O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

region creates a bright patch between n0 and p1, and hot plasma escapes out along the new open field to become the spire of Phase 1. The spire is collimated by the dominant strong open magnetic flux. Heat from the reconnection is magnetically confined to a small volume in the closed field below the reconnection location and so shows up as a brightening, but in the open field above the reconnection site it is spread over a much larger volume and so does not lead to a brightening in region n1. The continuous magnetic cancellation makes the jet move sideways. It can be seen, by comparing Figures 7 (b) and (c), that the location of the open field line that has just reconnected (and therefore the spire) moves to the left as reconnection proceeds. This transverse motion can be faster than the photospheric cancellation speed, since the transverse motion of photospheric sources can lead to a buildup of a current sheet that subsequently reconnects. Phase 2 is driven by the subsequent cancellation between n0 and p2 (Figure 7 (d)) and produces a spire and a brightening in the same manner as in Phase 1. It is possible that the two phases are independent of one another, but this is unlikely since they occur so close in time and space and the spire has a more or less smooth motion, which suggests that the first phase helped trigger the second phase or that the fragments p1 and p2 are not independent but are linked somehow by a common convection pattern in the moat below the photosphere. Figure 7. Schematic of the topology and magnetic reconnection in the two successive phases of a complex jet showing a few representative field lines marked by light-headed arrows before and after bursts of reconnections. (a) Before reconnection n0 and the outer parts of n1 and n2 are open magnetic fields with negative polarity. On both sides of n0, there are closed magnetic fields with positive polarities p1 and p2 linking to the inner parts of the negative polarities n1 and n2, as shown. Arrows mark the direction of magnetic field lines. (b) Phase 1 of the reconnection process driven by magnetic cancellation between n0 and p1. Reconnection takes place at the X-point, with plasma velocities shown by solid-headed arrows. The upward-moving outflow jet from the reconnection site is channeled upward by the open field lines as a spire. The separatrices and the field lines that have reconnected (a new open field line and a new closed field line) are marked in red. The location of a chromospheric brightening is also indicated below the reconnection location and straddling n0 and p1. (c) Phase 1 continues with more reconnection at the X-point and so creates a lateral motion of the spire. (d) Phase 2 repeats the same process, but at the X-point on the left side of n0, driven by magnetic cancellation as p2 approaches n0. The separatrices and the newly reconnected field lines are shown in red. The formation and evolution process of the jet is a process in which magnetic


O O O O O O O O O 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 B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation I-Citation 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 B-URL I-URL I-URL I-URL I-URL I-URL I-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 O O O O O O O O O O O O O O O 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 O O O O O O O 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

2015 ). For illustration, in Fig. 3 , we plot the radial profiles of various quantities for two models: inside-out scenario ( Case 1) and for constant short time-scale gas infall rate t f = 2.25 Gyr using the boundary τ b = 100 Myr. As we see, the distributions do not differ significantly for the two shown examples. Notice that, although near the corotation the reduced SFR for high-mass stars , their sum does not tend to zero at the corotation. 3 Our computed profiles for μ g , μ s and are close to observed ones derived by other authors (cf. our Fig. 3 with fig. 1 in Yin et al. 2009 or fig. 4 in Kubryk et al. 2015 ). Figure 3. Radial distributions of various quantities at present time. Solid lines: model with constant t f = 2.25 Gyr. Dashed lines: inside-out scenario. The boundary τ b = 100 Myr. The bend in μ g ( r ) at 4 kpc, seen for inside-out scenario (dashed lines), is due to change in t f approximation for r ≤ 4 kpc. The feature in at this distance is due to (see Sections 3.1 and 3.2). The upward jump in μ g , at r ≈ 12 kpc for the model with constant t f (solid lines) is associated with the outer Lindblad resonance r L , which is located at the same distance (see Section 3.3). The jump maybe easily explained by the cut-off at the same distance. 3.4 Oxygen synthesis in the Galactic disc In general, our ‘chemical’ equation, which describes the radial evolution of oxygen abundance along the Galactic disc in ISG, is close to the classical ones proposed by Tinsley ( 1980 ), Lacey Fall ( 1985 ), WS , PC , Matteucci ( 2003 ) and others with one correction that we work with composite SFR (see equation 8 ): where μ O is the mass density of oxygen in the disc, Z O = μ O /μ g , is the enrichment rate of ISG by newly synthesized oxygen: correspondingly P O is the mean mass of newly synthesized oxygen ejected per CC SN event. The lower limit in the integral, entering equation ( 18 ), we adopt to be equal to 10 M ⊙ since exploding CC SNe do not produce oxygen if the initial masses of their progenitors are less than 10 M ⊙ (e.g. Wanajo et al. 2009 ). The meaning of various terms in equation ( 17 ) is as follows. The second term on the right-hand side of the equation describes the increase of oxygen density due to intergalactic gas infall on to the disc. The third term describes the rate of oxygen return into ISG due to wind from low-mass stars and their pass to remnant; the fourth, fifth and sixth terms describe the depletion of oxygen in ISG due to capture it by the forming objects. The last term in equation ( 17 ) is the radial diffusion of oxygen that we associate with turbulence in ISG. The inclusion effect of diffusion was provoked by the following: if we do not take into account the diffusion, in our model we would have deep gap in oxygen radial distribution near the corotation because here ψ H → 0. To smooth away this sharp gap in the distribution, we must include the effect of diffusion. The combined effect of corotation resonance and


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation O O O O B-Telescope O O B-Instrument O O O O O O O B-CelestialRegion I-CelestialRegion O O O O O O O O O O O O O O O O O O O B-Wavelength B-Wavelength O B-Wavelength O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O 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-Wavelength O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-CelestialObject O O O O O O

inside the of each cluster. Many clusters have a so scarcely populated RGB that this parameter turns out to be null, which essentially points to negligible crowding in the cluster core compared to the environment of typical field-AGB stars. More populous clusters have a significant number of RGB stars, but their never exceeds 1.1 . At these maximum RGB densities, the magnitude bias turns out to be tiny (about mag), although the magnitude rms error (bottom panel of Figure 8 ) amounts to a very significant ∼0.12 mag. Assuming a Gaussian distribution of magnitude errors, the faintest among our candidate AGB stars could actually be TRGB stars (or real AGB stars slightly fainter than the TRGB) which entered into the AGB selection region just because of the photometric scatter. However, we verified that this fraction is very small: just 55 AGB candidates (shown in Figure 8 ), or ∼6 % of the sample, have a F160W magnitude compatible with it being a TRGB star scattered upwards by one rms. These cases include AGB candidates in dense globular clusters such as AP 1969 (B225-G280; Figure 4 ). Overall, these estimates of the cluster densities and crowding errors are quite crude and subject to many uncertainties: few RGB stars per cluster, no real fitting of cluster density profile, no real estimate of the likelihood of RGB stars being scattered into the AGB region, etc. Moreover, it suffices to examine Figure 4 to conclude that proper estimates of the effect of crowding would require extensive—and time-consuming—experiments of artificial star tests using the actual cluster images, or fully synthetic cluster tests. For the moment, we limit ourselves to making our estimates available in the final catalog, so that potential users can appreciate, with the help of Figure 8 , the chances that AGB candidates in a particular cluster are significantly affected by crowding. 2.6. C/M Classification with WFC3/IR Medium-band Filters We augment our catalog of cluster AGB candidates with estimates of their spectral subtypes where available. First, we use results from Boyer et al. ( 2013 , 2019 ), who performed an HST survey using WFC3/IR medium-band filters in 21 regions across the PHAT footprint, to classify their bright red giants as either C- or M-type. Their method uses the sensitivity of the filters F127M, F139M, and F153M to the presence of either CN + C 2 or H 2 O absorption features in the NIR. We cross-match our sample of 937 candidate AGB stars in clusters with the complete Boyer et al. ( 2019 ) catalog. We find a total of 59 robust matches, for which the differences between the catalogs are smaller than 004 in position, and smaller than 0.017 mag in both F110W and F160W magnitudes. All of them are classified as M stars. The lack of C stars is this small sample is not surprising, given the remarkable scarcity of C stars in M31, especially in its innermost regions (Boyer et al. 2019 ). Indeed the average C/M ratio across the M31 disk amounts to just ∼0.02. 2.7.


O B-Person O O O O B-Grant I-Grant O O B-Grant O B-Grant O O O O O O O O O O O O O B-Fellowship I-Fellowship B-Person O B-Person O O O O B-Person I-Person O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O B-Grant O O O O O O O O B-ComputingFacility B-ComputingFacility O O O B-Grant O B-Grant O O B-ComputingFacility O O O B-ComputingFacility I-ComputingFacility O O B-Organization I-Organization I-Organization I-Organization O O O B-Person I-Person O O O O O O O O O O O O O O O B-Grant B-Grant B-URL O O B-Grant O O O O O O O O B-Organization I-Organization I-Organization I-Organization B-Organization O O O O O O O O O O O B-Observatory O O O B-Observatory I-Observatory I-Observatory I-Observatory O B-Observatory O B-Proposal I-Proposal O O O O O O B-Software O O B-Organization I-Organization I-Organization I-Organization O O O O B-Collaboration I-Collaboration O O B-Person I-Person O O O O B-Software I-Software I-Software O B-Software O O O B-URL O

Acknowledgements CL was supported by the ILP LABEX (under reference ANR-10-LABX-63 and ANR-11-IDEX-0004-02) during the first part of this work and is now supported by a Beecroft Fellowship. JD and AS acknowledges funding support from Adrian Beecroft, the Oxford Martin School, and the Science and Technology Facilities Council (STFC). OI acknowledges the funding of the French Agence Nationale de la Recherche for the project ‘SAGACE’. This work relied on the HPC resources of CINES (Jade) under the allocation 2013047012 and c2014047012 made by GENCI and on the Horizon Cluster hosted by Institut d'Astrophysique de Paris. We warmly thank S. Rouberol for running the cluster on which the simulation was post-processed. This research is part of Spin(e) (ANR-13-BS05-0005, http://cosmicorigin.org ) and horizon-UK. This research is also partly supported by the Centre National d'Etudes Spatiales (CNES). This work is based on data products from observations made with ESO Telescopes at the La Silla Paranal Observatory under ESO programme ID 179.A-2005 and on data products produced by TERAPIX and the Cambridge Astronomy Survey Unit on behalf of the UltraVISTA consortium. We thank D. Munro for freely distributing his Yorick programming language and OpenGL interface (available at http://yorick.sourceforge.net/ ).


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

; Kudoh Basu 2003 ; Wiebe Watson 2004 ; Falceta-Gonçalves et al. 2008 ; Hildebrand et al. 2009 ; Houde et al. 2009 ). Reduction of due to averaging effects is of great importance in our paper. Roughly speaking, two main averaging effects exist. First, averaging along the LOS can reduce . That is, if there is more than one independent turbulent eddy along the LOS, the measured value of will be reduced (see Myers Goodman 1991 ; Zweibel 1996 ; Houde et al. 2009 ). Second, averaging the polarization angle within the telescope beam can also reduce (see Heitsch et al. 2001 ; Wiebe Watson 2004 ; Falceta-Gonçalves et al. 2008 ; Houde et al. 2009 ). The averaging effects in general make the step from Equation ( 2 ) to Equation ( 3 ) inaccurate. In the presence of the averaging effects, the CF method tends to overestimate . In this paper, we focus on the averaging effect along the LOS and propose a simple method to compensate for the effect. Using three-dimensional direct magnetohydrodynamic (MHD) turbulence simulations, we test the proposed technique. In Section 2 , we describe our numerical method and explain in detail how averaging along the LOS makes the conventional CF method overestimate . At the end of Section 2 , we describe our new technique. In Section 3 , we present the results of our numerical simulations. In Section 4 , we discuss our findings and summarize. 2. NUMERICAL METHOD AND THEORETICAL CONSIDERATIONS 2.1. Numerical Code To obtain turbulence data, we solve the following compressible MHD equations in a periodic box of size using an essentially non-oscillatory scheme (see Cho Lazarian 2002 ): with ∇ · and an isothermal equation of state , where C s is the sound speed and ρ is density. Here, is the velocity, is the magnetic field, and is the driving force. We use 512 3 grid points. In our simulations, C s = 0.1, , and . In all simulations, the rms velocity v rms is between ∼0.7 and ∼0.8, and the sonic Mach number is . Since the Alfvén speed of the mean field () is 1, the Alfvén Mach number is , which means that the turbulence considered in this paper is sub-Alfvénic. 2.2. Forcing In this work, we drive turbulence in Fourier space and consider only solenoidal () forcing. We use ∼100 forcing components isotropically distributed in the range , where k is the wavenumber and k f varies from simulation to simulation (see Table 1 ). Therefore, the peak of energy injection occurs at . More detailed descriptions of forcing can be found in Yoo Cho ( 2014 ). Table 1 Simulations Notes. a Sonic Mach number. b Alfvén speed of mean magnetic field. c Driving wavenumber. d L los is the system size and L f is the driving scale. In our simulations, L los = 2 π and . Therefore, we have . 2.3. Theoretical Considerations: The Effects of Averaging along an LOS Our main concern is to investigate the effect of the driving scale on the CF method. For this purpose, we change the driving scale by changing the driving wavenumber k f . If the driving scale is L f ,


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

region (black dashed line). For the viscous simulation on the other hand, we can see that the Poynting flux leaving the coronal shell region (solid black line) is substantially smaller than the Poynting flux entering the region (green dashed line). This difference is of the same order as the internal energy increase in the shell region (not shown here). The Poynting flux entering the shell region through the near TR-coronal boundary (green lines) differs in the ideal and viscous simulation due to the different mixture of propagating and standing waves in this region. For the ideal simulation, the standing wave component dominates, which reduces the amount of Poynting flux through the near boundary, as the standing regime creates a node in v z (see e.g. Prokopyszyn et al. 2019 ). Comparing with coronal energy requirements, the difference between the average Poynting flux entering and leaving through the TR-coronal boundaries of the shell region for the viscous simulation is of the order of 1.5−2 Jm −2 s −1 , several orders of magnitude too low, even for the Quiet Sun (∼3 × 10 2 Jm −2 s −1 , Withbroe Noyes 1977 ). Fig. 9. Time integrated Poynting flux , with S the boundaries of the left shell, for the viscous (solid lines) and ideal simulation (dashed lines). The green lines represent the lower TR-coronal boundary and the black lines the upper boundary. 4. Discussion and conclusions In this paper, we use 2.5D numerical simulations to investigate whether a pre-existing density profile is modified by the evaporative upflows following (viscous) heating by phase mixing of Alfvén waves. The Alfvén waves are driven through an additional forcing term in the momentum equation. The simulations account for the effects of gravitational stratification, thermal conduction, and optically thin radiation. A fully resolved atmospheric model (including the chromosphere as a mass reservoir) is achieved with relatively modest resolution by artificially broadening the TR using the approach proposed by Lionello et al. (2009) and Mikić et al. (2013) . To include a transverse density profile (perpendicular to the background magnetic field) in the initial setup, a heating function which varies in the cross-field direction is imposed. Throughout the simulations (running for a total time of more than 5000 s), a complex combination of Alfvén waves ( v z ) and longitudinal perturbations ( v y ) is present in the domain. The longitudinal perturbations are a combination of long-period oscillations resulting from the ongoing evolution due to the imposed cross-field heating profile, the ponderomotive effects associated with the driven Alfvén waves, and the evaporative upflows resulting from heating occurring in the coronal part of the shell regions of the loop due to phase mixing of the Alfvén waves. By comparing with the results from the ideal simulations, we are able to distinguish the evaporative upflows present in the viscous simulations from the other (ideal) longitudinal


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

PDSs obtained during the 20042005 outburst decay ( Qu et al. 2005 ). They found a QPO at 0.22 Hz in addition to a narrow peak (i.e. pulsation from the pulsar) close to that frequency (0.23 Hz). The QPO was detected when the luminosity was at a mid-flux level of the outburst, or even lower. The rms strength of this QPO also amounts to a few per cent in that work. The 0.22 Hz QPO was observed around the spin frequency in both the INTEGRAL ( Mowlavi et al. 2006 ) and RXTE data during the 2005 outburst decline ( Qu et al. 2005 ; Reig et al. 2006 ). In addition, Takeshima et al. (1994) discovered another QPO with a centroid frequency of 0.05 Hz and a relative rms amplitude of 5% in the 2.337.2 keV data from the 1989 outburst of V 0332+53. We do not find any signal of the QPO at 0.05 Hz, although we find the presence of a broad component at around that frequency (which may eventually turn into peak noise, i.e. QPO). The QPO detected in V 0332+53 at 0.22 Hz constitutes the first detection of a QPO riding on the spin frequency of a NS and points to a strong coupling between the periodic (i.e. the pulses) and the red-noise (i.e. broad-band QPO signal) components ( Qu et al. 2005 ). The existence of a QPO signal with a similar frequency to the spin of the NS suggests that they are related in some way. One model to explain this coincidence was given by Lazzati Stella (1997) and Burderi et al. (1997) . They proposed that the QPO originates in the magnetosphere around the NS. Additionally, they argued that the accretion flow is inhomogeneous near the surface of the NS, and that random shots are characterized by an arbitrary degree of modulation. The combination of rotation and radiative transfer effects should therefore produce a periodic modulation of the shots similar to that of any continuum X-ray emission from the polar caps. They proposed that a coupling between the periodic and red-noise variability should be frequently present in X-ray pulsars. In our case and in contrast to previous observations during giant flares ( Reig et al. 2006 ; Reig 2008 ) the QPO signal appears during the lowest of the measured fluxes ( ). If the QPO has an origin on the magnetosphere of the NS (and is not an artefact from our observations), it should be more visible when the accretion column is more tenuous (or even absent). In summary, it looks as if we might be witnessing the innermost parts closest to the magnetosphere surroundings during our latest observations, i.e. Obs. 611. 5. Summary and conclusions In this paper we present a multiwavelength study of the Be/X-ray binary system V 0332+53 with the main goal of studying its transient behaviour during its intermediate luminosity X-ray outburst in 2008. After being yr in quiescence in X-rays, the system underwent a new active period. A new X-ray outburst was detected around 17 October 2008, roughly six days before the periastron passage of the NS. We note that the optical companion entered the brightening state nearly


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

for further analyses. Fig. 2 shows the final image after co-adding. It clearly shows a central galaxy surrounded by an extend blueish arc in the south-west (labelled as C and D) and two other blobs in the north (A) and south-east (B), respectively. Both the central galaxy and the extended arc are observed spectroscopically by the SDSS, and their spectra are shown in the right-hand panel of Fig.1. With the aid of the better imaging resolution provided by the CFHT/Megacam, the blueish arc is resolved into two blobs (labelled as C and D). Furthermore, another faint blob in the south-east (B) and a red, almost full Einstein ring, are clearly detected for the first time. This is certainly a strong lensing system of quadruple images, and the background galaxy contains a quasar which is very special because we can see not only the quasar but also its host galaxy. Figure 1. Left-hand panel: The SDSS image of the lens system. The fibre subtend an angle of 2 arcsec (white circle). Right-hand panels: The SDSS-measured spectra of the lens galaxy (top) and the lensed quasar (bottom). Figure 2. The co-added data of g band, r band and i band taken by CFHT. 3 LENS MODELLING STRATEGY The system is modelled by the lens modelling tool lfit_gui developed by Shu etal. ( 2016c ). Here we briefly describe the settings used in this work. 3.1 Foreground-light and source models We model the surface brightness distribution of the lens galaxy with elliptical Srsic profile defined as in which I e is the surface brightness at the effective radius r e that encloses half of the total light. The constant b ( n ) is defined in Ciotti Bertin ( 2012 ) and MacArthur etal. ( 2003 ) 4 . As the CFHT data clearly resolve the Einstein ring formed from the quasars host galaxy, we model the source surface brightness distribution with one elliptical Srsic model. We choose not to model the quasar itself because the Einstein ring already provides robust constraints on the lens model. 3.2 Lens model The projected surface mass distribution of lens galaxy is modelled by singular isothermal ellipsoid profile (hereafter SIE) (for details, see Kormann, Schneider Bartelmann 1994 ). Let denote the two-dimensional position of source on the source plane and the impact vector of light ray in the lens plane, both measured with respect to an optical axis. The gravitational lensing equation shows where D d , D s and D ds denote the angular diameter distance to the lens, the source and from the lens to the source, respectively. is the deflection angle, related to the surface mass density by Introducing angular coordinates by we can transform equation ( 2 ) to the interpretation of the lens in equation ( 5 ) is that a source with true position can be seen by an observer to be located at angular positions satisfying equation ( 5 ). So, the dimensionless lens equation is obtained as where , and length scale 0 are defined as and SIE is the lensing velocity dispersion. We can express the scaled deflection


O O O O O O O O O O O O O O O O B-Person I-Person O B-Person I-Person O O O O O O O O O O B-Person I-Person O O O O O O O O O O O O B-Organization I-Organization O O B-Grant I-Grant I-Grant I-Grant O O B-Organization I-Organization I-Organization I-Organization O B-Location O O B-Grant I-Grant I-Grant B-Person O O O O B-Organization B-Grant I-Grant I-Grant B-Person O O B-Organization B-Grant I-Grant I-Grant B-Person O B-Organization B-Organization O B-Organization B-Person O O O O O B-Location I-Location B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O B-Organization I-Organization I-Organization O O B-Location B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O B-Grant I-Grant I-Grant O O B-Organization I-Organization O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O O B-Organization I-Organization O O O O O B-Grant I-Grant O B-Organization O O O O O O B-Dataset I-Dataset O O O B-Organization I-Organization I-Organization O O O O O O B-Grant I-Grant O O O O O O O B-Organization O O O O O O O O O O B-Survey I-Survey I-Survey I-Survey I-Survey O O O O O B-Organization I-Organization I-Organization I-Organization O B-Location B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O O B-Survey O O O O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility O O B-Organization I-Organization I-Organization O B-Survey O O B-URL O B-Survey O O O O B-Collaboration I-Collaboration I-Collaboration O O O O O O B-Collaboration I-Collaboration O O B-Collaboration I-Collaboration I-Collaboration O B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration O B-Collaboration I-Collaboration I-Collaboration B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-Organization I-Organization I-Organization B-Organization B-Location B-Organization I-Organization I-Organization B-Organization B-Location B-Organization I-Organization I-Organization I-Organization B-Organization B-Observatory I-Observatory I-Observatory I-Observatory I-Observatory B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Observatory I-Observatory B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Observatory I-Observatory I-Observatory B-Collaboration I-Collaboration I-Collaboration I-Collaboration B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization O B-Organization I-Organization

We thank the anonymous referee for useful comments which improved this paper. The authors also thank Sara Ellison and Mallory Thorp for many useful and enjoyable discussions regarding galaxy mergers and Gaoxiang Jin for discussions on merger stage classification. The work is supported by the Academia Sinica under the Career Development Award CDA-107-M03 and the Ministry of Science Technology of Taiwan under the grant MOST 107-2119-M-001-024-. P.B.T. acknowledges partial support from UNAB research grant 2019. M.B. acknowledges the FONDECYT regular grant 1170618. R.R. thanks FAPERGS, CNPq and CAPES. J.H.K. acknowledges financial support from the European Union's Horizon 2020 research and innovation programme under Marie Skłodowska-Curie grant agreement No. 721463 to the SUNDIAL ITN network, from the Spanish Ministry of Economy and Competitiveness (MINECO) under grant No. AYA2016-76219-P, from the Fundación BBVA under its 2017 programme of assistance to scientific research groups, for the project “Using machine-learning techniques to drag galaxies from the noise in deep imaging,” and from the Leverhulme Trust through the award of a Visiting Professorship at LJMU. This project makes use of the MaNGA-Pipe3D dataproducts. We thank the IA-UNAM MaNGA team for creating this catalog, and the ConaCyt-180125 project for supporting them. We also thank the MPA/JHU teams for making their catalogs publicly available. Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P. Sloan Foundation, the U.S. Department of Energy Office of Science, and the Participating Institutions. SDSS acknowledges support and resources from the Center for High-Performance Computing at the University of Utah. The SDSS website is www.sdss.org . SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration including the Brazilian Participation Group, the Carnegie Institution for Science, Carnegie Mellon University, the Chilean Participation Group, the French Participation Group, Harvard-Smithsonian Center for Astrophysics, Instituto de Astrofísica de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe (IPMU)/University of Tokyo, the Korean Participation Group, Lawrence Berkeley National Laboratory, Leibniz Institut für Astrophysik Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für Astrophysik (MPA Garching), Max-Planck-Institut für Extraterrestrische Physik (MPE), National Astronomical Observatories of China, New Mexico State University, New York University, University of Notre Dame, Observatório Nacional/MCTI, The Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, Universidad Nacional Autónoma de México, University of Arizona, University of Colorado Boulder, University of Oxford, University of Portsmouth, University of Utah, University of Virginia, University of Washington, University of Wisconsin, Vanderbilt University, and Yale University.


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

at the highest stellar masses ( M * > 10 10.5 M ⊙ ). The dashed vertical lines denote the 95 per cent completeness limits, determined at the upper redshift range ( z = 2). Representative error bounds for individual galaxies are shown on the left-hand panels, based on the median errors on the PSB sample. For the CANDELS sizes, data are taken from van der Wel et al. ( 2012 ), which include estimates for random and systematic errors from galfit . For the ground-based individual errors, we add in quadrature the scatter in δ R / R determined by the comparison with CANDELS (Section 3 ). The representative uncertainty on stellar masses is based on our Bayesian mass-fitting analysis described in Wild et al. ( 2016 ), as briefly outlined in Section 2.3 . The size–mass relations show the expected trends for star-forming and passive galaxies, consistent with previous studies (e.g. Daddi et al. 2005 ; Trujillo et al. 2006 ; van Dokkum et al. 2008 ; McLure et al. 2013 ; van der Wel et al. 2014 ). On average, passive galaxies appear significantly more compact than star-forming galaxies of equivalent stellar mass, but show a steeper size–mass relation, leading to convergence at the highest masses ( M * ∼ 10 11.5 M ⊙ ). Intriguingly, we find that PSB galaxies at this epoch are also extremely compact; they are comparable in size to the established passive galaxies, with evidence that they are smaller on average at high mass ( M * > 10 10.5 M ⊙ ). These trends are apparent with the large ground-based sample and with the smaller CANDELS sample. We performed a bootstrap analysis as a simple test of significance, randomly sampling the (ground-based) populations within each mass bin, with replacement. For the four bins above 10 10.5 M ⊙ , the fraction of the resampled populations in which the passive galaxies show mean sizes equal to (or smaller than) the mean of the PSB population are 0.07, 5 × 10 −5 , 1.2 × 10 −4 and 4 × 10 −5 (low-to-high mass, respectively). We note that the final bin contains 86 passive galaxies but only three PSBs, so the bootstrap comparison for this bin may be unreliable. Overall, assuming no systematic errors, we find evidence that massive PSB galaxies at z > 1 are significantly more compact, on average, than passive galaxies of comparable mass. Repeating the analysis using the median sizes produced very similar trends. The median analysis and further tests of robustness are presented in Appendix A . Our results are consistent with the findings of Yano et al. ( 2016 ), who also found evidence that high-redshift PSB galaxies are very compact. As an additional comparison, in Fig. 5 we display the distribution of for the three galaxy populations, measured for the redshift range 1 z 2 and stellar masses M * > 10 10.5 M ⊙ . Following Barro et al. ( 2013 ), we use this parameter to effectively remove the slope in the galaxy size/mass relation. Fitting a function of the form to the passive population, we find a best fit with α = 1.55, in very


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This paper is based upon work supported by NASA under award Nos. NNX12AC68G and NNX16AF42G. R.N. acknowledges support by FONDECYT grant No. 3140436. We would like to thank Moshe Elitzur for productive discussions that resulted in improvements to the manuscript and Ying Zu for assistance in the use of his code JAVELIN. We also thank the anonymous referee for useful comments that improved the clarity of the paper.


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

as local instances of a decreasing mean field. By way of illustration of the key features of the moderate- and ultra-high-beta regimes, we refer the reader to Fig. 13 . This shows two numerical experiments, one with β Ω/ S , and the other with β > Ω/ S , in which the sign of the shear is alternated several times, so the system goes through multiple successive periods of decaying (firehose-unstable) and growing (mirror-unstable) mean field (this is analogous to successive instances of the experiments described in Sections 3.1 and 3.2 ). The key point is that at ultra-high β, periods of firehose growth and decay alternate, the system spends most of its evolution close to the firehose threshold, the mirror instability is almost completely suppressed, while the mean magnitude of the magnetic field barely changes at all; in contrast, at moderate β, the periods of decaying/growing mean field feature (relatively) lively firehose/mirror fluctuations which, however, do not survive long past the point when they cease to be driven by the external shear. In the context of the emergence of the threshold value of β, we have also carried out a β scan of the driven firehose turbulence, to complement a previous study by Kunz et al. ( 2014a ), where only one value of β was used. It has turned out (Section 2.1 ) that the saturation level of firehose fluctuations depends on β, viz. , , so when β ≳ Ω/ S , we have . The latter saturation regime takes the system on the order of one shear time to achieve and follows after a long phase of secular growth, during which the pressure anisotropy is pinned at marginal stability purely by the increase in the fluctuation energy, with no appreciable scattering of particles. This is broadly in line with the earlier theoretical argument of Schekochihin et al. ( 2008 ) and Rosin et al. ( 2011 ), although unlike in their study, the fluctuations are oblique, rather than parallel. We do not as yet have a complete theoretical understanding of this regime, or of the β and S dependence of the saturated firehose amplitude. Figure 13. Time evolution of the magnitude of the mean field (solid black), mean magnitude of the field 〈 B 〉 (bold red), firehose fluctuation level (solid blue) and mirror fluctuation level (dashed blue) in two runs where the sign of shear was alternated several times: (a) the case of β Ω/| S |, (b) the case of β > Ω/| S |. Note the much-delayed onset (amounting to near-complete suppression) of mirror instability and near constancy of 〈 B 〉 in the ultra-high-β case. These plots should be compared to Figs 11 and 12 (a,c). 4.2 Implications for cosmic magnetogenesis As large-scale dynamical motions that drive pressure anisotropies are invariably associated with changing the macroscopic magnetic field and since the resulting instabilities give rise to microscopic magnetic fluctuations, the implications of all this for the long-standing problem of the origin (and maintenance) of cosmic magnetism are the obviously


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

of J H K photometry of the entire 3C 294 system. Notes. To derive the magnitudes from Steinbring et al. (2002) , the fluxes from components a, b, and c have been summed. Photometry of individual components have been derived by Quirrenbach et al. (2001) and Steinbring et al. (2002) . A comparison to our data is shown in Table 5 . The difference between the Quirrenbach et al. (2001) and Steinbring et al. (2002) data is large, approximately two magnitudes, while our measurements are somewhere in between. Again, the size of the aperture used is not given for either the Keck-data or CFHT-data. Table 5. Comparison of HK photometry of components a, b, and c of the 3C 294 system. Notes. The K images have been taken through different filters (see Table 4 ) but the differences are small and did not affect the large differences seen between the individual measurements. We also created J − H , H − K s , and J − K s color maps for 3C 294 to search for any evidence of spatially-dependent extinction in the three components. No obvious feature was detected. 3.2. Optical spectra of the <ext-link ext-link-type="aoi">3C 294</ext-link> system The one-dimensional and two-dimensional spectra of the 3C 294 system are shown in Fig. 4 . Despite our 2 h integration time, we do not detect any obvious continuum. When rebinning the spectra in spectral and spatial direction by a factor of five, a hint of continuum can be glimpsed in the red channel. However, with this rebinning, the potential continuum of components a, b, and c would overlap, preventing us from distinguishing between the two components (see below). We detected the Ly α λ 1215 Å, C IV λ 1550 Å, He II λ 1640 Å, and C III] λ 1907/1909 Å lines in the blue channel. The C III] line is blue-shifted with respect to the other lines. This is not unusual in AGN (e.g., Barrows et al. 2012 ) and may be a result of the increased intensity of the transition at λ 1907 Å relative to the one at λ 1909 Å at low densities ( Ferland 1981 ). Only one emission line at λ 6749.4 Å can be detected in the red channel. It is faintly present in the individual spectra from both MODS instruments and is not an artifact of the data reduction. Under the assumption that it originates from the same source as the emission lines in the blue channel, we identify this line with the Ne [IV] doublet λ 2424/2426 Å at z = 1.783. Similarly to our C III] λ 1907/1909 Å line in the blue channel we would not be able to separate the double lines individually given an instrumental resolution of ∼5 Å. If the identification is correct, we may even associate the very faint emission at λ ∼ 6485 Å with C II] λ 2326 Å at z ∼ 1.788. The position of this line coincides with a forest of night-sky emission lines, however, so this detection is tentative. To our surprise, we do not detect Mg II λ 2798 Å in our spectra, which we would expect at λ ∼ 7790 Å. However, Mg II is relatively weak in radio galaxies ( McCarthy 1993 ) and line ratios can vary strongly in


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Acknowledgements This work was supported by the Victorian Life Sciences Computation Initiative (VLSCI), grant reference UOM0005, on its Peak Computing Facility hosted at The University of Melbourne, an initiative of the Victorian Government. Part of this work was performed on the gSTAR national facility at Swinburne University of Technology. gSTAR is funded by Swinburne University of Technology and the Australian Governments Education Investment Fund. AM acknowledges support from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (grant agreement No 638809 AIDA). This research was funded by the Australian Research Council through the ARC Laureate Fellowship FL110100072 awarded to JSBW. Parts of this research was conducted by the Australian Research Council Centre of Excellence for All-sky Astrophysics (CAASTRO), through project number CE110001020 (PMG). Finally, we would like to thank the anonymous referees for their constructive comments which helped to improve this paper.


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ACKNOWLEDGEMENTS We thank the anonymous referee for useful comments. This work was partially supported by the Italian Space Agency (ASI) through the grant Attivit di Studio per la comunit scientifica di astrofisica delle alte energie e fisica astroparticellare (Accordo Attuativo ASI-INAF n.2017-14-H.0). TAD acknowledges support from a Science and Technology Facilities Council UK Ernest Rutherford Fellowship. IP acknowledges support from INAF under the PRIN SKA project FORECaST. This paper made use of the following ALMA data: ADS/JAO.ALMA#[2015.1.01572.S] and ADS/JAO.ALMA#[2015.1.00878.7]. 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. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. This paper has also made use of the NASA/IPAC Extragalactic Database, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with NASA. This research used the facilities of the Canadian Astronomy Data Centre operated by the National Research Council of Canada with the support of the Canadian Space Agency.


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The authors would like to thank the referee for the constructive comments. This project has received funding from the Science and Technology Facilities Council (UK) through the consolidated grant ST/N000609/1. This research has been co-financed by the European Union (European Social Fund—ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF)—Research Funding Program: Thales Investing in Knowledge Society through the European Social Fund. The authors acknowledge support by the Royal Society. This work was supported by computational time granted from the Greek Research Technology Network (GRNET) in the National HPC facility—ARIS. This work used the DIRAC 1, UKMHD Consortium machine at the University of St Andrews and the DiRAC Data Centric system at Durham University, operated by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility ( http://www.dirac.ac.uk ). This equipment was funded by BIS National E-infrastructure capital grant ST/K00042X/1, STFC capital grant ST/H008519/1, and STFC DiRAC Operations grant ST/K003267/1, and Durham University. DiRAC is part of the National E-Infrastructure.


O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-ObservationalTechniques I-ObservationalTechniques O O B-Grant 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 B-ObservationalTechniques I-ObservationalTechniques O O O B-Grant O B-Grant O O O O O O O O O O O O O O O O O O O B-Model O O B-ObservationalTechniques I-ObservationalTechniques I-ObservationalTechniques O O O O O B-Software B-Citation I-Citation O B-Citation O O O O O O O O O O B-Telescope O O O O O O O O O O O B-Model O O O O O B-Software O O O O O B-Model O O O O O O O O O O O O O B-Model 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 B-Model O O O O O B-Model O O B-Model O O O O O O O O O O O O O O O O O B-Model O O O O B-Software O O O O O O O O O B-Model O O O O B-ObservationalTechniques I-ObservationalTechniques O O B-Model O O O O O O O O O O O O B-Model O O O O O O O O O B-Model O O O O O O O O O B-Model O O O O O O O O O O O B-Model I-Model O B-Formula I-Formula I-Formula O O B-Model 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-Model O O O O O O O O O O O O O B-Software 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

12 of the exposures do not approach the “saturation” threshold (blue dots), while 14 of the exposures have one pixel with a significant nonlinearity correction applied (red dots). Aperture photometry of the individual HST -calibrated FLT files shows a a bimodal pattern with a systematic difference of 0.2 mag. The bimodality is a result of the dither pattern: in the exposures with a correction applied, the PSF of the star is centered perfectly on a single pixel while in the other exposures the center falls in a gap between pixels, lowering the peak flux in any one pixel below the nonlinearity threshold. Figure 1. Aperture photometry of the SNAP observations of XZ Cyg. Each point corresponds to a single frame, points are color-coded based on their dither position. The ∼0.2 mag difference caused by the dither pattern is a result of an overcorrection for nonlinearity in a single bright pixel at dither point a. Although the stars are well isolated, the presence of significantly nonlinear pixels without a proper correction means that we cannot apply simple aperture photometry to our direct SNAP and GO observations. Our solution to this situation is to mask pixels in frames with poor nonlinearity corrections and then undertake PSF photometry. 3.1. Direct Imaging Photometry Photometry was carried out with DAOPHOT (Stetson 1987 , 1994 ) on all individual direct imaging “FLT” frames with the HST Pixel Area Map correction applied. Because we cannot generate a unique PSF for each frame, we used DAOPHOT to generate and apply one PSF for use in the 64 × 64 images and then generated a separate PSF for the 128 × 128 images. To generate the PSF, we used stars that are “clean” (i.e., images that do not have pixels that approach the nonlinear regime): 156 images for the 64 × 64 subarray and 208 for the 128 × 128 subarray or 26 images of six and eight stars each, respectively. To determine which parameters to assign to our model PSF, we generated several thousand individual PSF models with PSF radius and fitting radius varied in integer pixel increments from 2 to 17 and the seven different PSF functional forms available in DAOPHOT. We then compared the magnitude derived from each model PSF for each star with aperture photometry and chose PSF parameters that, on average, best reproduced the aperture magnitudes. We assigned a PSF radius of 14 pixels to the 64 × 64 PSF model and 17 pixels for the 128 × 128 PSF model and used a fitting radius of 12 pixels and a Moffat function with β = 3.5 for both PSF models. We also use the “clean” images to test the effect of pixel masking on our PSF photometry. We chose the brightest pixel in each image, masked it, and redetermined the magnitude using the same range of PSF parameter values. Regardless of the parameters used, masking pixels did not significantly impact DAOPHOT PSF photometry measurements. When masking stars in our 64 × 64 images, we found a systematic offset of −0.0017 ± 0.0022 mag, and for 128 × 128 images we


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We acknowledge support from INAF under PRIN SKA/CTA FORECaST and PRIN SKA-CTA-INAF ASTRI/CTA Data Challenge. F.S. acknowledges partial support from the H2020 AHEAD project (grant agreement No. 654215) and a Leverhulme Trust Research Fellowship. E.P. acknowledges financial support from ASI and INAF under contract 2017-14-H.0 ASI-INAF. We thank the referee for the constructive comments that significantly helped to improve the paper.


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to Bolatto et al. ( 2003 ). This ratio of 0.9 is consistent with the massive star-forming region in the MW (e.g., Nishimura et al. 2015 ). For source A, of and of 186 K km s −1 pc 2 yield of cm −2 (K km s −1 ) −1 . In addition, we obtained a similar from source B, cm −2 (K km s −1 ) −1 , from of and of 81 K km s −1 pc 2 . The averaged of cm −2 (K km s −1 ) −1 is four times higher than that in the MW disk, which is in good agreement with that in N83 obtained by Bolatto et al. ( 2003 ), (7.0 ± 3.4) cm −2 (K km s −1 ) −1 . 4.2. Properties of Molecular Gas and Star Formation in N83C We summarize the properties of the molecular gas based on our ALMA observations and discuss their relation to star formation in N83C. The derived gas density of cm −3 is significantly higher than the typical gas density of cm −3 in the Orion A/B molecular clouds (Nishimura et al. 2015 ), even though both gas densities are derived from the same molecular line, 12 CO(). Such a difference in derived gas densities is presumably due to the low metallicity in the SMC. The low metallicity corresponds to the small-dust content in molecular clouds, which causes the reduction of the shielding against far-UV radiation. In this condition, external far-UV radiation from the ii region associated with N83C easily penetrates and photodissociates the outer layer of the 12 CO molecule in the molecular clouds. Thus we can only observe the innermost parts of the molecular clouds, whose gas density is cm −3 , even in 12 CO emission. It is to be noted that theoretical simulations examined by Glover Clark ( 2012 ) support our results: their simulations suggest that diffuse CO emission becomes unobservable, but dense gas continues to produce observable CO emission as metallicity decreases. The observational fact that even 12 CO emission traces the high-density ( cm −3 ) regions in N83C just corresponds to this situation. Then, we consider the meaning of the derived kinetic temperature of molecular gas, 30–50 K. Bolatto et al. ( 2003 ) suggested that warm (∼40 K) clumps exist in some regions of N83 whose 12 CO()/ 12 CO() ratios exceed 2. Although the 12 CO()/ 12 CO() ratio of 0.9 in N83C is not so high (Bolatto et al. 2003 , 2005 ), it is possible that the global gas temperature exceeds 30 K in N83C considering that the bright ii region, which is a likely heating source, spreads over N83. In addition, the kinetic temperature of molecular gas is consistent with the dust temperature of 35 K (Takekoshi et al. 2017 ). Recent observational studies in the MW can also support our results: Nishimura et al. ( 2015 ) reported that the kinetic temperature in Orion A/B molecular clouds is 20–50 K, which is similar to that in the N83C, although the typical temperature of molecular clouds in the MW is 10–20 K. Considering that both N83C and Orion A/B molecular clouds are associated with bright ii regions, it is suggested that their temperature increase is due to the heating by far-UV radiation. However,


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We thank Alex Heger for the data of his Z9.6 progenitor model, his numerous contributions in developing the KEPLER code,and many insights into the topics of this paper. The help of Feryal zel withcomparing our neutron star masses with observational data and of Gabriel Martnez-Pinedo with our analysis of 19 F production is also appreciated. T.E. and H.-T.J. thank L.Hdepohl, T.Melson, M.Ugliano, and A.Wongwathanarat for numerical support and R.Hix and F.-K. Thielemann for providing the NSE solver introduced into P-HOTB by K.Kifonidis. This work was supported by NASA (NNX14AH34G) and the UC Office of the President (12-LR-237070). At Garching, funding by Deutsche Forschungsgemeinschaft through grant EXC153 Excellence Cluster Universe and the European Research Council through grant ERC-AdG No.341157-COCO2CASA is acknowledged.


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Acknowledgements This project is funded by DST INSPIRE Faculty [IFA-12/PH-44](Department of Science and Technology (DST), Govt. of India) and DST-SERB Fast track scheme [SR/FTP/PS-118/2011] (Science and Engineering Board (SERB), Govt. of India). We are thankful to the Inter-University Centre for Astronomy and Astrophysics (IUCAA) for providing the HPC facility. RSJ would like to thank IUCAA for providing the research facilities as a visiting student. Computations described in this work were performed using the publicly available enzo code ( http://enzo-project.org ) and data analysis is done with the yt-tools ( http://yt-project.org/ ). Authors would also like to thank the editor and the anonymous referee for their critical comments that have definitely helped in improving the content of this paper.


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Acknowledgments We thank Biping Gong, Wei Xie and Wei Chen for helpful discussions and Likang Zhou and Senlin Yu for language polishing. This work is supported by the National Basic Research Program of China (973 Program, Grant No. 2014CB845800) and by the National Natural Science Foundation of China (Grants No. U1231101 and U1431124).


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A.C. and N.T.P. acknowledge support from the National Science Foundation under CAREER Grant No. 1455090. A.C. and N.T.P. also acknowledge partial support from the Swift Cycle 12 GI program (Grant No. NNX17AF93G). Support for this work was in part provided by the National Aeronautics and Space Administration through Chandra Award No. 19500451 issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of the National Aeronautics Space Administration under contract NAS8-03060. This work was also supported by the GROWTH project funded by the National Science Foundation under grant No. 1545949. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. These results made use of the Discovery Channel Telescope at Lowell Observatory. Lowell is a private, non-profit institution dedicated to astrophysical research and public appreciation of astronomy and operates the DCT in partnership with Boston University, the University of Maryland, the University of Toledo, Northern Arizona University, and Yale University. The upgrade of the DeVeny optical spectrograph has been funded by a generous grant from John and Ginger Giovale. This work made use of data supplied by the UK Swift Science Data Centre at the University of Leicester. This work is partially based on observations collected with the Liverpool Telescope, which is operated on the island of La Palma by Liverpool John Moores University in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias with financial support from the UK Science and Technology Facilities Council. The Pan-STARRS1 Surveys (PS1) have been made possible through contributions of the Institute for Astronomy, the University of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society and its participating institutes, the Max-Planck Institute for Astronomy, Heidelberg and the Max-Planck Institute for Extraterrestrial Physics, Garching, The Johns Hopkins University, Durham University, the University of Edinburgh, Queen’s University Belfast, the Harvard-Smithsonian Center for Astrophysics, the Las Cumbres Observatory Global Telescope Network Incorporated, the National Central University of Taiwan, the Space Telescope Science Institute, the National Aeronautics and Space Administration under grant No. NNX08AR22G issued through the Planetary Science Division of the NASA Science Mission Directorate, the National Science Foundation under grant No. AST-1238877, the University of Maryland, and Eotvos Lorand University (ELTE).


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region. This demonstrates that additional chemical changes occur at temperatures higher than 120 K during the warm-up, when molecules and radicals become more mobile and could react each other more readily. Both Sample #2 and Sample #3 contain hydrogen, carbon, nitrogen, and oxygen. However, their corresponding organic residues (Res #2 and Res #3) do not display the same functional groups that give rise to the 2200 cm −1 feature. This is evident looking at the infrared spectra of the two samples in the region 2300–2000 cm −1 : both show two multi-peaked bands, but with profiles and components different one another. Thus Res #2 exhibits a 2200 cm −1 feature comparable to those observed for Res #1, Res #4, and Res #5 (see the bottom panel of Fig. 5 ), whereas Res #3 displays a quite sharp feature centred at 2158 cm −1 . We think that the presence of water as component of Sample #3 can affect the chemical rearrangements during proton bombardment at 17 K and especially during the annealing to room temperature, preventing or reducing the formation of molecules containing nitrile and iso-nitrile groups and encouraging the formation of molecules containing amide groups, as already stressed by commenting the XPS spectra in the previous section. Looking at the IR spectrum of Res #3, we are not sure about the chemical groups responsible of the band centred at 2158 cm −1 , even if we hypothesize a contribution of OCN − still trapped in the organic residue (Res #3) at room temperature. OCN − ion is one of the new species formed at 17 K after energetic processing of a frozen icy mixture containing oxygen, carbon and nitrogen bearing species (e.g. van Broekhuizen et al. 2005 ). Indeed it has been detected both in Sample #2 and in Sample #3 after proton bombardment (see the top panel of Fig. 5 ). During the annealing of Sample #3, we have recorded the OCN − peak position as a function of the sample temperature: we recognize a gradual shift towards lower wavenumbers as the sample temperature increases, from 2167 cm −1 at 17 K–2160 cm −1 at 260 K. Therefore the frequency of the peak observed for the refractory residue at room temperature (2158 cm −1 ) could be compatible with the trend of the recorded peak position of the OCN − ion into the ice, as shown in Fig. 6 . In this section, we are mainly focusing on the spectral region 2300 – 2000 cm −1 due to its link with astrobiological studies. In fact the triple CN bond stretching mode of nitriles considered relevant to pre-biotic chemistry falls in this region. The role of nitriles in formation of various pre-biotic compounds has been illustrated by Matthews Minard (2006) . Our experimental results demonstrate that the presence of oxygen in the icy samples is not necessary for the formation, at room temperature, of the multi-component band at 2200 cm −1 that we identify with nitrile (–C≡N) and isonitrile (–N≡C) functional groups. The refractory residues containing nitrogen, such as those analysed in this


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Acknowledgements I thank the anonymous referee for valuable comments that helped me in improving the manuscript. I am grateful to Anatoly Zasov for fruitful discussion and his important comments on the manuscript. I thank my family for the support and inspiration. This work is supported by The Russian Science Foundation (RSCF) grant No. 17-72-20119. I acknowledge the usage of the HyperLeda data base ( http://leda.univ-lyon1.fr ).


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We thank the referee, Tony Moffat, for his useful comments that helped improve this paper. J.M.A. and A.S. acknowledge support from [a] the Spanish Government Ministerio de Economía y Competitividad (MINECO) through grants AYA2010-15 081, AYA2010-17 631, and AYA2013-40 611-P and [b] the Consejería de Educación of the Junta de Andalucía through grant P08-TIC-4075. J.M.A. was also supported by the George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy and he is grateful to the Department of Physics and Astronomy at Texas AM University for their hospitality during some of the time this work was carried out. I.N., A.M., J.A., and J.L. acknowledge support from [a] the Spanish Government Ministerio de Econoía y Competitividad (MINECO) through grant AYA2012-39 364-C02-01/02, [b] the European Union, and [c] the Generalitat Valenciana through grant ACOMP/2014/129. R.H.B. acknowledges support from FONDECYT Project 1 140 076. S.S.-D. acknowledges funding by [a] the Spanish Government Ministerio de Economía y Competitividad (MINECO) through grants AYA2010-21 697-C05-04, AYA2012-39 364-C02-01, and Severo Ochoa SEV-2011-0187 and [b] the Canary Islands Government under grant PID2 010 119. J.S.-B. acknowledges support by the JAE-PreDoc program of the Spanish Consejo Superior de Investigaciones Científicas (CSIC). STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555.


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P.N. acknowledges support from a Theoretical and Computational Astrophysics Network grant, award number 1332858, from the National Science Foundation. This work was completed at the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1066293. Useful conversations with Benny Trakhenbrot and Nicholas Stone at the Aspen Black Holes Workshop are gratefully acknowledged. B.A. and A.R. acknowledge support from the TCAN grant for a post-doctoral fellowship and a graduate fellowship, respectively. This research was supported in part (AF) by the National Science Foundation under Grant No. NSF PHY11-25915. E.Z. acknowledges funding from the Swedish Research Council (project 2011-5349). N.C. acknowledges the YCAA Prize Postdoctoral fellowship. N.C. and F.P. acknowledge the SAO Chandra grant AR6-17017B and NASA-ADAP grant MA160009.


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AS acknowledges support by the Natural Sciences and Engineering Research Council (NSERC) of Canada. AR is grateful for the Faculty of Science Undergraduate Student Research Award he obtained at the University of Manitoba.


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Acknowledgements D.S. and C.W.O are supported by the Netherlands Organization for Scientific Research (NWO; VIDI project 639.042.422). S.K. acknowledges support from NASA through Hubble Fellowship grant HST-HF2-51394 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. D.S. would like to thank Carsten Dominik for useful discussions and Shigeru Ida for pointing out a typographical error in Schoonenberg Ormel (2017) . We thank Beibei Liu, Joanna Dra̧żkowska, and the anonymous referee for constructive feedback on the manuscript.


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

show the regions which contain 95% of the models. The central blue line is the median line for Planck TT+lowP+BSH. Here Planck indicates Planck TT+lowP. One might wonder whether it is reasonable to stop at first order in . We have therefore tested a generic expansion in powers of the scale factor up to order : We find that all parameters are very stable when allowing higher order polynomials; the parameters are weakly constrained and going from (the linear case) to (quadratic case) to (cubic expansion) does not improve the goodness of fit and stays compatible with , which indicates that a linear parameterization is sufficient. 5.1.2. 1-parameter varying <italic>w</italic> A simple example of a varying model that can be written in terms of one extra parameter only (instead of ) was proposed in Gott Slepian (2011), Slepian et al. (2014) , motivated in connection to a DE minimally-coupled scalar field, slowly rolling down a potential , analogous to the one predicted in chaotic inflation ( Linde 1983 ). More generally, one can fully characterize the background by expanding a varying equation of state , where: at first order in , which is then the only extra parameter. Marginalized posterior contours in the plane – are shown in Fig. 6 . The tightest constraints come from the combination Planck TT+lowP+lensing+BSH that gives at 68% confidence level, which slightly improves constraints found by Aubourg et al. (2015) . Fig. 6 Marginalized posterior contours in the – plane are shown for 1-parameter varying models (see Sect. 5.1.2 ) for different data combinations. Here Planck indicates Planck TT+lowP. 5.1.3. Principal Component Analysis on <italic>w(z)</italic> A complementary way to measure the evolution of the equation of state, which is better able to model rapid variations, proceeds by choosing in fixed bins in redshift and by performing a principal component analysis to uncorrelate the constraints. We consider different bins in and assume that has a constant value in each of them. We then smooth the transition from one bin to the other such that: with , a smoothing scale , and a binning . We have tested also a larger number of bins (up to ) and have found no improvement in the goodness of fit. The constraints on the vector of values that can assume in each bin is difficult to interpret, due to the correlations between bins. To uncorrelate the bins, we perform a principal component analysis ( Huterer Starkman 2003 ; Huterer Cooray 2005 ; Said et al. 2013 ). We first run COSMOMC ( Lewis Bridle 2002 ) on the original binning values ; then extract the covariance matrix that refers to the parameters we want to constrain: where is the vector of parameters and is its transpose. We calculate the Fisher matrix, , and diagonalize it, , where is diagonal and is the orthogonal matrix whose columns are the eigenvectors of the Fisher matrix. We then define (e.g., Huterer Cooray 2005 ) and normalize this such that its rows sum up to unity; this matrix can be


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Funds from the Proyecto de Excelencia de la Junta de Andalucía, J.A. 2012-FQM1776 and from FEDER are acknowledged.