O O O O O O O O O O O O O O O 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 B-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software I-Software I-Software B-Software I-Software B-URL O O O O O O O O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

10 3 ]. In panel (b), C ranges from (0, 200] and γ ranges from (0, 0.2]. For the purpose of cross-validation, we split the entire data set into two subsets: the training set and the test set. Amari et al. ( 1997 ) found the optimal number of the test set as , where l and n are the number of data points and features, respectively. Taking l = 187 and n = 13 in our case, we found that the partition of the entire data set between the training set and the test set should be 80%:20% (145:37). Using the optimal pair of parameters C and γ found above, we fed the training set into the SVM regression algorithm to build a prediction engine. Next, we made a prediction of the CME transit times using the test set and calculating the R 2 score between the predicted and actual transit times. To find the best result with the highest R 2 score, we randomly shuffled the entire data set (the order of events in the data set is shuffled, which is a general practice to avoid bias, see, e.g., Géron 2017 ) and repeated the above steps (i.e., split the shuffled data set into the training and test sets, build an engine using the training set, and calculated the R 2 score of the test set). Theoretically, there are (∼6 × 10 38 ) possible combinations of the training set and test set. This is a huge number and it is impossible to exhaustively test all of the possibilities given the available computer power. Figure 5 shows the variation of the average (blue curve) and maximum (green curve) R 2 scores among all of the test sets with the increasing number of trainings. The average R 2 score increases continuously before the number of trainings reaches 1000, and remains almost unchanged after that. This suggests that when training is performed over 1000 times, the result can reflect the basic distribution of the R 2 scores for all possibilities. The maximum R 2 score increases steeply when the number of performed trainings is less than 100,000 and yields a similar value when it is increased by a factor of 10. This indicates that it becomes more feasible to find the best engine with an increasing number of trainings. Figure 5. Variation of the average (blue curve) and maximum (green curve) R 2 scores with increasing number of trainings. Considering the above results and reasonable CPU time consumption, we repeated 100,000 times of trainings to find the best training set, which results in a highest R 2 score of its corresponding test set, to construct the engine. This could be rather costly. However, via paralleling the process employing the open-source Message Passing Interface (Open MPI, http://www.open-mpi.org/ ), a 100,000-time training only takes ∼25 minutes on an Intel(R) Core(TM) i7-7770K desktop with 8 threads. However, we should note that training the SVM regression 100,000 times cannot always reveal the best result (as shown by the green dashed line in Figure 3 ), because 100,000 is only a fraction of all of the possibilities (). Multiple runs are sometimes needed to


O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O 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 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-CelestialObjectRegion I-CelestialObjectRegion O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O B-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 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 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 B-TextGarbage I-TextGarbage I-TextGarbage I-TextGarbage O O O O O O O O O O O O O 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 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 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 B-Model I-Model O B-Formula I-Formula I-Formula I-Formula I-Formula B-Formula I-Formula I-Formula I-Formula 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-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 B-Citation I-Citation I-Citation

of the warp causing reddening extends 1.07 and 0.68 R ⋆ above the disk midplane (for the Jan. 18 and 19 spectra, respectively). The CoRoT light curves indicate that the warp blocks part of the star during about half of the rotation period, which points to a ratio of roughly 3:1 between the azimuthal and vertical dimensions of the warp given the above size estimate. We note that, with the viewing geometry derived by Fonseca et al. (2014) , the star is unobscured only during phases when the disk does not significantly extend above the disk midplane. 4.3. Gas absorption The X-shooter spectra also contain atomic gas absorption lines that include nonstellar contributions, which we later correlate with the dust extinction. The spectral resolution of X-shooter renders it challenging to differentiate interstellar (expected to be narrow) from circumstellar absorption (expected to be broad) directly in the spectra. Hence, we concentrated on the evolution of the observed EW, because any “truly” interstellar (e.g., Pascucci et al. 2015 ) or stellar absorption is expected to stay constant. In this situation, observable changes in the absorption require that inter- and circumstellar column densities have roughly similar values. Circumstellar column density changes that are small compared to the interstellar absorption would remain unnoticed. Conversely, observing EW changes directly implies that the circumstellar column densities are sufficiently large. 4.3.1. Measured line properties The Na and K optical doublets are the strongest absorption lines in our spectra ( Fig. 4 ). They are common interstellar absorption lines (e.g., Welty Hobbs 2001 ), but can also have circumstellar contributions. In fact, accretion emission can also contribute to these lines, but the lack of strong accretion signatures 3 implies that this would affect the EW by≲ ≳ 10mÅ. Similarly, absorption by the accretion funnels has been suggested to cause broad absorption features in CTTS, mainly in the strongly accreting ones. Hence, we regard a funnel contribution to the Na and K absorption insignificant for V 345 Mon due to its very low accretion rate. In all three epochs, we clearly detect absorption in the Na and K optical doublets while the Na UV lines are not significantly detected with a combined EW upper limit of 0.7 Å. The depth of the Na and K doublets is mainly photospheric, the PHOENIX model ( T eff = 4900 K, log g = 4.50, solar metallicity, see Husser et al. 2013 ) gives stellar EWs of 3.6 Å (Na) and 0.6 Å (K). Neverthless, material between us and the photosphere causes extra and variable absorption since the measured EW is higher than the photospheric value for both doublets during all epochs. With the limited spectral resolution of X-shooter, we cannot localize the gas that causes this extra absorption, for example, through its velocity structure. However, some of this extra absorption is likely interestellar and thus constant between the observing nights ( Pascucci et al.


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


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

We thank the referee, Richard Alexander, for his useful and clarifying comments that improved the paper. E.M., G.A., M.O., J.M.T., and J.F.G. acknowledge support from MINECO (Spain) grant AYA2014-57369-C3 (co-funded with FEDER funds). S.L. acknowledges support from DGAPA-UNAM IN105815 and CONACyT 238631. C.C.-G. acknowledges support from UNAM-DGAPA PAPIIT IA102816. L.Z. acknowledges the financial support from DGAPA, UNAM, and CONACyT (Mexico). Facility: VLA.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software I-Software I-Software I-Software 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-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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

and magnetic reconnections. By sampling the shock profiles at different times and different locations of the bow shock and tracing the particles, we have shown the following results: 1. We identify different stages in the macroscopic evolution of the bow shock and the entire formation of the magnetosphere in the meridian plane. The macrostructures reach a quasi-stable state after several ion cyclotron cycles, consistent with previous 3D implicit PIC simulations (Peng et al. 2015b ). Furthermore, a relatively high temporal-spatial resolution employed in our simulation provides an opportunity to examine the microstructure of the bow shock and the magnetic reconnection. 2. In the southward IMF condition, the shock around the subsolar point is quasi-perpendicular, and the shock at the wings is oblique. The angle and solar wind speed along the shock normal decrease with the distance away from the subsolar point. At quasi-perpendicular regions of the shock, a self-reformation of the shock front is found and the cyclic period of the reformation is similar to those observed in 1D and 2D local simulations. At the oblique region, the shock becomes weak due to the slow solar wind speed in the shock normal direction. 3. Different from 1D and 2D local simulations, particles in the downstream region are more complicated at the bow shock. By tracing the ions and electrons in the simulation, we find that the solar wind ions injected at the subsolar point will become diffuse and can be convected to the cusp region and the downstream of the oblique region of the bow shock. Electrons are more diffusive than ions in the downstream region. The ions injected at the northern part of the bow shock will fill in the northern part of the magnetosheath. A fraction of electrons injected at the same place will be convected to the southern part of the magnetosheath. The particles injected and reflected by the quasi-perpendicular shock region can affect the local velocity distributions and electromagnetic fluctuations in the transition and downstream regions of the oblique shock at the wings of the bow shock. This feature makes the oblique shock regions become a little different from those observed in local planar shock simulations. 4. The impact of the upstream plasma beta β i and solar wind Mach number M A on the bow shock and the magnetosphere show that the shock front becomes quasi-stationary in the high beta and low Mach number cases. In addition, the magnetotail reconnection disappears in this quasi-stationary case due to the low compression of the magnetotail under a low solar wind pressure condition. If we keep the Mach number of the incident solar wind unchanged and only increase the beta value, the bow shock is still nonstationary. Contrasting the low beta case, the ripple scale becomes larger in the high beta case. 5. To confirm the impact of the solar wind condition on the bow shock front nonstationarity, we also studied the time evolution of shock


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

This work is supported in part by a Department of Energy Office of Nuclear Physics Early Career Award, and by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Divisions of Nuclear Physics, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231, and from NSF grant AST-1206097. Support for M.-R.W. and G.M.-P. is provided in part by the Helmholtz Association through the Nuclear Astrophysics Virtual Institute (VH-VI-417) and the BMBF-Verbundforschungsprojekt number 05P15RDFN1.


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

jet emanating from Sgr A*: the jet collides with the Eastern arm of the Sgr A West H ii region, driving a shock front which is observable in infrared and radio, and accelerating relativistic electrons which are seen in X-ray. The long axis of the hypothetical jet path corresponds to an azimuthal angle φ ∼ (−35 ± 2)°. If the jet propagates along the rotation axis, this measurement is consistent with our finding that φ ∼ (−32 ± 23)°. The rotation axis is also similar to that inferred by jet models of Markoff, Bower Falcke ( 2007 ), θ ≳ 75°, φ ∼ −25°, and model-dependent constraints on the spin axis by Meyer et al. ( 2007 ), φ ∼ − 25°. Surprisingly, this rotation axis is also nearly coincident with the Galaxy's rotation axis, φ = −317 (Reid Brunthaler 2004 ). Since we find a rotation axis misaligned with both the stellar clockwise disc (by ∼90°), and with G2 (by ∼60°), our model argues against scenarios in which gas in the accretion flow originates from either of these sources. The rotation axis we identify does align quite closely with the circumnuclear disc, a massive torus of molecular gas with an inner edge ∼1.5 pc from Sgr A* (θ = 118° ± 15°, φ = −25° ± 15°; Jackson et al. 1993 ). Our analysis suggests that the gas in the accretion flow hails from the circumnuclear disc, rather than from the young clockwise stellar disc as is commonly assumed. In addition to constraining the rotation axis of the accretion flow, we find degenerate relationships between the gas density and magnetic field strength, and between the rotation profile and the shape of the G2 cloud. These degeneracies could be broken with further observations, yielding first measurements of the gas density and rotation speed at radii of 100s of au in the Galactic centre. This is an exciting possibility, because these measurements would constrain the thermodynamics and momentum transport within the accretion flow, providing important information about the physics of black hole accretion in low-luminosity systems such as Sgr A*. We find that G2's motion is with the accretion flow rather than against it (Fig. 8 ; cf. Sadowski et al. 2013a ). With a relative inclination of ∼60° between G2's pre-pericentre orbit and the accretion flow, this is similar to the M3 simulation of Abarca, Sadowski Sironi ( 2014 ). This lowers the relative velocity somewhat, and may help explain non-detections of the bow-shock ahead of the cloud (e.g. Bower et al. 2015 ; Tsuboi et al. 2015 ). A potentially important effect we have not included in our analysis is the back-reaction of the drag force on to the accretion flow; since the combined mass of G1 and G2 is comparable to the total amount of gas in the accretion flow, the drag force acting on the clouds could also influence the evolution of the accretion flow. This is a complex process, as the back-reaction depends on angular momentum transport in the accretion flow and could be affected by magnetic fields, turbulent transport, and viscosity; we have


O O B-Archive I-Archive I-Archive O B-URL O O O O O O O O O O O O B-Person I-Person O O O O O O O B-Organization O B-Grant B-Grant O B-Grant

We thank Cluster Science Archive ( http://www.cosmos.esa.int/web/csa ) for providing the data for this study. The fruitful discussion with A. Vaivads is appreciated. This work was supported by NSFC grants 41574153, 41431071, and 41404133.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey O O O B-CelestialRegion I-CelestialRegion O O O O O O O O B-Survey O O O O O O O O O O O O O O O O O O B-Survey O O O B-CelestialRegion I-CelestialRegion

and our results not dominated by these corrections. This is discussed in more detail in Section 7 and Tables 2 and 3 . Table 2. Impact of the different corrections for observational systematic effects on the derived best-fitting bias b for the tomographic bins selected with our template method. The baseline mask is described in Section 4.2.3 and corresponds to all regions where our sample is complete (i.e. 10σ depth i ≥ 22.5). The third column corresponds to an additional masking of regions with high values of potential systematic variables such as seeing, where we observe large decrements in galaxy density (as described in Section 6.1 ). The fourth column refers to further corrections to w (θ) after these masks, in the cases where the data still correlate with maps for potential systematics (as discussed in Section 6.2 ). The fifth column reports the χ 2 /d.o.f. after all corrections applied. Empty entries refer to the cases where such corrections were not necessary. These values were obtained after fitting the ‘linear growth’ model for scales θ > θ min = (0.26, 0.18, 0.12, 0.08, 0.06) deg, from first to last z -bin. Table 3. Same as Table 2 but for the tomographic bins selected with the machine learning method. Different algorithms for photometric redshift estimation use different data quantities (most notably, template-based ones use magnitude errors while most machine learning do not). Thus, one expects a different response to potential systematics. 6.3 Stellar contamination Stellar contamination will affect the measured clustering signal, even if the cross-correlation between the galaxies and stars is negligible. This is due to the fact that rather than modulate the selection function of galaxies, stellar contamination introduces a separate population. In the limit where the stars are unclustered and the stellar contamination is constant, the observed galaxy density is δ o = (1 − f star )δ gal and thus i.e. the measured clustering is diluted by the square of the purity of the galaxy sample. We derive a general expression for the clustering of a galaxy population, given some stellar contamination (full details are shown in Appendix D ) where in this formalism, the number density of contaminating stars is allowed to be a function of not just the total density of stars, but also the survey observing conditions. The cross-correlation tests presented in the previous sections did not find stellar contamination to be a significant systematic contaminant. This suggests that the term in equation ( 26 ) proportional to w star, S is consistent with zero. However, the terms remain, and thus any stellar contamination must be accounted for. We estimate the stellar contamination in each photometric redshift bin by using DES observations in the COSMOS field. This region contains space-based observations which identify matching DES sources as point-like or not (as detailed in Section 4.1 ). Fig. 9 shows the purity of the DES sample in the COSMOS field


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

in marginally excited dynamos, we restrict ourselves in the following to being real. We now also assume that is constant. In that case, oscillatory solutions were previously thought impossible ( Rädler Bräuer 1987 ). Analogously to their approach, we multiply Eq. ( 8 ) by , where the asterisk denotes complex conjugation, and integrate by parts. Using Eqs. ( 9 ) and ( 10 ), we obtain Furthermore, , so Equation ( 8 ) yields altogether four terms, two of which are real and the other two imaginary. We obtain two integral constraints where denotes the value of on the second boundary at . This implies that (negative frequencies for positive ) and if and . Similar integral constraints can also be formulated for the complex magnetic field, . Unfortunately, the perfect conductor boundary condition, , is more cumbersome. Instead, one could formulate the problem for an artificially modified boundary condition, on . Together with the condition on , the problem for becomes equivalent to that for . In either case, the integral constraints are analogous to those of Rädler Bräuer (1987) ; see Appendix A for details. Fig. 1 Plots of a) real, b) imaginary, and c) absolute parts of . In a) and b) , the zero lines are marked in white, while in c) those of are dotted blue and those of are solid red. 4. The solution Given that Eq. ( 8 ) has constant coefficients, it has solutions proportional to where the index denotes one of two independent solutions. The are in general complex and obey the characteristic equation It has two solutions, To satisfy the boundary conditions ( 9 ) and ( 10 ), we write the solution as a superposition of and . Equation ( 9 ) is readily satisfied by writing where we have ignored the possibility of an arbitrary (complex) constant in front of . To satisfy Eq. ( 10 ), we now require that vanishes. The existence of solutions to is demonstrated by looking at a contour plot of ; see Fig. 1 , where we also plot separately the real and imaginary parts of . We see two zeroes in , which is confirmed by the crossing of the lines where and vanish. (At , there is no such crossing, so is not a solution.) The transcendental equation relating to can be written in more explicit form as To find solutions to , it is convenient to introduce the complex variable We seek solutions to via complex interpolation, where subscripts and refer to the current and previous iteration. This yields the first critical value as with the corresponding complex wavenumbers The wavenumbers and obey the relation which follows from Eqs. ( 9 ) and ( 18 ). The critical values of and were first obtained by Jabbari et al. (2017) using explicit time integration. Additional solutions exist in the second and fourth quadrant of the plane; see Fig. 2 . They are all oscillatory, in agreement with the integral constraints; see Eqs. ( 13 ) and ( 14 ) and Table 1 . However, those higher modes would generally be unstable in a nonlinear calculation and therefore only of limited interest (


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This work has made use of the HPC resources of CINES (Jade supercomputer) under the allocation 2013047012 and 2014047012 made by GENCI. Part of the analysis was performed on the DiRAC facility jointly funded by STFC and the Large Facilities Capital Fund of BIS. This work is partially supported by the Spin(e) grants ANR-13-BS05-0005 of the French Agence Nationale de la Recherche and by the ILP LABEX (under reference ANR-10-LABX-63 and ANR-11-IDEX-0004-02). The research of YD has been supported at IAP by ERC project 267117 (DARK) hosted by Université Pierre et Marie Curie – Paris 6. We thank S. Rouberol for running smoothly the horizon cluster for us, and D. Munro for freely distributing his yorick programming language and opengl interface (available at http://yorick.sourceforge.net/ ). SC and CP thank Lena for her hospitality during the course of this work. VD would like to thank the Institut d'Astrophysique de Paris for hospitality during the completion of this work, and acknowledges support by the Swiss National Science Foundation. JD and ASs research is supported by funding from Adrian Beecroft, the Oxford Martin School and the STFC.


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O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O B-Citation I-Citation I-Citation I-Citation O O B-CelestialObject I-CelestialObject I-CelestialObject O B-CelestialObject O O B-Telescope 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 B-Citation I-Citation I-Citation I-Citation O O O O B-Citation I-Citation I-Citation I-Citation O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O B-CelestialObject O O O O B-Citation I-Citation I-Citation I-Citation O O B-CelestialObject I-CelestialObject I-CelestialObject 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 I-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O B-CelestialObject I-CelestialObject I-CelestialObject 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 O O O O B-Formula I-Formula I-Formula I-Formula 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-CelestialObject I-CelestialObject I-CelestialObject O B-CelestialObject B-Citation I-Citation I-Citation I-Citation I-Citation O O O B-ObservationalTechniques I-ObservationalTechniques I-ObservationalTechniques O B-Telescope O O O O O O O O O O O O O O O B-CelestialObject O B-CelestialObject O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-CelestialObject 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 B-CelestialObject I-CelestialObject I-CelestialObject O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O B-CelestialObject O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O

the age-metallicity relation for stars in the solar neighbourhood 3 is often explained as due to radial mixing of stars in a Galactic disk with a gradient in [Fe/H]; stars presently in the solar neighbourhood were born at different Galactocentric distances (). However, in order to explain the low scatter in Mg/Fe and Y/Mg at a given age, the gradients in these abundance ratios should then be vanishingly small at all times, which requires that the ratios between the number of Type II SNe, Type Ia SNe, and AGB stars have evolved in the same way independent of . This corresponds to a weak or non-existent inside-out formation history of the Galactic disk ( Haywood et al. 2015 ). 4.2. 16 Cyg A and B Among the Kepler stars included in this paper, the two components of the 16 Cyg binary system are of particular interest. The very detailed set of oscillation frequencies for these relatively bright stars has made it possible to derive precise values of masses, radii and ages ( Metcalfe et al. 2015 ), He abundances ( Verma et al. 2014 ), and rotation periods ( Davies et al. 2015 ). Furthermore, a comparison of the seismic radii with those determined from interferometric angular diameters ( White et al. 2013 ) provides an important test of asteroseismology (see Silva Aguirre et al. 2017 ). The chemical compositions of 16 Cyg A and B are also very interesting. Cochran et al. (1997) discovered that 16 Cyg B has a Jupiter-sized planet with a mass in an eccentric orbit with a period of 800 days, whereas no planets have been detected around 16 Cyg A . Hence, a comparison of abundances of the two stars has the potential of revealing possible effects of planet formation or planet accretion on stellar surface composition as discussed by Laws Gonzalez (2001) , who in a high-precision spectroscopic analysis found a small metallicity difference, (A – B) = , between 16 Cyg A and B. This was supported by Ramírez et al. (2011) , who found systematic differences of the abundances of the two components corresponding to a mean difference of (A – B) = for 22 elements. However, in a similar study by Schuler et al. (2011) , the mean abundance difference for 15 elements was found to be only dex. In order to clarify the controversy about the chemical compositions of 16 Cyg A and B, Tucci Maia et al. (2014) made a new high-precision spectroscopic analysis using CFHT/ESPaDOnS spectra with and . From a strictly differential analysis of the two stars, they obtained (A – B supporting the abundance difference found by Ramírez et al. (2011) . Furthermore, they found the abundance difference between A and B to increase with elemental condensation temperature for the refractory elements, and interpreted this as a signature of sequestration of refractory elements in the core of the giant planet around 16 Cyg B . Table 4 Comparison of atmospheric parameters and [Fe/H] for 16 Cyg A and B between Tucci Maia et al. (2014) and this paper. Notes. (a) Tucci Maia et al. (2014) . (b) This


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

range from 9 to 12 in the H band. Fig. 2. Luminosity distribution function in the H band for the APOGEE – LAMOST stellar catalog. The catalog covers a broad magnitude range from 7 to almost 14 mag. Most of the stars are in the magnitude range from 9 to 12 in the H band. 2.2. Signal-to-noise ratio APOGEE aims to obtain high-resolution H -band spectra with high S/N (100 per half-resolution element of pixels) for stars in the bulge, disk, and halo of the Milky Way ( Zasowski et al. 2013 , 2017 ). Most APOGEE targets are observed in several visits. After multiple visits, a combined spectrum is produced ( Nidever et al. 2015 ). LAMOST DR3 provides the S/N per pixel for the targets as calculated in five different bands, u , g , r , i and z . Using the center wavelength and bandwidth, they obtain the wavelength range for each SDSS band, and then the S/N in each band is the median value at each pixel in this band ( Luo et al. 2015 ). The cumulative histograms of S/N in APOGEE and in LAMOST for the z band (left panel in Fig. 3 ) shows that the APOGEE survey has 80% of stars in common with S / N > 100, and 40% with S / N > 200. The LAMOST survey has 40% of stars in common with S / N > 100, and 10% with S / N > 200 2 . The right panel in Fig. 3 shows the S/N from APOGEE and LAMOST spectra for the common stellar catalog as a function of the H -band magnitude from the 2MASS survey ( Skrutskie et al. 2006 ). This figure shows a clear relation between magnitude and S/N in APOGEE. This relation is weaker in LAMOST DR3 data and the H band, where a given stellar magnitude has a wide range in S/N. Fig. 3. Left panel : cumulative histograms of S/N per half-resolution element (approximately a pixel) for APOGEE (solid line) and S/N per pixel for LAMOST (dashed line), as provided from the original catalogs. Right panels : S/N from APOGEE and LAMOST spectra for the common objects as a function of the H -band magnitude from the 2MASS survey. 2.3. Radial velocities In APOGEE DR14 ( Abolfathi et al. 2018 ), RVs are determined for each individual visit to identify stars with companion-induced Doppler shifts. The individual visit spectra are resampled and combined to generate a single spectrum for each object. Final RVs are obtained by cross-correlation against a grid of synthetic spectra spanning a wide range of stellar parameters. The APOGEE instrument and the existing RV software routinely deliver RVs per visit at a precision of ∼0.07 km s −1 for S / N > 20, while the survey provides external calibration sufficient to ensure accuracies at the level of ∼0.35 km s −1 . RVs in APOGEE are reported with respect to the center of mass (barycenter) of the solar system ( Nidever et al. 2015 ). The LAMOST 1D pipeline ( Luo et al. 2015 ) also measures the RVs using a cross-correlation method. The pipeline recognizes the stellar spectral classes and simultaneously determines the RVs from the best-fit correlation function between the observed spectra and the template. The RVs are


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This work was funded by INCT – Estudos do Espaço, CNPq and FAPESP (proc. 2011-08171-3). This support is gratefully acknowledged. We also thank Ernesto Vieira Neto for his contribution with the numerical integrator.


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the SPEX package 1 ( Kaastra et al. 1996 ). To help the user to see if a -value corresponds to an acceptable fit, SPEX gives, after spectral fitting, the expected value of and its rms spread, based on the best-fit model. Both quantities are simply determined by adding the expected contributions and their variances over all bins. 3. Simple approximations for the expected value and variance of <italic>C</italic> We obtained simple approximations to the infinite series involved in ( 4 ) and ( 6 ), with relative errors better than for and better than for , as follows: With the help of the above equations, the goodness of fit for the model can be easily assessed. Given the other properties of cstat , such as unbiased parameter estimates, in almost all circumstances cstat is the preferred statistic to be used and the use of -statistics in X-ray spectral analysis should be avoided. 4. Two practical examples Fig. 2 Simplified spectra of the Perseus cluster ( top ) with Hitomi and of Capella ( bottom ) with RGS. We tested our method to assess the goodness of fit with two examples. In the first example, we simulated a spectrum that has approximately the shape of the Perseus cluster as measured with the Hitomi SXS instrument ( Hitomi Collaboration et al. 2016 ). For this demonstration purpose we simplified the model by adopting an isothermal spectrum in collisional ionisation equilibrium with a temperature of 4 keV, proto-solar abundances, and an emission measure matching the flux of Perseus as measured by Hitomi. In our spectral fits, we used the temperature and emission measure of the source as free parameters. The spectrum has 5804 bins and is shown in Fig. 2 , without noise, but with instrumental features included. We scaled this spectrum in flux by factors of with ranging from 0–10, i.e. higher values of corresponding to lower fluxes. For each flux value, we simulated 1000 spectra, performed a best fit, and determined . We then produced a histogram of -values and calculated the 90%, 95%, and 99% percentile points , , and of this distribution. In an actual analysis of an observed spectrum, a model would be rejected at the 90% confidence level if , and this is similar for the other confidence levels. We compare these percentile points, scaled with the expected mean and variance , as delivered by SPEX and described in Sect. 2 , in Fig. 3 . Our second example is a simulation of the spectrum of Capella with the Reflection Grating Spectrometer (RGS) of XMM-Newton. This spectrum is approximated by a single isothermal component with temperature 0.5 keV and appropriate flux for Capella. All further steps are the same as for the Perseus example. The main difference between both spectra is that while Perseus is dominated by continuum emission, owing to its high temperature, Capella is dominated by line emission, owing to its low temperature. The Capella spectrum has 1433 bins and is also shown in Fig. 2 . Fig. 3 Percentile points 90%, 95%, and 99% for the


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This work is supported by the Science Challenge Project (grant No. TZ2016005), NSFC (grant No. 41674165), and the China Scholarship Council. The author also wants to thank A. Bhattacharjee, Y.-M. Huang, F. Pucci, F. Guo, and A. Spitkovski for 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 B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-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-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O B-Formula I-Formula I-Formula 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 B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O 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

3.5 }. We are interested in calculating the amount of mass ejected by the accelerating shock wave. First, we find the depth x esc ( E; n ), defined as the shock position at which the peak material velocity, just behind the shock is where the prefactor accounts for the velocity in the immediate downstream of a strong shock, and the acceleration factor C f ≈ 2 long after shock passage. All matter exterior to x esc eventually accelerates to beyond v esc and becomes unbound. The ejected mass is given by where we used equation ( 6 ) in the last approximation, valid when x esc ≪ R ⋆ . Fig. 3 shows the material velocity profile as the shock propagates through the star, for an explosion energy of E / E bind = 0.018. This figure demonstrates the definition of x s – the depth at which material velocity first becomes sonic (red curve), and x esc – where the post-shock material velocity is eventually accelerated to v esc (purple curve). Figure 3. The material velocity profile at different times after an explosion with energy E / E bind = 0.018 set at the centre of an n = 3/2 polytrope. The dashed green line is the speed of sound in the undisturbed star, and the horizontal solid blue line is the threshold post-shock velocity that results in mass ejection, as described in the text. Highlighted in blue is the velocity profile at the end of the Sedov–Taylor phase, when the shock first becomes weak. The pulse is then subsonic throughout most of the star, until it transitions to a strong shock, shown in red , when the material velocity becomes sonic. Finally, in purple we show the velocity profile when the ejection criterion is first met, at depth x esc ≈ 10 −2 R ⋆ measured from the stellar edge. Fig. 4 provides a complementary view on the results of the numerical simulations, showing the velocity evolution throughout the stellar interior, demonstrating the analytical picture portrayed in Fig. 2 . During the spherical phases, the shock and material velocities decrease while density remains roughly the same. Later on, the pulse continues to decelerate since the ambient temperature drops in the outer layers of the star, while the (subsonic) material velocity behind the shock increases. At some point, the material velocities approach the local sound speed, and the shock begins to accelerate, transitioning to a strong shock. The material outside the layer at which v sh = v esc / C f is being ejected by the explosion. Figure 4. Shock and material velocity as a function of unperturbed density, for a simulation of an explosion of energy E / E bind = 2.9 × 10 −3 set in an n = 3 polytrope. The numerical results in this figure mirror the analytic picture in Fig. 2 . Peak material velocity is plotted in black, and the unperturbed sound speed in blue. The shock velocity (in red) was calculated from the material velocity and the local Mach number with respect to the material lying just ahead of the shock. Finally, the horizontal dashed line is the threshold shock velocity


O O O O O B-Model O O O B-Model O O O O O O B-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 B-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula O O O B-Model O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O 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 B-Model 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-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O B-Model O O O O O O O O O O O O B-Model O O O O O O O O O O B-Model 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 O O O O O O O O O O O O O O O O O O O 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 B-Model O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength 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 O O O O O O O O O O O O O O O O O O O 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

is particularly true for the Ethos-4 model, where the DAOs are nearly absent as early as z = 20 (given the finite resolution of our numerical set-up). 4.2 The Lyman-α forest at a glance In the top row of Fig. 4 we present the transmitted flux fraction, F , measured along random lines of sight at z = 5 (left) and z = 4.2 (right) for the CDM and sDAO models. The spectra have been created following the procedure outlined in Section 3.2 , after rescaling the mean transmission in each simulation box to the observed transmitted flux. In each case, the lines of sight have been chosen so as to probe the same spatial region in the two simulation volumes. The lower sub-panels show the difference in the transmitted flux, Δ F = F CDM − F sDAO . This figure highlights the fact that the same line of sight probes different intervening structures in the IGM of the two simulations. In particular, it is clear that, just as in WDM, absorption lines are in general deeper for a random line of sight in the CDM simulation than for the sDAO model, signifying the presence of a more clumpy IGM. This difference is a direct consequence of the cut-off in the initial power spectrum. Figure 4. Top row : synthetic mock spectra extracted from our simulations at z = 5 (left) and z = 4.2 (right). Each panel shows the transmitted flux fraction, F , in velocity space for a specific randomly selected line of sight through the simulation volume at the corresponding redshift. The lines of sight are chosen such that the same spatial region is probed in the CDM (black) and sDAO (red) simulation volumes. Clearly, more intervening structure can be inferred from the CDM spectra as evidenced by the deeper transmission lines than in sDAO . The lower panels show the relative difference in transmitted flux, i.e. Δ F = F CDM − F sDAO . Middle row : The same lines of sight shown in the top row but before we rescale the mean flux to the observed values. Bottom row : The unscaled flux PDF at these redshifts. These panels show the ‘true’ difference in the transmitted flux between the CDM and sDAO models, i.e. by removing any artefacts that may be brought in by the different amount of rescaling required for the two DM models. The sDAO and CDM models have been rescaled by different amounts when matching the simulated spectra to the observed mean transmitted flux. To disentangle the implications of rescaling from the different line shapes due to the modified cosmology at a given UV background, the middle row of Fig. 4 shows the unscaled line-of-sight spectra at z = 5 and z = 4.2. Clearly, there are residual differences between the two models even in the unscaled case. Quantitatively, these effects are seen more clearly in the bottom row of Fig. 4 , which shows the probability distribution function (PDF) of the unscaled transmitted flux for the two models at these redshifts. Considering just CDM to begin with, it is noticeable that as time proceeds, there is a cut-off in the flux PDF at higher values


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

into the ring current, which extends the recovery phase of the storm (Gonzalez et al. 1994 ; Fok et al. 1995 ; Jordanova et al. 1997 ; Miyoshi et al. 2003 ; Søraas et al. 2004 ; Tsurutani et al. 2006a ; Kasahara et al. 2009 ). The prediction of time corresponding to the minimum value that the Dst index will reach is the main goal of geomagnetic storm forecasting research. However, many technological applications rely on the expected time of the disturbed magnetosphere returning to quiet time conditions. These predictions are even more important for extreme/severe geomagnetic storms (Cid et al. 2014 ). In the literature, a linear proportional relation is expected between the decay rate of the ring current and the Dst index through the Dessler–Parker–Sckopke relationship (Olbert, Siscoe Vasyliunas 1968 ; Greenspan Hamilton 2000 ). Therefore, an exponential function was accepted to fit the recovery phase Dst index data to find the decay time of the storm (e.g. Burton, McPherron Russell 1975 ; Hamilton et al. 1988 ; Ebihara Ejiri 1998 ; O’Brien McPherron 2000 ; Dasso, Gómez Mandrini 2002 ; Kozyra et al. 2002 ; Wang, Chao Lin 2003 ; Weygand McPherron 2006 ; Monreal MacMahon Llop-Romero 2008 ). In a few cases, the decay time was expected to be a constant value (Burton et al. 1975 ). Moreover, in some cases, this was dependent on the convective electric field E y (O’Brien McPherron 2000 ), or also dependent on the dynamic pressure (Wang et al. 2003 ). However, the intense and/or extreme storms show a two-phase recovery profile, i.e. an early fast recovery phase followed by slow recovery. Therefore, it was difficult to model the observational data assuming a unique exponential function (Akasofu, Chapman Venkatesan 1963 ; Hamilton et al. 1988 ; Gonzalez et al. 1989 ; Prigancová Feldstein 1992 ; Liemohn et al. 1999 ; Monreal MacMahon Llop-Romero 2008 ). This issue was resolved by assuming a hyperbolic decay function (Aguado et al. 2010 ; Cid et al. 2014 ). In this model the entire recovery phase is dependent on two parameters, i.e. the minimum Dst value ( Dst 0 , the intensity of the storm or the value of the Dst index when the recovery phase starts) and the recovery time (τ h , the time to get the value of Dst 0 /2). A superposed epoch analysis of recovery phases of intense storms from 1963 to 2003 suggests that the hyperbolic decay function reproduces the experimental data better than the exponential function for any type of storm, which indicates a non-linear coupling between the decay rates of Dst and Dst (Aguado et al. 2010 ; Cid et al. 2014 ). Generally, the recovery phase takes one to two days or sometimes more than two days, depending on the source of the magnetic storm (Dessler Parker 1959 ; Gonzalez et al. 1994 ; Kozyra et al. 1997 ; Tsurutani et al. 2006a ). ICMEs generate extreme storms with an exponential/hyperbolic recovery phase profile of one or two days whereas the CIR- and high-speed stream (HSS)-driven magnetic storms can last from


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We thank Dr. J. Puls for comments on the paper and for the discussion on the inclusion of clumping in the wind models. This research was supported by grant GA ČR 18-05665S. Computational resources were provided by the CESNET LM2015042 and the CERIT Scientific Cloud LM2015085, provided under the programme “Projects of Large Research, Development, and Innovations Infrastructures”. The Astronomical Institute Ondřejov is supported by a project RVO:67985815 of the Academy of Sciences of the Czech Republic.


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This work is based on observations taken at the ESO La Silla Paranal Observatory within the MUSE Commissioning. The authors wish to thank the anonymous referee for his/her comments and suggestions that allowed us to greatly improve the paper. E.I. wishes to thank the European Southern Observatory for the financial support, the hospitality and the access to the computer facilities during the several visits in 2014 and 2015 that allowed us to perform the fundamental steps of the work presented in this paper. F.C. acknowledges the European Research Council for the Advanced Grant Program Num 267399-Momentum. P.M.W. received funding through BMBF Verbundforschung (project MUSE-AO, grant 05A14BAC and 05A14MGA). R.B. acknowledges support from the ERC advanced grant 339659-MUSICOS.


O O O O O O O O O O O B-Survey O O O O O O O O O O O B-Telescope I-Telescope O B-Observatory I-Observatory I-Observatory I-Observatory I-Observatory 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 B-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O B-Grant I-Grant I-Grant I-Grant I-Grant B-Grant O B-Organization I-Organization I-Organization B-Organization O B-Organization I-Organization I-Organization I-Organization B-Organization B-Grant I-Grant O O O O O O O O O O O O O O O O O O O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O O B-Grant B-Grant O B-Grant O O B-Organization O O O B-Grant O O B-Organization B-Grant I-Grant I-Grant I-Grant I-Grant

ACKNOWLEDGEMENTS We are hugely grateful to those who contributed to the LiJET project. We would like to thank all the staff of the 2.4-m telescope of Lijiang station of Yunnan Observatories for their help and support during our observations. Funding for the telescope has been provided by the Chinese Academy of Sciences (CAS) and the People’s Government of Yunnan Province. We acknowledge the support from the Project Based Personnel Exchange Program (PPP) with China Scholarship Council (CSC) and German Academic Exchange Service (DAAD) ([2016] 6041). We also thank the anonymous referee for helpful comments and suggestions, which led to significantly improvement in our manuscript. This work was financially supported by the National Natural Science Foundation of China (NSFC) under grant Nos. 10373023, 10773027 and 11333006, and the CAS through project No. KJCX2-YW-T24, and the CAS ‘Light of West China’ Program.


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

B ). The trend is still visible with a lower slope 0.23 ms −1 d −1 . We present the RV and corrected RV of HD 186704A in Fig. 3 . The difference of one order of magnitude on the slope of the trend between Nidever et al. (2002) observations and ours can be explained by the fact that our observations were made when the SB was closer to the periastron or apoastron of its orbit. 3.1.6 HD 181321 We confirm that HD 181321 is an SB. Nordström et al. (2004) report a variation of 2.3 km s −1 over 9 yr, Guenther Esposito (2007) report a trend with a slope of 1.4 km s −1 yr −1 . Our observations spread on 3757 days (10.3 yr) cover at least two orbital periods. The star is active and show BVS variations with a period of 2−2.5 days that should correspond to the rotational period of the star. We use yorbit to fit the RV with two Keplerian models, one to fit the stellar activity variation and an another to fit the binary variations. We find two possible solutions for the companion, one with a period of 1600 days (2.7 au) and a minimum mass of 0.1 M ⊙ , and a second with a period of 3200 days (4.4 au) and a minimum mass of 0.18 M ⊙ . In both cases, the eccentricity is ~0.5. We present those two solutions in Fig. 4 . More data are needed in order to distinguish between those two solutions. Fig. 4 Solutions of HD 181321 RV fit by the sum of two Keplerian ( top ) and their residuals ( bottom ). Left : 1600 days solution. Right : 3200 days solution. 3.1.7 HD 206893 HD 206893 is a F5V star that hosts a directly imaged BD companion at a separation of 270 mas ( Milli et al. 2017 ; Delorme et al. 2017 ). We recently reported in Grandjean et al. (2019) a long-term trend in the star RV coupled with pulsations with periods slightly less than one day. We performed an MCMC on both the RV trend, imaging data, and H IPPARCOS - Gaia proper motion measurements to constrain the orbit and dynamical mass of the BD. We concluded that the trend can not be attributed to the BD as it leads to dynamical masses incompatible with the object’s spectra. The presence of an inner companion that contributes significantly to the RV trend is suggested with a mass of 15 M Jup , and a period between 1.6 and 4 yr. 3.1.8 HD 217987 HD 217987 is a M 2V, high proper motion star and exhibits a long-term RV trend induced by its secular acceleration. We therefore corrected the RV from the star secular acceleration in its proper motion we deduced from its paralax and proper motion reported in Gaia Collaboration (2018) (see Fig. 5 ). The corrected RV presents short period variations. The RV and BVS are correlated which indicate that the signal might be dominated by spots or plages (see Fig. 5 ). We observe a long-term variation in log , FWHM, and RV which are better fitted by a second degree polynomial model than with a linear model (see Fig. 5 ). This variation could be then attributed to a magnetic cycle of the star with a period greater than 5000 days. An analysis on a large number of M dwarf was


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Acknowledgments The authors would like to thank Sami Dib for valuable and constructive comments. Also M. Hosseinirad thanks Najmeh Mohammad-Salehi and Maryam Samadi for useful discussions. S. Abbassi acknowledges support from the International Center for Theoretical Physics (ICTP) for a visit through the regular associateship scheme. We also like to thank the anonymous referee for his/her helpful comments which improved the paper.


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ACKNOWLEDGEMENTS We thank the anonymous referee for their comments and suggestions that improved the analysis and the presentation of the results. FV and WNB thank NASA XMM–Newton grant 80NSSC18K0487 and the NASA ADAP program for support. BL acknowledges financial support from the National Key RD Program of China grant 2016YFA0400702 and National Natural Science Foundation of China grant 11673010. We warmly thank J. Runnoe and Z. Shang for useful discussion on UV SED shape of quasars.


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JRB and CAH were supported by the STFC under the grant ST/L000776/1. DS was supported by an STFC studentship. We would like to thank the anonymous referee for reading and providing constructive feedback to help improve the manuscript.


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Acknowledgements A.C. acknowledges support by CFisUC strategic project (UID/FIS/04564/2019), ENGAGE SKA (POCI-01-0145-FEDER-022217), and PHOBOS (POCI-01-0145-FEDER-029932), funded by COMPETE 2020 and FCT, Portugal. V.B. acknowledges support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (project Four Aces grant agreement No 724427). J.-B.D. acknowledges support by the Swiss National Science Foundation (SNSF). This work has, in part, been carried out within the framework of the National Centre for Competencein Research PlanetS supported by SNSF.


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from low SNR, individual exposures. At high SNR, we obtain abundances precise to ≈0.01 to and even at low SNR (SNR ≈ 50) we get precisions of ≈0.02 to for most elements. These precisions are confirmed by looking at the scatter in the abundances within open clusters, which we find to be . We also recovered the expected abundance trends in globular clusters, but found that the censoring in the network is crucial to obtain this, because training on the full spectrum for all elements causes the NN to depend too strongly on correlations between elements within the training set and therefore to fail when these correlations are absent, like in globular clusters. We also demonstrated that a large NN can work well with a limited amount of training data, finding barely degraded performance for training sets that only consists of thousands of spectra. The speed and flexibility of NN s mean that they are a highly useful tool for spectroscopic data analysis. They allow the results obtained from a detailed analysis of a small calibration set to be transferred to an entire large data set of millions of spectra in a matter of minutes and can thus be a great aid in the development of the next generation of spectroscopy tools. They could also be of use in earlier stages of the data processing, for example, for homogenizing spectra taken with different instruments (e.g. the northern and southern APOGEE spectrographs) or for removing instrumental systematics such as persistence (e.g. Jahandar et al. 2017 ). Such applications would be easy to pursue with the astroNN software package described in the Appendix. APPENDIX: ASTRONNN: A PYTHON LIBRARY FOR DEEP LEARNING IN ASTRONOMY Data-driven tools are becoming more and more popular in astronomy and deep learning in particular is becoming a popular technique to deal with big data sets. When we started on the research for this paper, we realized that a python package that (i) has a focus on deep learning, (ii) contains tools and data sets that are relevant to astronomers, (iii) is easy to use and well tested against errors, and (iv) acts as a platform to share astronomy-oriented NN s is needed to advance research in this area. astroNN is a python package for deep learning in astronomy designed to fulfill the points stated above. astroNN relies heavily on Tensorflow (Abadi et al. 2016 ), a standard deep learning python library, and is easy to set up on all common platforms. astroNN employs custom methods for storing and sharing models: models are saved in a folder and consist of the NN itself in HDF5 format, the training history in CSV format, model parameters, and the names of output neurons as well as normalization parameters in JSON format. Users simply have to give the reduced data as numpy array(s) to astroNN and get outputs back as numpy array(s); normalization of the inputs and outputs is handled internally. At this point, astroNN as used in this paper consists of about 8300 lines of code in the modules, 1200


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Acknowledgments We thank Volker Springel for allowing the use of his code pgadget3 and the anonymous referee for their suggestions that improved the presentation of our results. We acknowledge support by the Deutsche Forschungsgemeinschaft through the SFB 956, The Conditions and Impact of Star Formation and the TRR 33 The Dark Universe. MB thanks the Bonn-Cologne Graduate School for Physics and Astronomy for support. The authors acknowledge that the results of this research have been achieved using the PRACE-3IP project (FP7 RI-312763), using the computing resources (Cartesius) at SURF/SARA, the Netherlands.


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

the region. They found that for the region of interest studied here, mostly located outside the Galactic plane, the difference between the standard LAT diffuse model and their refined model is negligible. However, a more complete analysis of the effect of the uncertainties in the background emission model was carried out following Acero et al. ( 2016b ), who used a set of 8 alternative models 3 developed in Ackermann et al. ( 2012 ) by changing some crucial parameters that determine the intensity and distribution of the Galactic gamma-ray emission: the cosmic ray source distribution, the height of the cosmic ray propagation halo and the HI spin temperature. This is important since the standard diffuse emission models distributed for LAT data analysis are optimized for analysis of point sources and compact extended sources (Acero et al. 2016a ), and the analysis must be validated using different models. The estimation of the systematic errors was done as in Acero et al. ( 2016b ) by comparing the source parameters obtained with each alternative model and those with the standard model. The significant detection of G350.6-4.7 (above 15σ for all alternative models considered) gives confidence that the emission is indeed associated to a new extended high-energy source. Systematic errors related to the imperfect knowledge of the effective area were estimated following the LAT team recommendations. 4 Since this uncertainty and the resulting uncertainty from the background model are independent, the total systematic error was obtained by adding them in quadrature. 3 DISCUSSION It is reasonable to attribute the origin of the gamma-rays to the shell of a previously unknown SNR. If located at the distance to the pulsar PSR J1747-4036 (3.4 kpc), the object size would be around 200 pc and the centre of the disc would be located around 250 pc from the plane of the Galaxy. SNRs with diameters of the order of a few degrees are known and a significant number have been seen as extended objects by the LAT (Acero et al. 2016b ). Well-known examples are the Cygnus Loop (Katagiri et al. 2011 ) and RX J0852.0-4622 (Tanaka et al. 2011 ). However, not many SNRs are known to have a diameter greater than 100 pc, although large objects could not have detected due to observational selection effects (Green 1991 ). Dynamic considerations of the expansion and evolution of an SNR can give a physical justification for an upper limit in their size (e.g. Cioffi, McKee Bertschinger 1988 ; Slavin Cox 1993 ). It is possible then that if this new source is an SNR it is much closer than 3.4 kpc and hence unrelated to PSR J1747-4036. This pulsar is classified as a millisecond pulsar (e.g. Abdo et al. 2013 ), and thus if related to the G350.6-4.7, the SNR would also be too old to show a GeV spectrum as the one found here (see e.g. Acero et al. 2016b ). The Cygnus Loop SNR is located at about 540 pc (Blair, Sankrit Raymond 2005 ) and has a diameter of ∼35 pc. If the same physical


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I gratefully thank George M. Fuller, Yang Sun, and Surja K. Ghorui for fruitful discussions. I also owe gratitude to Projjwal Banerjee, Alice Shih, and Joe Semmelrock for their input in writing this manuscript. This research at Shanghai Jiao Tong University is supported by the National Natural Science Foundation of China (No. 11575112), by the National Key Program for ST Research and Development (No. 2016YFA0400501), and by the 973 Program of China (No. 2013CB834401).


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

a population of stars is present, and some studies suggest they may be somewhat common (Lauer et al. 2005 ) – further increases the TDE rate. 4.4 Other sources of emission: winds and accretion on to the primary From Fig. 1 , we see that accretion on to the secondary often proceeds at a super-Eddington rate. While most of the time the rate is only mildly super-Eddington, satisfying with N ≃ few, in some cases, and particularly towards the peak in the accretion rate, N can approach and even exceed 100. While these hyper-Eddington periods are predicted analytically (Rees 1988 ; Evans Kochanek 1989 ), the peak accretion rates in Fig. 1 can actually exceed the analytical one (shown by the dashed curve in the top-left panel in this figure), which is a consequence of self-gravity (Coughlin Nixon 2015 ) and the non-zero energy of the stellar centre of mass. In these highly supercritical regimes, one might expect winds (Strubbe Quataert 2009 ; Metzger Stone 2016 ) or, in the more extreme cases, jets (Giannios Metzger 2011 ; Coughlin Begelman 2014 ; Tchekhovskoy et al. 2014 ; Coughlin Begelman 2015 ) to be launched from the vicinity of the accreting SMBH. From these outflows one would expect an additional source of radiation, with properties distinct from the disc. While it is unlikely that this scenario explains the rebrightening seen in ASASSN-15lh – the accretion rate would have been super-Eddington prior to the increase, and the constancy of the X-ray emission (Margutti et al. 2017 ) suggests that there was no change in the source of harder photons – changes in the luminosity induced by a sudden super-Eddington surge of accretion would be possible in other systems. The disk feeding the SMBH should also become geometrically thicker once the Eddington limit is surpassed, and could perhaps inflate to a quasi-spherical envelope once L ≫ L Edd (Loeb Ulmer 1997 ; Coughlin Begelman 2014 ). The simulations performed here would not capture the important physical interactions between the radiation and the plasma that would lead to such an inflated disc structure (see Sa̧dowski et al. 2016 , who do find quasi-spherical envelopes from their simulations of TDEs). Nevertheless, if the photosphere of the disk coincides with the photon trapping radius (Begelman 1979 ), then we can estimate the size of the envelope as (equation 17 of Coughlin Begelman 2014 ) where in the final line we set the opacity equal to the value for electron scattering, κ = κ es = 0.34 g cm −2 . Interestingly, this radius is of the order of the Hill sphere of the secondary for the binaries considered here; thus, the discs from super-Eddington TDEs in tight binaries could fill their Roche Lobes, resulting in accretion on to the primary. This accretion would then provide an additional source of radiation, and it would also modify the structure of the envelope around the secondary and, conceivably, its accretion rate. While it did not occur in any of our simulations, one can also imagine


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and the horizontal axis shows the log of the effective temperature T eff . Each square represents one model. From left to right, the panels are evaluated for m 0 = 10 3 , 10 4 , and 10 5 , respectively. The dashed diagonal lines represent curves of constant Eddington ratio ( from left to right) and horizontal dashed curves show lines of constant mass ( from top to bottom) evaluated for the hottest annulus in the disk model. The white dashed curve in the left panel shows the variation as a function of radius for a relativistic α -disk model with a = 0, , and . The thick black solid curve corresponds to an analytical estimate (Equation ( 6 )) of where the annulus becomes photon starved. Note that we cap the color bar at f = 4 to better show the variation at lower values of f , but several of the hardest spectral models exceed this value. The black dashed lines show the values of Q and T eff computed at the radius where T eff reaches its maximum value in a relativistic accretion disk model for various values of the accretion rate and mass for a nonspinning black hole (Novikov Thorne 1973 ; Shakura Sunyaev 1973 ). For black hole spin a = 0, R max = 9.5 r g , where is the gravitational radius and G is Newton’s constant. We can then compute T eff , Q , and m 0 in the radiation pressure dominated limit via Here is the accretion rate scaled to , is the electron scattering opacity, is the Stefan–Boltzmann constant, η is the spin dependent radiative efficiency, α is the stress prescription parameter and . T rel , Q rel , and are relativistic correction factors (Novikov Thorne 1973 ). The diagonal lines in each panel correspond (from left to right) to , 0.1, and 1. The horizontal lines correspond (from top to bottom) to . Since the spectral hardening factor of a global disk model correlates closely with the value of f in the hottest annulus, this provides a good estimate of how f will vary for a global disk. Increasing the black hole spin shifts the diagonal lines to the right (i.e., toward higher T eff for a given M and ). In the left panel, we also show the variation of T eff and Q with radius in an accretion disk for and as a white, dashed curve. This shows that for a single disk model, f is generally largest at the radius with the highest T eff . Figure 4 shows the same quantities, but for lower values of m 0 . Here the ranges of T eff and Q with valid spectral models are narrower due to difficulties with convergence at these lower surface densities. The diagonal and horizontal dashed lines have the same meaning as in Figure 3 , but only cover masses of and 1000. Comparison with Figure 3 shows an accelerating trend for f to increase with decreasing m 0 . Equation ( 5 ) shows that the value of m 0 in the α -disk model is a function radius, mass, spin, and accretion rate. It is also sensitive to the details of the assumed stress prescription (Done Davis 2008 ) and thus likely to be the least robustly estimated parameter. Figure 4. Table of best-fit


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The author would like to acknowledge research support from the Australian Research Council through Discovery Grant programmes DP120101237 and DP150103294. He is also grateful for the support received during an extended visit to the Institute for Astronomy, University of Edinburgh during which this paper was largely written. Thanks also to Ken Freeman, Russell Cannon and Elizabeth Maunder who conducted the 2010 December observations, and to Andrew Cole for providing a copy of the line profile fitting code (whose heritage can be traced back to that of Armandroff Da Costa ‘plus ça change, plus c'est la même chose’). This research has made use of the WEBDA data base, operated at the Institute for Astronomy of the University of Vienna, and of the VizieR catalogue access tool, CDS, Strasbourg, France. The original description of the VizieR service was published in AAS, 143, 23.