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

estimates of the relative abundances of the COMs detected in L1157-B1. With this goal in mind, we obtained their excitation conditions and column density carrying out a simple rotational diagram analysis. We computed the molecular abundances with respect to H 2 by using the whole CO column density in the B1 direction, as estimated by Lefloch etal. ( 2012 ), N (CO) = and assuming a standard relative CO abundance X (CO) = N (CO)/ N (H 2 ) = 10 4 . The obtained temperatures, column densities and abundances are summarized in Table 1 . The rotational diagrams of the newly detected COMs are shown in Fig. 2 . For all the detected species, the line emission can be reasonably well fitted by one single gas component whose rotational temperature is around 2030K (Table 1 ). Glycolaldehyde has a slightly larger rotational temperature (50K) but also a larger error bar (10K). Considering only the lines observed with E up , a lower rotational temperature () would provide a very good fitting. Figure 2. Rotational diagrams of COMs detected towards L1157-B1. From the top to bottom: C 2 H 5 OH, H 2 CCO, HCOCH 2 OH and CH 3 OCH 3 . The best fit is drawn by the red line. For HCOCH 2 OH, the fit to the transitions with is drawn by the blue dashed line. Column densities vary from 210 12 cm 2 (formamide) to 110 15 cm 2 (methanol). Incidentally, the column density of the other COMs shows a relatively small range of variation, from 2 to 510 13 cm 2 , namely less than a factor of 3. In other words, with the exception of formamide, which is significantly less abundant, the other detected COMs have abundances a factor of 2050 lower than methanol. We searched for acetic acid (CH 3 COOH), the other isomer of glycolaldehyde and methyl formate, using the frequencies given in Ilyushin, Kleiner Lovas ( 2008 ). We failed to detect it. We could place an upper limit on its abundance, adopting T rot similar to that of methyl formate () and glycolaldehyde (), and the partition function given by Calcutt etal. (in preparation). We obtain a 3 upper limit of 510 9 at (10 8 at ): Acetic acid is less abundant by a factor of 35 with respect to methyl formate. 3.3 Comparison with hot corinos When compared to other solar-like star-forming regions where these COMs were previously detected (IRAS 162932422: Jaber etal. 2014 ; Coutens etal. 2015 ; Jrgensen etal. 2016 ; IRAS 2A and IRAS 4A: Taquet etal. 2015 ), L1157-B1 appears to be a site were COMs are very efficiently produced. The molecular abundances are higher in the shock than in the hot corinos by a factor of 210, depending on the species. The dimethyl ether abundance measured in IRAS 162932422 is the only exception. We note that only relatively small COMs are detected in the shock region, whereas larger COMs, for example, propanone (CH 3 COCH 3 ) and ethylene glycol [(CH 2 OH) 2 ], are detected in the inner protostellar environments (e.g. Maury etal. 2014 ; Jrgensen etal. 2016 ) but not yet in the shock. More observational data from


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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-Model I-Model I-Model 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 B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject 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-Wavelength O B-Citation I-Citation I-Citation I-Citation 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 B-Wavelength O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O 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 B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O B-Model 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 the angular velocity of the black hole. This could lead to quasi-periodic signatures in the observed radiation, especially if the radiation mechanism at the current sheet is to some extent beamed. However, in an actual accretion disc the flux tubes may be much more irregular and variable, leading to more stochasticity in the observed signal. The main dissipation mechanism is likely to be reconnection at these current sheets. Since the environment around the black hole is filled by soft optical/UV photons from the accretion disc, particles accelerated in the reconnection process will be quickly cooled through inverse Compton scatterings and may also initiate pair cascades on the soft photons. The reconnection outflow may be strongly Compton dragged, and the reconnection proceeds in a regime as described by Beloborodov ( 2017 ) where the spectrum is dominated by bulk Comptonization from the reconnection outflow and has a high-energy cut-off near the pair production threshold. To get an estimation of the dissipation rate in realistic systems, let us consider a typical Seyfert galaxy, MCG-6-30-15, which has a supermassive black hole of mass M = 2 × 10 6 M ⊙ , bolometric luminosity , and X-ray luminosity (Reynolds et al. 1997 ). Measuring B in terms of the characteristic field G (Phinney 1983 ), we get If the magnetic field near the black hole reaches a value B ∼ B Edd , then the amount of power dissipated due to the kink instability will be enough to account for all the X-ray emission. The kind of relatively strong magnetic field with small coherence length-scales may be a generic outcome of MRI in the accretion disc, or associated with hotspots on the accretion disc as the flux tubes emerge buoyantly similar to solar magnetosphere. As we have seen from GRMHD simulations, when the accretion disc is threaded by a strong net magnetic flux, it tends to become magnetically arrested and form a powerful jet (McKinney Blandford 2009 ; Avara, McKinney Reynolds 2016 ); however, in situations where the net magnetic flux is small, the disc magnetic field may be dominated by the locally amplified components. MRI and the subsequent buoyancy or gravitational instabilities can produce fields with alternating polarities (e.g. Davis, Stone Pessah 2010 ; Zhu Stone 2018 ); they may also be quite asymmetric. As these structures are fed to the black hole, we may see continuous flux tube inflation and kink instability happening on a much more stochastic basis. We have seen from the simulations that the kink instability tends to happen when the confinement from the surrounding field is strong; this confinement can be produced by magnetic field from currents in the outer disc, or a disc wind that exerts pressure towards the central axis region. We have so far approximated the black hole as a resistive membrane in a flat space–time model. Whether the other GR effects are important will be tested using a time-dependent, GR force-free code in the future. Meanwhile,


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O B-CelestialObject 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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

by allowing toroidal fields of opposite sign to exist on the two sides of the equator more easily. One way of capturing the physics of this in a 3D non-axisymmetric model may be to include a quenching of turbulent diffusivity in the regions of strong magnetic field. We plan to explore the effect of this in future. With these two opposite results at hand, one crucial question is: which of the two results is closer to reality? Although we cannot assert this with confidence at this stage, we believe that the 2D kinematic dynamo result that the dipolar parity is preferred on increasing diffusivity is the more appropriate result. Although in this paper we are taking account of the 3D nature of magnetic buoyancy and, in that sense, treating magnetic buoyancy more realistically, we still have not taken account of flux depletion from the convection zone and its bottom in an appropriate way. This is probably one important reason why our results are not matching with the results of previous 2D models (Chatterjee et al. 2004 ; Hotta Yokoyama 2010 ). We are right now exploring possible schemes to take account of the flux depletion due to magnetic buoyancy in a realistic way. We believe that this flux depletion is quite important in the solar dynamo. Choudhuri Hazra ( 2016 ) found that the Waldmeier effect cannot be reproduced from a theoretical dynamo model unless the flux depletion is taken into account. We have a future plan of incorporating flux loss due to magnetic buoyancy in a realistic way in our 3D kinematic dynamo model and then studying the parity issue more carefully. Since we are interested in a dynamo solution which has dipolar parity, we have converged on the reference solution presented here. If we decrease diffusivity, then we are led to the case where the meridional circulation provides the main transport mechanism for the poloidal field. On the other hand, if we increase diffusivity, then we obtain the quadrupolar mode. This is what has led us to choose the value 5 × 10 11 cm 2 s −1 for diffusivity inside the convection zone. 4. THE BUILD-UP OF THE POLAR FIELD After constructing the self-excited dynamo model, we now study how individual sunspot pairs contribute to the building up of the polar field and address the question of whether our understanding gained from this study necessitates the revision of some insights we have from SFT models. For this study, we shall put individual sunspot pairs on the solar surface by hand and look at the evolution of the magnetic field. In other words, we shall now not try to construct self-excited periodic solutions, although we shall keep using the same values of different parameters that we had used for constructing the self-excited periodic solution. We start our simulation by putting a single pair of bipolar sunspots in the northern hemisphere at different emergence angles λ emg and let it evolve under the axisymmetric mean flows and diffusion to see the development of the polar field. We have


O O B-Person I-Person O B-Person I-Person O O O B-Person O B-Person O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-Organization I-Organization I-Organization I-Organization B-Organization O O B-Organization I-Organization I-Organization B-Organization O O O O O B-Person O O O O B-Person O O O O B-Person O O O B-Grant I-Grant O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O B-Location B-Person O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O B-Fellowship I-Fellowship O B-Software O O O O O O O B-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O B-Organization I-Organization I-Organization O O O O O O O O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility B-ComputingFacility B-URL O O B-ComputingFacility I-ComputingFacility B-Person O O O O B-Organization I-Organization I-Organization O O B-Location I-Location B-Grant I-Grant I-Grant B-Grant O O B-Organization B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant B-Person O O O O O B-Organization I-Organization B-Organization O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant B-Grant I-Grant I-Grant I-Grant I-Grant O O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O B-Grant I-Grant O B-Grant I-Grant

We thank Bill Harris and Eric Pelligrini for interesting discussions. C.S.H. and R.E.P. thank the the Zentrum für Astronomie der Universität Heidelberg (ZAH), Institut für Theoretische Astrophysik (ITA), and the Max-Planck-Institut für Astronomie (MPIA), for their generous support during R.E.P.’s sabbatical leave (2015/16) and C.S.H.'s extended visit (2015 October–November). R.E.P. is supported by Discovery Grants from the Natural Sciences and Engineering Research Council (NSERC) of Canada. C.S.H. acknowledges financial support provided by the Natural Sciences and Engineering Research Council (NSERC) through a postgraduate scholarship. The FLASH code was in part developed by the DOE-supported Alliances Center for Astrophysical Thermonuclear Flashes (ASCI) at the University of Chicago. This work was made possible by the facilities of the Shared Hierarchical Academic Research Computing Network (SHARCNET: www.sharcnet.ca ) and Compute/Calcul Canada. R.S.K. acknowledges support from the European Research Council under the European Communitys Seventh Framework Programme (FP7/2007-2013) via the ERC Advanced Grant “STARLIGHT: Formation of the First Stars” (project no. 339177). R.S.K. further acknowledges funding from the Deutsche Forschungsgemeinschaft (DFG) in the Collaborative Research Center SFB 881 The Milky Way System (subprojects B1, B2, and B8) and in the Priority Program SPP 1573 Physics of the Interstellar Medium (grant nos. KL 1358/18.1 and KL 1358/19.2).


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The research leading to these results has received funding from the European Community’s Seventh Framework Program (FP7/2007-2013) under grant agreement No. 269194 and also under the auspices of the US DoE by Los Alamos National Laboratory under Contract No. DE-AC52-06NA25396


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

field is obtained using the cloud-in-cells particle assignment scheme (CIC; e.g. Hockney Eastwood 1981 ). We introduce some scatter before the mapping procedure in a way that is different from the original EZmock paper. The new scattering formula is where and are the ZA density field after and before the scattering, respectively, and G (λ) is a random number drawn from the Gaussian distribution with width λ. The exponential function, exp[ G (λ)], is used to avoid negative densities. The term including ρ a introduces a non-linear mapping, which converges to 1 when is large. It plays a similar role as the density saturation parameter in the original EZmock paper. Furthermore, we apply a density cut ρ c (called the density threshold in Chuang et al. 2015a ) on the ZA density field before applying the scatter formula to make sure that there is no object produced in a low-density region. The mock catalogue is then populated by randomly picking a fraction of the original ZA particles in each cell, which is equal to the number of haloes attributed to it by the PDF mapping procedure described above. Finally, we assign the velocity by multiplying the displacement field by a factor f , and combining it with a three-dimensional Gaussian random motion with width σ . The factor f is computed by where f () and H () are the growth rate and Hubble parameter, respectively, at the redshift of the simulation box. Thus, we have five effective bias parameters ( n d , A , λ, ρ c and σ ) to adjust EZmocks. In contrast to Chuang et al. ( 2015a ), we do not modify the input power spectrum for calibration because we want to observe the impact of different cosmological models, as explained in the next section. 2.2 Simulation set-up We use the same input power spectrum as the one used by Chuang et al. ( 2015a ), that is ΛCDM Planck cosmology with {Ω M = 0.307115, Ω b = 0.048206, σ 8 = 0.8288, n s = 0.96}, and a Hubble constant () given by h = 0.6777. The output galaxy catalogues are at redshift = 0.5618. Again, following Chuang et al. ( 2015a ), we calibrate the number density to 3.5 × 10 −4 , which is similar to that of the SDSS-III/Baryon Oscillation Spectroscopic Survey (BOSS) galaxy sample at ∼ 0.5 (Reid et al. 2016 ). The simulation boxes are 2.5 h −1 Gpc each side. The particle mesh used is 960 3 . We construct three sets of 3000 EZmock simulation boxes with three sets of parameters. These three sets of boxes share the same 3000 Gaussian random fields. Table 1 lists the values of these parameters. The first set is the reference, whose clustering statistics are similar to those in Chuang et al. ( 2015a ) but not the same, because the EZmock methodology we are using here is slightly different, as mentioned above. Table 1. The three sets of EZmock parameters used in this study. We construct 3000 EZmock simulation boxes for each set of parameters (i.e. 9000 boxes in total). The second set of 3000 EZmocks has a different amplitude in the input power spectrum (i.e.


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Thanks are given to the anonymous referee for the critical comments that motivated new calculations that reinforced the robustness of the analysis to be carried out. This work has been supported by the grant AYA2015-66506-P from the Spanish Ministry of Economy and Competitiveness (MINECO).


O B-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O 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 B-CelestialObject I-CelestialObject O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O B-Formula I-Formula I-Formula I-Formula 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 B-CelestialObject I-CelestialObject 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 B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O B-CelestialObject O 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-Wavelength O O O O O O O O O O O O O O O O O O O O O O O B-Software I-Software I-Software I-Software I-Software O B-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O B-Model O B-Citation I-Citation O O O O O O B-Database I-Database I-Database I-Database I-Database B-Database B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-Wavelength B-Wavelength B-Wavelength B-Wavelength B-Wavelength B-Wavelength B-Wavelength B-Wavelength 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

sources HD 100546 and TW Hya. 2. For both disks, we fitted fully parametric physical models to the spectral energy distribution, spatially resolved CO emission, and a range of far-infrared emission lines. The most important difference from past physical models is that spatially resolved CO line emission is also reproduced. 3. We confirm earlier findings that the HD 100546 disk atmosphere has either an interstellar gas-phase carbon abundance ([C]/[H] , if = 10) or is moderately depleted ([C]/[H], if = 100); and that the TW Hya disk atmosphere is two orders of magnitude deficient in gas-phase volatiles ([C]/[H], [O]/[H], and ). 4. Upper limits on HD emission for HD 100546 put an upper limit of on the gas to dust ratio in the disk. 5. The star HD 100546 has solar-like photospheric abundances of volatile elements (C, N, O) but a strong depletion of rock-forming elements (e.g. Fe, Mg, Si). 6. Most carbon atoms in the HD 100546 disk gas have not passed through a hydrocarbon more complex than CH during the lifetime of the system. 7. An underabundance of volatile elements in the disk atmosphere can develop when gas is mixed through the midplane and the temperature there allows freeze-out of major carrier species onto settled grains. An analytical formulation of this process is presented in Sect. 6.2 . 8. The volatiles return to the gas in the inner disk, as evidenced by their enhanced abundance relative to refractory elements in the gas accreting onto both stars. Appendix A: HD 100546 photospheric abundances Table A.1 Photospheric abundances derived for HD 100546. Notes. Number of lines used in the abundance fitting is shown in Col. 4. Asterisks denote very uncertain results. Solar abundances are from Asplund et al. (2009) . The photospheric properties of HD 100546 were derived through directly fitting synthetic spectra to the optical spectrum of the star. This process gives a measurements of , , , and chemical abundances. The synthetic spectra were calculated using the Z eeman spectrum synthesis program ( Landstreet 1988 ; Wade et al. 2001 ), using model stellar atmospheres from ATLAS9 ( Kurucz 1993 ), and atomic data from the Vienna Atomic Line Data Base (VALD; Kupka et al. 1999 ). The best-fit stellar parameters were derived using and automatic minimization routine, in which all parameters were fitted simultaneously ( Folsom et al. 2012 ). This fitting process was performed on none independent spectral windows (416427, 440460, 460480, 490510, 510520, 520540, 540560, 620650, and 710750 nm). The final best fit parameters are the averages of the individual windows, and the uncertainties are the standard deviations. In cases where a chemical abundance for an element was derived in only three or fewer windows, the uncertainties were increased to account for the full window-to-window variation, as well as any potential uncertainties due to line blending and continuum normalization. Great care was taken to avoid any lines contaminated by emission. Weak


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

We thank the Ulysses project at ESA and NASA/JPL for effective and successful mission operations and an anonymous referee for improving the presentation of our results. H.K. is also grateful to Klaus Hornung for valuable discussions during the preparation of this manuscript. This research was supported by the German Bundesministerium für Bildung und Forschung through Deutsches Zentrum für Luft-und Raumfahrt e.V. (DLR, grant 50 QN 9107). H.K. and P.S. gratefully acknowledge support by MPI für Sonnensystemforschung. P.S. acknowledges support by Deutsche Forschungsgemeinschaft (DFG) grant KR 3621/1-1. Facility: Ulysses .


O B-Dataset I-Dataset I-Dataset I-Dataset I-Dataset O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O B-Telescope 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-Telescope B-Instrument 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 B-Instrument O O B-CelestialObject I-CelestialObject O O O B-Archive I-Archive I-Archive I-Archive 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 B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula B-Citation I-Citation I-Citation O O O O O B-Model 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 B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O B-Instrument O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength B-Wavelength 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 B-Wavelength O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-CelestialObject I-CelestialObject 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 B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-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-Survey B-Wavelength B-Wavelength O O B-Wavelength I-Wavelength O O O B-Telescope B-Wavelength I-Wavelength B-Wavelength I-Wavelength B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O O O O O O B-Survey I-Survey B-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-Wavelength O B-Wavelength O O B-Wavelength O B-Wavelength 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 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

the 2MASS All Sky Data Release. 4 The zero-points with their standard errors are taken from Maíz Apellániz Pantaleoni González ( 2018 ). For the WISE photometry, we calculate synthetic magnitudes on the AB magnitude scale and then apply the corrections to Vega magnitudes from Jarrett et al. ( 2011 ) for which the estimated error is 1.45 per cent (0.016 mag). For the IUE NEWSIPS spectra, we adopted a zero-point error of 4 per cent from Nichols Linsky ( 1996 ). 3.3 Interstellar reddening Fig. 3 shows a selection of HARPS spectra of AI Phe obtained from the ESO Science Archive Facility in the region of the Na i doublet. There are no detectable interstellar absorption lines in this region and so the reddening towards AI Phe must be very close E ( B − V ) = 0 (Karataş Schuster 2010 ). Accordingly, we set a Gaussian prior on the reddening E ( B − V ) = 0 ± 0.005 and set a lower limit E ( B − V ) ≥ 0. Figure 3. HARPS spectra of AI Phe in the region of the Na i doublet. The spectra have been normalized and vertically offset for clarity. The rest wavelengths of the Na i lines are indicated by vertical dashed lines. 3.4 Priors on infrared flux ratios The near-infrared (NIR) flux from solar-type stars compared to the total flux or the flux at optical wavelengths shows a well-defined relationship with T eff that is almost linear and that has little dependence on metallicity or surface gravity. This is the basis of the infrared flux method (Blackwell, Shallis Selby 1979 ; Casagrande et al. 2010 ) or the use of colours such as () to estimate effective temperatures for FGK-type stars (Boyajian et al. 2013 ). There is only one direct measurements of the flux ratio for AI Phe at wavelengths longer than 1 μm. We were concerned that not imposing any additional constraints on the flux ratio at these wavelengths could mean that the resulting models become unrealistic, e.g. the () colours computed using samples from P ( M | D ) might show a much large scatter than is observed in real stars. This could happen if the use of distortion coefficients allows for models where the flux from one star is unrealistically high at NIR wavelengths while the other is too low, unless some constraint is placed on the flux ratio at these wavelengths. We address this concern by making the assumption that the stars in AI Phe behave similarly to other dwarf and sub-giant FGK-type stars in the solar neighbourhood in order to put some constraint on the flux ratio in the 2MASS J, H , and K s bands, and the WISE W 1, W 2, W 3, and W 4 bands. We use stars from the Geneva–Copenhagen survey (Holmberg et al. 2009 ) to define relationships between T eff and ( V − J ), ( V − H ), etc. The values of T eff , E ( B − V ), log g , and [Fe/H] for each star are taken from Casagrande et al. ( 2011 ). We define separate relations for the F7 V star and the K0 IV star based on a different subsample of stars with similar properties to each. For the F7 V star, the subsample is defined by the following


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

It is a pleasure to thank G. Bodo, M. Chandra, S. Davis, J. Dolence, J. Goodman, G. Lesur, V. Paschalidis, J. Simon, and J. Stone for useful discussions. We also thank the anonymous referee for a very useful report. The numerical calculations presented here were performed on the Blue Waters supercomputer at NCSA. B.R.R. was supported by an Illinois Distinguished Fellowship and by NSF grant AST-1333612. Work at Los Alamos National Laboratory was done under the auspices of the National Nuclear Security Administration of the US Department of Energy. C.F.G.’s work was also supported in part by a Romano Professorial Scholar appointment, a Simons Fellowship in Theoretical Physics, and a Visiting Fellowship at All Souls College, Oxford.


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We thank the referee for their insightful suggestions, which led to improvements in the presentation of the paper. IR also thanks F. Cattaneo for his important and informative discussions about magnetic field generation during WD smoldering. This work was supported by NSF Grant AST-0709181 and by NSF Graduate Research Fellowship Grant DGE-1144082.


O O O O O O O O O O O O O O O O O O O O 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 B-Citation I-Citation O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula B-TextGarbage I-TextGarbage I-TextGarbage O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Model I-Model I-Model 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 B-CelestialObject I-CelestialObject O O O O O O O O B-Wavelength O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O 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 B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula I-Formula I-Formula O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation 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 B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-CelestialObject I-CelestialObject 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-CelestialObject I-CelestialObject O O B-Instrument I-Instrument I-Instrument B-Instrument O O B-Telescope 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 B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O

from the Kerr solution is found, this approach is not suitable to measure the deviation from the Kerr geometry and it is necessary to use a different method. Among the many proposed parametric black-hole spacetimes in literature, here we use the Johannsen metric (Johannsen 2013 ). In its simplest form, which is the version employed in our work, the Johannsen metric has only one deformation parameter, named α 13 (see Johannsen 2013 for the origin of this parameter). In Boyer–Lindquist coordinates, the line element reads (we use units in which G N = c = 1)where , , , andFor α 13 = 0, we recover the Kerr metric. In order to have a regular exterior region, we have to impose (as in the Kerr metric, for there is no event horizon and the central singularity is naked) and the following restriction on α 13 (Tripathi et al. 2018 ) Note that α 13 enters the metric coefficients g tt , g tφ , and g φφ . It thus affects the structure of the accretion disk, modifying the Keplerian gas motion and moving the ISCO radius. Qualitatively speaking, α 13 > 0 ( 0) increases (decreases) the strength of the gravitational force, so it moves the ISCO radius to higher (lower) values and this explains the strong correlation with the spin parameter in the plots that will be presented in the next sections. 3. Data Reduction and Analysis LMC X-1 was discovered in 1969 as the first extragalactic X-ray binary (Mark et al. 1969 ; Price et al. 1971 ). The system consists of a stellar-mass black hole and an O-giant companion star. The distance of the source, the black-hole mass, and the inclination angle of the orbit, which are three key-quantities in the continuum-fitting method, have been estimated to be D = 48.10 ± 2.22 kpc, M = 10.91 ± 1.54 M ⊙ , and i = 3638 ± 202, respectively (Gou et al. 2009 ; Orosz et al. 2009 ). LMC X-1 is characterized by a quite stable bolometric luminosity, which is about 16% of its Eddington luminosity L Edd (Gou et al. 2009 ) and thus nicely meets the standard criterion required to use the continuum-fitting method: sources with an accretion luminosity in the range 5%–30% L Edd (McClintock et al. 2014 ). The measurement of the spin parameter of the black hole in LMC X-1 using the continuum-fitting method was presented in Gou et al. ( 2009 ), and here we follow that study. There are 55 pointed observations of LMC X-1 with the Proportional Counter Array (PCA) on board RXTE (Swank 1999 ). To use the continuum-fitting method, it is desirable to choose thermal dominant spectral data, which are defined by three conditions (Remillard McClintock 2006 ): (i) the flux of the thermal component accounts for more than 75% of the total 2–20 keV unabsorbed flux, (ii) the root mean square (rms) variability in the power density spectrum in the 0.1–10 Hz range is lower than 0.075, and (iii) quasi-periodic oscillations are absent or very weak. Imposing these three conditions, we only have three observations, which are named “gold spectra” in Gou et al. ( 2009 ) as


O O O O O O O O O B-Organization I-Organization O O B-Collaboration I-Collaboration I-Collaboration O O O O O O B-Person I-Person I-Person O O O B-Person I-Person O O O B-Person I-Person O O O O B-Person I-Person O O O B-Person O O O O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization O O B-Fellowship I-Fellowship O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Person O B-Organization O B-Grant B-Person O O O O O B-Organization I-Organization I-Organization O O B-Organization I-Organization B-Person O O O B-Organization O B-Grant B-Instrument O O O O B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization O O O O O B-Grant O O O O O O B-ComputingFacility O O B-Organization B-Grant O O O O O O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility O O B-ComputingFacility I-ComputingFacility I-ComputingFacility O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization O B-Organization O B-Grant O B-Grant O B-ComputingFacility I-ComputingFacility I-ComputingFacility O O B-Organization I-Organization I-Organization B-Location O B-ComputingFacility I-ComputingFacility I-ComputingFacility O B-Organization O O O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility B-ComputingFacility B-ComputingFacility O B-Organization I-Organization O O O O O O O O O O B-Software O O B-URL O B-Software O O B-URL O O O O O O B-Instrument O O B-Identifier

The authors are grateful for useful suggestions from the CBC group of the LIGO Scientific–Virgo Collaboration. In particular, we are grateful to Walter Del Pozzo for useful advice, Vivien Raymond for helpful discussions, Simon Stevenson for careful reading, and Neil Cornish for beneficial comments. B.F. was supported by the Enrico Fermi Institute at the University of Chicago as a McCormick Fellow. This work was supported in part by the Science and Technology Facilities Council. P.B.G. acknowledges NASA grant NNX12AN10G. S.V. acknowledges the support of the National Science Foundation and the LIGO Laboratory. J.V. was supported by STFC grant ST/K005014/1. LIGO was constructed by the California Institute of Technology and Massachusetts Institute of Technology with funding from the National Science Foundation and operates under cooperative agreement PHY-0757058. This work used computing resources at CIERA funded by NSF PHY-1126812, as well as the computing facilities of the LIGO Data Grid including: the Nemo computing cluster at the Center for Gravitation and Cosmology at the University of Wisconsin–Milwaukee under NSF Grants PHY-0923409 and PHY-0600953; the Atlas computing cluster at the Albert Einstein Institute, Hannover; the LIGO computing clusters at Caltech, and the facilities of the Advanced Research Computing @ Cardiff (ARCCA) Cluster at Cardiff University. Some results were produced using the post-processing tools of the plotutils library at http://github.com/farr/plotutils and skyarea library at https://github.com/farr/skyarea . This paper has been assigned LIGO document reference LIGO-P1500117.


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energy. Figure 7. Drift along time of the CoM of the bound core with respect to the CoM of the whole system, for one of the simulations of set 1A. The Lagrangian radii are evaluated in percentage of the total mass of the cluster and so all the bodies, including possibly escaping IMBHs and growing (in mass) objects, are taken into account. Of course, the escaping IMBHs lead to a natural increase of the high-percentage Lagrangian radii so that in Fig. 5 we display only up to the 50 percent Lagrangian radius ( R 1/2 ). Note that growing massive objects, although they remain inside the bound core of the system and close to its CoM, do not a priori coincide with this CoM (see Fig. 8 that shows, also, how the growing BH movement is since the beginning well within the half-mass radius) and could, consequently, induce sharp variations in the latter evolution of the low-percentage Lagrangian radii. Figure 8. Black line gives the distance ( r smo ) of the growing supermassive object to the CoM of the bound ‘core’ of the system, for one arbitrarily chosen simulation of set 1A, taken as example. For comparison, we also give in purple the half-mass radius of the system. The curves are plotted starting from the time when the SMBH ‘seed’ is already grown by 42 IMBH mergers. The late time evolution of the average half-mass radius R 1/2 (50 percent Lagrangian radius), which is a good definition of the system radial scale, is well fitted by a linear relation: For set 1 and t > 15 yr, the values of the parameters are leading to a root mean square error of the fit equal to 0.8 mpc for R 1/2 . For set 2 and t > 500 yr, the values are giving a root mean square error equal to 5 mpc. The average half-mass radius at the final simulation time for set 1 is equal to 24 mpc (37 mpc for set 2), that is 50 times (8 times for set 2) the initial half-mass radius, R 1/2 (0) = 2 −1/3 R 0 . Even with our original safety margin of one order of magnitude for the initial cluster radial size, at the end of the simulation the core of the cluster extends much farther out than the area allowed for our purpose of mimicking the presence of an SMBH by a dense cluster of IMBHs. This is true for every simulation of set 1 and not only on average. This is even more the case for set 2, where no safety margin was taken. This result is not surprising: We actually expected that the extreme conditions required (a stable system of IMBHs of total mass and maximal size ≤5 mpc) were very unlikely to be reached. As we see in the next section, in both set 1 and set 2 the IMBH cluster undergoes various merger episodes. This has relevant consequences, whose main result is the formation of a very massive BH as coming out from the dominant object growing up after successive merger events. Hence, we conclude that, as expected on basic theoretical understanding, the answer to the first of the issues we raised in introduction is negative: A cluster of IMBHs dense enough to mimic the dynamical role of an


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Acknowledgements The authors thank the referee for their comments that allowed us to improve the article. D. Hypolite and S. Mathis acknowledge funding by the European Research Council through ERC SPIRE grant 647383 and the CNES PLATO grant at CEA Saclay. The authors also wish to thank the MESA website. M. Rieutord acknowledges funding by the French Agence Nationale de la Recherche (ANR), under grant ESRR (ANR-16-CE31-0007-01). This work was also supported by the Centre National de la Recherche Scientifique (CNRS, UMR 5277), through the Programme National de Physique Stellaire (PNPS), and by the CNES PLATO grant at IRAP.


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The authors wish to thank the anonymous referee, whose helpful comments greatly improved the quality of this manuscript. This work was supported by Kepler Cycle 2 GO grant NNX11AB71G and Cycle 3 GO grant NNX12AC79G and NSF grant AST13-11678. We are pleased to thank John Gizis for advance use of his GO program’s long-cadence data on GJ 1243. We thank John P. Wisniewski and Adam F. Kowalski for continuing discussions on stellar activity, and Rakesh Yadav for very useful comments on an early draft of this manuscript. J.R.A. Davenport thanks Morgan Fouesneau for help with Python code. Kepler was competitively selected as the tenth Discovery mission. Funding for this mission is provided by NASA’s Science Mission Directorate.


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We thank the anonymous referee for their thoughtful comments and useful suggestions. This material is based upon work supported by the National Science Foundation under grant No. 1716260. Additional support for this work was provided by a NASA Keck PI Data Award, administered by the NASA Exoplanet Science Institutem and by the Department of Astronomy and the Institute for Astrophysical Research at Boston University. A.W.M. is supported through Hubble Fellowship grant 51364 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555. F.A. received funding from the French “Programme National de Physique Stellaire” (PNPS) and the “Programme National de Planetologie” of CNRS (INSU). D.H. is supported by the Collaborative Research Centre SFB 881 “The Milky Way System” (subproject A4) of the German Research Foundation (DFG). This research made use of the Massachusetts Green High Performance Computing Center in Holyoke, MA. The data presented herein were obtained at the W.M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W.M. Keck Foundation. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain.


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We would like to thank Carlos de Breuck and Theresa Nilsson for their support for the observations. This publication is based on data acquired with the Atacama Pathfinder EXperiment (APEX) which is a collaboration between the Max-Planck-Institut für Radioastronomie, ESO, and the Onsala Space Observatory. We acknowledge the use of the GILDAS software for the data reduction. The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Advanced Grant RADIOLIFE-320745.


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We acknowledge the comments received from an anonymous referee, which helped to improve the quality of this paper. GALC acknowledges the support of an STFC PhD studentship. This research utilised Queen Mary's MidPlus computational facilities, supported by QMUL Research-IT and funded by EPSRC grant EP/K000128/1.


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The authors acknowledge the continuous and fruitful interactions with Jorma Harju, and an anonymous referee for helping improve the manuscript. S.K. acknowledges support from Xueying Tang and an NRAO Student Observing Support grant. J.C.T. acknowledges support from the University of Florida Research Opportunity Seed Fund and the Florida Space Inst. V.W. acknowldeges funding by the French INSU/CNRS program PCMI, the Observatoire Aquitain des Sciences de l’Univers and the European Research Council (ERC Grant 336474: 3DICE).


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ACKNOWLEDGEMENTS We thank Robert Izzard and Conor Byrne for helpful discussions. The Armagh Observatory and Planetarium is funded by direct grant from the Northern Ireland Dept for Communities. The authors acknowledge support from the UK Science and Technology Facilities Council (STFC) Grant No. ST/M000834/1.


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hot Jupiters from Kepler , coupled with the complex targeted nature of the survey (cf. the untargeted surveys used in our sample), means that these results need to be approached with some caution. Our result () confirms the giant planetmetallicity correlation seen in previous studies, but suggests that it is marginally weaker for hot Jupiters than it is for the longer period giant planets such as in the survey outlined above. We summarize our result and the previous results in Table 1 . Table 1. values. Our value is lower than all previously published results in Table 1 . We are within 1 of the result of Johnson etal. ( 2010 ); however, if we accounted for the mass dependency in our calculation as they have, we would expect our value for to decrease further (though not significantly so, as the stellar masses in our sample have a range of only 1M ). We have 2.32 and 2.31 from Valenti Fischer ( 2005 ) and Schlaufman ( 2014 ), the two other results from RV surveys, respectively. While these hint at a difference in the strength of the correlation between cool and hot Jupiters, we have 1.55 from Guo etal. ( 2017 ) and 2.75 from Petigura etal. ( 2018 ), the two hot Jupiter specific studies. Though again it should be noted that both hot Jupiter studies have a very small sample size. 5.2 Potential biases The metallicity offset ( c ) is needed to calibrate between the metallicities in Besanon and SWEET-Cat, but adds an extra degree of uncertainty compared with a survey that has a uniformly determined set of metallicities for both hot Jupiter hosts and field stars. However, the metallicity offset appears fairly well constrained from the sample distribution in Fig. 4 , and is relatively small in comparison to the overall spread of metallicities (cf. Fig. 3 ). The metallicity offset does correlate with (see Fig. 4 ), which results in a relatively large and slightly asymmetric uncertainty on . There is also a correlation between the radius of a star and its metallicity: the increase in opacity with the presence of metals results in the star having a larger radius. As transit depth decreases with the square of a stars radius, planets would be more difficult to detect around higher metallicity stars via the transit method. This would act to decrease our value of , but it has been found by Petigura etal. ( 2018 ) that planet detectability does not significantly depend on stellar metallicity. RV surveys will preferentially find planets around metal-rich stars as it is easier to perform the method when there are stronger and/or more metal lines present in the host star spectra. We do not expect the detection of a planet via the transit method to depend significantly on metallicity of the host star and this is one of the advantages of using a sample of hot Jupiter planets from transit survey discoveries. However, it should be noted that confirmation of planets from transit surveys is based on RV follow-up, which will still be subject to the bias described above.


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J. A. López-Vázquez and S. Lizano acknowledge support from PAPIIT-UNAM IN101418 and CONACyT 23863. J. Cantó acknowledges support from PAPIIT-UNAM-IG 100218. We thank an anonymous referee for useful suggestions that improved the presentation of this paper.


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The authors were supported by a grant from the NASA Living with a Star Program to Ames Research Center. The HMI data used are courtesy of the NASA/ SDO and the HMI science teams. We gratefully acknowledge many useful discussions with Nagi Mansour, Alan Wray, Alexander Kosovichev, and Philip Scherrer.


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We thank the entire Herschel Gould Belt Survey team for their efforts in obtaining and preparing the data used for the dense core catalogs we employed in this paper. We particularly appreciate the efforts of Bilal Ladjelate, Vera Könyves, and Alexander Men’shchikov in their contributions to the getsources extractions used for our analysis. J.K., J.D.F., E.R., M.C.C., and C.D.M. acknowledge the financial support of a Discovery Grant from NSERC of Canada. R.K.F. is a Dunlap Fellow at the Dunlap Institute for Astronomy Astrophysics. The Dunlap Institute is funded through an endowment established by the David Dunlap family and the University of Toronto. P.C., J.P., A.P., and A.C.T. acknowledge the financial support of the European Research Council (ERC; project PALs 320620). The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. This research made use of astrodendro, a Python package to compute dendrograms of Astronomical data ( http://www.dendrograms.org/ ). This research also made use of Astropy ( http://www.astropy.org ), a community-developed core Python package for Astronomy (Astropy Collaboration et al. 2013 ). Facilities: GBT , Herschel .


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Acknowledgements AM acknowledges funding support from Spanish public funds for research under project ESP2015-65712-C5-5-R from the Ministerio de Industria, Economía y Competitivida (MINECO) and the Fondo Europeo de Desarrollo Regional (FEDER), and from project RYC-2012-09913 under the Ramón y Cajal programme of the Spanish MINECO. The authors want to acknowledge the efforts and very constructive comments and suggestions of the anonymous referee. We also acknowledge Brian Boland and Jose Delgado for the English edition of this manuscript.


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case, even if the Coulomb collision scenario outlined above was not valid, the waves generated during the magnetic field reconfiguration could discriminate between fully stripped and normal ions for a short time before being dissipated, resulting in a charge state composition similar to the Outlier one. If such a reconnection event occurred high in the corona where the plasma density is low enough, ionization would not be able to replenish the ions left behind, leaving the decrease in their abundance intact. However, if the wave–plasma interaction was depositing energy to all ions except the fully stripped ones, the Outlier wind should exhibit larger ion temperatures in normal ions than in the fully stripped ones. Also, the presence of an additional energy source to this wind, which is unavailable to the normal slow wind and not directly associated with the reconnection region, would cause the ion temperature in the Outlier wind to be larger than in the normal wind. Figure 10 shows, however, quite the opposite: (1) all heavy ions have the same temperatures in the Outlier wind, and (2) these ion temperature values are lower than in the normal slow wind. However, the signatures of wave–plasma interaction at the reconnection point could easily be lost during the Outlier wind propagation in the heliosphere after the initial release, so that the comparison shown by Figure 10 does not necessarily rule out this scenario. The acceleration of ions during magnetic reconnection in solar flares has also been investigated with simulations and analytic studies by Drake et al. ( 2009 ). They found that the ions with a high mass-to-charge ratio can behave like pickup particles and be strongly heated more easily than protons as they cross the reconnection exhaust boundary; the threshold for ions to be heated also depends on the plasma β . Whether the depletion of the fully stripped ions in the Outlier slow wind is attributed to the lack of this type of acceleration needs further exploration. 5. CONCLUSIONS In this work, we have studied the Outlier slow solar wind, a subset of slow solar winds that shows a peculiar charge state distribution, and compared its characteristics to those of the normal slow solar wind. The Outlier wind, initially identified through a C 6+ /C 5+ ratio that is much lower than expected, was found to be a subset of slow solar winds with the same properties and source regions as the latter, with the exception of a very large decrease in the abundance of fully stripped ions, which causes a decrease of C and He abundance, and much lower ion temperatures. We argue that no matter what the Outlier wind origination mechanism is, the source region must be above 1.6 solar radii and the generating process must be episodic. We discuss three possible scenarios that could explain the peculiar properties of the Outlier wind: wave–plasma interaction, depletion already contained in coronal loops, and Coulomb collisions. In the first scenario, waves


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This work used the COSMA 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 a BIS National E-infrastructure capital grant ST/K00042X/1, DiRAC Operations grant ST/K003267/1, and Durham University. DiRAC is part of the National E-Infrastructure. The authors are indebted to the Virgo Consortium, which was responsible for designing and running the halo simulations of the Aquarius Project. They are also grateful to Gabriella De Lucia, Amina Helmi, and Yang-Shyang Li for their role in developing the semi-analytic model of galaxy formation used in this paper. They also thank Jorge Pearrubia and Carlos Vera-Ciro for valuable discussions and suggestions. They especially thank Nicolas Martin for generously sharing his new position angle measurements. ES gratefully acknowledges the Canadian Institute for Advanced Research (CIfAR) Global Scholar Academy and the Canadian Institute for Theoretical Astrophysics (CITA) National Fellowship for partial support. CB thanks the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013)/ERC Grant agreement 278594-GasAroundGalaxies for partial support. This work was supported in part by the National Science Foundation under Grant No. PHYS-1066293 and the hospitality of the Aspen Center for Physics.


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

their stellar mass by less than 10% across cosmic time. This result illustrates the uniqueness of these galaxies, suggesting a minimal contribution from merging events. Upcoming surveys such as WAVES ( Driver et al. 2016 ), covering wider regions of the sky, and deeper in flux than GAMA, will allow us to produce a high enough number of MUGs, to explore their formation channels in detail. It is remarkable that our sample of massive compact galaxies appear – at least in projection – in a relatively crowded environment (see Figs 1 and 2 ), complicating the photometric and spectroscopic analysis. Therefore, the inferred sizes and densities only provide upper bounds, as the light from the minor companions may contaminate the surface brightness profiles in a way that is impossible to mitigate at the spatial resolutions available to us. Follow-up observations, including imaging at high spatial resolution with HST or JWST, and deeper spectroscopy with IFU cameras at 8–10m-class telescopes, such as MUSE or MEGARA, will be required to better comprehend the intriguing properties of massive ultracompact galaxies. Appendix A: Robustness of the measured structural parameters We simulated 3840 galaxies, both in the KiDS r -band and the VIKING Z -band, with the tools described in Buitrago et al. (2013) . We explored the range of structural parameters shown by our sample, namely: where mag, R e , n , a r and p a stand out for magnitude (either in the r - or Z -band), effective radius, Sérsic index, axis ratio and position angle. The structural parameters of the mock galaxies were randomly distributed in a linear way, considering the full parameter space defined by the previously mentioned values. The mock galaxies were placed randomly on the KiDS and VIKING images, only imposing the condition that they should not overlap with any detection defined by the SExtractor segmentation map of each survey. Each mock galaxy was convolved with a representative PSF from those images, and analyzed with the same code we utilize to investigate the real galaxies. According to Figs. A.1 and A.2 , our ability to recuperate the structural parameters degrades at fainter fluxes and higher Sérsic indices. This result is expected, because dimmer and more concentrated objects are more difficult to analyze (a similar behaviour is found in the simulations of Buitrago et al. 2013 ). In the Z -band, the results are somewhat worse because of the coarser pixel scale (0.21 arcsec pix −1 versus 0.339 arcsec pix −1 ). However, for the data at hand, caution needs to be taken only for faint objects with a high Sérsic index. Fig. A.1. Relative errors – (output-input)/input – of the structural parameters (magnitude, effective radius and Sérsic index) of our simulated KiDS galaxies in the r -band. The right-hand column shows the average values in 1 mag bins (derived after a 5 σ clipping). The error bars represent the standard deviation within each bin. Fig. A.2. Relative errors –


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CN acknowledges financial support from PRIN MIUR 2010-2011, project ‘The Chemical and Dynamical Evolution of the Milky Way and Local Group Galaxies’, prot. 2010LY5N2T. JB was supported by STFC by grants R22138/GA001 and ST/K00106X/1. The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement no. 321067.


O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O B-Survey O O O O O O O O O O O O O O O B-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 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 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 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-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

for the 77 pairs with r proj > 5 kpc (blue). Primaries with more than one companion were counted more than once. The pairs with r proj r vir are shown in red. In the case of pairs having both their primaries and secondaries in the parent sample, only the most massive companion was considered. Table 1. Uncertainties associated with the use of z grism on the fraction of pairs. Very close pairs with r proj 5 kpc are superimposed in the CANDELS images so it was not possible to identify them as two distinct objects using the 3D-HST photometric catalogue (see example in the last panel of Fig. 5 ). The images of the galaxies in the parent sample were visually inspected to identify such cases. 10 pair candidates were found. Six of them had z spec , so we visually inspected the associated slit data. For three of them, both nuclei were included into the slit width (see Appendix A ) so we considered them as real pairs, which brings the total number of pairs in the parent sample to 80. The seven remaining ones correspond to a possible systematic underestimation of the number of pairs. Correcting factors to the number of pairs related to, e.g. projection effects are discussed in Section 2.2.4 . 2.2.2 Comparing observational and theoretical merger rates The goal of this paper is to compare observational estimates of the (major) merger rate to the predictions of the ΛCDM model. To avoid introducing systematics in the comparison, one therefore needs to adopt consistent definitions and assumptions. Merger rates in simulations can be defined in several ways. One of them consists in defining the merger rate as the rate at which a secondary halo is accreted on to a primary halo and becomes a sub-halo. This halo–halo merger rate then needs to be corrected by an estimate of the extra time needed for the secondary galaxy entering the primary halo to actually merge with the primary galaxy. Estimates based on semi-analytical or semi-empirical models need to explicitly account for such a correction, which can rely on several methods (e.g. based on the dynamical friction time). This can introduce a systematic uncertainty of a factor of ∼2 on the expected merger rate (see extensive discussion on these aspects in, e.g. section 2.4 of Hopkins et al. 2010a ). Using cosmological simulations, one can directly estimate the resulting galaxy–galaxy merger rate by intrinsically accounting for this delay. However, they are not immune to other uncertainties such as how and when the mass ratio and infall time are defined (Rodriguez-Gomez et al. 2016 ). In this paper, we choose to rely on the semi-empirical approach in which dark matter haloes are populated with realistic galaxies using the halo occupation distribution and empirical scaling relations that are relatively well constrained in the redshift and mass ranges considered in this study. 2.2.3 Identifying merging pairs Since the halo–halo merger rate is the most direct predictions of semi-empirical models, we designed a method


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 O O B-Person I-Person O B-Person I-Person O O O O

We thank Nicole Nesvabda, Pierre Guillard, and Nicolas Bouché for useful discussions of the SNe and SMBH feedback. We also thank Jérémy Blaizot and Andrea Cattaneo for very insightful 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Model I-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 low-temperature value for the rate constant of reaction FAR2 compared to FAR1 . For FAR2 a C–O bond is formed and as heavy-atom tunneling is less efficient than hydrogen atom tunneling, the rate constant is much lower than what would be expected from the barrier height only (compare for instance MF4 , GA6 , and FAR2 ). Similarly for the reaction of FA with , where a C–C bond is formed ( FAR3 ), again the low-temperature rate constant is very low. Note also the lower values for the T c of FAR2 and FAR3 compared to the hydrogen transfer reactions, indicating that tunneling also sets in at lower temperatures. Comparing the rate constant to the typical value assumed for radical–radical barrierless reactions, ∼10 12 s −1 , it is clear that these reactions are much less likely to contribute to COM formation. On that note we do wish to stress, however, to keep in mind that although radical–radical reactions may be able to proceed without a barrier, this does not mean that all reaction pathways are open, see for instance Lamberts ( 2018 ). 5 ASTROCHEMICALLY RELEVANT CONCLUSIONS Unimolecular reaction rate constants have been calculated and are provided for hydrogen addition and abstraction reactions from methylformate, glyoxal, glycoaldehyde, an ethylene glycol and are thus available to be implemented in both rate-equation and kinetic Monte Carlo models aimed at studying the formation of COMs at low temperatures. Our results are generally in agreement with experimental work, although some discrepancies exist on the efficiency of specific reaction paths, such as the formation of or after hydrogen abstraction from methanol, which impacts on the ease of methylformate formation (for which is needed) or ethylene glycol formation (for which is required). A microscopic model aiming to reproduce experiments may be able to provide a clear picture of how the reactions are intertwined with each other. The reaction could not be studied and thus deserves further attention. We found that one cannot predict average rate constants solely based on the type of the reaction. The spread in the low-temperature rate constant can be roughly seven orders of magnitude for a single reaction type (e.g. hydrogen addition to an aldehyde carbon) showing a strong dependence on the other functional groups that are attached to the carbon backbone. Within a single molecule, on the other hand, one can loosely say that hydrogen abstraction from an aldehyde group is faster than hydrogen addition to the same carbon. Both of these have a rate constant that is larger than hydrogen abstraction from a methyl group. Care should be taken with extrapolating rate constants based on the height of the barrier alone, as calculations show that reactions with narrow barriers can have rate constants at low temperature that are higher than those with a lower activation energy. Reactions that include the breakage or formation of a bond between two heavy atoms generally have low-temperature rate


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

Results of our simulations indicated the following: 1. Considering the current range of impact velocities in the asteroid belt, the depth of an impact crater is only slightly larger than 10 m even when the target is assumed to be of the softest material. This suggests that if the activation of MBCs is due to the sublimation of water–ice, ice must be buried in the top few meters of the object. The latter is consistent with the model by Schörghofer ( 2008 ), who showed that a layer of dust with a thickness of only a few tens of centimeters can prevent water–ice in asteroids from sublimating for the age of the solar system; 2. A substantial amount of ice may be exposed on the inner surface of an impact crater, contributing to the activation of an MBC. The size and therefore the inner area of a crater is larger for targets with a higher water-mass fraction; 3. Some of the ejected material may be re-accreted when the impact velocities are low (e.g., ≲100 m s −1 ), and may contribute to the activation of MBCs. Calculations by Hsieh et al. ( 2004 ) and Hsieh Jewitt ( 2006 ) suggested a very large ice exposure area to account for the activity of MBC 133P/(7968) Elst-Pizzaro. Our simulations indicated that while for an object similar to this MBC, the exposed ices on the bottom and interior surface of an impact crater, combined with the ice re-accreted on the surface of the object may be large enough to account for its activation, in general, due to the small gravity of MBCs, the amount of re-accreted material on the surfaces of these objects is too small to contribute to their activity. The latter implies that the activity of MBCs is most likely due to ice sublimation from multiple impact craters and/or the water content of these bodies are larger than the anticipated 5%, providing more ice in exposed areas for sublimation. Although the simulations presented here portray the impact scenario as a viable mechanism for exposing sub-surface ice to ignite the activity of MBCs, they contain some limiting assumptions. First, we did not consider porosity for our targets. Including porosity is a complicated task that requires developing complex mathematical models. This is currently under development and we expect the results to be ready for publication in the not-so-distant future. However, given the simulations presented here, we do not expect the result to change drastically, even when porosity is included. We considered the target material to be basalt or tuff. However, MBCs are most likely made of carbonaceous chondrites. That means, in order to simulate impact events, the knowledge of the equation of state of this material, as well as the flaw distribution for the fracture model, are required, which are unknown. Our approach, that is, simulating impacts using a very hard (basalt) and a very soft (tuff) target, allows us to portray a general picture of the impact scenario as a mechanism for ice exposure that can be applied to a variety of targets with


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light curve, which may help discriminate between different explosion scenarios. 4.1. Circumstellar Setup For some guidance in what sort of mass distributions to consider, we turn to studies of post-merger density distributions as presented by Pakmor et al. ( 2012 ), Schwab et al. ( 2012 ), and Shen et al. ( 2012 ), and summarized in Figure 9 . These calculations roughly show how circumstellar material evolves from immediately following the merger (∼seconds), to many viscous times (∼hours), to many thermal times (∼1000 years), respectively. Even over this large range of timescales, this comparison demonstrates that a profile is a good description of all of these density profiles. This is because the large heating near the base of the material leads to a roughly constant flux and a radiative envelope with an n = 3 polytropic index. Motivated by this, here we consider similar density distributions for extended material of , so that the mass of the extended material is simplywhere is the radius of the underlying WD and is a normalization constant for the density profile. Strictly speaking, the models that evolve for large periods of time following the merger are not expected to necessarily make SNe Ia, and instead lead to accretion-induced collapse (Saio Nomoto 1998 ; Shen et al. 2012 ; Schwab et al. 2015 ). Nevertheless, in the spirit of this work, we will still explore a variety of density distributions with different values of M e and R e , even for those cases that might not reach an SN Ia, to see what the corresponding observational signatures should be. Figure 9. Example density profiles showing a diversity of possible outcomes for the circumstellar material following a double WD merger. These profiles are a WD (green dashed line), equatorial material during a violent merger (Pakmor et al. 2012 , purple dot–dashed line), the nearly spherical profile after the material has viscously relaxed (Schwab et al. 2012 , red solid line), and the material after it has expanded to a red supergiant-like size (Shen et al. 2012 ; blue dotted line). 4.2. Extended Material Light Curves Our first set of circumstellar calculations are shown in Figure 10 . Here, we set the external mass to and vary the outer radius from up to . The explosion is triggered in the same way as all previous models, and the 56 Ni mixing is kept low with a boxcar width of , that is, the same as the red curves in Figures 1 , 2 , 5 , 7 , and 8 . The impact of the extended material on the light curve is dramatic, resulting in a bright first peak from the shock cooling of this extended material. This is reminiscent of the double-peaked light curves of some SNe IIb, which have also been attributed to extended material around the progenitor star (Bersten et al. 2012 ; Nakar Piro 2014 ). Furthermore, the roughly parabolic shape is similar to the analytic light curve expected for this material (Piro 2015 ). The observation of such a feature would be extremely useful for constraining the