(Barnes et al. 2018 ). 5 THE LINK TO AGN EFFICIENCY The inclusion of ATC leads to an increased CC fraction, increased central cumulative gas fraction, and flattens the CC fraction redshift evolution relative to simulations that neglect it. The temperature profiles and the gas fraction profiles both suggest that the central black hole injects less energy into the ICM when thermal conduction is included. Therefore, we now examine the energy injected by the central black hole and how this energy couples to the ICM. We define the central black hole of each cluster as the most massive black hole within of the potential minimum at z = 0. Its properties are then traced as a function of redshift. During the formation of the ICM ( z ≤ 2) the low accretion rate, kinetic mode feedback dominates (Weinberger et al. 2018 ). In Fig. 9 , we plot the median cumulative energy injected by the central black hole in the kinetic mode feedback for simulations with and without ATC. At z = 0, the inclusion of ATC results in a 24 per cent reduction in the energy injected by the low accretion rate kinetic feedback mode, which agrees with the results from the temperature and gas fraction plots. Figure 9. Median cumulative energy injected in the kinetic mode (solid lines) as a function of redshift for the central black hole compared to the energy lost via radiative cooling within r 500 (dash–dot-dotted lines) for simulations with (red) and without (blue). For simulations with ATC, we plot the conductive heating (short dashed line) within as a function of redshift. The right scale shows the median stellar mass (long-dashed) and black hole mass (dash-dotted) with (dark red) and without (dark blue) ATC. When ATC is included the central black hole injects less energy, but the stellar and black hole masses are unchanged. Conductive heating only contributes a small fraction of the energy difference. The right axis of Fig. 9 shows the median stellar mass of the brightest cluster galaxy, defined as the mass within twice the stellar half-mass radius for the most massive subhalo, and the median central black hole mass as a function of redshift. Despite the reduction in energy produced by the inclusion of ATC, the masses of the galaxy and black hole have a negligible difference for simulations with and without ATC, especially for z ≤ 1. Therefore, the central black hole is still able to self-regulate and control its growth and the growth of the galaxy. One explanation of the difference in injected energy with and without ATC is that there is significant heat transfer from outer radii into the core of the cluster, providing the additional energy required to offset radiative losses. To investigate this we define the conductive heating with a sphere by its conductive luminosity. This is defined as the heat flux integrated over the surface of the sphere where we chose a sphere of radius to account for the collapse and growth of the cluster with cosmic time. Only gas that is

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


Fig. 9 favour periodic models more strongly when the light curve is sinusoidal and favour QPO models more strongly when the light curves are sawtooth like. We introduced the higher order p 4 QPO models with periods locked in a 2:1 ratio and a common coherence time to explore if this difference was driven by the assumption of sinusoidal waveforms in the one-component QPO model. We show in Fig. 10 that using the two-component QPO models halves the number of RRab and RRd variables that prefer a QPO compared to the one-component model. The increase in periodic preference going from a one-component to the two-component QPO models for the more sinusoidal RRc and RRe sources is marginal. An even larger shift is seen for the fundamental mode Cepheids. These results are in agreement with the behaviour we found in Section 3 for the experiments comparing artificial light curves with sawtooth or sinusoid waveforms. It is not surprising, therefore, that a higher order QPO model results in a greater preference for periodicity. The two-component QPO is a better approximation to the sawtooth-like light curves of RRab, RRd and fundamental mode Cepheids, so the coherence time can act more like the desired physical parameter, and less as a proxy for light-curve shape. Figure 10. Distribution of the RRab+RRd, RRc+RRe, fundamental Cepheids and first overtone Cepheids in the AIC likelihood difference for the QPO and periodic models when using either the standard QPO model (dotted) or the higher order model (solid). The changes are small for the more sinusoidal RRc+RRe and first overtone Cepheids, but shift strongly towards the periodic case for the more sawtooth-like RRab+RRd and fundamental mode Cepheids. In addition to light-curve shape, we also noted in Section 2 that mischaracterized errors can bias the results, irrespective of light-curve shape. If some of the noise level assumed in the model is less than the true noise, the extra variance will be interpreted as signal. The natural way to model this extra variance is to move the model away from periodic to model the mischaracterized noise as stochastic variability. If we take the best-fitting model and re-estimate the errors so that it has 2 /dof1, then the fraction of Cepheids and RRLyrae favouring the periodic model increase significantly, from 70 and 10percent to 90 and 65percent in the case of first overtone and fundamental Cepheids, respectively, and increasing from 80 and 15percent among RRc/RRe and RRab/RRd to 95 and 90percent, respectively. 4.3 Variable distributions in QPO parameters The lesson from Section 3 is that the QPO parameter cannot simply be interpreted as a measure of coherence because it is significantly affected by light-curve shape. This is, however, no barrier to using the QPO parameters to classify variables. Fig. 11 shows the distribution of all the sources in the P , P and QPO parameter spaces. We see that the P plane maps physically distinct variable types to nearly unique spaces.

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


of dust extinction. Generally, the single-band SFRs are in agreement or are slightly lower than those derived from SED modeling with MAGPHYS. If we are unable to use either of the first two methods and we have at least one detection in another filter, we scale the SEDs from the DLA counterparts that were fit with the first method to match the detected host galaxy flux. We then use the scaled SEDs to estimate the rest-frame UV flux and use the median and standard deviation of the scaled SEDs to calculate the rest-frame UV SFR. Finally, if there are no detections in any band but there are upper limits in the rest-frame UV band, we calculate SFR upper limits using the second method. Photometric measurement were made using the aperture photometry technique, using the HST point-spread function (PSF) for GRB-DLA counterparts with HST data and the DCT 12 PSF for the ground-based data (corresponding to ∼2 and ∼17 kpc diameter apertures respectively). The large difference in apertures comes from the fact that HST is able to resolve the host galaxy. We assume that the light from unresolved sources is solely from the host galaxy and background sky. All SFRs are calculated from dust-corrected observations unless otherwise stated. The host extinction, A V , is taken either from SED models or from GRB afterglow measurements using a Small Magellanic Cloud (SMC)-like extinction law which has been shown to best depict the GRB explosion environment (e.g., Schady et al. 2012 ). We assume the host extinction is the same as the GRB line-of-sight extinction, which Perley et al. ( 2013 ) has shown is fairly consistent within a factor of two to three. If the host extinction is an upper limit, we use that value in all dust-corrected calculations and report SFR upper limits. In Table 1 , we report these GRB-DLAs with SFR error estimates but treat these as SFRs upper limits in all plots using dust-corrected SFRs. Our host extinction is, in general, higher than the reported for DLAs in the SDSS survey for our sample’s column densities (Murphy Bernet 2016 ). This may likely be because GRB-DLAs are found at a smaller impact parameter of (Blanchard et al. 2016 ) than the general DLA population of (Fumagalli et al. 2015 ) or more simply because our DLA sample traces, in general, metal-rich, and likely dust rich, systems (for example, see the correlation between and metal line equivalent widths in Murphy Bernet 2016 ). 3.1.1. SED Fitting Star Formation Rate We use MAGPHYS with the HIGHZ extension (da Cunha et al. 2008 , 2015 ), to model the host galaxy SEDs from photometry. MAGPHYS models templates to the data and returns an SED with fitted parameters which include SFR, stellar mass ( M ), dust mass ( M ), and A V . This particular package is well suited for galaxies and takes into account bursty star formation which is appropriate for GRB host galaxies as suggested by Hunt et al. ( 2014 ). MAGPHYS uses a continuous model of star formation with superimposed random bursts that

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


image for illustration purposes and to help explain the caveats of the algorithm (compare it to the segmentation obtained for COR2B). Figure 7. CME event observed on 2008 December 12 on COR2A (upper panels) and COR2B (bottom panels) FOVs. The red line indicates the CME segmentation obtained by CORSET. Earlier stages of the CME development in the FOV of the COR2 instruments are not shown in Figure 7 . At these earlier time instances, CORSET was able to segment the CME; however, these results had to be ignored because they led to NARD equal to zero on the application of CORSET3D. The radial speeds derived by CORSET3D as a function of latitude and longitude are shown in Figure 8 . The CORSET3D reconstruction shows that this CME event propagates in the inner portion of northwest quadrant of the solar corona (as seen from Earth, see Figure 8 ) up to at least a heliocentric distance of 16 solar radii (de-projected distance by the time the event reached the end of the time period selected, i.e., 13:37 UT). Figure 8 indicates that the radial speed is lowest at the northernmost portion of the reconstructed CME front. Further analysis is necessary to assess whether the speed differences along the front are artifacts resulting from the segmentation or a true effect. Byrne et al. ( 2010 ) also studied this event using a technique based on triangulation and found a speed of about 400 km s −1 between 10 and 15 solar radii. Using the GCS model, Möstl et al. ( 2014 ) found that the initial speed of this CME was about 497 km s −1 . Figure 8. Radial speeds of the front of the CME event observed on 2008 December 12 as a function of latitude and longitude (in the Stonyhurst coordinate system), as derived by CORSET3D. If we assume that this event continues propagating radially after 13:37 UT, it would be observed at Earth with its center in the negative side of the y axis of the Geocentric Solar Ecliptic (GSE) coordinate system. This assumption seems to be in agreement with the magnetic flux estimated by Howard DeForest ( 2014 ). According to these authors, the corresponding magnetic structure reached Earth first in the negative portion of the y axis, i.e., westward of the Sun–Earth line. A previous study from Liu et al. ( 2010 ) used triangulation in both STEREO /COR2 and STEREO /Heliospheric Imagers’ FOVs to track this CME event along its evolution to Earth (see, e.g., Figure 9 in Liu et al. 2010 ). They identified two structures in the time-elongation maps constructed from running difference images along the ecliptic plane. They called these two structures “feature 1” and “feature 2,” although they seem to be part of one complex CME structure, which is the one CME event considered in this work. Liu et al. ( 2010 ) found that the speed of both features ranged between 300 and 600 km s −1 , developing westward during their entire evolution from the Sun to the Earth. Lugaz ( 2010 ) computed the direction of this complex event with respect to the Sun–Earth line

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 B-Instrument O O O B-Instrument 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 B-Instrument 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 B-Software O O O O O B-Software O O O O O O O O O O O O O O B-Software O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation 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-Software 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 B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O B-CelestialObject O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O B-Telescope B-Instrument O B-Telescope B-Instrument O O O O O O O O O O O B-CelestialObject O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O 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-CelestialObject O O B-CelestialObject B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-CelestialObject O


for the freedom in the low-order gravity field, because the likelihood function used to obtain our posterior distribution of interior models assumed an inflated variance on J 2 to accord with the numerical precision of our theory of figures implementation (see Section 2.1 ). Because the resulting distribution included a diversity of heavy-element and helium distributions, envelope transition locations, and core masses, the seismology suggests a tension with the Voyager rotation rate commonly assumed for Saturn’s interior that different three-layer interior models seem unlikely to resolve. This conclusion based on the ring seismology adds support to the notion that periodicities in Saturn’s magnetospheric emission (e.g., Desch Kaiser 1981 ; Gurnett et al. 2005 ; Giampieri et al. 2006 ) may not be consistently coupled to the rotation of Saturn’s interior (e.g., Gurnett et al. 2007 ; Read et al. 2009 ). The present model is potentially oversimplified in two major ways. First, the model is not suited to address the close multiplets of waves observed to have the same azimuthal wavenumber m , namely, the multiplets of waves in the C ring with m = 2 and m = 3. The bulk of these seem naturally explained by the model of Fuller ( 2014 ), wherein avoided crossings between the f -modes and deep g -modes of higher angular degree give rise to a number of strong perturbations with the same m value. However, in the wealth of new OLR and OVR wave patterns that have been measured from increasingly low signal-to-noise VIMS data since Hedman Nicholson ( 2014 ), it seems that only two waves add to the mixed-mode picture, both with m = 2: the close-in W76.44 wave, and the Maxwell ringlet wave whose frequency and m number were predicted by Fuller ( 2014 ). The f -modes of higher angular degree have less amplitude in the deep interior and so are less likely to undergo degenerate mixing with any deep g -modes strongly. Indeed, there is not yet any direct evidence for f -modes with l > 3 undergoing avoided crossings with deep g -modes, although the outlying (5, 4) OVR warrants closer scrutiny in the mixed-mode context. The second major simplification of the present model is the assumption that Saturn rotates rigidly. While upper limits can be established for the depth of shear in Jupiter or Saturn’s envelopes on magnetohydrodynamic grounds (Liu et al. 2008 ; Cao Stevenson 2017 ), evidence gathered from spacecraft indicates that zonal wind patterns do penetrate to significant depths (Smith et al. 1982 ; Kaspi et al. 2018 ). It has been proposed that the insulating molecular regions of these planets may be rotating differentially on concentric cylinders (Busse 1976 ; Ingersoll Pollard 1982 ; Ingersoll Miller 1986 ), the zonal winds being the surface manifestation of these cylinders of constant angular velocity.The mode identifications made in Section 5 and Table 1 reveal that the seismological data set now samples a variety of radial (via the angular degree l ) and

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Mission 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 B-CelestialObjectRegion I-CelestialObjectRegion 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 O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion 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 B-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula 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-Instrument O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O B-Identifier I-Identifier O O B-CelestialObjectRegion I-CelestialObjectRegion 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 B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O B-CelestialObject O B-CelestialObjectRegion I-CelestialObjectRegion 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 B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O 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 burst spectrum (see Lewin et al. 1993 ; Strohmayer et al. 2006 , for a review). We scrutinised the NICER, XMM-Newton EPIC-MOS/PN, Swift -XRT, and NuSTAR data for the presence of thermonuclear bursts at different time scales (1, 10, and 100 s), but we found none. Next we focused on INTEGRAL JEM-X (3–35 keV) data and identified one thermonuclear burst candidate. We describe the analysis of the JEM-X data covering the event below. 6.1. Properties of the type-I X-ray burst We searched INTEGRAL/JEM-X data for bursts within revolutions 1986–2009, following the same approach as Mereminskiy et al. (2017) . We focussed on one of the two JEM-X cameras, JEM-X1; JEM-X2 was operating simultaneously, but this instrument seems to be experiencing reduced sensitivity in recent years. We identified one candidate thermonuclear (type-I) burst from IGR J17591−2342, in Scw-500010 of INTEGRAL revolution 2001 on Sept. 19, 2018; 23:07:33 (MJD 58380.96358 TT). The key properties of the burst are listed in Table 3 . Based on its intensity, this burst should have also been detectable by ISGRI; however, due to the loss of sensitivity over time in the lower ISGRI energy band, 18–27 keV, we did not detect this event in those data. Table 3. Parameters of the type-I X-ray burst observed by INTEGRAL JEM-X during the outburst of IGR J17591−2342 in 2018. Notes. (a) 58380.96358 MJD. (b) The τ fit has been measured after a plateau of ∼10 s. (c) Burst peak flux in 0.1–40 keV energy band. (d) Burst peak temperature. (e) Pre-burst unabsorbed flux in 0.1–250 keV energy range. (f) Burst fluence in 0.1–40 keV energy band. The type-I X-ray burst occurred ∼60 d after the outburst commenced, just after the source was at the highest X-ray luminosity (see Fig. 2 ). We defined the burst start time as the time at which the X-ray intensity of the source first exceeded 10% of the burst peak flux (above the persistent intensity level). The event showed a fast (∼1–2 s) rise time, followed by a ∼10 s long plateau at its peak (Fig. 8 ). Therefore, we conclude that most likely a photospheric radius expansion took place (see e.g. Falanga et al. 2007 ; Galloway et al. 2008 ; Bozzo et al. 2010 ). After the plateau, the burst decay profile could be well fitted with an exponential function and the correspondingly derived e-folding time is τ fit ∼ 9 s. The total duration of the burst was ∼40 s. Fig. 8. Light curve of the type-I X-ray burst detected by JEM-X and reported for the first time in this paper. The burst start time was 58380.96358 MJD. The JEM-X light curve was extracted in the 5–25 keV energy range with a time bin of 2 s. For the burst spectral analysis, we first determined the persistent flux before the burst onset by converting the ISGRI counts from Rev-2001 to the total broadband spectrum obtained from Revs. 1994–1995 (see Sect. 5 ). We note that during the outburst, the ISGRI data in the 20–150 keV band alone were fitted by a power-law model, and the spectral parameters were

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 B-Telescope B-Telescope B-Instrument B-Observatory B-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 B-Telescope B-Instrument B-Wavelength I-Wavelength 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 B-Wavelength O O O B-Telescope 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-Instrument O B-Instrument 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-CelestialObject I-CelestialObject O B-Dataset 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 B-Telescope O O O O O O O O O O O O B-Telescope O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O B-Wavelength O O O B-Telescope B-Instrument O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O B-Wavelength I-Wavelength O O O O B-Wavelength O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O 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 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 B-Wavelength O O O B-Instrument O O O O O O O O O O O O O O O O O B-Instrument O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Telescope O O O B-Wavelength I-Wavelength I-Wavelength O O O O O B-Model I-Model O O O O O


in star formation: both in short bursts (during close passages of the satellite) as well as sustained high star formation rates lasting several Gyrs. In Starkenburg et al. (2016) we show that the general properties of our simulated dwarf systems compare very well to a large sample of dwarf irregular galaxies and blue compact dwarfs from the literature. In this paper we provide a quantitative characterization of the morphological and kinematic properties of the dwarf systems during the minor merger events and thereby facilitate a more detailed comparison to observations. For the analysis we used morphological descriptions that have been applied to characterise where galaxies lie along the Hubble sequence, to disentangle interacting from isolated systems, and to describe the stellar distributions in major mergers of or larger spiral galaxies, such as the CAS (concentration, asymmetry and smoothness) and GM (Gini coefficient and M20) indicators (see e.g. Conselice et al. 2000 ; Conselice 2003 ; Abraham et al. 2003 ; Lotz et al. 2004 , and references therein). These have also been applied to describe the stellar components of isolated irregular dwarf galaxy samples ( Conselice 2003 ; Lotz et al. 2004 ), to characterise the gas distribution in starbursting dwarf galaxies ( Lelli et al. 2014 ) and in simulations of major mergers ( Holwerda et al. 2011a ), as well as a variety of observational samples ( Holwerda et al. 2011b , c , d , e , 2012 , 2013 , 2014 ). This paper is organised as follows. The hydrodynamical simulations are described concisely in Sect. 2 , while in Sect. 3 we focus on one specific simulated system and highlight key tidal features as the merger takes place. In Sect. 4 we introduce the morphological and kinematic indicators used and compare the results to some observational samples. We present a brief comparison to two dwarf galaxies with peculiar properties, namely IC10 and NGC 6822 in Sect. 5 . The summary and conclusions are given in Sect. 6 . 2. Method We analyse the structural properties of dwarf galaxies during minor mergers with dark satellites for a suite of hydrodynamical simulations recently presented in Starkenburg et al. (2016) . The simulations span a range of initial conditions for the dwarf galaxy, its satellite and a variety of orbital configurations for the interaction. They were performed using the OWLS ( Schaye et al. 2010 ) version of Gadget-3 (based on Springel et al. 2001 ; Springel 2005 ) with implementations for star formation and feedback as described in Schaye Dalla Vecchia (2008), Dalla Vecchia Schaye (2008) . Table 2 Parameters for the orbits. Notes. (a) The apo-to-peri ratio is an average for the first pericentric passage for different main and satellite masses and inclinations. Fig. 1 Evolution of the model-A dwarf galaxy with , merging with a 20% mass ratio dark satellite with on a co-planar relatively radial orbit (the intermediate orbit in Table 2 ). All figures show an inclined view of the

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


and in quiescence, along with their rates of change. We have also refined the supercycle length (and possible changes in superoutburst occurrence rate). The structure of this paper is the following: Sect. 2 presents details about observations, data reduction, and photometry analysis. Section 3 contains information about the photometric behaviour of the system and a thorough study of positive and negative superhumps. We discuss this information in Sect. 4 and present a summary of our campaign dedicated to MN Dra in Sect. 5 . 2. Observations and data reduction The observational data of MN Dra presented here were collected throughout three observation campaigns. The first data were obtained during 6 nights from 2009 October 12 to October 22, in the Skinakas Observatory, Greece. At that time, the star was in a quiescent state. The second campaign was conducted during 15 nights from 2013 July 09 to September 10. On that occasion, data were gathered in Poland, at the Borowiec station of the Poznań Astronomical Observatory, at J. Kochanowski University in Kielce, and at the Ostrowik station of the Warsaw University Observatory. During the 2013 campaign we detected two superoutbursts of MN Dra. The longest campaign was organized in 2015, from June 4 to December 18. Data covering 84 nights of observations were collected at the Borowiec Station, in Pisa in Italy, at Antelope Hills Observatory and at the MDM Observatory in the USA. Once again, two superoutbursts in MN Dra were observed. In Table 1 we present the journal of CCD observations of MN Dra. In total, the star was observed 374.37 h, and 8717 useful exposures were obtained. To summarize, eight telescopes with diameters ranging from 0.25 to 1.30 m were used to collect data during the 2009, 2013, and 2015 campaigns. All data of MN Dra were gathered in a clear filter (“white light”). This approach allowed us to obtain reliable photometry around 18–20 mag when the object was in quiescence. Bias, dark, and flat-field correction of raw files was made in a standard way. For the data reduction we used the IRAF package. The profile (point-spread function) photometry was obtained with the DAOPHOTII package ( Stetson 1987 ). Relative unfiltered magnitudes of MN Dra were derived from the difference between the magnitude of the star and the mean magnitude of two comparison stars marked as C1 and C2 in Fig. 1 , where the map of the observed region is shown. The equatorial coordinates of comparison stars C1 (, , mag in filter) and C2 (, , mag in filter) were taken from the 2MASS All-Sky Catalog ( Cutri et al. 2003 ). Instrumental magnitudes were transformed into the passband, which is very close to observations made in white light. Fig. 1 Finding chart with the position of MN Dra marked as V1 and two comparison stars C1 and C2. The field of view is about . 3. Light curves 3.1. Global photometric behaviour Fig. 2 Global photometric behaviour of MN Dra. For convenience, we use only a day number HJD-2 450 000 [d]

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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-Observatory I-Observatory B-Location O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Location O O B-Observatory I-Observatory O O B-Observatory I-Observatory I-Observatory O B-Organization I-Organization I-Organization O B-Location O O O B-Observatory I-Observatory O O B-Observatory I-Observatory I-Observatory 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 B-Observatory I-Observatory O B-Location O B-Location O B-Observatory I-Observatory I-Observatory O O O B-Observatory I-Observatory O O B-Location O O O O O B-CelestialObject I-CelestialObject 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 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 B-Software O O O B-Model I-Model O O O O O B-Software O O B-Citation I-Citation 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-TextGarbage I-TextGarbage O O O O O B-TextGarbage I-TextGarbage O O O O O O O B-Dataset I-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 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 B-CelestialObject I-CelestialObject O O O O O O O O O O O O


so the shell velocity equals the ratio of the swept-up momentum and the swept-up mass M sh ( t ) ≈ f Ω M ej + M w,sh ( t ), where the swept-up mass of the pre-dynamical wind is given by and t end = t run ( v w / v sh ) is the time required for shock to reach the outer edge of the pre-dynamical outflow. Although the time evolution of v sh is complicated by the implicit dependence of M w,sh on v sh , we find that for fiducial parameters its value varies by less than a factor of 2 from its asymptotic value of where in the final line we have taken M w ≲ M ej , f Ω = 0.3 and . In our analytic estimates that follow we assume a temporarily constant value of , where ξ ≈ 0.5–1. Emission escapes on the photon diffusion time-scale through the fast ejecta, which at the shock radius R sh ≈ v sh t is given by where we have used equation ( 3 ) for δ o = 5 and δ i = 2. If the opacity remains roughly constant in time, then equating this to the expansion time t gives the time-scale for the shock-powered emission to rise to its peak (Arnett 1982 ) where κ 0.3 ≡ κ/(0.3 cm 2 g −1 ) is normalized to a typical value (Fig. 4 ). In the second line, we have normalized the ejecta mass to a fixed fraction of the total stellar mass; the fast ejecta velocity to the binary escape speed; and the semimajor axis of the binary to 10 times the main-sequence stellar radius R ms ≈ R ⊙ ( M / M ⊙ ) 0.8 . All else being equal, equation ( 21 ) shows that mergers between more massive stars, or evolved stars with radii much larger than their main-sequence values, will result in later peaking light curves, consistent with our full numerical solutions (Fig. 5 ). However, overall the dependence on binary parameter is relatively weak, consistent with the factor of ≲5 range of observed values t pk ≈ 30–150 d for a ∼ 2–100 R ms and M ∼ 1.5–30 M ⊙ (Fig. 1 , Table 1 ). Also note that, by assuming a fixed, relatively high value of the opacity in deriving equation ( 21 ), we cannot account for cases when the shock heating is insufficient to keep the ejecta ionized (e.g. the 2 M ⊙ model in Fig. 5 ). Table 1. Properties of LRN and their stellar progenitors. References: (1) Mason et al. ( 2010 ), (2) Munari et al. ( 2002 ), (3) Tylenda et al. ( 2005 ), Afşar Bond ( 2007 ) but see Munari et al. ( 2005 ), (4) Blagorodnova et al. ( 2017 ), (5) Smith et al. ( 2016 ), (6) Mauerhan et al. ( 2015 ), (7) Mauerhan et al. ( 2017 ), (8) MacLeod et al. ( 2017a ). a Ejecta velocity inferred from optical spectra (note that this may not always represent the velocity of the bulk of the ejecta, but instead the fastest components). b Approximate peak luminosity of second peak. c Assuming the second peak was bolometrically about 1 mag fainter than the first. If the forward shock dominates the shock power (equation 7 ), then the peak luminosity of the shock-powered second light-curve peak is given by (in the limit v sh ≫ v w ) where we have used equations ( 1 ) and ( 2 ). Normalizing again to the

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


Rincon, Ogilvie Proctor ( 2007 ), where a subcritical dynamo generated by the interaction between (fluctuating) non-axisymmetric and (mean) axisymmetric toroidal magnetic field leads to ultimate saturation in a bounded domain with zero initial magnetic field. Indeed, in our theory the domain-integrated helicities of the flow and the magnetic field are both zero, while the domain-integrated cross-helicity vanishes because and are out of phase. The theory also allows us to investigate the astrophysically relevant weakly dissipative regime. We do this by showing that the inviscid limit of the theory, Re ≫ 1, is well behaved, and then examine the further limit of nearly ideal MHD by considering large values of Re m . Although the zonal magnetic field fluctuation becomes very large in this regime the angular momentum flux remains well behaved for all wavenumbers and decreases as | m | −1 (equation 34 ). A simple prediction for the magnitude of this flux follows from the assumption that the dominant wavenumber m corresponds to the optimum wavenumber from linear theory that yields the fastest MRI growth rate. The resulting expression for the angular momentum flux, , resembles the prescription of the α-model of Shakura Sunyaev ( 1973 ) but with the sound speed replaced by the Alfvén speed. A similar dependence of the momentum flux on the square of the magnetic field was observed in the simulations of a compressible but magnetic field dominated disc by Hawley et al. ( 1995 ), although subsequent computations by Sano et al. ( 2004 ) and Pessah, Chan Psaltis ( 2007 ) suggest a weaker dependence on v A . We emphasize that throughout this paper the symbols Re and Re m refer to scaled values of the Reynolds number and the magnetic Reynolds number, i.e. the condition Re m ≫ 1, for example, refers to Re m * ≫ ε −1 while the condition Re m ≪ 1 refers to Re m * ≪ ε −1 . The latter condition can therefore be satisfied for the large Re m * expected of astrophysical systems provided only that these are small compared to ε −1 , a quantity defined here in terms of the shear rate. Our approach has several attractive features, one of which is the fact that angular momentum is inevitably transported outward. In this connection we mention that Lesur Longaretti ( 2007 ) find that the transport coefficient F v /|σ| in a turbulent disc increases with the magnetic Prandtl number Re m / Re . In our (non-turbulent but fully non-linear) study we find a similar tendency when m is fixed (cf. Fig. 7 a): in the supercritical regime, above the marginal stability curve, F v decreases as Re increases for fixed Re m ; when Re is fixed, F v increases as Re m increases. Possible concerns include neglecting the possibility that saturation is accompanied by net outflow in the vertical direction, as measured by the quantity although this is a consistent assumption that follows from the relation obtained from equation ( 1a ). This relation is identically satisfied by . A further concern is

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


that the mass point C is under the action of an arbitrary additional force F (per unit mass) that is not gravitational and acts on the gas component of the supercloud. In our case, F will represent an hydrodynamic force due to the friction between the gas supercloud and the surrounding interstellar medium or due to the pass of a shock wave that affects the gas supercloud. Then, the motion equations in the reference system ( x, y ) are given by Figure 1. Illustration of the stationary coordinate system ( x, y ) centred at the Galactic centre and the rotating coordinate system (η, ξ) of origin O moving on a circular orbit of radius R 0 . The figure plane represents the Galactic plane and the rotation sense is clockwise. The angle θ, between the y -axis and ξ-axis, increases in the sense of the Galactic rotation. where F x and F y are the components of F and subscript c refers to the coordinates of the point C. Because the force K ( R c ) is equal to the centripetal force at R c , we will write K ( R c ) = R c ω( R c ) 2 , where ω( R c ) refers to the Galactic angular velocity at R c and for short will be written as ω c . Since we are interested in referring the motions to the rotating system, we should convert equations ( 1 ) into ones depending on (η, ξ). The formulae that govern this transformation are which are obtained from simple geometrical considerations of Fig. 1 . Besides, we should have into account that F x = F ξ sin θ + F η cos θ and F y = F ξ cos θ − F η sin θ, and that θ is a function of time t given by θ = θ 0 + ω 0 t . We adopt θ 0 = 0, i.e. the y -axis and ξ-axis agree at t = 0. Differentiating twice equations ( 2 ) with respect to the time t, we obtain where and . From the second members of equations ( 1 ), with the corresponding replacements, we get that where and . By equating equations ( 3 ) to the corresponding equations ( 4 ), we have The system of equations ( 5 ) is equivalent to the system a 1 = c 1 and a 2 = c 2 . Thus, the exact epicyclic equations of motion for the mass point C are If we adopt a flat rotation curve for the Galaxy, with a rotation velocity V 0 = 220 km s −1 , in approximate agreement with the measurements in a large range of Galactocentric distances (e.g. Sofue, Honma Omodaka 2009 ; Bovy et al. 2012 ), and . Since (see Fig. 1 ), we have For the study of the orbit of the local supercloud, the origin of the system (η, ξ) should be located in the solar neighbourhood at the Galactocentric distance of the Sun (i.e. R 0 ≈ 8 kpc). Replacing equation ( 7 ) into equations ( 6 ), this equation system can be solved numerically. The initial conditions needed to solve the differential equation system ( 6 ), i.e. η c (0), ξ c (0), , , will be calculated from the LSR velocity and position of the supercloud's gravitational centre at t = 0. With this purpose, we use the relations ( 2 ) to obtain η c = x c cos θ − y c sin θ and ξ c = x c sin θ + y c cos θ − R 0 . Hence, and . Since θ = ω 0 t = 0 at t = 0, the former

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


Figure 8. The dependence of dimensionless critical accretion rate on IBHs dimensionless mass m M /(10M ). Solid, dashed, and dotted curves correspond to JWST detection limit, that of MM without the confusion effect being taken into account, and that of MM with this effect being accounted, respectively. Figure 9. The dependence of the parameter on m M /(10M ). Curves of different styles describe the same cases as in Fig. 8 . Figure 10. Same as Fig. 9 , but now the dependence of parameter eff is shown. Figure 11. The minimal number of black holes within CMZ needed for observations with JWST and MM, for fixed values of the efficiency parameter , as a function of mass. Solid, dashed, and dotted curves corresponding to observations with JWST and MM without and with the confusion limit being taken into account. Curves with progressively larger values of N bh for a given value of m correspond to progressively smaller values of . The accretion rate given by expression ( 1 ) should be smaller than its critical value for 1. This requirement sets a limit of the possibility of observations of IBHs by a given instrument and for a given value of the density of the interstellar medium, IBH mass, and velocity. In order to compare ( 1 ) with , we express the accretion rate given by equation ( 1 ) in terms of our characteristic unit: , set c s 0 in equation ( 1 ), substitute there our chosen value of density of interstellar medium 3.34 10 22 gcm 3 and assume that a typical IBH velocity 225kms 1 . We obtain where . To begin with, let us consider a black hole travelling at the typical velocity and set in equation( 17 ). In this case from the requirement that for 1, we get lower limits on black hole masses, M crit , available for observations. For larger black hole masses, the condition gives a lower limit on the efficiency parameter , which is shown in Fig. 9 . One can see from this figure that JWST and MM without taking into account the confusion effect could be able to observe IBHs with masses larger than M crit 30M , while allowing for the confusion effect MM is able to detect IBHs only when M 90M , respectively. The range of available values of is rather limited to 0.1 even for the largest considered black hole mass 100M when the confusion effect is neglected and 0.8 in the opposite case. That should be relatively large may be a problem for observations since some works suggest significantly smaller values, see e.g. Igumenshchev Narayan ( 2002 ). On the other hand, assuming that high accretion efficiency is sustained and taking into account that the available volume of CMZ 10 6 pc 3 , it could be possible to observe IBHs with number density as small as 10 6 pc 3 . Available values of and M crit can be smaller in a situation when there are many IBHs within CMZ, with their number N bh 1 and, accordingly, their number density 10 6 pc 3 . In this case, assuming the Maxwellian statistics of distribution of IBHs over velocities we can estimate the number of IBHs

O 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 B-Telescope O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-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 B-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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Model O O O O O O O O O O O O O O


circles mark the mass coordinate . The last few profiles show the envelope oscillating due to mass transfer rates falling below the steady He-burning regime. On the low mass donor end, however, carbon may not ignite at all. The model with initial donor mass stays at lower accretion rates and falls far enough below the steady helum burning range that the mild helium oscillations become powerful enough to blow off mass. The blue dashed line shows how the maximum temperature in the shell will oscillate between the flashing helium burning shell and the hot, compressed C/O ashes below the burning layer. At these accretion rates, however, the accretion efficiency stays above 70%, allowing the WD to gain enough mass to trigger carbon ignition in the core. We compare our accreted mass retention efficiency calculated in the final stages of this model using super-Eddington winds to the analytical estimates of Kato Hachisu ( 2004 ) and Wang et al. ( 2015 ) in Figure 7 . Wang et al. ( 2015 ) used MESA (r3661) for their study, but used the default super-Eddington wind settings, whereas we triggered super-Eddington winds while the WD is still in a compact configuration in order to speed the computation. Systems with donor mass , therefore, will fall to lower accretion rates and efficiencies, and ultimately lose contact before a core ignition occurs. The components, now both C/O WDs, will spiral in due to GWR and contribute to the double-degenerate channel for SNe Ia, as discussed in Section 6 . Figure 7. The top panel shows the accreted mass retention efficiency during the last stages of the system with the donor stars. The black line shows what we calculated by taking the ratio of the growth rate of the accretor and the mass loss rate of the donor. The red short-dashed lines show the retention efficiency given analytically by Kato Hachisu ( 2004 ) for 1.3 and cores. The blue long-dashed lines show the retention efficiency given analytically by Wang et al. ( 2015 ) for 1.3 and cores. The bottom panel shows the mass transfer rate being donated to the WD. Between the high and low mass donor limits is the region where core carbon ignitions occur. This is where the donor mass is high enough that the accretion rates do not fall too far below the stability boundary before is reached, but also low enough that it avoids a carbon shell ignition from long sustained high accretion rates. A clear example of this is shown in Figure 8 , with the trajectories of the core and envelope shown with profiles in space for a system with . In Figure 9 we show the composition and temperature profile when this model has grown to , the same profile as that in Figure 8 . As the C/O envelope is , this shows that the base is at a temperature minimum, and the temperature maximum in the envelope is only deep. The core ignition in these models indicates that they are likely SN Ia progenitors. Figure 8. Profiles of of the WD in the binary system with . Markings have the same meaning as

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


unobscured sources, to dex for faint and highly obscured sources. The average value of the error is dex, with standard deviation . We show the average errors with a black cross in the left panel of Fig. 4 , while the specific value for each source is used in the following analysis. In order to look for intrinsic correlations between these two quantities, one possibility is to compute the partial Spearman rank correlation between two variables in the presence of a third, and to assess the statistical significance of such correlation (e.g., Macklin 1982 ). To derive the correlation coefficient between and , conditioned by the distance, (, , ), we evaluate the Spearman coefficient related to each pair of parameters and then combine them according to the expression (Conover 1980), which returns the partial correlation between and , corrected for the dependency on . The resulting is 0.15, and the associated confidence level, in terms of standard deviations, that the first two variables are correlated, independently of the influence of the third, is , following Eq. (6) of Macklin ( 1982 ). Therefore, the two quantities appear to be significantly correlated, after the effect of redshift on both of them is taken into account. 3.2. Redshift bins The second approach, often used in the literature, is to define redshift bins that are as narrow as possible to minimize the distance effect, and to look for correlations between the two quantities. Thanks to the large sample collected in this work, we can divide the sample into five redshift bins. For every redshift bin, a large distribution in both luminosities can be observed, with the typical luminosity increasing with redshift (Fig. 4 ). Most of the observational works mentioned in Sect. 1 looked for the distribution of average in bins, or average in bins (but see Gruppioni et al. 2016 ). Both hydrodynamical simulations (e.g., Volonteri et al. 2015 a,b) and semi-analytic models (e.g., Neistein Netzer 2014 ) show that, in the - plane, there may be the superimposition of a weak correlation for the bulk of the population, and a strong correlation only for the most extreme merger phases, corresponding to the highest and . If the underlying distribution shows such a complex shape, the results of the two approaches (average in bins or average in bins) may be very different. In Fig. 5 (left) we show the result of plotting average in bin of (both in log scale) in five redshift bins. As can be seen, there is no correlation at all and, as expected, there are no sources below the relation computed for a pure AGN template in Mullaney et al. ( 2011 ), similar to the one used in Netzer et al. (2009). Following this approach, we are therefore able to reproduce the results of Shao et al. ( 2010 ), Rosario et al. ( 2012 ), and others that claim no correlation between AGN activity and SF over several orders of magnitude in luminosity. On the other hand, computing average in bins (in log scale) from the same bivariate

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


by a Gaussian probability density function (PDF) with mean and standard deviation . For the flux limits, we used the 1 σ upper limits as as well as σ for the PDFs. All PDFs are set to zero for negative fluxes. Each of these Gaussian PDF representations of the measurements are corrected by the lens magnifications listed in Table 2 , using the intrinsic flux as simply the observed flux divided by the magnification and that the variance on the intrinsic flux is given by:Here is the estimated lensing magnification for each image. The uncertainties on the magnification factors quoted in Table 2 are not symmetric, and we therefore, conservatively, use the largest absolute value of the upper/lower magnification ranges as . The product of the individual magnification-corrected PDFs for each image gives us a representation of the intrinsic flux of the background source including information from both the detections and the upper limits. If any of the detections and/or upper flux limits were in disagreement such a product would be driven to 0. Within 3 σ, all of our measurements are in agreement with each other. Sampling the distribution resulting from taking the product of the individual PDFs, we obtain the combined intrinsic magnification-corrected line fluxes or line flux limits. In Table 3 , we quote the median value and 68% (∼1 σ ) confidence intervals for the final distribution. Comparing these values with the measurements performed directly on the stack also given in Table 3 scaled by the average HFF lens magnification of images A–E (), the de-magnified Ly α and C iv fluxes agree within the errors (especially if the large uncertainties on the magnification are folded into the error budget). The intrinsic flux limits appear to be roughly a factor of three tighter from the stack than from the Gaussian PDF if the uncertainties on the lens magnification are ignored. The tentative detection of the O iii ]-doublet in the stacks agree with the magnification-corrected flux limit set by the Gaussian PDF combination. 5.2. Interpreting UV Line Fluxes and EWs As mentioned in Section 1 , EWs and flux ratios of rest-frame UV lines are strongly correlated with the ionization strength and the gas-phase metallicity of the stellar populations dominating the SEDs of the emitters (e.g., Stark et al. 2015b , 2017 ; Feltre et al. 2016 ; Gutkin et al. 2016 ; Jaskot Ravindranath 2016 ; Mainali et al. 2017 ; Pérez-Montero Amorín 2017 ). Hence, the obtained flux ratios (limits) from the GLASS spectra can be used as an indicator of the physical properties of the multiply imaged source behind RXC J2248.7–4431 as described in the following. The C iii ] EW and the flux ratio between C iv and C iii ] are sensitive to the gas-phase metallicity and the ionization parameter of the stellar populations (Feltre et al. 2016 ; Gutkin et al. 2016 ; Jaskot Ravindranath 2016 ; Pérez-Montero Amorín 2017 ). From the GLASS spectra, we get rest-frame (1 σ ). As shown by Rigby et al. (

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


α and are the polar and azimuth angles of the wave vector of a transverse electromagnetic wave. In this case, the angle α is the observation angle. The spectral power of radiation at the emission frequency Q ω can be obtained in accordance with the expression for the total radiation power: Comparing expressions ( 4 ) and ( 5 ) we obtain: In our work, we will not apply head-on approximations, which, as noted in the work of Willes et al. ( 1996 ), can be violated at small wavenumbers of Langmuir waves and their narrow spectra. We will also not use the narrow-spectrum approximation proposed in Willes et al. ( 1996 ). The cited work also contains a scheme with the spatial orientation of the wave vectors of the merger of Langmuir waves and the generated transverse wave. In order not to limit ourselves to particular cases, we present the results of calculations according to direct expressions ( 2 ), ( 3 ), without using the simplifications usually inherent in these models, which are described in detail in Willes et al. ( 1996 ). Let us now consider radio emission at different spectra of Langmuir waves. Taking into account the work of Willes et al. ( 1996 ), we consider the case of axial symmetry of the radiating region and the spectrum of Langmuir waves in the form: where B is the normalizing coefficient in accordance with the normalization condition: W is the total energy density of Langmuir waves; and φ are the polar and azimuth angles of the Langmuir wave, where the angle is calculated relative to the axis of symmetry of the radiating region, δ is an even positive number. Let us first consider the case when , i.e. when does not depend on the Langmuir wave vector. Fig. 1(a) shows the distribution of radiation ( Q k ) over the wavenumber for different viewing angles α at δ = 2, k max = ω pe /(3 V T e ), k min = ω pe /(15 V T e ), and T e = 3 × 10 6 K, n = 10 16 m −3 . These values of k max and k min are chosen for the following reasons: Langmuir waves with a value greater than k max are effectively absorbed by thermal electrons as a result of Landau damping, and therefore we will not consider them. Langmuir waves in plasma are usually generated by beams of superthermal electrons, so we consider the region of phase velocities up to 15 V T e and assume that there are no Langmuir waves with large phase velocities (smaller wavenumbers). The observation angle α is the angle between the symmetry axis of the radiating region and the vector k . In this case, we assume that k 0 = ( k min + k max )/2, and σ is less than the value of k 0. Fig. 1(b) shows the distribution of radiation ( Q ω ) as a function of the frequency of the transverse electromagnetic wave. The calculation results for this case are shown in Figs 1 and 2 for different σ. At a small standard deviation (e.g. σ = 0.1 k 0 , Figs 1a , b ) the radiation is concentrated in a narrow frequency range. A similar type of Langmuir spectra can be generated, for example, by a fast electron beam. With

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


and the fraction of mass of formed stars that are NSs iswith being the IMF, Ψ( t ⋆ ) is our best-fit SFH, and Θ NS ( M ⋆ ) is 1 for star mass ranges of 8 M ⊙ M 20 M ⊙ , and zero otherwise. We drop the metallicity dependence in Θ NS because we only consider a solar metallicity for the galaxy, as a result of our spectroscopic fit. t ⋆ is the time when the progenitor of the NS was formed, therefore satisfying t ′ = t ⋆ + t life , with t life being the lifetime of the progenitor before becoming an NS. We assume a t life = 0.02 Gyr, but our calculation is insensitive to this choice as the typical lifetime of these massive stars (∼0.01–0.03 Gyr) is much shorter than the timescale over which the SFH found for NGC 4993 is changing at late times. We assume a Chabrier IMF, but this choice is not relevant, as we are only exploring the high-mass end of the IMF. Assuming α = 0.002 and the distribution of Δ t NSM from Vangioni et al. ( 2016 , their Figure 3 for solar metallicity), and our best-fit SFH from Equation ( 1 ) with t 0 = 3 Gyr and τ = 0.3, we get an NS formation rate of and a BNS merger rate of for the whole galaxy. Errors reflect the uncertainty on the SFH, which dominates our errors: they represent the two central quartiles of the rates distribution computed with the SFHs of the pixel SED fitting over the galaxy. Given the sensitivity of the BNS merger event rate to the recent SFR of a galaxy, it is somewhat surprising that GW170817 occurred in an old, early-type galaxy. We therefore ask what is the probability of observing such an event in any early-type galaxy within the LIGO-detectable volume. To make this estimate, we integrate the stellar mass function of early-type galaxies from Weigel et al. ( 2016 ) and scale the per-solar-mass rate from Equation ( 2 ) to the mass contained within the LIGO-detectable volume (radius 80 Mpc). We find resulting in expected events. This calculation assumes that the SFH of NGC 4993 is representative of local early-type galaxies. In fact, much of the mass will be contained in more massive, and on average older and less star-forming, galaxies. We contrast this with a similar calculation for all galaxy types, using the cosmic SFR density from Gladders et al. ( 2013 ), finding and ∼0.5 expected events. This result shows that it is unlikely that we observed one such BNS merger with LIGO over the combined nine months of operations in an early-type galaxy. The assumptions in the calculation include the fraction of NS that form in binaries ( α = 0.002) and the delay time distribution, both coming from binary star models (where the progenitors of the BNS were already a bound system) and satisfying Milky Way constraints. If the BNS formation mechanism is via dynamical interaction, our result could point to a higher value of α or a shorter Δ t NSM for systems that recently underwent a galaxy merger, more so for those that have high stellar density (such as early-type galaxies). It is therefore of interest to know the

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 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 B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject 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 B-Model O B-Formula I-Formula I-Formula O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Instrument 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 B-Instrument 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 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-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O B-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 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


(e.g. Narayan et al. 2012 ; Yuan, Wu Bu 2012b ; Yuan et al. 2015 ). In the hydrodynamic (HD) simulation, there is no magnetic field, wind is found to be driven by the combination of gas pressure gradient and centrifugal forces. In the magneto-hydrodynamic (MHD) simulation, it is found that wind is driven by the combination of gas pressure gradient, magnetic pressure gradient and centrifugal forces (Yuan et al. 2015 , see also Moller Sadowski 2015 ). Recently, observations of both LLAGNs (e.g. Tombesi et al. 2010 , 2014 ; Crenshaw Kramemer 2012 ; Wang et al. 2013 ; Cheung et al. 2016 ) and the hard state of black hole X-ray binaries (Homan et al. 2016 ) show that winds are present in hot accretion flows. The reason for the existence of wind is also investigated by analytical works (e.g. Begelman 2012 ; Gu 2015 ; Mosallanezhad, Bu Yuan 2016 ). Bu et al. ( 2016a , b ) study whether wind can be produced beyond the Bondi radius. In these studies, the gravity of nuclear star cluster is taken into account. It is found that the radial profile of the gravity becomes flatter when stars gravity is taken into account. Also, it is found that wind cannot be produced in the presence of star gravity. Wind production can occur only within the Bondi radius of hot accretion flows. The simulations introduced above neglect radiative cooling. Non-radiative simulations of hot accretion flows can only be applied when the black hole accretes at very low rate, , where is the Eddington accretion rate (Sadowski et al. 2017 ). With the increase of mass accretion rate, radiative cooling effects will become important. Strong radiative cooling can decrease the gas pressure. As mentioned above, gas pressure gradient is an important force for driving wind. We can expect that when radiation becomes strong, wind should become weak. In this paper, we study how the wind strength changes with mass accretion rate. We are interested in wind due to the following two reasons. First, wind can take away mass, which can change the density profile of accretion flows. The change of density profile can affect the emitted spectrum of an accretion flow (e.g. Quataert Narayan 1999 ; Yuan, Quataert Narayan 2003 ). Secondly, it is now widely believed that AGN feedback plays an important role in the evolution of their host galaxies (e.g. Ciotti Ostriker 1997 , 2001 , 2007 ; Proga, Stone Kallman 2000 ; Proga 2007 ; Kurosawa Proga 2009 ; Novak, Ostriker Ciotti 2011 ; Gan et al. 2014 , 2017 ; King Pounds 2015 ; Ciotti et al. 2017 ). Wind can push away the gas outside an AGN. This can reduce the feeding rate of the central black hole. Also, the star formation rate may also be changed (e.g. Ciotti et al. 2017 ). In order to study wind feedback, we first need to study the strength of wind. The effects of radiative cooling on hot accretion flow have been taken into account recently (e.g. Wu et al. 2016 ; Ryan et al. 2017 ). In these papers, the effects of radiative cooling on wind strength have not

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


we do not consider the spherical reprocessor further. Figure 6. The spherical reprocessor of Brightman Nandra ( 2011 ), compared to the data. Colours as for Fig. 5 . 5 MYTORUS The toroidal X-ray reprocessor model, mytorus (Murphy Yaqoob 2009 ; Yaqoob et al. 2010 ), is illuminated by a central X-ray continuum source. The global covering factor of the reprocessor is 0.5, corresponding to a solid angle subtended by the structure at the central X-ray source of 2 (an opening half-angle of 60 o ). mytorus self-consistently calculates the Fe K α and Fe K β fluorescent line emission and includes the effects of absorption and Compton scattering on both the continuum and lines. mytorus offers the ability to leverage constraints on the Fe K line emission and spectral curvature together, to obtain both the global and line-of-sight column density. The model is therefore one of the most powerful available for fitting X-ray spectra. Although the nominal covering factor is fixed at 50 per cent of the sky as seen by the continuum source, one can model other physical possibilities using the ‘decoupled’ mode that allows for a different line-of-sight column to the gas responsible for reflection (the Fe line emission strength can still be linked self-consistently to the column of the reflector). Such a decoupling is often required in spectral analyses of high-quality broad-band X-ray spectra, because the column density in and out of the line-of-sight column density are not always the same (e.g. Risaliti et al. 2009 ; Marchese et al. 2012 ; Yaqoob et al. 2015 ). In our fits, a single power law was assumed to be seen in transmitted and scattered light, and this was implemented by linking the photon indices of these components in all fits. The general model form was where MYTZ designates the line-of-sight absorption, MYTS the scattered X-rays, and MYTL the line emission (both from material out of the line of sight, hereafter referred to as the ‘global’ gas), from mytorus . zg(10) represents 10 individual Gaussian lines (Table 2 ) present in the data that are not accounted for by the mytorus model. gs is a Gaussian smoothing component convolved with the torus neutral Fe line profile, using a kernel of σ = 30 eV at 6 keV. The power-law continuum is split over two sightlines, one is absorbed my MYTZ and the other is absorbed only by N H , a full-covering column of gas whose lower limit is set at the Galactic line-of-sight absorption, but whose upper limit is not constrained. 5.1 Coupled model fits Taking the ‘Coupled Model’ to mean one for which the line of sight and global column densities are tied together, we performed two variations on this fit. First, the angle of the global gas was fixed at θ = 90 o and the normalization of the global-scattered light and line emission were directly tied to the illuminating continuum. This model did not provide an acceptable fit to the data, yielding χ 2 = 709/438 dof with , while the full covering gas component gave , exceeding

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


light reflections. To further reduce the negative effects of the background filament radiation, its spectrum was recorded under high vacuum conditions (5 × 10 −8 mbar) and subtracted from measured molecular spectra. The electron energy was calibrated by measurement of the cross section of the (0, 0) band of (C 3 Π u –B 3 Π g ) at 337 nm (Zubek 1994 ; Országh et al. 2012 ) and the He i (1s2p 3 –1s4d 3 D 1,2,3 ) 447.14 nm emission line (NIST 2015 ). The (C 3 Π u –B 3 Π g )(0, 0) cross section exhibits a pronounced peak at 14.1 eV. The cross section for the He i (1s2p 3 –1s4d 3 D 1,2,3 ) transition exhibits a step at 23.736 eV. The electron energy calibration was performed in the mixture of C 2 H 2 :N 2 :He 1:1:1 (established by an absolute pressure gauge) to avoid problems with different charging effects of the electron monochromator electrodes in different gases. The difference between energy scales calibrated by nitrogen and helium was less than 0.015 eV. Two different measurement modes were used in the present study: (i) fluorescence spectra induced by monoenergetic electrons at fixed electron energy, and (ii) PECs—the intensity of photons of a specific wavelength detected as a function of the electron energy, sometimes referred to as the relative excitation function. PECs are proportional to a dissociative excitation-emission cross section (DEE CS) and can be calibrated to its absolute values. Additionally, PEC curves can be used for determination of the apparent thresholds in PEC, which are related to the thresholds for the dissociative excitation reactions (Stano et al. 2003 ). 3. Results and Discussion 3.1. Spectrum We have recorded the electron-induced UV–VIS spectrum of acetylene in the spectral range from 190 to 700 nm. The spectral range 190–257 nm was recorded at an electron energy of 70 eV and low resolution of the optical monochromator (2 nm FWHM), and the rest was recorded at 50 eV and higher resolution of the optical monochromator (0.4 nm FWHM). The spectral range 305–530 nm is presented in Figures 2 (a) and (b). All the spectra presented in this paper were corrected for the spectral response of the apparatus. The intensities in the spectra were calibrated to absolute values according to the known emission cross sections for the dissociative excitation-emission channel, which we will give more details on later. The spectra exhibit lines and bands corresponding to dissociative excitation of acetylene by electron impact (Beenaker et al. 1975 ; Tsuji et al. 1975 ). Figure 2. Acetylene spectrum in the wavelength region of (a) 310–420 nm and (b) 420–660 nm at electron energy 50 eV with slits set to 100 μ m (optical resolution ∼0.4 nm). Due to the lower sensitivity of the optical system in the region 190–257 nm, it was necessary to decrease the resolution of the optical monochromator (using 500 μ m for both slits). We were able to identify two C i lines at 193.1 nm (C i (2s 2 2p3s 1 P 0 –2s 2 2p 2 1 D)) and 248.4 nm (C i (2s 2

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the spectrum, particularly below 4400 Å; in the data of WR102, a broad peak in the degree of polarization (∼1 per cent deviation) and polarization angle (∼8° deviation) is seen between 7100 and 7600 Å. The latter feature cannot be a line effect as it is located in a region of the spectrum that is devoid of strong lines, and although its origin remains unknown (the details of our investigations are given in Section 3.2 ), we are confident it is of spurious nature. Given these considerations, the analysis presented in the rest of this study was performed without the spectral region below 4400 Å in WR93b, and the range 7100–7600 Å in WR102. Figure 1. Spectropolarimetric data of WR93b (left) and WR102 (right). The panels, from top to bottom, respectively, the degree of polarization (red) and best Serkowski law fit (black); the residuals after Serkowski fit removal (orange); the polarization angle (blue); Stokes I (grey) and line identification. The grey areas represent the discrepant regions of the spectrum described in Section 3.1 . Excluding these wavelength ranges, the polarization in the direction of WR93b and WR102 rises up to ∼4.5 per cent and ∼10 per cent, respectively. Their polarization angles have distinct behaviours: WR93b exhibits a constant polarization angle of θ = 28.2°, whereas the polarization angle of WR102 shows a downward trend that can be fit with a line of the form θ = −1.08 × 10 −3 λ + 18.4 deg. A non-zero Δθ/Δλ can be explained either by the superposition of intrinsic and interstellar polarization (Coyne 1974 ) or by the presence in the line of sight of dust clouds with different particle sizes and alignments (Coyne Gehrels 1966 ). The merit of these interpretations is discussed in Section 3.5 . 3.2 7300 Å feature in WR102 In Section 3.1 , we highlighted a prominent feature in WR102 spanning the wavelength range 7100–7600 Å. This peak was labelled as spurious and disregarded in our analysis. Here, we detail the steps taken in investigating the nature of this feature. First, we explored whether the spike in polarization is intrinsic to the data. The fact that the feature is not associated with any strong line (as would be expected for a line effect present in the WR star) is, however, inconsistent with this idea. Additionally, plotting the polarization, calculated for each of the 12 sets of observations at four half-wave retarder plate angles (see Fig. 2 ), reveals that the shape and orientation (peak or trough) are highly variable from set to set, and no one set is consistent with another. To formally check whether the data are spurious, we look at the difference in instrumental polarization corrections (Δε, see Maund 2008 ) in this region of the spectrum. This property is expected to be 0 for polarization signals ≤20 per cent, and deviations indicate that the polarization does not reflect a real signal (Maund 2008 ). In Fig. 2 , it is clearly visible that Δε is consistent with 0 across the spectrum but deviates

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