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

varies less with MC sampling rate than the ejected mass (see below). Figure 4 also shows why it is so difficult to accurately estimate the amount of unbound material in a simulation: the steepness of the Lorentz factor distributions implies that a very small error in the estimated location of the boundary between bound and unbound material has large effects on the predicted mass of unbound material. The second, more minor difference is that the cutoff of the velocity distribution is slightly lower in both MC simulations ( v max ∼ 0.5) than with M1 ( v max ∼ 0.55). We can compare these results to Sekiguchi et al. ( 2016 ), who performed a longer simulation with M1 transport, the same equation of state, and slightly more symmetric masses. They find 0.005 M ⊙ of ejecta with and , and a Y e distribution fairly similar to those obtained with our M1 code—results that are broadly consistent if the higher mass asymmetry led to the ejection of an additional 0.003 M ⊙ of neutron-rich material. The properties of neutrinos escaping the system are summarized in Figure 5 . After the first 2 ms, the average energy of neutrinos and the ν e and luminosities in the M1 and MC simulations agree within ∼20%. The ν x luminosity, on the other hand, is nearly twice as large in the MC simulation. Differences between the two MC simulations are negligible compared to differences between MC and M1. The luminosity of heavy-lepton neutrinos is one of the most uncertain observable in our M1 scheme, because a large region close to the neutron star surface has negligible κ a but large κ s . In that region, neutrinos are trapped, but out of thermal equilibrium with the fluid. As the energy closure is the most ad-hoc part of our M1 algorithm, and the diffusion rate of neutrinos strongly depends on the choice of energy spectrum, this is a particularly difficult situation. The MC scheme has no particular reason to perform poorly in that regime: while it corrects large absorption opacities, its treatment of high-scattering regions is better motivated than that of the gray M1 scheme. Nevertheless, it may be premature to assume that the MC scheme provides the better answer, as the two schemes may be impacted in different ways by the grid resolution. In Sekiguchi et al. ( 2016 ), neutrino luminosities reach values similar to those measured here within ∼5 ms, before decreasing on the cooling timescale of the remnant. Figure 5. Left panel: angular distribution of the electron antineutrinos leaving the grid (3–5) ms after merger; θ is the angle with respect to the angular momentum vector, i.e., polar neutrinos are on the left, equatorial neutrinos on the right, and each bin covers the same surface area. Middle panel: neutrino luminosity in the high-resolution MC simulation and the M1 simulation. Right panel: average (number-weighted) energy of neutrinos leaving the computational grid in the same simulations. The angular distribution of neutrinos shows clearer differences between


O O O O O O O O O O O O O O O O O O O O O B-Organization I-Organization I-Organization B-Grant I-Grant I-Grant I-Grant B-Organization B-Location O B-Grant B-Organization O B-Grant O B-Grant O B-Organization O B-Grant B-Person O O O O O O B-Organization I-Organization I-Organization I-Organization O O O O O B-Organization I-Organization I-Organization O O O O B-ComputingFacility B-Location O O B-Grant I-Grant O B-Software B-Citation I-Citation I-Citation I-Citation O

We would like to thank the anonymous referee for useful comments that improved the paper. This work was supported by the European Research Council (ERC-2015-AdG grant No. 695008), FCT (Portugal) grant SFRH/IF/01780/2013, DOE grants DE-SC0008409 and DE-SC0008655, and NASA grant NNX16AB28G. D.A.U. gratefully acknowledges the hospitality of the Institute for Advanced Study and the support from the Ambrose Monell Foundation. Simulations were carried at MareNostrum (Spain) under a PRACE award. Software: OSIRIS (Fonseca et al. 2002 ).


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

We thank the anonymous referee for their detailed comments and suggestions that improved this study. We also thank Anahita Alavi, Philip Best, Rychard Bouwens, Naveen Reddy, and Irene Shivaei for their insightful discussions and comments. The catalogues used in this analysis are publicly available from Sobral et al. ( 2013a ). DS acknowledges financial support from the Netherlands Organization for Scientific research (NWO) through a Veni fellowship, from FCT through an FCT Investigator Starting Grant and Start-up Grant (IF/01154/2012/CP0189/CT0010) and from FCT grant PEst-OE/FIS/UI2751/2014. IRS acknowledges support from ST7C (ST/L00075X/1), the ERC Advanced Grant DUSTYGAL (321334) and a Royal Society/Wolfson Merit award. BD acknowledges financial support from NASA through the Astrophysics Data Analysis Program (ADAP), grant number NNX12AE20G. JPS gratefully acknowledges support from a Hintze Research Fellowship.


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

ACKNOWLEDGEMENTS I thank Marek Sikora for valuable discussions and suggestions, Łukasz Stawarz for providing the quiescent spectra of Mrk 421 and Mrk 501, and the referee for valuable comments. This research has been supported in part by the Polish National Science Centre grant 2015/18/A/ST9/00746.


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

et al. 2017 ). To decouple the effect of Z and Y , we compute five tracks of mass 1.50 M ⊙ and Z = 0.031 ([Fe/H] = 0.25), but with initial helium Y = 0.25, 0.28, 0.30, 0.35 and 0.40 (with Y = 0.28 as our default value). Fig. 4 , right-hand panel, shows the evolution of ΔΠ 1 with central helium for the five tracks. We note that the effect on ΔΠ 1,max and ΔΠ 1,min grows linearly with Y . However, for a variation of Δ Y = ∼0.02 from the default value ( Y = 0.25 and 0.30), the deviation on ΔΠ 1,max (ΔΠ 1,min ) lies within the observed uncertainty on ΔΠ 1 (∼3–4 s). The deviation we tested is compatible with typical spread on disc populations (Casagrande et al. 2007 ). Nevertheless, the effect becomes substantial for extreme enrichments, for example, in bulge or globular clusters where populations with very different He abundances and the same metallicity may coexist (Renzini et al. 2015 ). Figure 4. Left-hand panel: RC-ΔΠ 1 evolution as a function of central helium mass of an M = 1.50 M ⊙ solar metallicity star with three different mixing schemes and four different 12 C(α, γ) 16 O reaction rates. Right-hand panel: RC-ΔΠ 1 evolution as a function of central helium mass fraction of an M = 1.50 M ⊙ star computed assuming three different combinations of Z and Y . 5 ADDITIONAL UNCERTAINTIES ON ΔΠ<bold>1</bold>: <bold>12</bold>C(α, γ)<bold>16</bold>O NUCLEAR REACTION RATE As shown above, ΔΠ 1 is strongly dependent on assumptions related to core convection and metallicity; however, additional parameters and uncertainties may also have impact on ΔΠ 1 , in particular the 12 C(α, γ) 16 O reaction rate, which, along with triple-α, plays a fundamental role, especially at the end of the HeCB (e.g. see Cassisi et al. 2003 ; Straniero et al. 2003 ; Constantino et al. 2015 ). We compute a series of HeCB evolutionary tracks ( M = 1.5 M ⊙ , solar abundance) in which we adopt four 12 C(α, γ) 16 O reaction rates in conjunction with three mixing schemes: Bare–Schwarzschild model (BS), 1.0 H p step function overshooting (HOV) and 1 H p penetrative convection (HPC). The 12 C(α, γ) 16 O reaction rates considered are the tabulated values given by JINA (Cyburt et al. 2010 ), K02 (Kunz et al. 2002 ), CF88 (Caughlan Fowler 1988 ) and NACRE (Angulo et al. 1999 ), and already made available in mesa . While no difference can be noted at the beginning of the phase, the impact of the different mixing schemes is evident at the maximum period spacing (end of the HeCB), where HOV tracks show a scatter of around 6–7 s between them, compared to only ∼2 s for BS (Fig. 4 ). We therefore expect an uncertainty between 6 and 2 s on the MPC and MOV models. This value is comparable with the observed average ΔΠ 1 uncertainty for clump stars (∼4 s). 6 DISCUSSION AND CONCLUSION The precise measurements of gravity-mode period spacing (ΔΠ 1 ) in thousands of HeCB stars have opened the door to detailed studies of the near-core structure of such stars, which


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O 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 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 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 B-Telescope 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 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 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 B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O

to the distance of 2I. The small apertures sample near-nucleus variations, whereas the 15,000 km aperture is a better measure of the total light scattered by the comet. The use of fixed linear (as opposed to angular) apertures provides a measure of the scattering cross section within a fixed volume surrounding the nucleus and obviates an otherwise necessary geocentric distance correction that is dependent on the surface brightness distribution. We obtained background subtraction from the median signal in a concentric annulus with inner and outer radii of 20,000 km and 30,000 km, respectively. The apparent magnitudes, V x , with x = 500, 1000, 2000, and 15,000 are listed in Table 2 , along with absolute magnitudes, H x , computed fromwhich corrects for the inverse square law and for the phase function, f ( α ) at phase angle α . In the absence of a measured value, we assumed f ( α ) = 0.04 mag degree −1 . The table also lists the scattering cross section, in square kilometers, computed fromwhere p V is the geometric albedo. We use p V = 0.1, as appropriate for dust in solar system comets (Zubko et al. 2017 ), while noting that the albedo of this unique interstellar object is likewise unmeasured and could be significantly different. The dust albedo is ∼2.5 times higher than the average comet nucleus albedo. Table 2 HST Fixed-aperture F350LP Photometry a Note. a For each date and aperture radius, l , the table lists the apparent magnitude, V , the absolute magnitude, H , and the scattering crossection, C e (in units of square kilometers), in the form V / H / C e . H and C e are computed using Equations ( 1 ) and ( 2 ). Temporal variations in the absolute magnitudes are plotted in Figure 4 , in which the UT 2020 March 4.3–9.3 dates of photometric outburst (Drahus et al. 2020 ) are marked by a vertical gray band. Our data show that the outburst was preceded by a progressive brightening of 2I by about 20% in all apertures. This brightening is not correlated with the phase angle, which changes modestly and nonmonotonically in this period (Table 1 ), and therefore cannot be ascribed to uncertainties in the phase function. Neither does it vary with the angle from the orbital plane. Instead, the data show a steady brightening from January 3 to February 24, indicating a period of increasing activity. We conjecture that this is due to a seasonal effect on the nucleus: according to the pole solution proposed by Kim et al. ( 2020 ), the subsolar latitude on the nucleus moved from the southern hemisphere to the northern during this period, bringing the Sun’s heat to previously unexposed ice. Figure 4. Absolute magnitudes vs. date for the 500, 1000, 2000, and 15,000 km radius apertures. Smoothed dashed lines are added to guide the eye. The shaded vertical band marks March 4–9, the dates of the reported photometric outburst. Our first postoutburst HST observation occurred about 2 weeks later (March 23), by which time the near-nucleus brightness had jumped


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

does not need to precompute and store anything for these surfaces. To solve equation ( A4 ), we need only the current position and direction, and the θ boundaries of the current cell. A1.3 Constant phi surfaces The constant φ surfaces are planes. Determine the Cartesian coordinates for the four edgepoints of the surface. Then, define, for the k plane, the vectors Take the cross-product and normalize to get the normal vector to the plane . Note that an intersection point on the plane will obey . For the k + 1 plane use instead and then corresponding operations for and d . The intersection point ( x i , y i , z i ) and the distance to this point, d s , are then found from solving the linear equation system No solution means the packet is moving parallel to the plane and will not impact it. If d s 0, the packet is moving in the wrong direction and will not impact the plane. The four numbers are computed once and stored for all surfaces. A1.4 Entry surface flagging If the surface through which the packet entered the cell is allowed also an as exit surface, small numeric errors could lead to the packet getting stuck at the boundary. To avoid this the entry surface is initially flagged to be disallowed as solution for which next boundary to encounter. This flagging is removed if an interaction occurs inside the cell. For two surfaces, the ‘convex out’ boundaries at the constant r outer radius and constant θ conical boundary closer to the equatorial plane, it is possible for the packet to enter and exit the same boundary on a straight path. However, this occurrence is very rare, in particular for a high-resolution grid as those used here. We therefore kept the flaggings also for these cases, and was removed only after a small distance into the cell had been travelled. This treatment implies a small distortion to the flight path for photons gracing these surfaces but the effect of this should be very small, and this treatment avoids an more expensive algorithm for doing the transfer exactly. A1.5 Positional corrections Once the shortest distance has been calculated, the new Cartesian coordinates of the packet are calculated from . The spherical coordinates are then calculated from these. It may sometimes happen that in these transformations small numeric errors lead to the new spherical coordinates being (slightly) outside the limits of the new cell. If that happens severe errors can occur in calculating the next movement. Therefore, at each new cell entry, this is checked and if a discrepancy has arisen, the coordinates are adjusted to be just inside (by a multiplicative factor 1 ± 10 −5 ) the surface in question. A1.6 Next interaction point For continuum opacity, standard Monte Carlo procedures are followed by drawing a random optical from τ = −ln z where z is a random number between 0 and 1. Then As the distances are computed in the stellar rest-frame one should ideally use the direction-dependent opacity in this frame. We did not make the


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

in Fig. 7 . As can be seen, we now require 3 × 3 sets of MNn discs (i.e. 27 parameters) to obtain a fit at better than 10 per cent accuracy over 0.1 s ′ / r s 10. Figure 6. The twisted triaxial NFW density profile. The mass distribution is axisymmetric close to the centre and triaxial in the outskirts. Figure 7. MNn fit (dotted line) for a twisted triaxial NFW density profile (solid lines). We require 3 × 3 MNn discs for this more complex profile to get a good fit (better than 10 per cent accuracy over the range 0.1 s ′ / r s 10). 3.4 The potential and the force field So far, we have compared the original density profile with the one we obtain with our potential-density pair. It is interesting also to compare the potential generated by these density profiles and the force field as well. An important advantage of our potential-density pair is that the potential and the force field can be calculated analytically which is not the case, for instance, for the triaxial and twisted NFW profiles which have to be calculated numerically. We now compare the potential and the force field generated by a triaxial NFW density profile with those generated by our potential-density pair. We first calculate the potential generated by the original function, using the Chandrasekhar formula (Chandrasekhar Press 1969 ): This is an improper integral over the variable τ, where Once we have calculated the potential generated by the original density profile, now we calculate the potential generated by our superposition of MNn discs. This is just the sum of the potential generated by each single MNn disc that follows analytically from equation ( 3 ). We compare our MNn potential and force field with the true solution in Fig. 8 for the case of a triaxial NFW profile. Figure 8. Residuals of the potential and force field for a 3 × 2 MNn fit to the triaxial NFW density profile. 4 CONCLUSIONS We have presented a novel positive potential-density pair expansion for modelling galaxies, based on the MN disc. The key novelties of our method are: (i) we use three sets of such discs aligned along each symmetry axis, allowing us to model triaxial and twisted triaxial systems; (ii) we increase the efficiency of our expansion by allowing the scalelength parameter of each disc a to be negative; (iii) we introduce a constraint equation that ensures that the total density is everywhere positive; and (iv) we allow arbitrarily many discs in our expansion, allowing us to accurately model a wide range of density distributions relevant for modelling galaxies. We find that at better than 10 per cent accuracy in our density reconstruction, we can represent a radial and vertical exponential disc over 0.1–10 scalelengths/scaleheights with four MNn discs; an NFW profile over 0.1–10 scalelengths with four MNn discs; and a twisted triaxial NFW profile with three MNn discs per symmetry axis. Our potential-density pair is efficient, fully analytic, and well suited to reproducing the density


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

Distribution parameters, namely , and δ , show significant positive correlations with the cycle strengths. These correlations are in general agreement with the previous findings of Solanki et al. ( 2008 ), although there are some differences in the values of the correlations, as the cycle lengths are computed differently in their study. In general, the observed correlations imply that stronger cycles begin sunspot eruptions at relatively higher latitudes, and they have wider extends of sunspot eruption latitudes. Another interesting result from this study is the hemispheric asymmetry in the distribution parameters, especially in the center values ( C ). We find that the parameter oscillates around the zero value, whereas the amplitude of this oscillation seems to decrease with the increase of the cycle number. To explore these features, we have applied a flux transport dynamo model in which polar field at the solar minimum is varied randomly. Although this model produces many features of the solar cycle correctly, the latitudinal distribution of sunspots is not in good agreement with observation because of the fewer sunspots near the equator. Despite of this dissimilarity, all correlations among the distribution parameters, as obtained in observation, are reproduced correctly. Our results are in broad agreement with that of Solanki et al. ( 2008 ), who reproduced similar correlations using a simplified thin shell dynamo model. While our model has a fixed single-cell (in each hemisphere) meridional flow, Solanki et al. ( 2008 ) showed that the model with and without meridional flow produce slightly different results. Our model also reproduces the detailed variation of these parameters within the cycle, as demonstrated by Cameron Schüssler ( 2016 ). Thus, our study supports a considerable variation in the polar field as the cause of the irregular solar cycle and variations in the latitude distributions. The variation in the polar field is directly and indirectly observed in the Sun (Muñoz-Jaramillo et al. 2013 ; Priyal et al. 2014 ). This variation is primarily caused by the the scatter in the tilt angles of active regions around Joy’s law (Cameron et al. 2013 ; Jiang et al. 2014 ; Hazra et al. 2017 ; Karak Miesch 2017 ), which is actually observed in the Sun (e.g., Dasi-Espuig et al. 2010 ; Stenflo Kosovichev 2012 ). While it is known that the variation in the meridional flow is expected to cause some variations in the solar cycle (e.g., Karak Choudhuri 2011 ; Belucz Dikpati 2013 ), due to difficulties in the measurements, we are uncertain about the amount of variation present in the deep meridional flow. However, the surface meridional flow is observed to change with the solar cycle and most of this variation is probably caused by the inflows around the active regions (Gizon et al. 2010 ). This meridional flow perturbation can change the polar field from cycle to cycle (Jiang et al. 2010 ; Hathaway Upton 2014 ; Shetye et al. 2015 ). In our


O O O O B-Person I-Person O O O O O O O O B-Telescope O O B-Person I-Person O O O O O O O O B-Database I-Database O O B-Person I-Person O O O B-Model I-Model I-Model O O O O O O O O O O O O O O O O O B-Person I-Person B-Person I-Person B-Person I-Person O O O O O O O O O O O O O O O B-Person O B-Person I-Person O O B-Event I-Event I-Event I-Event I-Event O O O O O O O O O O O O O O O O B-Organization O O B-Grant B-Person O O O O O B-Organization O O B-Grant O O O O O B-Telescope I-Telescope I-Telescope O O O O B-Telescope I-Telescope I-Telescope O O O O O O B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization B-Observatory I-Observatory I-Observatory O B-Organization I-Organization I-Organization I-Organization O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization O B-Survey I-Survey I-Survey I-Survey O O O O O O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O O O O O O O O O O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O O O O O O O O O O O B-Archive I-Archive I-Archive I-Archive I-Archive I-Archive O B-Database O O O B-Organization B-Location I-Location O O B-Database O O O B-Organization B-Location I-Location B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-Survey I-Survey I-Survey I-Survey B-Survey O O O B-Organization I-Organization I-Organization I-Organization I-Organization

We are grateful to Eran Ofek for his help scheduling and carrying out the PTF observations, to Adrian Price-Whelan for his help extracting light curves from the PTF database, and to Aaron Dotter for providing a 125 Myr isochrone with colors computed in the specific filters used during the course of this analysis. We also thank John Stauffer, Luisa Rebull, Kristen Larson, and the anonymous referee for comments that improved our analysis and presentation of our results. K.R.C. thanks Hilary Schwandt and the WWU Faculty Research Writing Seminar for sage advice that accelerated the completion of this manuscript, and acknowledges support provided by the NSF through grant AST-1449476. M.A.A. acknowledges support provided by the NSF through grant AST-1255419. Observations were obtained with the Samuel Oschin Telescope as part of the Palomar Transient Factory project, a scientific collaboration between the California Institute of Technology, Columbia University, Las Cumbres Observatory, the Lawrence Berkeley National Laboratory, the National Energy Research Scientific Computing Center, the University of Oxford, and the Weizmann Institute of Science. The Two Micron All-Sky Survey was a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center (California Institute of Technology). The University of Massachusetts was responsible for the overall management of the project, the observing facilities and the data acquisition. The Infrared Processing and Analysis Center was responsible for data processing, data distribution and data archiving. This research has made use of NASA's Astrophysics Data System Bibliographic Services, the SIMBAD database, operated at CDS, Strasbourg, France, and the VizieR catalog access tool, CDS, Strasbourg, France (Ochsenbein et al. 2000 ). This research was made possible through the use of the AAVSO Photometric All-Sky Survey (APASS), funded by the Robert Martin Ayers Sciences Fund.


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 B-Wavelength I-Wavelength I-Wavelength I-Wavelength B-Wavelength B-Wavelength O B-Wavelength B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O B-Wavelength I-Wavelength O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength B-Wavelength 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 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 B-Wavelength I-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O B-Model I-Model B-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 I-Instrument I-Instrument I-Instrument I-Instrument O O O B-Telescope I-Telescope I-Telescope I-Telescope I-Telescope B-Telescope O O B-URL O O O O O O O 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 I-Wavelength I-Wavelength O O O O O O O O O O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength I-Wavelength I-Wavelength O B-Wavelength I-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 B-Software I-Software I-Software I-Software I-Software B-Software O O B-Software O O O O B-Observatory I-Observatory I-Observatory I-Observatory O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O

expected line ratios of the prominent O i lines, when collisional excitation and Ly β fluorescence (referred to as photoexcitation by accidental resonance—PAR process—in Bhatia Kastner 1995 ) are the dominant excitation mechanisms. From a comparative analysis of the theoretical estimates with the observed emission strengths of O i λλ 7774, 8446, 11287, and 13165, Mathew et al. ( 2012b ) demonstrated that Ly β fluorescence is the dominant excitation mechanism for the production of O i λλ 8446, 11287 lines in CBe stars. CBe stars share similar spectral characteristics with HAeBe stars, such as emission lines of H α , O i , Fe ii , and Ca ii triplet. It is worth exploring whether both CBe and HAeBe stars share similar excitation mechanisms for the formation of O i lines. There could be considerable difference between the O i line forming regions in both the stellar systems. CBe stars are found to have a circumstellar gaseous decretion disk wherein the O i λ 8446 line is formed at a mean radial distance of ∼8 R ⋆ , considering Keplerian motion (Mathew et al. 2012b ). However, the location of the origin of the O i λ 8446 line in HAeBe is far from clear. Most of the accretion related emission lines in HAeBe stars (e.g., H α , Pa β , Br γ ) are thought to be formed in the magnetospheric accretion columns (Muzerolle et al. 2004 ). This work is an attempt to bring more clarity to our understanding of the formation mechanisms of O i emission lines in HAeBe stars. The paper is organized as follows. In Section 2 , we present the optical and near-infrared (near-IR) spectroscopic observations carried out over a period of 3 years and describe the data reduction techniques employed. We describe the methods and the python routines used for the spectral analysis and to estimate line flux in Section 3 . The dominant excitation mechanism for the formation of O i lines in HAeBe stars is evaluated in Section 4 . The main results of the paper are summarized in Section 5 . 2. Observations and Data Reduction The optical spectroscopic observations were carried out using the Himalayan Faint Object Spectrograph Camera mounted on the 2 m Himalayan Chandra Telescope (HCT). 6 6 http://www.iiap.res.in/iao/hfosc.html The spectroscopic observations were obtained with Grism 8 in combination with 167 l slit (192 wide and 11′ long), providing an effective resolving power of ∼1050. The spectral coverage is from 5500 to 9000 Å, which included the spectral lines relevant to this study, viz., H α , O i λ 7774, and O i λ 8446. After each on-source exposure, FeNe lamp spectra were obtained for wavelength calibration. We have followed the regular procedure of reducing the spectra after bias subtraction and flat-field correction using the standard tasks in Image Reduction and Analysis Facility (IRAF). 7 7 IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement


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ACKNOWLEDGEMENTS The authors thank Volker Springel for help with gadget 4 and helpful discussion about the convergence, Alexandre Barreira for providing the data for G 1 , and Titouan Lazeyras for data of the separate universe simulations and helpful discussions. AS is supported by DFG through SFB-Transregio TR33 ‘The Dark Universe’. FS acknowledges support from the Starting Grant (ERC-2015-STG 678652) ‘GrInflaGal’ from the European Research Council.


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The authors would like to thank the anonymous referee for providing detailed and constructive suggestions to improve this paper. J.L. acknowledges support from the Research Grants Council of Hong Kong through grant 17319316. J.L. also acknowledges a Seed Fund for Basic Research from the University of Hong Kong. T.B. was supported by a Visiting Research Professor Scheme from the University of Hong Kong, during which major parts of this work were conducted. J.M.D. acknowledges the support of projects AYA2015-64508-P (MINECO/FEDER, UE), AYA2012-39475-C02-01, and the consolider project CSD2010-00064 funded by the Ministerio de Economia y Competitividad. Y.O. is supported by the Ministry of Science and Technology ( MOST ) of Taiwan, MOST 106-2112-M-001-008.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O 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 B-Wavelength I-Wavelength 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O B-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

plot summarizing the relative marginal errors on parameters, , for all the parameters, the flux thresholds, the ELG samples and redshift bins, and the sky areas considered. In particular, each row refers to a specific parameter, namely from the top to bottom; each column refers to a specific flux threshold, i.e. from the left- to right-hand side; red, green, and blue lines, respectively, refers to refer to H α , O iii + H β , and O ii galaxies; and diamond, triangle, square, and circle markers refer to , respectively. Figure 7. Relative 1 σ marginal errors on redshift-dependent parameters from the clustering of galaxies detected through different line emission: H α in red, O iii + H β in green, and O ii in blue. Circles, squares, triangles, and diamonds refer to survey areas of 1, 5, 15, and 30 in , respectively, whereas the four columns illustrate the dependence of the constraints on the flux threshold, set to from the left- to right-hand side. The main conclusion one can draw from this plot is that – not counterintuitively – sensitivity is possibly more important than area for high-redshift observations. This is further demonstrated in Fig. 8 , where we focus on the extraction of RSDs in terms of constraints on the redshift-dependent quantity f σ 8 ( z ). We adopt the same colour code as before for the various ELG samples, and the two panels show forecast 1 σ marginal error bars on measurements of f σ 8 ( z i ) in each redshift bin, for a wide and shallow survey (left-hand panel) or a narrow and deep survey (right-hand panel). Clearly, measurements extracted from the original target, namely the H α -galaxy sample, are optimized for the former survey specifications, with error bars tighter than those obtained with the latter experimental configuration. It turns out that a large area and a relatively larger flux threshold is also better for RSD estimation from the O iii + H β sample, with error bars smaller than for a narrow and deep survey. On the other hand, when it comes to the extraction of cosmological information from redshift 3−5 O ii galaxies, it is better to observe as much as 30 times a smaller sky area, but with twice as deep a survey, which yields f σ 8 ( z ) measurements more constrained. Figure 8. Relative 1 σ marginal errors on f σ 8 ( z ) from the clustering of galaxies detected through different line emission: H α in red, O iii + Hβ in green, and O ii in blue, for two different surveys: on the left-hand side a lower sensitive but wide surveys (, ); on the right-hand side a narrow but more sensitive survey (, ). Finally, let us touch upon the importance of high-redshift oxygen-line galaxies to constrain cosmological parameters. Hitherto, we have focused on model-independent parameters related to the redshift evolution of the matter power spectrum, and on its modulation by BAOs, galaxy bias, and RSDs. The next stage will now be to translate constraints on those parameters to more fundamental cosmological parameters as, for


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

S.R. thanks Chris Matzner, Eliot Quataert, and Yan-Fei Jiang for useful conversations. S.R. appreciates the referee for their comments and suggestions. This research was funded by the Gordon and Betty Moore Foundation through Grant GBMF5076.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O 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 B-Software O O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Survey I-Survey I-Survey O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O B-Survey I-Survey O O O O O O O O O O O O O O O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

spectra belong to the bright configuration, while lower panel spectra belong to the faint configuration. V total magnitude is in the bottom right inset. The overall S/N is 55, 39, and 15 for the bright spectra, and 9, 6, and 4 for the faint ones. 5. Redshifts We measured galaxy redshifts on the spliced spectra, that is, those extending over the entire wavelength range (3800–9000 Å), in order to gather information both from the blue part of the spectra (where at our redshifts, most optical absorption lines are present) and from the red part of the spectra (where the H + NII region is located). The night sky residuals, present in specific regions of the spectra, have been replaced by interpolated values before measuring the redshifts. On these cleaned spectra we measured both the redshift obtained by cross-correlating the spectrum with that of a template at zero velocity (using the IRAF/xcsao package) and the one obtained from the match of emission lines ( IRAF/emsao ). Each single spectrum was visually inspected by members of the team (A.M., B.P., D.B., J.F., M.G., A.P., A.C.) to ensure that the automatic estimation was correct, and to assign a flag that was then used to derive the final redshift determination. We used: the weighted average of the two determinations if both wereflagged as good; the emission line redshift if the cross-correlation was not convincing; and the cross-correlation redshift if spectra did not contain emission lines (and the cross correlation was reliable). Errors on the redshifts are the errors of the combined measurements of both absorption features and emission features if the two redshift estimates were averaged together, and are single errors on the measurements that do not have emission lines, or where we did not trust the absorption line cross-correlation. Among the original 18 995 spectra, we were able to measure 17 985 redshifts, with a median error of 50 km s and average completeness 95. Figure 4 shows the distribution in redshift of all the OmegaWINGS targets (black line). The filled histogram represents the redshift determinations obtained with the previous WINGS spectroscopic survey ( Cava et al. 2009 ), all in the inner cluster regions. The red histogram shows the new Omega WINGS redshifts. When a new redshift was present, we used this determination instead of the old WINGS one (the difference between the two determinations being peaked at , with a few cases of real mismatches in spectra with low S/N). The number of cluster members with a AAOmega redshift is 7497, that adds to the 2732 galaxies belonging to the clusters for which we had a previous WINGS measurement. This means that the total number of cluster members rises to 10 229 in total. 5.1. Completeness To ensure that we could properly derive global properties from the clusters under scrutiny, and from their galaxy populations, we calculated the spectroscopic completeness as a function of both magnitude and radial distance. The first term is


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AC acknowledges support from the National Aeronautics and Space Administration under Grant No. 12-ADAP12-0139 issued through the ADAP programme. EI acknowledges funding from CONICYT/FONDECYT post-doctoral project No.: 3130504. JWa is supported by a European Union COFUND/Durham Junior Research Fellowship under EU grant agreement number 267209, and acknowledges additional support from STFC (ST/L00075X/1). RJI acknowledges support from the European Research Council in the form of the Advanced Investigator Program, 321302, COSMICISM. SJO acknowledges support from the Science and Technology Facilities Council (grant number ST/L000652/1). SRS acknowledges support from NASA NESSF. The construction of MUSIC was supported by JPL RTD, NASA APRA, NSF ATI and NSF AAG. The Dark Cosmology Centre is funded by the Danish National Research Foundation. This paper makes use of the following ALMA data: ADS/JAO.ALMA#2013.1.00449.S. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (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. SPIRE has been developed by a consortium of institutes led by Cardiff Univ. (UK) and including Univ. Lethbridge (Canada); NAOC (China); CEA, LAM (France); IFSI, Univ. Padua (Italy); IAC (Spain); Stockholm Observatory (Sweden); Imperial College London, RAL, UCL-MSSL, UKATC, Univ. Sussex (UK); Caltech, JPL, NHSC, Univ. Colorado (USA). This development has been supported by national funding agencies: CSA (Canada); NAOC (China); CEA, CNES, CNRS (France); ASI (Italy); MCINN (Spain); SNSB (Sweden); STFC (UK) and NASA (USA). HCSS/HSpot/HIPE are joint developments by the Herschel Science Ground Segment Consortium, consisting of ESA, the NASA Herschel Science Center and the HIFI, PACS and SPIRE consortia. This research has made use of data from the HerMES project ( http://hermes.sussex.ac.uk/ ). HerMES is a Herschel Key Programme utilizing Guaranteed Time from the SPIRE instrument team, ESAC scientists and a mission scientist. HerMES is described in Oliver et al. ( 2012 ). The data presented in this paper will be released through the HerMES Database in Marseille, HeDaM ( http://hedam.lam.fr/HerMES/ ).


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OHP and MR acknowledge support from NASA grant NNX10AH10G, NSF CDI-typeII grant CMMI1125285, and the Theoretical and Computational Astrophysics Network (TCAN) grant AST1333514. The authors acknowledge the University of Maryland supercomputing resources ( http://www.it.umd.edu/hpcc ) made available in conducting the research reported in this paper. This work also used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by NSF grant number ACI-1053575. We thank the anonymous reviewer for helping improve the quality and clarity of this paper.


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

the size of the halo scatter in GR. For the mapping defined using the effective density field, given by equation ( 17 ), it has been expected that the GR X-ray luminosity should be equal to the f ( R ) gravity value multiplied by the factor . From Fig. 6 , the rescaled data in F5 appear to be higher than in GR by on average for both the non-radiative and the full-physics simulations. A similar level of deviation is also observed for the true density results, where equation ( 22 ) predicts that the GR and f ( R ) gravity X-ray luminosity should be equal after the values in f ( R ) gravity are divided by the factor . Again, the rescaled F5 X-ray luminosity is significantly greater than in GR on average. As for the Y SZ and Y X mappings, the disparity found here can be explained by looking at the gas density profiles in Fig. 2 . For both the non-radiative and full-physics data, the gas density in the inner halo regions is greater for F5 (with appropriate rescaling applied) than for GR. Because the inner regions have a greater contribution to the X-ray luminosity than for other proxies, as described above, this causes these differences in the inner regions to become significant overall, even for the non-radiative data for which the F5 and GR profiles are converged above a lower radius. This results in the general offset for the full range of masses as shown in Fig. 6 . As described above, the X-ray luminosity is also more strongly influenced by feedback processes, which can further increase the offset between F5 and GR if the feedback behaves differently in these two models. Our observation that the mappings have a poorer performance for the X-ray luminosity than for the other proxies is consistent with He Li ( 2016 ), who observed a disparity of . Unless further corrections are applied to account for the unpredictable effects of feedback in the mappings therefore the X-ray luminosity is unlikely to be a reliable proxy for mass determination in accurate cluster tests of f ( R ) gravity. 4.1.4 Further comments As described in Section 3.2 , we have excluded the core region of r 0.15 R 500 when calculating the thermal properties of our simulated FOF groups. We have also experimented excluding core regions of size r 0.1 R 500 and r 0.2 R 500 : for the scaling relations Y SZ – M, Y X – M , and – M , the relative differences between f ( R ) gravity and GR are barely affected; on the other hand, the effect is larger for the L X – M scaling relation, because L X is more sensitive to the inner halo regions than the other proxies. However, the L X – M relation is not ideal for reliable tests of gravity anyway, as noted above, and is mainly included in this work for completeness and for comparison with the other relations. Even if the entire core is included in the calculations, we have found that the effect on the Y SZ – M and Y X – M results is still very small, providing further confirmation that these relations can be used for reliable tests of


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

and is very likely a few degrees. Thus in total we see that the observed bend is ∼70° at angle θ ≈ φ int /1.4. In other words, an intrinsic bend in the jet of only a few degrees will produce the overall projected bend in the jet axis of ∼70° that we see in Figure 4 (c) when viewed from within a few degrees of the jet axis. Of course, the observed bend angle tends to 180° as θ → 0. The simplest possible bending model is a monotonic bend that lies all in a single plane, as assumed above. Given a small viewing angle near the base of the jet, this would normally result in an apparent one-sided jet, due to the strong Doppler boosting of the approaching jet emission and de-boosting of the receding jet emission. The approaching jet would also rapidly fade with distance from the core as the viewing angle increases. However, if the bending plane lies perpendicular to the sky, the jet can cross our line of sight, resulting in apparent emission from the approaching jet on both sides of the core. Statistically, the odds of this alignment appear at first to be low, but in a flux-limited AGN sample, there is a strong preference for those jets that have maximum Doppler boosting factor. The latter occurs when a portion of the jet is pointing directly at us, which is the case for a jet crossing our line of sight. Lister ( 1999 , p99) showed that in fact a simple parabolic bent jet will have a total apparent flux density much larger than a straight jet with identical inner jet viewing angle, provided the bending occurs in a plane nearly perpendicular to our line of sight. One notable case of this azimuthal favoritism is the blazar PKS 1510−089, where Homan et al. ( 2002 ) provide strong evidence of a highly superluminal jet that makes a 180° apparent bend in the sky plane, with resulting collinear jet emission on either side of the AGN core. We do therefore have to consider the possibility that all of the radio emission seen in this blazar is associated with the jet, but just happens to appear to straddle the nuclear core due to projection effects. One clear difference between the radio structures of PKS 1413+135 and PKS 1510−089 is the inner counterjet component C in PKS 1413+135 seen in Figures 4 (c)–(f). An even closer component of the inner counterjet, which is connected to the core component, is seen in the 8.1 GHz and 23.8 GHz images of Figure 5 . No such inner counterjet, close to the core, is seen in PKS 1510−089, and it is very hard to imagine that these two components close-in to the core, which are so well aligned with the jet position angle projected across the core, are actually components of the approaching curving jet that have been projected across the core to the counterjet side after the approaching jet curves through an apparent bend of ∼70° from components N through G as seen in Figure 4 (c). There is also the surface brightness of the components to consider. The components within 10 mas on the northeast side of the core have much higher


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ACKNOWLEDGEMENTS AS and AW would like to acknowledge a support of Beethoven Grant No. DFG-NCN 2016/23/G/ST1/04083. KB and KN were supported by NCN Maestro Grant No. 2012/06/A/ST1/00258. We also want to thank the GOES, STEREO, SDO, and SOHO teams for developing and operating the instruments as well as for their open data policy. We are grateful to the referee for extensive and constructive comments and suggestions that helped us to improve the quality of the manuscript.


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We thank the anonymous referee for the helpful comments that helped us to improve the manuscript. This work is based on observations obtained with XMM-Newton , an ESA science mission with instruments and contributions directly funded by ESA Member States and the USA (NASA). M.D. thanks Paola Grandi, Daniele Dallacasa for useful discussions. M.D. and M.C. aknowledge financial support from the Italian Space Agency under grant ASI-INAF I/037/12/0 and extended PRIN INAF 2012. GL acknowledges financial support from the CIG grant “eEASY” No. 321913, from ASI-INAF 2014-045-R.0 and ASI/INAF I/037/12/0–011/13 grants. G.P. thanks the DLR: the Bundesministerium für Wirtschaft und Technologie/Deutsche Zentrum für Luft-und Raumfahrt (BMWI/DLR, FKZ 50 OR 1408).


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Acknowledgements We thank Alexandre Faure for providing collisional excitation rates at low temperatures, and Luca Matrà for sharing the model of the dust radiation field and the ALMA data of CO. We also thank the referee for helpful and thorough comments. HIFI has been designed and built by a consortium of institutes and university departments from across Europe, Canada and the United States under the leadership of SRON Netherlands Institute for Space Research, Groningen, The Netherlands and with major contributions from Germany, France and the US. Consortium members are: Canada: CSA, U.Waterloo; France: CESR, LAB, LERMA, IRAM; Germany: KOSMA, MPIfR, MPS; Ireland, NUI Maynooth; Italy: ASI, IFSI-INAF, Osservatorio Astrofisico di Arcetri-INAF; Netherlands: SRON, TUD; Poland: CAMK, CBK; Spain: Observatorio Astronómico Nacional (IGN), Centro de Astrobiología (CSIC-INTA). Sweden: Chalmers University of Technology - MC2, RSS GARD; Onsala Space Observatory; Swedish National Space Board, Stockholm University - Stockholm Observatory; Switzerland: ETH Zurich, FHNW; USA: Caltech, JPL, NHSC. This work was supported by the Momentum grant of the MTA CSFK Lendület Disk Research Group and by JSPS KAKENHI Grant Number JP16F16770. This research has made use of NASA’s Astrophysics Data System.


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We thank David Bacon, Alan Heavens, Enrique Gaztanaga, Catherine Heymans and Elisabeth Krause for useful conversations. RC and FP acknowledge support from STFC grant ST/H002774/1. This work was also supported in part by the National Science Foundation under Grant No. PHYS-1066293 and the hospitality of the Aspen Center for Physics.


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We enthusiastically thank the staff of Siding Spring Observatory and the W. M. Keck Observatory and its AO team, for their dedication and hard work. The authors wish to pay their respects to the Elders – past, present and future – of the traditional lands on which Siding Spring Observatory stands and to those of Hawai'ian ancestry on whose sacred mountain we are privileged to be guests. Without their generous hospitality, these observations would not have been possible. AMM, LJK, and MAD acknowledge the support of the Australian Research Council (ARC) through Discovery project DP130103925. This work was also partially funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, under grant no. (5-130/1433 HiCi). The authors acknowledge this financial support from KAU. AMM and CEM also acknowledge support by the National Science Foundation under award number AST-0908796.


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

magnitude, but also on the stopping time. Fig. 11 Rootmean square of in the midplane as a function of r (lower abscissa) and the dimensionless gas pressure gradient parameter Π in the midplane (upper abscissa). The root mean square is calculated using the mass-weighted mean over 500 yr after an equilibrium value of the dust scale height is reached. In the simulation adi_Z=0.02_Lr=90au_taustop=0.1 (blue line), in which the dimensionless dust stopping time τ stop is fixed at 0.1, the Mach number increases with the pressure gradient parameter if Π ≲ 0.09, but is approximately constant if the pressure gradient is stronger. The Mach number in this one and the simulation adi_Z=0.02_Lr=90au (green line), in which the stopping time increases from 0.046 to 0.46, is comparable at all radii. That is, the turbulent strength does not depend significantly on the stopping time in this stopping time regime. The Mach number is lower overall, but depends more strongly on the radius in the simulation adi_Z=0.02_Lr=90au_a=3mm (orange line) in which the stopping time ranges from 0.0046 to 0.046. In this regime, the turbulent strength increases with both the strength of the pressure gradient and the stopping time. 5.3 Radial gas velocity In Fig. 12 , we show the radial velocity of the gas. The gas moves outward on average as a consequence of the inward radial drift of the dust and, as the total angular momentum is conserved, the transfer of angular momentum from the dust to the gas. Yet, the turbulent motions that are induced by the streaming instability lead to the variance in the gas velocity being greater thanthe speed of this mean outward motion. That is, the streaming instability does not cause a sustained inward transport of gas mass (and outward transport of angular momentum) that contributes to the observed stellar accretion ( Alcalá et al. 2017 ). 6 Discussion 6.1 Implications for turbulence and planetesimal formation in protoplanetary disks We have studied the interaction of two instabilities, the vertical shear instability and the streaming instability. Both instabilities appear to be robust: operation of the vertical shear instability requires a vertical rotation profile and a sufficiently short gas cooling timescale. Lin Youdin (2015) show that in the MMSN model, the instability can grow between r ≈ 5 and 50 au. On the other hand, only dust and a radial gas pressure gradient are necessary for the streaming instability to be active. Fig. 12 Radial gas velocity (solid line) as a function of r in the simulations adi_Z=0.02_Lr=9au and adi_Z=0.02_Lr=90au . (The dashed lines marks the boundary between the domains of the two simulations.) The velocity is computed as the mass-weighted average over the vertical domain extent and a time-span of 50 and 500 yr, respectively,after an equilibrium dust scale height has been attained in each simulation. The average radial velocity at r ≥ 3 au is plotted as a dotted line and amounts to 0.035 m s −1 . This outward


O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O B-Telescope 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 O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O B-Observatory I-Observatory O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O B-Model O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O B-Dataset I-Dataset I-Dataset I-Dataset B-Dataset O O O O O B-Formula I-Formula I-Formula I-Formula B-Citation I-Citation I-Citation I-Citation I-Citation O O O B-Model O B-CelestialObject I-CelestialObject O O O O B-ObservationalTechniques I-ObservationalTechniques O O B-Wavelength B-Wavelength O B-Wavelength O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O B-Database

two very weak periods were also detected, at 20 minutes and 90 minutes, but cannot be confirmed. Figure 10. Multiband PDM analysis of the oscillatory variation on a timescale of days. A period of 3.9 ± 0.005 days is clearly detected (upper panel) from light curves based on the superposition of two independent observations. The bottom panel is the phased light curves folded with the detected 3.9 day period, in which the symbols are the same as in Figure 2 , revealing a sinusoidally shaped light curve. Figure 11. Variability of HO Pup down to a timescale of hours. Panel (a) presents the SLT r -band photometric data taken from 2019 December to 2020 March. The blue curve represents the 3.9 day cycle fitted with a sinusoidal function (see Figure 10 ). To uncover the variability shorter than one day, a sinusoidal function of 3.9 days has been subtracted from this light curve and the residuals are displayed in panel (b). After removing the 3.9 day cyclic variations, we found a new cycle of 50 minute variations using Lomb–Scargle periodogram analysis, based on the light-curve data taken from 2019 December to 2020 January, as shown in panel (c). As can be seen from this panel, the variation signal is well above the false-alarm probability (FAP, indicated by the red and cyan dashed lines for the 95% and 99% FAPs, respectively). The variability with 50 minute period can be easily seen in the phased light curve as presented in panel (e). However, the 50 minute variations were barely resolved or undetected for the data collected between 2020 February and March, as evident in panels (d) and (f). Instead, complicated variations can be seen in the nightly chunks of light-curve data during this period of observations. 3.6. Polarization Variation We have also observed variations in polarization for HO Pup. Based on polarization level P and position angle θ measured from Lulin Observatory (see Table 3 ), a small and yet significant polarization was observed on 2018 October 24 and 26. However, the polarization drops back to an insignificant value on 2018 October 25 and 2018 October 28. The observed variation in polarization suggested that HO Pup exhibits intrinsic polarization. 4. Discussion 4.1. Spectral-energy-distribution Fitting Prior to our work, classification of HO Pup in the literature was done via inspection of its light curves, either as a Be star with GCAS-type variability (Samus et al. 2017 ) or as an IW And-type DN (Kimura et al. 2020a ). Here, we first estimated its spectral and luminous class using spectral-energy-distribution fitting together with distance estimation based on the parallax measurement from Gaia Data Release 2 (DR2) (1.6165 ± 0.0311 mas, or d = 618.6 pc, Gaia Collaboration et al. 2018 ). The observed SED of HO Pup was constructed using available broadband photometry covering from near-UV (NUV) to mid-infrared. In Table 5 we list all available broadband photometric data on HO Pup queried within 1′′ radius using the VizieR


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We thank the referee for the constructive report, which greatly improved the manuscript. We thank Patrick Ogle for the helpful comments. This work uses observations obtained with XMM-Newton , an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA. In this work, the NASA/IPAC Extragalactic Database (NED) have been used. Á.B., C.J., W.R.F, and R.K. acknowledge support from the Smithsonian Institution.


O O B-CelestialObject O O O O O B-ObservationalTechniques I-ObservationalTechniques I-ObservationalTechniques B-ObservationalTechniques O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O B-Survey I-Survey I-Survey I-Survey B-Survey O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O B-Survey O B-Instrument O B-Survey O B-Telescope O B-Telescope O O O O B-Survey O B-Citation I-Citation I-Citation I-Citation O O O B-Survey B-Citation I-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 O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O B-Citation I-Citation I-Citation I-Citation O O O B-Wavelength 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 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 B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Wavelength O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey 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-Wavelength B-Wavelength 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 B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O 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 O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation

the inhomogeneous Universe, in particular, by using the baryon acoustic oscillation (BAO) as a standard ruler (e.g. Cole et al. 2005 ; Eisenstein et al. 2005 ). The Baryonic Oscillation Spectroscopic Survey (BOSS) experiment demonstrated the ability of BAO measurements to provide a standard ruler to the per cent level at redshift 0.5 (Anderson et al. 2014 ). Though the BAO is known to be largely free of systematic errors (e.g. Vargas-Magaña et al. 2014 ; Ross, Percival Manera 2015 ), precise measurement requires surveys of a large number of sources over a large cosmic volume. The current and future dark energy surveys aim to efficiently sample tens of millions of faint galaxies/quasars at redshift 0.5 ≲ z ≲ 2.3 over the entire observable sky to measure BAO at the per cent level (e.g. eBOSS, 1 DESI, 2 PFS, 3 4MOST, 4 EUCLID . 5 ) The eBOSS survey (Dawson et al. 2016 ) in the SDSS-IV (Blanton et al., in preparation), started in Fall 2014 and is currently mapping the large-scale structure at redshift z > 0.6 with four different tracers: luminous red galaxies (LRGs; Prakash et al. 2015 ), emission line galaxies (ELGs; Comparat et al. 2015a ), QSOs, and Lyα absorption (Myers et al. 2015 ; Palanque-Delabrouille et al. 2016 ). It will provide the first density map covering the redshift range 0.6 z 2.5 over a large portion of the sky (7500 deg 2 of LRGs and QSOs, 1500 deg 2 of ELGs). To achieve these goals with a 2.5-metre telescope, eBOSS requires efficient methods to pre-select targets using both magnitude and colour cuts. For ELGs, there is an additional source of complication: their redshifts will be mainly determined by emission lines, and it is therefore important to characterize the sampling efficiency of ELGs with broad-band magnitude and colour selections (e.g. Comparat et al. 2015a ; Raichoor et al. 2016 ). Studies have shown that the future ELG surveys will sample the or the Hα emitters in an incomplete manner (Comparat et al. 2015b ; Tonegawa et al. 2015 ). A more precise quantification of this incompleteness is critical for a more detailed understanding of the selection effects and to enable more precise cosmological analysis. In the redshift range targeted by eBOSS (0.6 z 1.2 for ELGs), the strongest emission lines that can be observed in the optical are the oxygen , lines and the hydrogen Hβ (λ4861) Balmer line. All other lines are either outside of the optical window at these redshifts, or an order of magnitude weaker and therefore will not drive the completeness of the ELG survey. Of these three line luminosity functions (LFs), the LF is the most well-known. Its LF has been measured from redshift 0 to 4.7 (e.g. Ly et al. 2007 ; Zhu, Moustakas Blanton 2009 ; Gilbank et al. 2010 ; Bayliss et al. 2011 ; Sobral et al. 2012 ; Comparat et al. 2015b ; Khostovan et al. 2015 ), mostly due to interests in using as an empirical star formation rate (SFR) indicator (see Kennicutt 1998 ; Kewley, Geller Jansen 2004 ; Moustakas, Kennicutt Tremonti


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We thank the referee for constructive suggestions. We also thank R.J. van Weeren for comments on the manuscript. H.K. was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2014R1A1A2057940). D.R. was supported by the National Research Foundation of Korea through grant NRF-2014M1A7A1A03029872.


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I would like to especially thank Geoff Marcy for extensive discussions and advice, Howard Isaacson for sharing samples from his MCMC fits to the Keck RV data, and an anonymous reviewer whose comments helped to improve this manuscript. I am also grateful for helpful discussions with Lauren Weiss, Rebekah Dawson, Tim Morton, Brice-Olivier Demory, Brian Jackson, Jack Lissauer, Tom Loredo, Eric Ford, David Hogg, and John Johnson. I acknowledge support provided by NASA through Hubble Fellowship grant #HF-51313 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5–26555. This work also benefited from the Summer Program on Modern Statistical and Computational Methods for Analysis of Kepler Data, held at SAMSI, Research Triangle Park, NC in 2013 June. This research has made use of the Exoplanet Orbit Database and the Exoplanet Data Explorer at exoplanets.org.


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constituting a plasma. Importantly, the observed β = 1 and the obtained Γ = 4/3 indicate that the longitudinal current, though in general not obliged to conserve along the magnetic tube, appears as an exact integral of motion at the scales under consideration, Since ρ ∝ r −2 − β = r −3 , we have for a hot flow h ∝ ρ Γ − 1 = ρ 1/3 ∝ r −1 ; therefore, by equation ( 2 ) the equality ( 49 ) holds, whatever the nature of the force balance in the jet. Energy conservation ( 10 ) then leads us to the above conclusion. This is direct evidence of a stable longitudinal current structure in the jet. It is interesting to consider what happens at 8 marcsec. Mertens et al. ( 2016 ), taking into account the results of Lyubarsky ( 2009 ), discuss that the jet may there enter a non-equilibrium regime or rather exhibit an early saturation of Poynting-flux conversion. Meanwhile, an alternative explanation may be a change of the jet thermodynamics. The relativistic gas is not characterized by a single polytropic index, and the general expression for its enthalpy is h = K 3 (1/Θ)/ K 2 (1/Θ), where K ν ( z ) is the Macdonald function of order ν and Θ = p /ρ is the temperature (Synge 1957 ). Useful simpler analytic approximations of the exact expression are presented in Mathews ( 1971 ), Meliani et al. ( 2004 ), Chattopadhyay Ryu ( 2009 ). In the two opposite limiting cases it corresponds to a polytrope with index Γ = 4/3 when Θ ≫ 1 and with index Γ = 5/3 when Θ ≪ 1. From equations ( 2 ) and ( 3 ) we have which allows us to formally estimate the polytropic index, respectively, for the case of a dominating longitudinal magnetic, transverse electromagnetic, and centrifugal pressure: Since Γ TEM = Γ CH 4/3, a hot flow with a dominating transverse electromagnetic or centrifugal pressure is not realized over 8 marcsec. The two other indices correspond to a cold flow: Γ LM is close to but yet slightly larger than the maximum possible 5/3, while, surprisingly, Γ CC almost coincides with 5/3 ≈ 1.67. Therefore, a transition from γ ∝ z 0.58 to γ ∝ z 0.16 at z ∼ 8 marcsec may be explained by the plasma cooling and transition from a hot flow with p ∝ ρ 4/3 to a cold flow with p ∝ ρ 5/3 . Over 8 marcsec we likely have a cold flow whose pressure is determined mainly by centrifugal forces, possibly with some contribution from the pressure of longitudinal magnetic field, while transverse electromagnetic fields give forces that almost compensate each other and result in a modest net effect. Determination of Γ from the jet acceleration and collimation profiles has power in revealing plasma composition, which is important for conclusions about exact mechanisms of jet launching. The transition directly from 4/3 to 5/3 as cooling occurs may be a sign of a pure electron–positron plasma component: electrons and positrons have the same mass and behave as the mentioned single-component perfect Synge gas. In the case of an electron–proton plasma, however, the transition from 4/3 to 5/3


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ACKNOWLEDGEMENTS Calculation of this work is performed of the XC30 and XC50 system at the Center for Computational Astrophysics (CfCA), National Astronomical Observatory of Japan (NAOJ). This work supported by JSPS KAKENHI Grant Number JP 19J13373 (RT), Society for the Promotion of Science Grant-in-Aid for Scientific Research (A) (17H01102 KO; 16H02170 TT), Scientific Research (C) (16K05309 KO; 18K03710 KO), and Scientific Research on Innovative Areas (18H04592KO; 18H05463 TT). This research is also supported by the Ministry of Education, Culture, Sports, Science and Technology of Japan as ‘Priority Issue on Post-K computer’ (Elucidation of the Fundamental Laws and Evolution of the Universe) and JICFuS. RT acknowledges the support by JSPS Overseas Challenge Program for Young Researchers. CD acknowledges the Science and Technology Facilities Council (STFC) through grant ST/P000541/1, and visitor support from Kavli IPMU.