O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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

width of 0.26 Å for H and [OIII]. As an example, two performed fits are presented in Fig. 2 , including the central spaxel (with a ) and the lowest S/N spaxel () of the spatially binned MUSE observations. To quantify the impact of our fitting parameters on our results, we performed similar analyses but varying one parameter at a time. Firstly, we used additive polynomials of the 4th order, commonly used for fitting spectra on narrower, SAURON-like, wavelength range. Secondly, we masked all the potential emission lines from the galaxy, e.g. H, [OIII], H, [NII] and [SII]. Finally, we fitted the MUSE spectra on a restricted wavelength range (50005500 Å) that contains the Fe lines and the Mg triplet, which on their own strongly constrain the derived stellar kinematics. In all cases, we measured similar kinematics structures, with mean differences of only a few kilometers per second for the two first LOSVD moments, and , and mean differences of 0.001 to 0.02 for and . We should emphasise, however, that there are still clear systematic errors mostly regarding the third- and fourth-order moments and . The corresponding maps show some odd features, for example a clear offset of the level at the edges of the field (see Figs. 3 and 4 ). This is not surprising considering the original strong variation of the sky background (see Sect. 2.2 ), between exposures and also within the field of view of individual exposures (residual gradient). Assuming symmetric (odd or even) moment maps for and (with respect to the photometric minor axis), we estimate these systematic errors to 0.02 for and 0.05 for . 3.2. Stellar kinematics results Fig. 4 One-dimensional curve of the first four line-of-sight velocity distribution (LOSVD) moments: a) stellar radial velocity, V; b) stellar velocity dispersion, ; c) third-order Gauss-Hermite moment, ; d) fourth-order Gauss-Hermite moment, . The points were extracted from the two-dimensional maps of the respective quantities (see Fig. 3 ), by taking the light-weighted mean value within a 2 wide slit, aligned with the major axis (orange points), and offset by +8 (green points) and +20 (blue points) along the minor axis. We present in Fig. 3 the stellar kinematics maps of NGC 3115, obtained as described in Sect. 3.1 from our MUSE reduced cube. The mean radial stellar velocity map (Fig. 3 , panel a) exhibits a fast-rotating structure, similar to a thin disc, embedded in a slower spheroidal component, but still rotating fairly rapidly. The thin disc structure has an apparent vertical extent (with respect to the major axis) widening from a few arcseconds near the centre to (i.e. 930 pc) at about two effective radii (i.e. 70 or 3.4 kpc) where it becomes blended with the spheroidal part of the galaxy. The thinness of the kinematic disc also confirms that NGC 3115 is viewed almost edge-on. Along the major axis, the mean radial stellar velocity curve exhibits a double maximum (see Fig. 4 , panel a) with a first steep rise to 150 km s


O O O O O O B-Person I-Person O O O O O O O O O O O O O O O B-Person I-Person O O O O O O B-Dataset I-Dataset O O B-Model I-Model B-Person O B-Person I-Person O O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-Person O O O O B-Fellowship I-Fellowship I-Fellowship I-Fellowship O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Grant O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility O B-Organization I-Organization O O O B-Organization I-Organization I-Organization I-Organization O O O O B-Organization B-ComputingFacility I-ComputingFacility I-ComputingFacility O B-URL O O O O O O B-Organization B-ComputingFacility I-ComputingFacility B-Grant I-Grant I-Grant B-Organization O O B-Grant O B-Grant B-Organization B-Grant I-Grant I-Grant I-Grant O B-Organization I-Organization B-ComputingFacility O O O O B-ComputingFacility I-ComputingFacility

ACKNOWLEDGEMENTS The authors are grateful to Joop Schaye and the anonymous referee for helpful comments and suggestions. Furthermore, we would like to thank Volker Springel for providing the particle data of snapshot 54 of the MXXL simulation. JS thanks Daniele Sorini for helpful discussions and acknowledges financial support from the Heidelberg Graduate School of Fundamental Physics (HGSFP). CMB acknowledges receipt of a Leverhulme Trust Research Fellowship. This work was supported by the Science and Technology Facilities Council [ST/L00075X/1]. We used the DiRAC Data Centric system at Durham University, operated by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility ( www.dirac.ac.uk ). This equipment was funded by BIS National E-Infrastructure capital grant ST/K00042X/1, STFC capital grants ST/H008519/1 and ST/K00087X/1, 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

select dimensions corresponding to non-zero diagonal values of . A similar selection of dimensions on gives of size below the dimension of the oversampled discrete Fourier grid, thus leading to the dimensionality reduction operator We see that the full measurement operator preserves the null space of , following from , thus retaining any original NSP. The diagonal dominated nature of has already been shown, which leads to an appropriate modelling of the noise. Also, applying is fast owing to the sparsity of . Note that in the context of this dimensionality reduction with , the weighting matrix , in fact designed for optimal weighting of the embedded visibilities, also operates as uniform weighting. Indeed, the diagonal values of are a measure of the density of continuous visibilities at each discrete grid point. As with , we also approximate the initial noise covariance matrix in this case by assuming , leading to the dimensionality reduction . This variant is included in comparisons of reconstruction quality. 3.4 Feature comparison A comparison of the different dimensionality reduction methods , and is shown in Table 1 . We note in the listing that provides a good combination of the desired final dimension, the guarantees for compressed sensing-based imaging to reconstruct images and a largely diagonal noise covariance matrix that enables us to embed this technique in the convex optimization algorithm we employ for imaging. embeds the data to image size while maintaining any original NSP of , and has a fast implementation; however, it fails to appropriately model the noise and is therefore less suitable for the minimization problem which requires i.i.d. Gaussian embedded noise to enable a simple 2 -norm data fidelity term. continues to maintain the NSP of and the i.i.d. Gaussian properties of the noise, which are essential for image reconstruction using our convex optimization algorithms. However, the data reduction is limited to a size . As mentioned in Sections 3.2 and 3.3 , for each of , and , an attempt is also made to further approximate the initial noise covariance matrix by the identity matrix in order to render the application of the respective dimensionality reduction methods even faster. Equations ( 19 ), ( 22 ) and ( 25 ) are then simplified to , and , respectively. However, this approximation is seen to be inappropriate, leading to poorer modelling of the noise and consequently lowering image reconstruction quality. , , and their respective variants are used to reduce dimensionality before performing image reconstruction in different settings and with varying data sizes. 3.5 Further reduction by thresholding As a conservative dimensionality reduction method, would embed to a final data size under the assumption that there are very few zero-valued singular values of , within limits of numerical precision, and all corresponding singular vectors are thus necessary to retain the information content of . Similarly, embeds to a size


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

Support for Program number GO–12600 was provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Incorporated, under NASA contract NAS5-26555. B.B. received partial support from NSF grant AST-0808201.


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

zero frequency lag component. Similarly, the autocorrelation of the (unfiltered) 2019-03-07 epoch (left-hand panels of Fig. 7 ) shows a strong zero frequency lag peak centred at 5.447 ± 0.008 h. Note that the quoted uncertainties are estimates based on the sample distribution of periods from the simple top-hat pulse model described in Sections 3.1.1 and 3.1.2 . Figure 7. Two-dimensional autocorrelation function, and the corresponding zero frequency lag components for the 2019-03-07 (left-hand panels) and 2018-10-02 epochs (right-hand panels). Dashed lines indicate the time lag of the major peak in the autocorrelation, which measures the periodicity of the pulses. The dash–dotted lines in the autocorrelation of 2019-03-07 are spaced every h from the zero time lag component, and around the major peak at a time lag of 5.447 h, and show the quasi-periodic nature of the pulses 19-1A, B, C and 19-2A, B, and C. The pulse periods measured between the two epochs are consistent with one another, and consistent with the 5.4432 ± 0.0072 h period measured by Barnes et al. ( 2017 ). We note that this disambiguates which component of the L726-8AB binary the emission originates from – the primary component BL Ceti (L726 − 8A) is also known to be active at radio frequencies (e.g. Gary et al. 1982 ), and is separated from UV Ceti by ∼4′′, well below the ∼15′′ resolution of our ASKAP observations. However, BL Ceti has a rotational period of 5.832 ± 0.012 h (Barnes et al. 2017 ). Along with the h periodicity revealed by the autocorrelation of the 2019-03-07 observation, there are also three minor peaks in the autocorrelation spaced every h from the zero time lag component, and to either side of the primary period of h. This gives strong evidence for the quasi-periodic nature of the faint pulses 19-1A, B, C and 19-2A, B, C. 3.3 Comparison of the two epochs We find notable similarities between the pulses occurring in both epochs when inspecting the dynamic spectra side by side. Most striking is the faint pulses occurring in both epochs: 18-1A, 18-2A, and 19-1A, B, C, 19-2A, B, C – all these pulses have very similar drift rates (, virtually indistinguishable within the bandwidth of our observations), durations (∼12 min), and are similar in their average flux densities (∼40–50 mJy). However, in the 2019-03-07 epoch, three faint pulses with equal drift rates occur every rotation, where as in 2018-10-02 only one faint, negative-drifting pulse occurs per rotation. Pulses 19-1B and 19-2B are morphologically most similar to the faint pulses 18-1A and 18-2A occurring once per rotation in the 2018-10-02 epoch, 18-1A and 18-2A. Furthermore, the time difference between 19-1B and 19-1D, and 19-2B and 19-2D (∼60 min) is similar to the time difference between 18-1A and 18-1B (∼50 min). While there are some morphological similarities between the bright pulses in both epochs, the bright burst in 2018-10-02 has a slower bulk drift rate, a longer duration, and overall a more complex


O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O B-Grant O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O B-Location I-Location O B-Grant O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O B-Location I-Location O B-Grant

ACKNOWLEDGEMENTS This work is supported by the National Natural Science Foundation of Chinaunder Grant No. 11474079, the Science and Technology Platform and Talent Team Program of Guizhou province (No. 2017-5610), and the Major Research Project of innovative Group of Guizhou province (No. 2018-013).


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

Numerical computations and analyses were carried out on Cray XC30 and computers at Center for Computational Astrophysics, National Astronomical Observatory of Japan, respectively. This work was supported in part by Grant-in-Aid for Scientific Research (B) by JSPS (15H03638).


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

We thank Timothy Brandt for helpful comments and discussion on earlier drafts of this paper. We would also like to thank the anonymous referee for their comments in improving the clarity of the paper. S.G. acknowledges the National Science Foundation Graduate Research Fellowship under grant No. DGE1745303. C.C. acknowledges support from NASA grant AST-1313280, and the Packard Foundation. This paper is based upon work supported by the National Aeronautics and Space Administration (NASA) under Contract No. NNG16PJ26C issued through the WFIRST Science Investigation Teams Program. Some of this material is based upon work supported by the National Science Foundation under Award No. 1501205. We would also like to thank Bill Paxton and the MESA community for making this work possible.


O B-Survey I-Survey I-Survey O O O O O O O B-Telescope I-Telescope B-Telescope O B-Instrument I-Instrument I-Instrument I-Instrument I-Instrument B-Instrument O O O O O B-Organization I-Organization I-Organization O O B-Observatory I-Observatory I-Observatory O B-Dataset I-Dataset I-Dataset O O O O O O O B-Survey I-Survey I-Survey I-Survey O B-Survey I-Survey O O B-Survey I-Survey I-Survey O B-Survey I-Survey I-Survey O O O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-Grant O O O O O B-Survey I-Survey I-Survey O O B-URL O O O O O O O O B-Telescope O O O O B-Instrument O B-Instrument O O B-Person O B-Person O O O O O O B-Organization I-Organization I-Organization O O B-Fellowship I-Fellowship I-Fellowship B-Organization B-Grant O B-Fellowship B-Person O O O O O B-Organization B-Fellowship I-Fellowship B-Fellowship B-Person O O O O O B-Fellowship I-Fellowship I-Fellowship I-Fellowship O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Location B-Person O O O O B-Organization I-Organization I-Organization B-Grant I-Grant I-Grant I-Grant B-Grant B-Person O O O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O O O O B-Software O O O O B-Software O O O B-Citation I-Citation I-Citation

The SAMI Galaxy Survey is based on observation made at the Anglo-Australian Telescope (AAT). The Sydney–AAO Multiobject Integral field spectrograph (SAMI) was developed jointly by the University of Sydney and the Australian Astronomical Observatory. The SAMI input catalogue is based on data taken from the Sloan Digital Sky Survey, the GAMA Survey and the VST ATLAS Survey. The SAMI Galaxy Survey is funded by the Australian Research Council Centre of Excellence for All-sky Astrophysics (CAASTRO, CE1100010200) and other participating institutions. The SAMI Galaxy Survey website is http://sami-survey.org . We thank the dedicated staff at the AAT whose support in interfacing SAMI with AAOmega is invaluable. MSO and JTA acknowledge the funding support from the Australian Research Council through a Super Science Fellowship (ARC FS110200023 and FS110200013). SMC acknowledges the support of an ARC future fellowship (FT100100457). ISK is the recipient of a John Stocker Postdoctoral Fellowship from the Science and Industry Endowment Fund (Australia). LC acknowledges support under the Australian Research Councils Discovery Projects funding scheme (DP130100664). CJW acknowledges support through the Marie Curie Career Integration Grant 303912. This research made use of astropy , a community-developed core python package for Astronomy (Astropy Collaboration, 2013).


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

ACKNOWLEDGEMENTS The authors would like to thank the anonymous reviewer for his comments, and Jerry Sellwood, Jim Stone, and Charles Gammie for advice and encouragement. This work was partially funded by STFC grant ST/L000636/1.


O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility O O B-Person I-Person O B-Person I-Person O O O O

We thank the Korea Institute for Advanced Study for providing computing resources (KIAS Center for Advanced Computation Linux Cluster System). We thank Seokcheon Lee and Graziano Rossi for many helpful discussions.


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

require high sodium abundances at low oxygen abundances. In the following, we list the three quantitative discrepancies between AGB nucleosynthesis yields and observed abundance patterns that are solved if we allow for smaller mass-loss rates. (1) The oxygen depletion in the most massive super-AGBs is not large enough. To address this problem, we have invoked deep mixing in the giant progenitors of the most extreme population, a mixing which should be favoured by the large helium abundance of these stars (D'Antona Ventura 2007 ), and we adopt this solution also here (see Section 4.1 ). Nevertheless, smaller mass-loss rates in the super-AGB phase would lead to the required large depletion of oxygen and would provide an additional possible solution to this problem. (2) Apart from 24 Mg depletion, some other HBB proton captures require a longer time than allowed by the mass-loss rates chosen in our Ventura et al. ( 2013 ) paper and in the previous computation. In particular, the silicon increase by proton captures on aluminium is found in Ventura et al. ( 2013 ) at the level of ∼0.05 dex, while ∼0.15 dex are required by Carretta ( 2015 ) data for NGC 2808. Also in this case, a larger production requires longer evolutionary times. (3) Taking at face value the modest δ Y implied by the observational width of the MS of some clusters in recent observations, Bastian, Cabrera-Ziri Salaris ( 2015 ) found a discrepancy between the range covered by data in O–Na plane and the range allowed by models. Below, we discuss some limitation of this analysis, and other possible ways to overcome this problem. However, taking this result at face value, also in this case the difficulty is removed if the models have a larger oxygen depletion for a given T HBB , and this can be achieved assuming smaller mass-loss rates during the AGB evolution. If models with smaller T HBB can describe well the O–Na data, they are progeny of lower initial masses and have smaller Y yield, as required by the comparisons in Bastian et al. ( 2015 ), solving the discrepancy. The mass-loss rates in the AGB models by Ventura et al. ( 2013 ) were originally calibrated on a comparison with the luminous lithium-rich stars in the Magellanic Clouds (Ventura, D'Antona Mazzitelli 2000 ), but this calibration is also able to provide a positive sodium yield, in spite of the contemporary burning of sodium and oxygen. If we allow for a mass-loss rate smaller, say by a factor of 3 – that is, we triple the time for p-captures in the AGB envelope – we may find a solution for the four problems listed above, at the expenses of burning too much sodium (see e.g. Ventura et al. 2011 ; Doherty et al. 2014 ). The problem of the sodium destruction is examined in detail in Renzini et al. ( 2015 ), where it is suggested that a reduction by a factor of 5 of the reaction rate 23 Na(p,α) 20 Ne would allow sodium to be destroyed at a slower rate, so that its global yield may be in the range of the observed sodium


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

in the Upper Scorpius region, assuming only an age evolution from one region to another. Fig. 6. Comparison between median and percentiles of the mass accretion rates as a function of disk mass for the Lupus and Upper Scorpius regions ( left ), and for the Upper Scorpius region and the expectations from viscous models at 1 Myr and 8 Myr ( right ). 5.2. The impact of photoevaporation and variable accretion The observations are even more discrepant from models predicting the Ṁ acc − M disk relation by means of both viscous evolution and internal photoevaporation. As shown by Somigliana et al. (2020) , the effect of photoevaporation is the reduction in the number of accreting targets at low disk masses and mass accretion rates to an extent that, by ∼10 Myr, only a fraction of massive disks still survive. This is not observed here, where we see low-mass disks with high Ṁ acc . It is unclear whether this disagreement is due to the fact that the models assume only one stellar mass and two fixed mass-loss rates, or whether this is an issue of internal photoevaporation models in general. On the other hand, external photoevaporation would predict that the disks have low mass, while still low values of M disk / Ṁ acc ∼ 0.1 Myr (see Fig. 4 , and Rosotti et al. 2017 ; Sellek et al. 2020 ), more in line with what is observed here. In this context, it is worth mentioning that the environment of Upper Scorpius is different than the one of Chamaeleon I and Lupus, having more nearby massive stars (e.g., de Zeeuw et al. 1999 ). In such an environment, the effect of external photoevaporation could have been relevant for the evolution of disks, possibly more than dynamical interactions (e.g., Winter et al. 2018 ). Whether this effect has been dominant for the evolution of the disks observed here is still an open question. Further modeling is mandatory here, but it is nevertheless puzzling how the mass accretion rates can be retained for such long time with so little disk mass available. A possible solution to the fact that the accretion rates measured here are high given the measured M disk might be variable accretion. However, studies in younger star-forming regions have shown that, in general, typical variation of Ṁ acc are 0.4 dex in most disks (e.g., Costigan et al. 2014 ; Venuti et al. 2014 ), with only a small fraction of targets showing extreme variability of Ṁ acc > 1 −2 dex (e.g., Audard et al. 2014 ). We could imagine that the variability is larger in the old region of Upper Scorpius, but in this case we could expect a larger dispersion in accretion rates than in younger regions, which, however, was not observed. Further studies on variability in older star-forming regions is needed. The mass-budget issue given the observed Ṁ acc and M disk is therefore important. Indeed, under the assumption that Ṁ acc is constant with time, these high values of Ṁ acc would imply that over the lifetime of the disk 10 −8 M ⊙ yr −1 ×10 7 yr ∼ 0.1 M ⊙ of disk


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 I-Organization O B-Grant B-Grant O B-Grant O B-Organization I-Organization I-Organization I-Organization O B-Grant B-Grant O B-Grant O O B-Location I-Location O B-Grant B-Grant

ACKNOWLEDGEMENTS We acknowledge useful comments and suggestions from the anonymous referee. This study is supported by the National Natural Science Foundation of China (Nos 11873085, 11673059, and 11521303), the Chinese Academy of Sciences (Nos QYZDB-SSW-SYS001, KJZD-EW-M06-01, and Y9XB016001), and the Yunnan Province (Nos 2017HC018, 2018FB005).


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

We would like to thank the referee for the comments and suggestions. The authors thank very much Richard Harrison for the careful reading and comments on the manuscript. C. M. and L. X. thank the National Natural Science Foundation of China (41474150 and 41627806). The AIA and HMI data are provided courtesy of NASA/SDO and corresponding science teams. The AIA and HMI data have been retrieved using the Stanford University’s Joint Science Operations Centre/Science Data Processing Facility. M.M. and K.G. thank the ISSI Bern for the support to the team “Observation-Driven Modelling of Solar Phenomena”.


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

In the case of ErisMod Low simulation pair the first replacement was made at redshift 1.1 and the last at redshift 0.1. In total, there were four replacement epochs. The final count of high-resolution objects in each of the ErisMod Low runs was 17. The progenitors as well as other halos found in the proximity of the main halo at an epoch of replacement went through a process of selection. If the respective dark matter cloud was found to be monolithic, not elongated, not part of a group of overlapping halos, and with no identifiable satellites, then a high-resolution model will be generated and used as a replacement. This procedure leads to the exclusions of between 40% and 60% of all considered halos at a certain epoch of replacement. Thus, the objects that are replaced are in general more resilient to the tides due to their compactness. The two simulation pairs ErisMod High and ErisMod Low should be seen as complementary since they are both derived from the same simulation ErisDARK and the first epoch of replacement for ErisMod Low starts after the last epoch of replacement in the ErisMod High simulation. Information regarding the orbits, the original virial mass, as well as the redshift of the first pericenter passage for all replaced objects is available in Figure 1 . Figure 1. Dwarf galaxy distances from host ranges for the four ErisMod simulations are plotted as bars. The dwarf galaxy number is sorted by halo mass at infall. At the top of each bar, the marked number (blue color) denotes the pre-infall virial mass of the objects in units of 10 9 M ⊙ . Near the bottom of each bar, the neighboring number (red color) indicates the count of the pericenter passages done by the galaxy until redshift zero. 3. RESULTS For the following analysis we consider subsets of the satellite populations presented in Figure 1 . We are interested in objects that at z = 0 are within 247 kpc of the center of the main halo, namely, inside the virial volume of the host halo. This was done in order to achieve consistency with previous analysis of the TBTF problem from the literature. Moreover, we exclude from analysis all the objects that have lost more than 99% of their mass before redshift zero, as the low number of particles will make the results of the analysis not trustworthy. This class of objects includes galaxies that have lost such a large fraction of their mass that they become irrelevant for the TBTF problem. The circular velocity of the satellites is defined as the function of distance from center: The results are shown in Figures 1 and 2 . In Figure 1 , the profiles of the halos at the epoch of replacement are plotted for comparison. Moreover, in Figure 2 , we have added the estimated circular velocities at the half-light radius available for the MW dSph satellites based on the data compiled by McConnachie ( 2012 ). They are derived from the line of sight velocity dispersion data using the equation:originally proposed by Klypin et al. ( 1999 ) and later


O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O B-Grant B-Grant B-Grant B-Grant B-Grant B-Grant O B-Grant O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O O O O O O B-Collaboration I-Collaboration I-Collaboration I-Collaboration B-Collaboration O O O O B-Observatory I-Observatory I-Observatory O O O O B-Organization I-Organization O O O O O O B-Organization I-Organization I-Organization O O O O O O O O O B-Observatory I-Observatory I-Observatory I-Observatory B-Observatory I-Observatory I-Observatory B-Observatory I-Observatory I-Observatory B-Observatory I-Observatory I-Observatory B-Organization I-Organization I-Organization I-Organization I-Organization O B-Observatory I-Observatory I-Observatory I-Observatory O O O O O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility O B-Location I-Location O O O O O O B-ComputingFacility I-ComputingFacility O O O O O O O O O O O O O O

The work is jointly supported by the National Natural Science Foundation of China (grant Nos. 41531073, 41731067, 41874202, 41861164026, 41574171, 41774184, and 41874205) and the Specialized Research Fund for State Key Laboratories. This work utilizes data obtained by the Global Oscillation Network Group (GONG) program, managed by the National Solar Observatory, which is operated by AURA, Inc., under a cooperative agreement with the National Science Foundation. The data were acquired by instruments operated by the Big Bear Solar Observatory, High Altitude Observatory, Learmonth Solar Observatory, Udaipur Solar Observatory, Instituto de Astrofísica de Canarias, and Cerro Tololo Inter-American Observatory. The work was carried out at the National Supercomputer Center in Tianjin, China, and the calculations were performed on TianHe-1 (A). The authors thank the reviewer for constructive suggestions for the improvement of the manuscript.


O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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-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-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 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 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 B-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 significant (and measurable) differences between the two models at the resolution of our spectrophotometric data, especially for the Mg UV and D4000 indices (marked in both plots as coloured areas). In Fig. 10 , we present the stacks built for the mature and senior galaxy populations together with the models characterized by their average properties. We also show the indices measured in the stacks of the mature, intermediate, and senior galaxy populations, and the tracks predicted by the model characterized by the average time-scales and dust attenuations quoted in Table 3 for each sub-population. The indices measured directly from the stacks are consistent with those predicted by the tracks of the models with the average properties of each sub-population. We demonstrate that the spectrophotometric data directly show the differences in the stellar population properties for the three sub-samples. Note that the origin of the average stellar population properties is the full SED spectral fits, and here we are comparing those models with finer resolution data in a limited wavelength range. The two analyses are not completely independent, but the information encoded in the data at the resolution which makes index measurements possible could easily be erased or degraded by fitting the whole SED from the UV to the mid-IR. Our test demonstrates that we are seeing differences in the galaxy populations in both the global SED and the spectral indices. We, thus, conclude that our results about the ages of MQGs at z = 1.0–1.5 are robust and not an artefact linked to the SED-fitting degeneracies. Figure 10. Left-hand panel: stacks for the senior (thick red line) and mature (thick blue line) populations normalized in the Mg UV (upper panel) and D4000 regions (lower panel). The average error of the stacks is ∼10 per cent. We used the dispersion as uncertainties (actual errors calculated by propagating the observed flux uncertainties were negligible). We also plot the normalized models with the average properties of each sub-population (thin red and blue lines). Right-hand panel: Mg UV versus D4000 plane, with the indices measured in the stacks for the mature, intermediate, and senior galaxies (blue, green, and red diamonds with error bars). For comparison, we also show the evolutionary tracks for two models with different star formation time-scales (an SSP and a delayed exponential model with τ = 1000 Myr) and two different dust attenuations ( A v = 0.0 mag and A v = 1.0 mag). The open circles represent the expected index values for each track at different ages (given in Gyr in the plot). The three coloured lines show the tracks predicted by the models with the average properties of each galaxy population (given in the legend). The filled coloured circles mark the indices values at different ages (0.5, 1.0, 2.0, 3.0, 5.0 Gyr, from smaller to larger symbols). The indices measured in the stacks are compatible with the average properties derived from 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 B-Person I-Person I-Person B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O O B-Instrument O O O O O O O O O B-Proposal B-Person O B-Person O O O O B-Organization I-Organization I-Organization O O O O O B-Person O O O O B-Location O B-Grant O B-Grant

The authors thank the anonymous reviewer for a thorough and careful reading and many useful and critical comments that resulted in significant improvements to the paper. The authors thank Professor J. Krelowski (Centre for Astronomy, Nicholas Copernicus University) for his comments on our analysis. The HARPS CH spectrum was observed in 2007 March under program 078.C-0403(A). L.B. and F.C. appreciate sponsorship through a Spectral Sciences, Inc. internal research and development project. G.A.G. acknowledges the support of Chilean fund FONDECYT-regular (project 1120190).


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

ACKNOWLEDGEMENTS AKB, TD, SE and ADM were supported by the National Science Foundation through grant number 1616168. ADM also acknowledges support through the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0019022. AKB is thankful to Duncan Campbell and Francois Lanusse for useful discussions.


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

ACKNOWLEDGEMENTS This work was financially supported by the Grant-in-Aid for JSPS Fellows for young researchers (MK). CD acknowledges the Science and Technology Facilities Council through grant ST/P000541/1 for support.


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

Collaboration XIV 2016b ); see Wen Wang ( 2017 ) for more details on the calculations of CMB (represented by the green contours in Figs 3 and 4 ). 2 We can see that when the observations of lensed GWEM systems are verified in the future, CMB constraints would benefit from having the constraints of lensed GWEM systems overlaid. 4 SUMMARY AND DISCUSSION Although the constraints on cosmological parameters have reached a high precision, all of the constraints so far have relied on EM observations alone. New multimessenger signals exploiting different emission channels are worth exploring in cosmology. Recently, Liao etal. ( 2017 ) proposed that future time-delay measurements of strongly lensed GW signals and their EM counterparts have great potential to infer cosmological parameters. Compared with the traditional approach of using strongly lensed quasar systems observed in the EM domain, the approach with lensed systems observed in both GW and EM windows has two advantages in constraining cosmological parameters. First, the time delays () between lensed images inferred from the GW signals would reach an extremely high accuracy (0.1s) from the detection pipeline, and such accurate measurements of would play an important role in boosting the development of precision cosmology. Secondly, with gravitationally lensed GWs and EM signals, the accuracy of lens modelling could be improved to some extent, leading to better constraints on cosmological parameters. In the EM window, Paraficz Hjorth ( 2009 ) suggested that the joint observations of the time delay () between lensed quasar images and the velocity dispersion () of the lensing galaxy are more effective to constrain cosmological parameters than or 2 separately. In this work, we apply the / 2 method, for the first time, to the strongly lensed systems observed in both GW and EM windows. We prove that both and / 2 from strongly lensed GWEM systems can serve as powerful cosmic rulers. From the comparison of the two different methods, we confirm that the / 2 method can provide tighter constraints on m than the method (i.e. using / 2 can make it easier to differentiate different cosmological models). Furthermore, we show that with a moderate sample size of 50, a constraint on the dark-energy equation of state w can be reached that is comparable to the 580 Union2.1 SNe Ia sample. Combining the and / 2 methods, it is possible to achieve higher accuracy in constraining w . The recent Advanced LIGO observations of binary black hole mergers GW150914 (Abbott etal. 2016a ), GW151226 (Abbott etal. 2016b ) and GW170104 (Abbott etal. 2017 ) have initiated the era of GW astronomy. Because of the high sensitivity, the planned third-generation GW detectors, such as the ET, could observe strongly lensed GWs. Recent works (Pirkowska etal. 2013 ; Biesiada etal. 2014 ; Ding etal. 2015 ) have carefully studied the prospects of observing strongly lensed GWs from merging double compact objects, which predicted that the ET


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

(McCourt et al. 2018 ; Mandelker et al. 2019 ) and by estimates of cool-phase cloud sizes inferred from measured column densities and derived number densities (e.g. Pieri et al. 2014 ; Crighton et al. 2015 ; Stern et al. 2016 ). Furthermore, with current computational capabilities it is infeasible to maintain even kpc-scale resolution throughout volumes that are tens of Mpc on a side, and standard Lagrangian or mesh refinement schemes will not automatically resolve the regions of the CGM where gas phases interact. Physical processes in addition to radiative hydrodynamics, such as thermal conduction, viscosity, and magnetic fields, may also have significant effects on cloud evolution (Marcolini et al. 2005 ; Orlando et al. 2005 ; Vieser Hensler 2007 ; McCourt et al. 2015 ; Armillotta, Fraternali Marinacci 2016 ; Brüggen Scannapieco 2016 ; Armillotta et al. 2017 ; Li et al. 2020 ), but they are rarely incorporated self-consistently in cosmological simulations. In the approach proposed here, we eject wind particles as in previous simulations but follow their evolution and interaction with the ambient CGM using an analytic subgrid model. We model the gas in each wind particle as a collection of cold clouds, and we calculate the exchange of mass, momentum, energy, and metals between these clouds and the surrounding CGM gas. A wind particle loses mass as it evolves, and it is dissolved when its mass falls below some threshold, or when its velocity and physical properties sufficiently resemble the surrounding gas, or when it rejoins a galaxy and contributes its remaining mass and metals to the ISM. This general method can be implemented in cosmological simulations that use smoothed particle hydrodynamics (SPH) or Eulerian or Lagrangian mesh codes. In future work, we will present results from implementing this Physically Evolved Wind (PhEW) model in cosmological simulations with the gizmo hydrodynamics code (Hopkins Raives 2016 ), employing the star formation and feedback recipes described by Davé et al. ( 2019 ) and the wind launch prescriptions described by Huang et al. ( 2020 ), which are themselves tuned to reproduce outflows in the FIRE simulations (Muratov et al. 2015 ). In this paper, we present the wind model itself. This model is based on results from very high resolution simulations of the ‘cloud-crushing problem’, which examine the evolution of an individual cold clouds moving supersonically relative to an ambient, hotter flow (see Banda-Barragán et al. 2019 for a recent compilation of such simulations). We concentrate in particular on the cloud-crushing simulations of Scannapieco Brüggen ( 2015 , hereafter SB15 ), which do not include thermal conduction, and the simulations of Brüggen Scannapieco ( 2016 , hereafter BS16 ), which do. These simulations model idealized situations with mass and spatial resolutions far higher than that achieved in any galaxy formation or cosmological hydrodynamic simulations. PhEW provides a method to


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

ACKNOWLEDGEMENTS We thank the anonymous referee. EB, JRM, and CT acknowledge STFC grant R/151397-11-1. EB thanks C.M. Harrison and J. Scholtz for useful discussions that helped improving the clarity of the results and discussion.


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

component is induced. As a result, a weaker toroidal field pressure is available for the disk wind ejection and acceleration. In this sense, the increasing magnetic diffusivity also suppresses the ejection process in the system. 7.2. Efficiency of Outflow Launching We have discussed above the influence of magnetic diffusivity on the ejection process. In general, magnetic diffusivity lowers the ejection rate. However, we have noticed that the magnetic diffusivity may lead to a higher outflow efficiency . Here we define the outflow efficiency aswhere and are the total ejection rate and the inner accretion rate, respectively, defined in Section 3.5 . We note that outflow efficiencies ξ > 1 are possible. In Table 2 we show the outflow efficiency ξ for the different simulations averaged from t = 2000 to t = 3000. In general, the outflow efficiency of disks with η 0 > 10 −4 is much larger than that of weakly diffusive disks with η 0 10 −4 . At this stage we may only speculate about the reason for this trend. One possibility may be the field structure just above the disk. The region above the accretion disk evolves as in ideal MHD. Material is frozen to the field lines and either flows along the field or needs to “push” the magnetic field component that is perpendicular to the motion. We find that the simulations with lower disk magnetic diffusivity result in a more tangled field structure (as discussed above, most probably due to the not fully stable initial disk hydrodynamics). One may argue that the tangled field is advected upward along with the outflow and then lowers the efficiency of acceleration. Also, mass loading is known to be governed by the physical conditions at the disk surface or the sonic surface. In our case of a super-Alfvénic injection, Lorentz forces will play a major role. We conjecture that for a tangled magnetic field the Lorentz forces are also tangled and thus less efficient in launching. In Figure 16 we show the field-line structures for simulations D 1 (left panel) and D 10 (right panel) at t = 2000. In the nondiffusive simulation D 1 (outflow efficiency ξ = 0.5), the matter flow inside the disk becomes turbulent, also disturbing the smooth structure of field lines. The disturbance propagates outward, leading to a field structure that is suppressing efficient acceleration. On the other hand, the field lines in simulation D 10 (outflow efficiency ξ = 2.9) still keep their original smooth structure at t = 2000. Figure 16. Density and magnetic field line distribution (zoomed in) for simulations D 1 (left) and D 10 (right) at t = 2000. In simulation D 1 the field lines inside the disk have a more turbulent distribution (especially within r 20), most probably due to the MRI. Another possibility for the observed interrelation between diffusivity and mass loading can be ohmic heating. This will result in a somewhat higher sound speed at the disk surface for the more diffusive disk. From steady-state MHD wind theory and


O O O O B-Organization I-Organization O O O O B-Fellowship I-Fellowship I-Fellowship

ACKNOWLEDGEMENTS I thank the Leverhulme Trust for award of a Leverhulme Emeritus Fellowship.


O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O B-Model I-Model I-Model I-Model I-Model I-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 O O O 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 B-Model O O O O O O O O O B-Telescope O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula 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 B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-CelestialObject 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 B-CelestialObject O O O O O O O B-Organization O O O O B-Instrument O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-CelestialObject O O O O O O O O B-CelestialObject B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O 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 B-Formula I-Formula I-Formula B-Formula I-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O

differences between spots and the photosphere Δ T spot (= T phot − T spot ) are listed in Table 2 . We follow Unruh et al. ( 2008 ) and use a 1D radiative equilibrium stellar atmosphere model with a cooler effective temperature than the quiet photosphere to represent spots. Mean MURaM quiet star spectra and 1D model spectra with equivalent effective temperature agree very well, although small differences are present for all spectral types. To minimize the effect of model differences on the resulting spot intensities, ATLAS9 spectra were calculated from 1D model stellar atmospheres at effective temperatures T phot and T spot for the quiet star and spots, respectively. The ratio of intensities was multiplied with the quiet star intensities from MURaM to provide spot intensities for our models. We show Kepler band spot intensity contrasts, I ( T spot )/ I ( T phot ) − 1 in Fig. 3 (bottom panel) for all spectral types. In the Kepler band, spots always have negative contrasts several times larger than that of facular regions, regardless of limb distance. Spot contrasts become more negative with increasing stellar effective temperature (a direct consequence of the spot temperature differences chosen). 3 MODEL SETUP We performed a number of investigations using the light-curvemodelling approach described in Section 2 : obtaining typical variability levels assuming a Sun-like feature distribution and evaluating the impact of spot temperature, active region latitude, and facular-to-spot coverage fraction on variability. Here, we describe how Sun-like feature distributions are generated and the assumptions made. 3.1 Latitude and longitude distributions We aim to model brightness variability on rotational time-scales. Focusing on the Sun, spots, and facular regions are observed to occur in latitudinal bands in both the northern and southern hemispheres. The central latitudes of these ‘active bands’ are known to change throughout the solar activity cycle, beginning at higher latitudes at the start of each 11-yr cycle and moving towards the equator as the cycle progresses (Hale et al. 1919 ). To model this, we use typical solar cycle averaged latitudinal distributions. These distributions are based on Borgniet et al. ( 2015 ), in which average spot and facular latitude distributions are presented for solar cycle 23 (1996 May–2007 October), derived from USAF/NOAA sunspot group data and MDI/SOHO magnetograms (Scherrer et al. 1995 ), respectively. Transit mapping observations of the K4V star HAT-P-11 show a very similar spot distribution to the Sun (Morris et al. 2017 ). This result indicates that the solar cycle averaged distributions in our simulations can also apply to some K-type stars. We fitted the solar spot and facular region latitude data with equatorially symmetric Gaussian distributions (for spots, 〈φ〉 = ±16°, σ φ = 8°; for faculae, 〈φ〉 = ±16°, σ φ = 12°) shown in Fig. 4 (top panel). Feature longitudes are randomized. As the number 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation 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 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 B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Model B-Citation I-Citation I-Citation I-Citation O O B-Model I-Model I-Model B-Model B-Citation I-Citation I-Citation O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O B-Model O O O B-Model 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

as done for the RMS . For the following analysis, we used these mean P2P RMS trends to identify, for each star, the best photometry: for each star in the input catalogue with a given T magnitude, we selected the light curve obtained with the photometric method that at the given T returns the lower mean P2P RMS . In this phase we also excluded all the light curves that have 300 photometric points and whose mean magnitude differs from that expected from the input catalogue >2 magnitudes. Panel (c) of Fig. 6 shows the 6.5-h RMS distribution (gray points) for the previously selected light curves. This transit noise 6.5-h RMS is obtained as described by Gilliland et al. ( 2011 ), Gilliland et al. ( 2015 ), and Van Cleve et al. ( 2016 ): we flattened each light curve interpolating to it a 5th-order spline with 65 break points and removing out the outliers. We computed the standard deviation of a running mean with a window length equal to 6.5 h (13 points). The azure line in panel (c) is the mean trend of the 6.5-h RMS distribution, calculated as previously described: the trend reaches a minimum at ∼34 ppm. For T 10, the distribution is bi-modal: stars that are not variable or whose period variability is >6.5 h have 6.5-h RMS ∼ 20 ppm. The stars with 6.5-h RMS ≳ 30 are highly variable on short time-scales and the flattening is not perfect. For stars with 10 ≲ T ≲ 14, we are able to detect exoplanets transits with depth 1 mmag, while for T ≳ 14 it is possible to find transits with depth 0.01 mag. 3 CANDIDATE EXOPLANET TRANSIT FINDING We searched for transiting signals among the light curves selected in the previous section. As described in Section 2.5 , we flattened all the light curves using 5th order splines defined on 65 knots. For each light curve, we removed out the outliers and the photometric points with 1347.4 t BTJD 1349.4, whose photometry is affected by pointing problems and that, despite the cotrending, still have some residual systematic artifacts. For each light curve, we extracted both the Box-fitting Least-Squares (BLS, Kovács, Zucker Mazeh 2002 ) and Transit-fitting Least Squares (TLS, Hippke Heller 2019 ) periodograms. For both techniques we searched for transiting objects having period 0.6 ≤ P ≤ 14 d, and for each star we extracted the parameters useful to discriminate between light curves with and without candidate transits, such as the signal detection efficiency (SDE), the signal-to-noise ratio (SNR), the depth of the transit. To detect candidate transits we performed two independent analysis on BLS and TLS outputs and at the end we joined the results. In Fig. 7 , we summarize the procedure adopted for the selection of candidate transiting exoplanets both for TLS (left-hand panels) and BLS (right-hand panels) technique. As described in Nardiello et al. ( 2015 ), we excluded spurious periods due to systematic errors by constructing the histogram of the period and removing the stars that form the spikes in the histogram: the red


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

and afterglows can be used to constrain the angular structures of energy and Lorentz factor (Beniamini Nakar 2018 ), which are consistent with our results. In Figure 2 , we show the fitting results of the characteristic Lorentz factor (Γ ∼ 2 η 0 γ B ) for GW170817 and 14 short GRBs. GW170817 has Γ ≈ 150, which fits well within the range of short GRBs (Γ = 135 ± 47). For GW170817, the Lorentz factor long the line of sight to the observer is 5.3, which fits the expectation that the early emission is effectively dominated by radiation from mildly relativistic material. Figure 2. Fit results of the characteristic Lorentz factor Γ (left) and the spectral index p (right) for GW170817 (red circle) and 14 short GRBs (blue squares). Markers with error bars indicate median values and symmetric 68% quantiles. In Figure 2 , we show the fitting results of the spectral index p . GW170817 has a tight constraint , as it has good observational data from all three bands. The mean and standard deviation of short GRBs is p = 2.26 ± 0.22. The spectral index of GW170817 is consistent with those of short GRBs. Figures 3 shows the distributions of GW170817 and 14 short GRBs in the ( n 0,0 , E 0,50 ) plane. GW170817 has n 0 ≈ 10 −2 proton cm −3 and E 0 ≈ 6 × 10 49 erg. Considering the jet opening angle θ 0 ≈ 0.11 rad, the corresponding isotropic equivalent energy is E iso ≈ 8 × 10 52 erg. These values are located within the typical ranges of short GRBs. Because n 0,0 and E 0,50 are degenerate parameters, most of the bursts display large error bars. Due to the scaling relations, our model is better at constraining outflow structures rather than estimating accurate values of degenerate parameters. Even though these degenerate parameters are not well constrained, we note that their uncertainties can be marginalized out, and thus will not affect the constraints on non-degenerate parameters. In Wu MacFadyen ( 2018 ), we broke the degeneracies by fixing density as n 0,0 = 10 −3 , and the outflow structure of GW170817 remains consistent. The values of e for the short GRBs is found to be around 0.3, which is consistent with other studies (Cenko et al. 2010 ; Beniamini van der Horst 2017 ). Figure 3. Fit results of explosion energy E 0,50 and ISM density n 0,0 for 14 short GRBs (blue squares) and GW170817 (red circle). Markers with error bars indicate median values and symmetric 68% quantiles. 4.3. On-axis Light Curves We have found that GW170817 and short GRBs share similar outflow structures and other physical parameters, except for the observation angle. Viewed off-axis, GW170817 displayed exceptional behaviors, such as late onset and early brightening. Short GRBs are viewed on-axis and show a general decline shortly after prompt emission. This leads to an interesting question: what would be observed from GW170817 if the observer were located on-axis? In Figure 4 , we show the X-ray afterglow observations for GW170817 (red circles with error bars) and 27 cosmological short


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

computed with the STAREVOL code so far ( Palacios et al. 2003 , 2006 ; Decressin et al. 2009 ; Lagarde et al. 2012 ), while the prescription of Maeder (1997) has been systematically used for the rotating models computed with the Geneva code ( Eggenberger et al. 2012 ; Georgy et al. 2013 ). Meynet et al. (2013) have shown that the choice of the turbulent transport prescriptions may dramatically affect predictions for the structural, chemical, and rotational evolution of massive stars, but they were unable to clearly determine a best combination for fitting the observational chemical constraints. In Sect. 5 we discuss this in a similar way within the framework of the rotational evolution of solar-type stars. Table 3 Parameters and assumptions of the different models computed in this study. Reference. MPZ04 refers to Mathis et al. (2004) , TZ97 to Talon Zahn (1997) ; Matt+15 to Matt et al. (2015) ; Matt+12 to Matt et al. (2012) ; RM 12 to Reiners Mohanty (2012) ; and GB13 to Gallet Bouvier (2013) . SB is for solid-body rotation. 2.4. Transport of chemicals The transport of chemical species in radiative region is computed as a purely diffusive process ( Chaboyer Zahn 1992 ) but accounts for vertical advection and a strong horizontal diffusion. For a chemical species , the concentration follows the equation with the total diffusion coefficient, given bywhere and were defined previously (see Table 2 ). Finally, the term refers to the temporal evolution of the concentration of chemical species due to nuclear burning. 3. Physics of the models For all the models reported in Table 3 , the basic input physics (equation of state, nuclear reaction, opacities) can be found in Lagarde et al. (2012) . The initial abundances and mixing length parameter are calibrated without microscopic diffusion to reproduce a non-rotating Sun with respect to the Asplund et al. (2009) solar mixture with a precision for luminosity and radius at the age of the Sun. We used a mixing length parameter , an initial helium abundance , and an initial metal abundance . These values differ slightly from Lagarde et al. (2012) because we included a non-grey atmosphere treatment based on Krishna Swamy (1966) , which better agrees with observations for Sun-like stars (e.g. Vandenberg et al. 2007 ). In addition to the treatment of transport and loss of angular momentum and mass as described in Sect. 2, we included the modification of the effective gravity by the centrifugal forces and its effect on the stellar structure equations following Endal Sofia (1976) . This effect is slightly visible on the evolutionary track in the Hertzsprung-Russell diagram when the stars rotate fast. Rotation can have a non-negligible impact on the effective temperature for the fastest rotators around the ZAMS. Fig. 2 Evolution of the angular velocity as a function of time for the reference models. Plotted on the left as the rotational periods in days and during the right as the angular velocity in solar


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

We acknowledge Matthew Bayliss, Kathy Cooksey, Francesco Di Mille, Steven Elhert, Michael Florian, Tolga Guver, Traci Johnson, Dan Kelson, Michael McDonald, Andy Monson, David Osip, Benjamin Rackham, Nathan Sanders, Anil Seth, Meghin Spencer, Brian Stalder, Tony Stark, Rik Williams, and Amanda Zangari for their assistance in Magellan target-of-opportunity observations. Partial support for this work was provided by NASA through Einstein Postdoctoral Fellowship grant number PF4-150121 and Chandra Award Number G04-15055X, issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for NASA under contract NAS8-03060. B.A.Z. acknowledges support from NSF grant AST-1302954, E.B. acknowledges partial support from NSF grant AST-1107973, and R.M. acknowledges support from the James Arthur Fellowship at NYU. Additional support was provided by several NASA/ Swift grants. This work made use of data supplied by the UK Swift Science Data Centre at the University of Leicester. The scientific results reported in this article are in part based on observations made by the Chandra X-ray Observatory and data obtained from the Chandra Data Archive. This paper includes data gathered with the 6.5 m Magellan Telescopes located at Las Campanas Observatory, Chile. Observations reported here were obtained at the MMT Observatory, a joint facility of the University of Arizona and the Smithsonian Institution. Based on observations obtained at the Gemini Observatory acquired through the Gemini Science Archive and processed using the Gemini IRAF package which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia), the Ministèrio da Ciência, Tecnologia e Inovação (Brazil), and the Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina). The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.


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

Acknowledgements This work is based in part on observations made with the NASA/ESA Hubble Space Telescope , obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. These observations are associated with programs 9744, 12889, 14254. Financial support was provided by NASA through grants from the Space Telescope Science Institute. We are grateful to Vivien Bonvin, Geoff C.-F. Chen, Frederic Courbin, Matthew A. Malkan, Cristian E. Rusu, Jong-Hak Woo and Andreas Schulze for useful comments and suggestions that improved this manuscript. We thank Chien Peng for his help with the estimates of black hole mass. XD is supported by the China Scholarship Council. TT acknowledges support by the Packard Foundations through a Packard Research Fellowship and by the NSF through grants AST-1450141 and AST-1412315. SHS gratefully acknowledges support from the Max Planck Society through the Max Planck Research Group. CER acknowledges support from the NSF grant AST-1312329. DS acknowledges funding support from a Back to Belgium grant from the Belgian Federal Science Policy (BELSPO). KCW and DP are supported by an EACOA Fellowship awarded by the East Asia Core Observatories Association, which consists of the Academia Sinica Institute of Astronomy and Astrophysics, the National Astronomical Observatory of Japan, the National Astronomical Observatories of the Chinese Academy of Sciences, and the Korea Astronomy and Space Science Institute. VNB gratefully acknowledges assistance from a National Science Foundation (NSF) Research at Undergraduate Institutions (RUI) grant AST-1312296. Note that findings and conclusions do not necessarily represent the views of the NSF. VB acknowledges the support of the Swiss National Science Foundation (SNSF).


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

explosions, exceeds its binding energy (see Matteucci 1994 ; Bradamante, Matteucci D’Ercole 1998 ; Vincenzo et al. 2014 ): The thermal energy of the gas is produced by SN explosions (of all types) and by stellar winds, while the binding energy of the gas is computed as where W L ( t ) is the potential well due to the luminous matter and W LD ( t ) represents the potential well due to the interaction between dark and luminous matter. This last term mainly depends on the mass of the DM halo ( M DM ) and on the ratio S = R L / R DM between the galaxy effective radius ( R L ) and the radius of the DM core ( R DM ) (see Bertin, Saglia Stiavelli 1992 ). The last term R i ( t ) represents the fraction of matter that is returned by stars into the ISM through stellar winds, SN explosions, and MNS, in the form of the element i . In other words, it represents the rate at which each chemical element is restored into the ISM by all stars dying at the time t . R i ( t ) depends also on the initial mass function (IMF). Here we adopt a Salpeter ( 1955 ) IMF for all galaxies: normalized to unity between 0.1 and 100 M ⊙ . 4 NUCLEOSYNTHESIS PRESCRIPTIONS For all the stars sufficiently massive to die in a Hubble time, the following stellar yields have been adopted. For LIMS we included the metallicity-dependent stellar yields of Karakas ( 2010 ). For massive stars we assumed yields of Kobayashi et al. ( 2006 ). For Type Ia SNe (SNeIa) we included yields of Iwamoto et al. ( 1999 ). We adopted the single-degenerate scenario for SNeIa, in which SNe arise from the explosion via C-deflagration of a C–O white dwarf in a close binary system as it has reached the Chandrasekhar mass due to accretion from its red giant companion. The same stellar yields have been adopted in Vincenzo et al. ( 2015 ). Also, a complete and detailed description of those yields can be found in Romano et al. ( 2010 ). 4.1 Eu and Ba yields For both Eu and the r-process fraction of Ba we considered two different production sites: MNS and MRD-SNe. We assume r-process elements to be produced by (i) only MNS, (ii) only MRD-SNe, (iii) both MNS and MRD-SNe. In our simulations, MNS are systems of two 1.4 M ⊙ neutron stars with progenitors in the 9–50 M ⊙ mass range. In order to include the production of r-process elements from MNS in our chemical evolution code, we need to specify the following parameters (see Matteucci et al. 2014 ): the mass of each elements that is produced per merging event, and ; the time delay between the formation of the double neutron star system and the merging event, τ; the fraction of neutron stars in binaries that produce a MNS, α MNS . For what it concerns the yields of r-process elements from MNS, they have been obtained by assuming that there is a scaling relation between them and those of strontium (Sr). The adopted scaling factors are equal to 0.03 for Eu and to 3.16 for Ba, and have been found from the Solar system r-process contribution, as determined by Simmerer et


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

fact is also illustrated in Fig. 12 , where the contour plots at 75% of the population are depicted. Figure 12 shows the mass range split over four bins for DAE diagram on the top row, for the PCA at the center, and for the RJ NUVR diagram on the bottom row. We note that the overlap is significantly lower for the DAE diagram, compared to the PCA diagram and to the RJ NUVR plane. The data-driven representations present a clear evolution over the axis in terms of mass for both star-forming and quiescent populations, while this evolution is barely observed in the classical RJ NUVR diagram. These distinct behaviors of the stellar mass distributions in the diagrams thus reveal variations of the galaxy SED properties that are again more efficiently extracted with the unsupervised learning techniques than when just taking the NUV and rest-frame colors into consideration. Given that the stellar mass of galaxies tightly correlates with their near-infrared luminosities, the mass distributions observed in Fig. 9 may suggest that the PCA and the DAE results at a given redshift are partially driven by the variations of the near-IR magnitudes that can be probed at this kind of redshift. On the other hand, the stellar mass also correlates with other physical properties such as the dust extinction and the activity of star formation, which both modify the overall shape of galaxy SEDs and necessarily also impact the DAE outputs. For instance, galaxies with enhanced recent star formation display SEDs characterized by a more important contribution of young and massive stars, which produces intense radiations of UV photons boosting the overall galaxy emission at short wavelengths. The star formation rate (SFR) of galaxies also correlates with their stellar mass, but in a non-linear relation such that the SFR per unit of mass mildly decreases in more massive sources ( Speagle et al. 2014 ). The relative level of star-forming activity in galaxies could thus also contribute to the apparent variation of the DAE and PCA distributions with the stellar mass. Fig. 12 Contour plots for different mass bins on the DAE diagram, on the PCA diagram and on the RJ – NUVR plane. The mass range is split over four bins and the contour plots are displayed at of the samples in the different mass bins. The DAE diagram is displayed on the top, PCA diagram at the center, and the RJ NUVR diagram on the bottom. The contour’s colors grow from grey to green for star-forming galaxies, and from yellow to purple for quiescent galaxies, respectively. These plots attest to the relationship with the stellar mass captured by the DAE and PCA diagrams for both star-forming and quiescent populations, while the overlap in the RJ – NUVR diagram is considerably higher. 4.3. Specific star formation rate To further explore the impact of the galaxy star-forming activity in the different diagrams, we conducted a similar analysis, taking into consideration this time the influence of the specific star


O O O O O O O O O O O O O O O O O O O O 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 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 B-Model I-Model 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 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 B-Model O O O B-CelestialObject O O O O O O O B-Model 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 B-Model I-Model I-Model I-Model I-Model 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 B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O B-Telescope B-Mission 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

of 0.47, but we do not draw any interpretation from it. Figure 12. Distribution of the peak intensity, duration, fluence and wait time t + for a subsample of flares with peak intensities in the range , durations in the range 2.8 min Δ t ≤ 49 min totalling 1198 flares. This range is chosen to select power-law behaviours of all these quantities, in order to test the SOC hypothesis (see the text). Orange lines represent the power-law fit on each distribution, characterized by a the index α. The fits were made using the integral of the distribution (as in Fig. 10 ). In the case of the fluence and the wait time, fitting interval had to be restricted to the area between the two vertical dashed red lines. We also remark that the power-law index of the Fourier spectrum of the light curve with flares but without orbital modulation is −1.11 ± 0.05 while without flares it is only −0.70 ± 0.05 (see Section 4 ). The pink noise (power-law index of −1) is one of the main characteristics of SOC processes, as this theory was introduced to explain the ubiquitous presence in natural processes of this type of noise (Bak, Tang Wiesenfeld 1987 ). Therefore, the fact that the index is closest to −1 with flares included suggests that these are only the larger-amplitude tail of an overall SOC signal. This is further re-enforced by the previously mentioned fact that the distribution of peak intensities behaves like the upper tail of a broader distribution. 6.3.1 A comparison with low accretion rate CVs The most obvious SOC mechanism to compare J1023 during its accretion phase with is the SOC possibly present in low accretion rate cataclysmic variables (e.g. Dendy, Helander Tagger 1998 ). Low accretion rate non-magnetic CVs often undergo brightening events called dwarf novae during which the systems brightness increases by 2–7 mag. Dwarf novae events are suspected to arise due to a combination of an instability in the accretion disc (disc instability model, or DIM; Osaki 1974 ) and a variable mass accretion rate. At low accretion rates, the discs are cool and stable. Once the discs reach a critical density, the viscosity of the disc changes, and material begins to move rapidly inwards through the disc, increasing the temperature of the disc while rapidly transferring material on to the white dwarf. This continues until the density of the disc drops below the critical value, and the disc becomes stable again. For a review, see Lasota ( 2001 ). While the mechanisms between the outbursts in dwarf novae and the flares in J1023 are very different, future work should be done on investigating the similarities between these systems, especially since the driving force behind dwarf novae and the flares in J1023 is accretion. 7 CONCLUSIONS The Kepler K2 light curve of J1023 has revealed more about the nature of tMSPs during their accreting state. In particular, we have found that the amplitude of the underlying orbital modulation in the accretion state is similar to that in the