om ( z i , z j ) for the ΛCDM model are closer to zero than for the wCDM or CPL models, irrespective of the sample. From Table 4 one can see that the residuals of the wCDM or CPL models summarized in the weighted mean scheme are more than 15 σ away from the expected value of zero (for the full sample). This deviation in terms of median statistics is even bigger. One can also see this clearly in Figure 8 where the histograms of R Om ( z i , z j ) are shown. In the case of the Omh 2 ( z i , z j ) diagnostics the performance of the ΛCDM and wCDM models is similar: using the full sample, the weighted mean of residuals is at 7 σ away from zero. As shown in Figure 10 , the bulk of the distributions for the ΛCDM or wCDM models contain zero in their tails, while the distribution for the CPL model is considerably away from zero (it corresponds to 26 σ for the weighted mean). It seems that despite the presence of some tension between the ΛCDM model and the two-point diagnostics evaluated on the most recent H ( z ) data, as noted, e.g., in Sahni et al. ( 2014 ) and Ding et al. ( 2015 ), this model still performs better than its immediate extensions, wCDM or CPL, in particular the latter. It should be stressed that the above mentioned performance of different models refers only to the two-point diagnostics considered. Therefore, this cannot be treated as a


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 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 B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Observatory I-Observatory I-Observatory I-Observatory I-Observatory 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 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 B-ObservationalTechniques O O B-Telescope I-Telescope 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 B-ObservationalTechniques O O O O B-Telescope I-Telescope O O O O O O O O O O O O O O O O O O B-Observatory B-Instrument O O O O O O O O O O O O O B-Telescope B-Instrument I-Instrument I-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 B-Observatory O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

a small fraction of the light to the photon counter of the profiling subsystem. In an AO system, typically about 97 per cent of the light of the LGS is directed towards the WFS by a beam splitter. The remaining 3 per cent of the light from the LGS follows the path to the science camera. This fraction could be notch-filtered and redirected to a high-speed photon counting detector, used to measure sodium density profiles. While the retrieved profiles taken at the LZT demonstrate that the CW lidar profiles are consistent with the ‘standard’ lidar profiles, our results obtained with a large area APD sensor used in linear mode were affected by a robust radio-frequency interference. In a photon-noise limited case the CW lidar method should have provided profiles with an accuracy of 20–40 m RMS centroid offset. Instead, the spread found in our experimental data is of the order of 150–200 m. We believe that this discrepancy is due to electromagnetic interference in the linear APD signal detected. Our theoretical analysis and the numerical simulations show the potential of the method. The method could yield sodium centroid profiles with high accuracy. Different scenarios could be realized, either one LGS modulated with a higher modulation strength (>60 per cent) or multiple LGS modulated with low modulation strength (≈30–40 per cent) could be used. We note that laser amplitude modulation strengths of 30–40 per cent result in 15–20 per cent decrease in the LGS return flux, which can be acceptable already with current 22W CW sodium lasers. Recent experiments done at the ESO WLGSU in La Palma (Haguenauer, Boanccini Calia Pfrommer 2019 ) have demonstrated the feasibility of splitting the uplink laser beam in two, to create two LGS angularly separated. The subsequent reduction of 50 per cent of the LGS flux corresponds to the loss of power due to a modulation of 100 per cent (ε = 1), in our CW lidar. The multiconjugate AO system at Gemini South (GeMS) splits one 20W CW laser into five LGS which reduces the return flux from one LGS to 20 per cent. For the new AO system under development for Gemini North, it is planned to split one 20W CW laser into two LGS. Calculations in the frame of the ESO Mavis project Phase A study indicate that using the 20W CW lasers in the VLT Galacsi LGS-AO system, with 20 × 20 cm sub-apertures Shack-Hartmann wavefront sensor, will still be able to support MCAO systems at visible wavelengths. Considering also that RD work is in place at ESO to both, enhance the LGS return flux by frequency chirping, and by increasing the laser power beyond 50 W at 589 nm, there is a good outlook for the CW lidar method to be used in operations, turned on when necessary. As this is the time of designing the extremely large telescope AO systems, we solicit the system experts to take provisions for the CW lidar implementation into account. Besides providing sodium laser profiles and abundances on time-scales of several seconds, of general use


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

for its mass. Changing any parameter in a reasonable range does not lead to a consistent solution. As shown by Lorenz et al. ( 2005 ), the secondary of V1331 Aql reaches about 96% of the Roche radius. Thus, V1331 Aql exhibits a detached configuration, but the secondary is about to fill its Roche lobe. It was not possible to obtain a consistent age for the binary V413 Ser because of a disagreement on the HR diagram for all searched values of Z and α ov . V413 Ser is located in the Serpens star-forming region (Chavarria-K et al. 1988 ). The Serpens dark cloud contains an extremely young star cluster and most probably both components of V413 Ser are pre-main-sequence objects (Çakırlı et al. 2008 ) and not the main-sequence ones as we assumed in our age determination. Results for IM Mon, Ori V1388, and V380 Cyg will be presented below. IM Monocerotis : Till now, IM Mon was studied in detail only in two papers, i.e., Bakiş et al. ( 2010 ) and Bakis et al. ( 2011 ). In Bakis et al. ( 2011 ), the analysis of all available photometric and spectroscopic observations allowed them to determine the absolute values of masses: M A = 5.35(24) M and M B = 3.32(16) M , and radii: R A = 3.15(4) R and R B = 2.36(3) R . Moreover, it has been shown that IM Mon is a member of Ori OB1a association and the age of the system is about 11.5 Myr. The age was estimated from a comparison of the location of stars on the diagram with the isochrones of Girardi et al. ( 2000 ). A comparison of the observed high-resolution spectrum with Kurucz atmosphere models gave atmospheric parameters and metallicity [Fe/H] = +0.2. The age of IM Mon determined by Bakis et al. ( 2011 ) is in agreement with earlier determinations for Ori OB1a association by Blaauw ( 1991 ) and Brown et al. ( 1999 ). Using the masses and radii, we tried to re-determine the age of the system, as illustrated in Figure 9 . We found that metallicity of at least Z = 0.025 is needed to find a common age of the components that is in line with the values of [Fe/H] obtained by Bakis et al. ( 2011 ). Then, the age of the system is about 9.7(2.9) Myr, which is in agreement with the previous determinations. However, when we put the stars on the HR diagram (the bottom panel of Figure 9 ), it turned out that the secondary component is overluminous for its mass. The evolutionary tracks for the metallicity typical for galactic B-type stars, Z = 0.014, would be consistent, although marginal; but in this case, there is no common age for both components even if the large overshooting ( α ov = 0.5) is assumed for the primary star. One reason for that could be an effective temperature that is too high. The lower value of T eff would move the star to the right and down in the HR diagram. The second explanation could be a more complicated configuration of this binary, i.e., maybe the system is not fully detached or there is a third light. Figure 9. The similar plots as in Figure 6 but for components of IM Mon. V1388


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We would like to thank the referee, Albert Bosma, for comments that improved the quality of the paper.


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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Tag O O O O O O O O O O O O O O O O B-Model I-Model O B-Software I-Software B-Citation I-Citation I-Citation I-Citation O B-Citation O O O O O O O O O O O O O B-Software I-Software B-Citation I-Citation I-Citation I-Citation O O O 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 B-ComputingFacility B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-Software I-Software O O O O O O O B-Software O O O O O O O O O O B-Software I-Software O O O O O O B-Software O O B-Software O O O O O O O O O O O O O O B-Software I-Software O O O O O O O O O O O O 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 B-Software O O O O O O O O O O

from equation and L circ is determined by the radius of the circular orbit r circ , To avoid the singularity at L = L max , it is helpful to introduce a new variable s by α = (1 − s 2 ) 1/2 L max ( r )/ L circ . Equation ( 4 ) then reads: As zero-order approximation, Φ * was set to zero, and an approximation was obtained for ρ( r ). The normalization constant A was recalculated after each iteration to provide the total mass M * for the cluster. The next approximation for the potential Φ * was obtained from a numerical solution of the Poisson equation After obtaining self-consistent profiles ρ( r ) and Φ * ( r ), one can build a random realization of the DF. First, we find L of the particle using the standard von Neumann rejection technique for equation ( 3 ). Energy E = E 0 and angular momentum L determine the orbit. Secondly, we set the radius of the particle, which is uniformly distributed in the radial angle variable, w . The dependence r ( w; E, L ) can be obtained directly by orbit integration, if the number of particles is not too large, or interpolating between reference orbits from a library. The radius r immediately gives the square of radial velocity , and the absolute value of transversal velocity . The velocity components ( v θ , v φ ) are uniformly distributed over a polar angle ψ in the velocity polar coordinates ( v ⊥ , ψ). Finally, the spatial coordinates are obtained as a uniform distribution on a sphere. For our default model with N = 10 5 and the central point mass M = 100, this procedure gives a nearly spherically symmetric N -body realization with centre-of-mass offset 1.5 × 10 −3 . Due to numerical noise, the initial amplitudes of the spherical harmonics A l (see equation 12 ) for 1 ≤ l ≤ 4 are of the order of 10 −3 . 2.3 <italic>N</italic>-body simulations The simulations presented in this work have been carried out using the specially adapted direct N -body code φ- gpu (Berczik et al. 2011 , 2013 ). The basic concepts of the code are based on the publicly available φ- grape (Harfst et al. 2007 ) code, an Aarseth N -body 1-like code (Aarseth 1999 ) including an efficient mpi parallelization and support for the special-purpose hardware GRAPE (Fukushige et al. 1991 ) (currently Graphic Processing Units – GPU). The current version of the φ- gpu code has been fully rewritten in the C++ programming language for the most effective use of GPUs. The φ- gpu code is fully parallelized using the mpi library. The mpi parallelization was done in the same ‘j’ particle parallelization scheme as in the earlier φ- grape code. All particles are divided equally between the working nodes (using the MPI_Bcast() command) and in each node we calculate only the fractional forces for the particles in the current time-step, i.e. the so-called ‘active’ or ‘i’ particles. We get the full forces from all particles acting on the active particles after the global MPI_Allreduce() communication routine is applied. The code supports the use of


O B-Telescope I-Telescope I-Telescope O O O O B-Organization I-Organization I-Organization O O B-Grant O O O O O O O B-Organization I-Organization I-Organization I-Organization O B-Grant O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization O B-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Grant I-Grant O O O O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O B-Organization I-Organization I-Organization O O B-Location B-Organization I-Organization I-Organization O O O B-Grant O O O O O O B-Archive I-Archive I-Archive I-Archive I-Archive I-Archive I-Archive B-Archive O O B-Archive O O O O B-Organization I-Organization I-Organization I-Organization I-Organization 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-Organization B-Grant O O O O O B-Organization I-Organization O O O B-Person I-Person O B-Organization I-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Location B-Organization I-Organization I-Organization O O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Person I-Person O O O O B-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship B-Person I-Person O O O O B-Location B-Organization I-Organization I-Organization O O B-Grant B-Person I-Person I-Person O O O O B-Fellowship I-Fellowship I-Fellowship O O O B-Observatory O O O B-Organization O B-Grant

The South Pole Telescope is supported by the National Science Foundation through grant PLR-1248097. Partial support is also provided by the NSF Physics Frontier Center grant PHY-1125897 to the Kavli Institute of Cosmological Physics at the University of Chicago, the Kavli Foundation and the Gordon and Betty Moore Foundation grant GBMF 947. This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. We acknowledge the use of the Legacy Archive for Microwave Background Data Analysis (LAMBDA). Support for LAMBDA is provided by the NASA Office of Space Science. This work was supported in part by the Kavli Institute for Cosmological Physics at the University of Chicago through grant NSF PHY-1125897 and an endowment from the Kavli Foundation and its founder Fred Kavli. The McGill group acknowledges funding from the National Sciences and Engineering Research Council of Canada, Canada Research Chairs program, and the Canadian Institute for Advanced Research. M. Dobbs acknowledges support from an Alfred P. Sloan Research Fellowship. S. Dodelson is supported by the U.S. Department of Energy, including grant DE-FG02-95ER40896. T. de Haan is supported by a Miller Research Fellowship. Cluster studies at SAO are supported by NSF grant AST-1009649.


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We would like to thank the anonymous referee for providing many insightful suggestions which have led to improved clarity of the work presented here. MRG would like to thank the generous hospitality of Kirk and Angela Korista and the Department of Physics Astronomy at Western Michigan University during the initial stages of this work. KTK would like to thank the University of Leicester for their hospitality during the completion of this work.


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variables, and powerful radio pulsars, such as the pulsar in the Crab nebula. In laboratory plasmas, jets, or directed flows, are observed in devices such as plasma focus (Beskin et al. 2017a ). The main puzzle of jets is their high degree of collimation. It is not clear how hot matter of jets, ionized gas in a strong magnetic field, confined in the cylindrical radius direction, which is the direction perpendicular to the axis of the jet. Neither hot gas nor external magnetic field is usually observed in the interstellar and intergalactic environment surrounding a jet. We will study the problem of radial equilibrium of the jet in the framework of ideal magnetohydrodynamics (MHD). This approximation is well suited for astrophysical jets. Dissipative effects are weak in hot plasma. In addition, large mean-free paths of particles, the presence of a strong magnetic field, in which cyclotron radii play the role of particle mean-free paths, and small cyclotron radii of ions in comparison with the characteristic scales of jets allow us to use ideal MHD for the description of astrophysical jets. It has been shown before that the problem of equilibrium of the jet in the radial direction within the framework of MHD is related to electric currents flowing inside the jet. If the jet carries uncompensated current, i.e. the total current of the jet is not zero, the current can be pinched to keep the hot jet in equilibrium (Blandford Payne 1982 ; Heyvaerts Norman 1989 ; Sulkanen Lovelace 1990 ; Li, Chiuch Begelman 1992 ; Pelletier Pudritz 1992 ; Sauty Tsinganos 1994 ). However, the question arises how to close the uncompensated current loop. If you let the return current flow outside the jet, it is not clear where it goes since track of the return current is usually not visible. It is more convenient to assume that return current flows inside the jet on its periphery. This raises the problem of the equilibrium of the jet in the region of return current. The return current repels from the direct one, and within the framework of a purely radial structure, there is no equilibrium, if there is no contribution of the surface current at the edge of the jet (Lery et al. 1998 ; Beskin Malyshkin 2000 ; Lyubarsky 2009 ; Beskin Nokhrina 2010 ). Here we will explore another possibility – the emergence of spiral structure in the region of return current flow. 2 CYLINDRICAL FLOW Let us consider stationary MHD equations in a coordinate system moving with the plasma flow along its axis with the velocity u . Here ρ is the plasma density of the jet, is velocity of the plasma, B is the magnetic field, and P (ρ) is the plasma pressure, which is a function of the density through the equation of state of the matter in the jet. Suppose first that all quantities depend only on the cylindrical radius coordinate r , that is, the jet is axisymmetric and homogeneous along axis z . In this case, the velocity and the magnetic field can be expressed as functions of r , Velocity v φ