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Our understanding of the problem of bubble stream RADAR reflectivity has been greatly helped by discussions with Dr. Jason Hofgartner of the Jet Propulsion Laboratory; it is our pleasure to acknowledge our indebtedness to him. We also thank the anonymous reviewer, who led us to significantly clarify our manuscript.


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

this exercise is not to make a complete analysis of the origin of the spiral arm that we detect with our observations, but to test the viability of a scenario. We investigated the effect of each of the aforementioned parameters, and inspected the results visually. Figure 8 shows the time evolution for a given simulation, over a span of several hundreds years. For this example, we took t 0 = 2 yr and δt = 0.3 yr. Shortly after t = t 0 a spiral, devoid of particles, appears in the disk (where the particles originally were), but its width decreases for each orbit owing to Keplerian shear. On the other hand, the grains that experienced the wind are set on an elliptical orbit once the wind has stopped (and provided that β wind is not too strong), with their apocentre farther than the original radius of the disk. All these particles tend to travel all-together, therefore, a spiral arm appears in the image at two distinct moments per orbit: when the group of particles is entering or leaving the birth ring (middle and rightmost panels of Fig. 8 ). In our simulations, given that collisions are not taken into account, this phenomenon will persist over time. Nonetheless, if the optical depth is low enough, the train of particles may not collide too often with other particles of the birth ring, and thus the spiral could be long-lived. A movie of the simulation can be found online 4 . Fig. 8 N-body simulation of the effect of anisotropic stellar winds on an ensemble of massless particles, creating a spiral arm in the disk. Nonetheless, the δt timescale is far too long compared to the stellar rotation period for the CME to stay in one preferential direction (0.3 yr compared to ~5 days; Watson et al. 2006 ). The stellar wind would most likely sweep across the entire disk multiple times. If we require δt to be much lower than a typical stellar rotation period, or of the order of the typical duration of the flaring event reported by Uzawa et al. (2011) , then the corresponding β wind value becomes much higher. As an example, for δt = 0.5 days, we find that a similar spiral arm requires β wind = 7500, a value that seems unrealistically high. Indeed, β wind is directly proportional to stellar mass loss rate and inversely proportional to grain sizes following the relation ( Augereau Beust 2006 ): with C D a factor close to 2, Ṁ ⋆ the stellar mass loss rate, v sw the speed of the stellar wind, G the graviational constant, and ρ the dust density. Even though TWA 7 is younger than AU Mic, and therefore potentially more active, a β wind = 7500 value seems rather improbable, as it would require extremely small dust grains (which would not scatter the stellar light efficiently in H -band) or an extremely large mass loss rate. For AU Mic, Augereau Beust (2006) found Ṁ ⋆ ~ 47 Ṁ ⊙ in quiescent state, ~ 2450 Ṁ ⊙ during flares (leading to β wind ~ 40−50), which averaged to ~ 300 Ṁ ⊙ (assuming flares occur 10% of the time). This means that the flares of TWA 7 should be


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope I-Telescope O O O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey B-Citation I-Citation I-Citation I-Citation O O O O O O B-Survey B-Citation I-Citation I-Citation I-Citation O O B-Survey B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation 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 B-CelestialObject I-CelestialObject O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

it is difficult to assess the probability that such candidates will be confirmed as pulsars, because confirmation strategies differ between surveys and usually limit the number of reobservations n REOBS to a handful because of constraints on telescope time. As a result, in an extreme case like PSR J1929+1357, the probability of confirming a discovery is approximately , so that the probability of making a confirmed discovery is . In 2013, with and a reasonable value of , the probability of making a confirmed discovery of a pulsar was 3 × 10 −4 . We note that, ideally, reobservations should also be made on a specifically designed set of timescales in order to capture pulsars with the wide range of switching timescales that we now see to be possible in this class of objects. In the case of PSR J1929+1357, it was fortunate that the pulsar was ON during the second attempted reobservation; in the next 93 observations, it was OFF. Had the first 5 reobservations been unsuccessful, it is possible that even such a strong pulsar would remain unconfirmed. Similar pulsars, but with one tenth of the flux density, must surely exist and would be clearly detected in the survey observations, particularly with the high sensitivity of the Arecibo Telescope used for the PALFA survey, but the case for extended reobservation efforts would be even less compelling: unconfirmed detection would be attributed to radio-frequency interference or to the detection of a normal pulsar in a distant sidelobe. For these reasons, there may be as many as several thousand strong pulsars like PSR J1929+1357 in the sky, which happen to be OFF when surveyed or, if ON, are OFF during confirmation observations. Similar but less severe selection effects preventing the discovery of objects like other long-term intermittent pulsars also contribute to what must be a population of neutron stars of significant size compared to that of normal pulsars. As we noted earlier, RRATs also suffer similar selection effects in one-pass surveys. It is likely that UTMOST (Caleb et al. 2016 ) and upcoming new projects, like CHIME (Bandura et al. 2014 ) and MeerTRAP (B. W. Stappers et al. 2016, in preparation) on MeerKAT, will be useful for finding more such objects as they will make many searches of the same piece of sky on various timescales for single-pulse and periodic sources. The discovery of two new long-term intermittent pulsars, PSRs J1910+0517 and J1929+1357, significantly expands the known population of such objects, whose properties are summarized in Table 2 . Although their number is still small (only five such pulsars), we are now in a position to make a few general remarks regarding their properties. They seem to have a rather narrow range of spin periods, from about 0.3 to 0.9 s. Furthermore, there seems to be a positive correlation between the spin period and its derivative, as we can see from their ON positions in the P – diagram (Figure 7 ). This correlation is similar to that observed


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Acknowledgements The authors would like to thank Saleem Zaroubi and Adi Nusser for providing useful suggestions on this work. KKD would like to thank the University Grant Commission (UGC), India for support through UGC-faculty recharge scheme (UGC-FRP) vide ref.no. F.4-5(137-FRP)/2014(BSR). SM acknowledges the financial support from the European Research Council under ERC grant number 638743-FIRSTDAWN.


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

off free electrons (Heitler 1954 ; Chen Kamionkowski 2004 ), and at high enough energies undergo electron–positron pair production (PP). We here distinguish the cross-section for PP off of the CMB (Agaronyan, Atoyan Nagapetyan 1987 ; Ferrigno, Blasi De Marco 2005 ), atomic and ionized hydrogen and helium, as well as free electrons (Joseph Rohrlich 1958 ; Motz, Olsen Koch 1969 ; Zdziarski Svensson 1989 ). Photons also undergo photon–photon scattering where the injected photon transfers part of its energy to a CMB photon (Svensson Zdziarski 1990 ); however, this process is highly subdominant in the redshift range considered here. The mean free paths (mfp) at mean gas density for selected processes undergone by injected electrons, positrons, and photons are outlined in Fig. 2 for a neutral 10 7 M ⊙ halo at redshift 40. Solid and dot–dashed lines show interactions for the leptons while the dashed show those for photons. The dashed red, magenta, and orange lines show photoionization, Compton scattering, and pair creation off of the gas field, respectively. Electroionization and excitation are shown in green and blue, IC scattering in black, and annihilation via positronium for positron in purple. For a fully ionized halo, the yellow line shows the mfp for Coulomb interaction. For each process, the lines indicate the mfp at the average density of the halo while the shading either side of the curves shows the mfp at r vir and r vir/100 . Figure 2. mfpin units of the virial radius for the various interactions undergone by injected particles within a neutral gas 10 7 M ⊙ halo at redshift 40. Solid lines show interactions for charged particles and dashed for photons. The grey line indicates the virial radius of the halo. Processes shown are photoionization (red), Compton scattering (magenta), and pair creation off of the gas (orange) for photons and ionization and excitation (green and blue) for electrons, as well as IC scattering (cyan) and annihilation via positronium for positrons (purple, dot–dashed line). In all cases, lines show the mfp for the process at the average density of the halo, while the shaded regions either side indicate the mfp at r vir and r vir /100. For reference, the yellow curve shows the mfp for Coulomb scattering in an equivalent, fully ionized halo. The grey line is indicative of the halo's virial radius. Particles with energies such that their interaction mfp are no longer smaller than or comparable to the virial radius will readily escape the halo without either interacting with the gas and/or depositing energy. For the DM annihilation products considered here, the primary interaction of the injected electrons and positrons is IC scattering (injected photons first undergo electron/positron pair creation off of the gas field). The actual energy transfer process occurs via the secondary particle produced in those interactions, in this case, the upscattered IC photons. Therefore, the energy spectrum of the secondary cascade


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The authors would like to thank the anonymous reviewer for constructive comments that improved the manuscript. We also thank Claire Cousins and Clara Blättler for useful discussions. This work was supported by a grant from the Simons Foundation (SCOL awards 339489 to SR and 290357 to LK). This work has made use of the MUSCLES M dwarf UV radiation field database.


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

arise from a multiphase ISM. This is also supported by the maximum velocity of the CO (2–1) emission (FWZI/2 ∼ 1000 km s −1 ; Fig. 1 b), which is consistent with the maximum velocity of a warm molecular outflow traced by blueshifted OH absorption (∼1200 km s −1 ; Veilleux et al. 2013 ) and H α emission (≥1000 km s −1 ; Heckman, Armus Miley 1990 ). As seen in other LIRGs (e.g. NGC 1068; García-Burillo et al. 2014 , NGC 3256; Sakamoto et al. 2014 , and NGC 1614; Saito et al. 2017 ), molecular outflows are often spatially extended (a few kpc) and concomitant with (or entrained by) ionized gas outflow. Considering all pieces of evidence described above and some similarities with other LIRGs, we suggest that the four peaks of the broad CO (2–1) components trace molecular outflows in NGC 6240. We derive physical parameters of the molecular outflows found in NGC 6240. The spatially resolved map (Fig. 3 c) allows us to estimate the mass and projected distance of the line width peaks from the launching points. We assume the launching points are the double nuclei, that is, the northern and eastern (southern and western) components of the molecular outflow come from the northern (southern) nucleus (see grey arrows in Fig. 4 ). This spatial configuration is supported by radio continuum observations with very long baseline interferometers (Gallimore Beswick 2004 ; Hagiwara, Baan Klöckner 2011 ), showing that the northern nucleus has an east–west bipolar structure. The direction of those bipolar structures is similar to our assumed morphology of the molecular outflows. We also assume that the inclination (α), CO (2–1)/CO (1–0) line intensity ratio, and CO (1–0) luminosity to H 2 mass conversion factor of the molecular outflows in NGC 6240 are 45°, unity, and 0.8 M ⊙ (K km s −1 pc 2 ) −1 , respectively, for the sake of simplicity. Figure 4. Peak velocity map of the broad component. The velocity field in colour scale ranges from 6850 to 7350 km s −1 . Data points around the four peaks in Fig. 3 c are shown. To estimate the mass outflow rate (), we employ the expression, where v out, proj is the projected velocity of the outflow, is the gas mass of the outflow, R out, proj is the distance from the launching point to the outflowing gas, and α is the inclination of the outflow. This equation assumes a uniformly filled cone geometry (Maiolino et al. 2012 ). All derived parameters related to are listed in Table 1 . v out, proj of the northern and eastern (southern and western) outflows is derived by using the projected velocity of the outflowing gas (Fig. 4 ) and the systemic velocity of the northern (southern) nucleus of 7122 (7164) km s −1 in the radio LSRK velocity frame (Hagiwara 2010 ). Table 1. NGC 6240 molecular outflow properties. The derived mass of each broad component is ∼10 7.9–8.2 M ⊙ (∼10 8.7 M ⊙ in total, which is consistent with the value derived from unresolved CO data; Cicone et al. 2014 ). Since the ionized gas mass of the butterfly


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magnetic field and the brightness ridges on the sky. 2. Data sets Planck observed the sky polarization in seven frequency bands from 30 to 353 GHz ( Planck Collaboration I 2014 ). In this paper, we only use the data from the High Frequency Instrument (HFI, Lamarre et al. 2010 ) at the highest frequency, 353 GHz, where the dust emission is the brightest. This is the best-suited Planck map for studying the structure of the dust polarization sky ( Planck Collaboration Int. XIX 2015 ; Planck Collaboration Int. XX 2015 ). We use the Stokes and maps and the associated noise maps made with the five independent consecutive sky surveys of the Planck cryogenic mission, which correspond to the DR3 (delta-DX9) internal data release. We refer to previous Planck publications for the data processing, map-making, photometric calibration, and photometric uncertainties ( Planck Collaboration II 2014 ; Planck Collaboration VI 2014 ; Planck Collaboration V 2014 ; Planck Collaboration VIII 2014 ). The and maps are corrected for spectral leakage as described in Planck Collaboration Int. XIX (2015) . As in this first Planck polarization paper, we use the IAU convention for the polarization angle, measured from the local direction to the north Galactic pole with positive values towards the east. For the dust total intensity at 353 GHz we use the model map, , and the associated noise map, derived from a fit with a modified blackbody of the Planck data at GHz, and IRAS at m ( Planck Collaboration XI 2014 ). This map has a lower noise than the corresponding 353 GHz Stokes Planck map. Furthermore, is the dust specific intensity corrected for zodiacal emission, cosmic microwave background (CMB) anisotropies, and the cosmic infrared background (CMB) monopole. The and maps are initially at 48 resolution, and at . The three maps are in HEALPix format 2 with a pixelization . To increase the signal-to-noise ratio of extended emission, we smooth the three maps to resolution using the Gaussian approximation to the Planck beam. We reduce the HEALPix resolution to (71 pixels) after smoothing. To finely sample the beam, we also use the smoothed map with in Appendix A . For the polarization maps, we apply the “” routine of HEALPix that decomposes the and maps into and maps, applies the Gaussian smoothing in harmonic space, and transforms the smoothed and back into and maps at resolution. Most of our analysis is based on the , , and maps, but we also use the maps of the de-biased polarization fraction and angle produced by Planck Collaboration Int. XIX (2015) . The contribution of the CMB polarization to the and maps at 353 GHz is negligible for this study. 3. Structures in the polarization maps We introduce dust polarization (Sect. 3.1 ) and present all-sky images highlighting localized structures in the dust Stokes and maps correlated with corresponding features in intensity (Sect. 3.2 ). Fig. 1 Top : all-sky Mollweide display of the dust emission intensity at 353 GHz after


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line and the corrected as a dashed line after an overall shift of 0.09 dex; different markers and colors stand for different reporters. The right panel shows the distribution of differences between A (Li) LAMOST and A (Li) H.Res. and the result of the Gaussian fit overplotted with a red solid line. Table 1 Information of the Li-rich Giants Reported by Previous Works 3.3.2. Random Errors In our results, 2746 giants have repeated observations; these could be used to estimate the random errors. We plotted the differences in A (Li) between repeated observations as a function of S/N, T eff , log g , [Fe/H], and A (Li) in Figure 6 . In panel (a), all the 2746 objects with repeated observations are included, which shows that the random errors are sensitive to the S/N decreasing from 0.3 to 0.1 dex with an increasing S/N. In order to avoid the influence of the S/N, only 1118 objects with high-quality data (S/N ≥ 200) were used in the rest panels. Panels (b) and (c) show that the random errors increase from 0.1 to 0.2 dex with increasing T eff or log g , which may be due to the fact that the lithium line at 6708 Å is stronger at low T eff or log g . The random errors have no obvious relation to the [Fe/H], as shown in panel (d), which may be because the strength of the lithium line has no obvious relationship to [Fe/H]. And panel (e) shows that the scatter of the differences of A (Li) remains same when A (Li) goes from 2.0 to 4.5 and is slightly larger in the bin of 1.5 ≤ A (Li) 2.0. Note that the lithium line at 6708 Å is strong enough to be detected when A (Li) is higher than 2.0. The typical value of random errors is 0.2 dex. Figure 6. Differences in A (Li) between multiple observations vs. S/N, T eff , log g , [Fe/H], and A (Li). All the 2746 objects with repeated observations are included in panel (a); only 1118 objects with high-quality data (S/N ≥ 200) were used in the rest panels. The bin sizes are 100, 200 K, 0.3 dex, 0.3 dex, and 0.5 dex, respectively. The red dots are the mean value and the error bars are the standard deviation of the differences in every bin. 4. Results The giants with A (Li) ≥ 1.5 are usually defined as Li-rich giants. In our results, 10,535 Li-rich giants are identified. Their information is listed in Table 2 , including the LAMOST ID, positions, stellar atmospheric parameters provided by LASP, A (Li), and the observed date. Figure 7 shows the histograms of the number of our Li-rich giant sample versus T eff , log g , and [Fe/H], respectively. For the distribution of temperature, there is a peak around 4800 K, and there might be another peak around 5100 K. There are two clear peaks around log g ∼ 2.5 and 3.5 dex, the first is corresponding to the red giant branch and red clump stars. In addition, the distribution of metallicity shows a clear peak around [Fe/H] ∼ −0.15 and a symmetric profile from ∼−0.8 to +0.5 dex. For the stars with metallicity lower than −0.8 dex, there seems to be a second peak in the range of −1.5 to


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This work is supported by NSFC grants under contracts 41774157, 41231069, 41231068, 41474147, 41574168, and 41421003, and the Specialized Research Fund for State Key Laboratories. The work was carried out at National Supercomputer Center in Tianjin, China and the calculations were performed on TianHe-1 (A). The authors appreciate the invaluable suggestions and comments that were provided by the anonymous reviewer. Special thanks go to Dr. Xiang in our laboratory for the instructive discussions and helpful suggestions to amend the paper.


O O O O O O O B-Grant O O O O O O O B-Archive I-Archive I-Archive I-Archive O O O O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O O O O O O B-Telescope I-Telescope I-Telescope O O O O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O O O O B-Organization O O O O O O O O O B-Telescope I-Telescope I-Telescope I-Telescope O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O O O O B-Organization I-Organization I-Organization B-Organization O B-Telescope O B-URL O O O O B-Telescope B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-URL O O O O B-Organization O O O O O O O O O O O O O B-Collaboration I-Collaboration I-Collaboration O O O O O O O B-Database O O O B-Database O O O O O O B-Organization B-Location I-Location O O O O O O O O O B-Survey I-Survey I-Survey I-Survey I-Survey O O O O O O O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization O O O O O O O O O O O B-Survey I-Survey I-Survey I-Survey I-Survey I-Survey I-Survey I-Survey I-Survey I-Survey B-Survey B-URL O O O O B-Organization I-Organization I-Organization B-Organization O B-Telescope O O O O B-Location I-Location I-Location I-Location O O B-Organization I-Organization I-Organization O O B-Location B-Observatory I-Observatory I-Observatory I-Observatory I-Observatory I-Observatory O O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Survey O O O O O B-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Dataset I-Dataset O O O O B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O O B-Organization O B-Grant O O O O O B-Software O O O O O B-Organization I-Organization I-Organization O O O B-Grant O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Grant I-Grant I-Grant O O O B-Grant O B-Organization O O B-Organization I-Organization I-Organization I-Organization O O O O O B-Software O O O B-Software O O O O B-Citation I-Citation I-Citation O


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is: (1) ID number used for cross-reference with the web version ofthis catalogue; (2) Name of the system and optical counterpart when known; (3) Peak X-ray flux in erg s cm, standardized to the 210 keV band. To do so, we begin with the X-ray flux that has been published in the literature (or in archive). We assume a power-law spectrum with a photon index ( Belloni et al. 2011 ) and the total neutral Galactic Hydrogen column density (), published by Kalberla et al. (2005) . If there is a measured published in literature derived from direct X-ray spectral analysis, we use this instead of the radio-derived interstellar one; (45) Optical or IR magnitude in the peak of the outburst and quiescence, respectively, in the AB system. To document the original observed band, we provide the name of the band in its original system; (6) Optical Galactic extinction [] reported in the literature. If unknown, we list the total Galactic line-of-sight absorption given by the Schlafly Finkbeiner (2011) dust maps; (7) Reported or estimated orbital period of the binary in hours; (8) References for all the parameters above. Table A.3 lists the optical/NIR photometry of the dynamical BHTs in quiescence: (1) Preferred name of the dynamically confirmed BHT; (29) Quiescent magnitudes of the dynamically confirmed BHTs. All the magnitudes were transformed to the AB system using the transformation coefficients taken from Table 2 in Frei Gunn (1994) and Eqs. (5) in Blanton et al. (2005) . To document the original observed band, we provide the name in its original system; (10) References of the magnitudes. Table A.4 provides the dynamical parameters of the BHTs: (1) Preferred name of the dynamically confirmed BHT; (2) Spectral type of the companion star; (3) The orbital period of the binary in hours; (4) The radial velocity of the companion star () in ; (5) The mass function of the BH in ; (6) The mass of the BH () in . If there is an uncertain value, we prefer to show a range of masses; (7) The binary mass ratio ; (8) The inclination of the system () in degrees; (9) The rotational broadening () in ; (10) References of all the parameters. At the bottom of each table, we present a detailed list with the particularities marked in Table A.1 and Table A.2 . This census is the most updated available and, compared to previous catalogues (e.g. Gottwald et al. 1991 ; Chen et al. 1997 ; Remillard McClintock 2006 ; Ritter Kolb 2003 ; Liu et al. 2006 , 2007 ), represents a substantial improvement in both statistics and observational parameters. While it only focuses on the population of BHs, it provides a thorough and more complete coverage of optical and NIR data and dynamical parameters 2 . 3. Analysis of the spatial distribution of BHTs Table A.1 allows us to perform a statistical study of the distribution of BHTs in the Galaxy. In Fig. 2 , we plot the 35 objects with estimated distances as viewed from the pole of the Milky Way. Filled orange circles represent the


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ACKNOWLEDGEMENTS We are grateful to the referee for helpful comments on the manuscript. This work was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. EdUHK 28300518) and the grants from the Education University of Hong Kong (RG2/2019-2020R and RG7/2019-2020R).


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O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject B-Citation I-Citation 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 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 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-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O B-Organization I-Organization I-Organization B-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject B-Citation I-Citation I-Citation I-Citation O B-CelestialObject I-CelestialObject B-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O B-CelestialObject I-CelestialObject 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 B-Dataset I-Dataset I-Dataset 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 B-Citation I-Citation I-Citation I-Citation O B-Identifier I-Identifier I-Identifier I-Identifier O O O O O O O O O O O O O O O O O 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

short ones (lasting a few days) and superoutbursts, which can last two weeks or longer in their rather bright ‘plateau’ phase. Typical superoutburst cycle lengths of these ‘ordinary’ SU UMa stars range from 100–500 d. Two additional subgroups can be distinguished: WZ Sge stars have longer superoutburst cycle lengths (several thousand days) and lack the normal short outbursts, while ER UMa-type dwarf novae are characterized by very short superoutburst cycles (20–40 d), and even more frequent normal outbursts in between. More than four decades ago, periodic ‘superhumps’ were detected in the SU UMa star VW Hyi (Vogt 1974 ; Warner 1975 ) during a plateau phase; later they turned out to be a characteristic feature of all SU UMa stars, but they also appear occasionally in other CV types, as classical nova remnants and nova-like stars (Patterson 1999 ). Since then, and till now, most observational efforts on SU UMa stars have been concentrated on the detection of superhumps and the determination of their properties (Kato et al. 2017 and the previous papers of that series), widely neglecting the systematic coverage of the general outburst behaviour of these and other dwarf novae. The semiregular outburst behaviour of DNe has attracted the interest of amateur astronomer societies for a long time, such as the American Association of Variable Star Observers (AAVSO), the British Astronomical Association (BAA), and the Royal Astronomical Society of New Zealand, Variable Star Section (RASNZ, VSS), and very valuable long-term light-curve studies have already been published decades ago, containing catalogues of individual outbursts with their main properties as maximum brightness, amplitude, width, and classification according to light-curve shape, as well as some statistical analyses of these properties. As typical examples, we can mention here extensive studies on SS Cyg (Mattei, Saladyga Waagen 1985 ), U Gem (Mayall 1957 ; Mattei et al. 1987 ), and VW Hyi (Bateson 1977 ). To our knowledge, no long-term studies like those of the 1960s and 1970s have been published more recently. Simultaneously, there was and still is a boom in the number of detections of new CVs, especially dwarf novae. The VSX AAVSO catalogue (Watson 2006 ) lists more than 9000 DNe, but does not give any cycle length information. The latest online version of the CV catalogue of Ritter Kolb ( 2003 , version 7.24, 2017 February) list a total of 852 DNe with known orbital period, 631 of them (74 ) classified as SU UMa, ER UMa, or WZ Sge stars. Only for 121 (19 ) are some cycle length data given. Discounting the doubtful cases, Ritter Kolb ( 2003 ) give, for a total of only 73 cases (12 ), reliable information on the lengths of the superoutburst cycle (hereafter ‘supercycle length’). However, no references are given for the cycle lengths, and it is often very difficult and time-consuming to check these data. Therefore, we here determine supercycle length values of other SU UMa stars, for which


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The calculations were carried out in the CFCA cluster of National Astronomical Observatory of Japan. We thank Andrea Mignone and the PLUTO team for the possibility to use the PLUTO code. We especially thank to Claudio Zanni for technical support. The visualization of the results used the VisIt package. V.B.-R. acknowledges support by the Spanish Ministerio de Economía y Competitividad (MINECO) under grants AYA2013-47447-C3-1-P. V.B.-R. also acknowledges financial support from MINECO and European Social Funds through a Ramón y Cajal fellowship. This research has been supported by the Marie Curie Career Integration Grant 321520. B.M.V. acknowledges partial support by the JSPS (Japan Society for the Promotion of Science): No. 2503786, 25610056, 26287056, 26800159. B.M.V. also acknowledges MEXT (Ministry of Education, Culture, Sports, Science and Technology): No. 26105521 and RFBR grant 12-02-01336-a. M.P. is a member of the working team of projects AYA2013-40979-P and AYA2013-48226-C3-2-P, funded by the Spanish Ministerio de Economía y Competitividad.


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

envelope for the AGB case, apparently because outward energy transport by spiral shocks is impeded by a dense inner envelope in the RGB case. For the volume-integrated energy terms (normalized by the total initial energy), there was a high level of agreement between the two runs, but with a few notable differences. The potential energy term involving the primary core and envelope is relatively more important in the AGB case (higher particle mass, more centrally condensed envelope), while the potential energy terms involving the secondary and envelope and self-gravity of the envelope are relatively more important in the RGB case (larger envelope mass). Our setup can eventually be improved by using a synchronously rotating primary initialized at the Roche limit separation (MacLeod, Ostriker Stone 2018 ; Reichardt et al. 2019 ), although this comes at a much higher computational cost. Radiative transfer and a more realistic non-ideal equation of state are needed. Including these ingredients will allow us to model ionization and recombination, radiative cooling, and convection, all of which are likely important for the budget and redistribution of energy in the envelope, and more accurate modelling of envelope unbinding. Despite these caveats, the projection of to unbind the envelope suggests that the universal failure in previous simulations to eject it without recombination is unlikely a consequence of insufficient physics, but the result of a combination of numerical limitations and insufficient run time. Nevertheless, the need to improve both the physics and the numerical capabilities of simulations remains, while also expanding into new regions of phenomenologically relevant parameter space. APPENDIX A: INITIAL CONDITIONS Initial profiles for the AGB primary star used are presented in Fig. A1 . We refer the reader to Chamandy et al. ( 2019a ) for the same profiles for the RGB star used. Figure A1. Top panel: radial profile of gas density for the AGB star modelled using mesa (thick orange curve) and the envelope of our 3D AGB star in the simulation at t = 0 (thin black curve). Middle panel: comparison of the internal energy density profiles in the mesa model, the simulation initial envelope, and the mesa model with the equation of state replaced with an ideal gas equation of state, as in the simulation (dashed red curve). Bottom panel: comparison of (negative of) potential energy density profiles in the mesa model and the simulation initial envelope. APPENDIX B: ENERGY NON-CONSERVATION The degree to which energy conservation is satisfied for our AGB run (denoted Model A) and two lower resolution AGB runs (Models B and C) is shown in Fig. B1 , where the fractional change in the total energy (accounting for flux through the domain boundaries) is plotted. The level of adherence to energy conservation is sensitive to the resolution around the primary core particle, and, after the first periastron passage, also to the resolution around the


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

the UDGs: to −15.5 mag, and M * = 5 × 10 7 to 5 × 10 8 M ⊙ . The slanted solid lines represent the varying surface brightness, = 23, 24, 25, 26, and 27 mag arcsec −2 (from left to right). For given surface brightness, the larger the UDGs are, the brighter (more massive) they are. The stellar masses of the UDGs are much lower than those of the bright red sequence galaxies. Figure 6. Left and middle panels: circularized effective radii vs. r ′-band absolute magnitudes (lower x -axes) and stellar masses (upper x -axes) of the UDGs and other galaxies in Abell S1063, Abell 2744, and the parallel fields. Symbols are the same as in Figure 5 . Solid lines represent isosurface brightness magnitudes of = 23, 24, 25, 26, and 27 mag arcsec −2 from left to right. Right panels: red line histograms are for the UDGs and LSB dwarfs in Abell S1063 and Abell 2744, and gray line histograms are for the UDGs in Coma. The numbers and dotted lines represent mean values of Sérsic index n for UDGs. In the right panels of Figure 6 we plotted the histograms of effective radii for Abell S1063 and Abell 2744 in comparison with that of the Coma UDGs (Yagi et al. 2016 ). The mean values, kpc for Abell S1063 and kpc for Abell 2744, are similar to that of the MW-sized UDGs in Coma, kpc. The histograms of the combined sample of UDGs and LSB dwarfs are similar to those of the large UDGs in Coma. 3.5. Spatial Distributions of the UDGs Figure 7 (left panels) displays the spatial distribution of the UDGs, LSB dwarf galaxies, and bright red sequence galaxies in the Abell S1063 and Abell 2744 fields. The circles in the left panels represent the boundaries of the radial bins used for deriving radial number density profiles. We excluded the central circular region in the UDG survey because of high surface brightness of the central galaxy. Figure 7. Spatial distributions (left panels) and radial number density profiles corrected for detection completeness (right panels) of the UDGs (large red starlets), LSB dwarfs (small red starlets), and bright red sequence galaxies (blue circles) in Abell S1063 and Abell 2744. Black dots denote the compact galaxies with . The circles in the left panels represent the boundaries of the radial bins used for deriving radial number density profiles. The central gray circle denotes the region not used for the UDG survey. Yellow starlets in the right panels are for the sum of the UDGs and LSB dwarfs. Yellow and cyan regions represent the cluster and parallel fields, respectively. We derived the radial number density profiles of the galaxies, subtracting the background contribution using the data for the HXDF. As the center for the radial profiles we adopted the center of the cD galaxy in Abell S1063 and the center of CN-1 in Abell 2744. Note that Lee Jang ( 2016 ) adopted the center of CN-2 at the southeast of CN-1, which is the brightest galaxy in the HST field of Abell 2744, for deriving radial number density profiles of the point sources (mostly


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

± 0.10, assuming no change in flux between the two observations), similar to the compact jets of other X-ray binaries, although we cannot rule out a steep spectrum within uncertainties. We find that the spectral index measurements within the 10 GHz band on the other observing epochs are typically unconstraining (with a typical error of ±0.5, due to the faintness of the radio emission and the small lever arm in frequency), so we cannot distinguish between optically thin and thick emission. The spectral index measurements for all epochs are listed in Table 3 . 4.5 The radio–X-ray correlation The radio ( L R = 4π D 2 ν S ν , where D is the distance to the source) and X-ray luminosities of our sample are displayed in Fig. 5 individually, and together in Fig. 6 , with the addition of other black hole and neutron star systems from the literature. Figure 5. The radio and X-ray luminosities of Cen X−4, SAX J1808.4−3658 and IGR J00291+5934. Hollow symbols mark upper limits. The labelled data points of SAX J1808.4−3658 refer to the same observations in Fig. 4 . IGR J00291+5934 (and possibly SAX J1808.4−3658, but with larger scatter) seems to follow the familiar correlation seen in black holes and some atoll sources, with β = 0.77 ± 0.18 (90 per cent confidence interval, shaded area). Positions of X-ray binaries on the radio–X-ray plane are best measured from strictly simultaneous observations. Among our multiwavelength campaign, Cen X−4 has strictly simultaneous data. For the other sources, we interpolate the X-ray light curve to estimate the X-ray flux at the time of the radio observations, by fitting a piecewise linear function in the log L X /time space. The 3 σ upper limit of 14 μJy on the radio emission of Cen X−4 in quiescence only constrains its radio luminosity to being less than that of the radio-fainter black hole jets (e.g. XTE J1118+480; Gallo et al. 2014 ). The limit lies just above the proposed tMSP track, slightly below the quiescent black hole systems. In addition, we also place the 1979 outburst of Cen X−4 on the radio/X-ray plane for the first time. For the radio luminosity, we use the data reported by Hjellming et al. ( 1988 ) in two bands (at 1.49 and 4.9 GHz). For days when observations were carried out in both radio bands, we use the measurement with smaller uncertainties, with the assumption of a flat spectrum. We find that during the 1979 outburst, Cen X−4 reached radio and X-ray luminosities similar to the atoll sources. Assuming it follows a single, continuous radio–X-ray correlation from the peak of the outburst down to quiescence (like the black hole systems V404 Cyg, Corbel et al. 2008 ; and GX 339–4, Corbel et al. 2013 ), we obtain a lower limit for its correlation slope β ≳ 0.5. The upper limits for IGR J17511–3057 make it less luminous in the radio band than typical atoll sources (Fig. 6 ), but we cannot rule out radio emission at a level similar to that of EXO 1745−248, the radio-detected neutron star with the lowest


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ACKNOWLEDGEMENTS We would like to thank the referee for a constructive and useful comments on the manuscript. AK is very grateful to Rick Kessler and Dan Scolnic for many enlightening discussions on the cosmological analyses using supernovae type Ia samples and effects of survey selection function. AK was supported by a NASA ATP grant NNH12ZDA001N, NSF grant AST-1412107, and by the Kavli Institute for Cosmological Physics at the University of Chicago through grant PHY-1125897 and an endowment from the Kavli Foundation and its founder Fred Kavli. EJ is supported by the Argonne Leadership Computing Facility, a U.S. Department of Energy, Office of Science User Facility operated under Contract DE-AC02-06CH11357. CM and JW were supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research (ASCR) under Contract DE-AC02-06CH11347. JW was also supported by ASCR through award DE-SC0014205. Numerical experiments presented in this paper were carried out on the midway computing cluster maintained by the University of Chicago Research Computing Center. We acknowledge the Center and its staff for support.


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We thank Paule Sonnentrucker for useful comments and Robert Snuggs for technical assistance.


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

we present two other spectral extraction methods for the SPI data. B.1. Method 2: Using different event selection In this method, we consider the threshold of the PSD events, as set in the SPI telescope electronics. These are from 400 keV to 2.2 MeV after revolution 1170 and from nearly 650 keV to 2.2 MeV before. In this energy range, we used the PSD events only. This selection has been prescribed in Roques Jourdain (2019) in order to avoid spectral artifacts caused by potential spurious events. These spurious events appear at high energies (> 400 keV) for very bright sources (typically above 1 Crab). They are caused by a displacement of low-energy photons toward high energy, when the source is so bright that many photons can be detected in the same detection electronics time window. The energy reconstruction for the SE chain is then not reliable. This does not happen in the PE chain, which records the same event much more rapidly. B.2. Method 3: Using SPIDAI In this method, we use the SPI Data Analysis Interface 6 (SPIDAI) to reduce the data from SPI. We created a sky model containing Cyg X-1 and Cygnus X-3 and set the source variability to ten scws for Cygnus X-3 and five scws for Cyg X-1 (e.g., Bouchet et al. 2003 ; Cangemi et al. 2021 ). We then created the background model by setting the variability timescale of the normalization of the background pattern to five scws. In order to avoid the effects due to solar flares, radiation belt entries, and other nonthermal incidents, we removed scws for which the reconstructed counts compared to the detector counts give a χ 2 > 1.5. This selection reduces the total number of scws by ∼10%. The shadowgrams were then deconvolved to obtain the source flux, and spectra were extracted between 20 and 2000 keV using 27 logaritmically spaced channels. Given the large number of scws in both states, we extracted six and four different spectra for the LHS and HSS, respectively, each of them was extracted from data of 500–600 scws and corresponds to a distinct period. For each spectrum, we applied a correcting factor of 1/0.85 [above 400 keV or 650 keV according to the considered period, Roques Jourdain 2019 ) to account for the change efficiency. We then computed two average spectra for both states. In the HSS, the normalization of the spectrum has a slight variability over the four different periods which explain the larger error bars that we observe in this state when computing the average spectrum. B.3. Comparison between the methods The right panel on Fig. B.1 shows the broad SPI spectra (20–2000 keV) used in this paper along with the spectra extracted with the aforementioned methods. The left panel on Fig. B.1 shows the same spectra between 400 keV and 700 keV, that is to say the range for which the selection between SEs and PSD events is different from the the method described in this paper and method 2, described in Appendix B.1 . Fig. B.1. Left panel: spectra extracted with three different methods:


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The author gratefully acknowledges partial financial support by the Portuguese Fundação para a Ciência e Tecnologia under contract SFRH/BSAB/1420/2014.


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

angles and distances of events with joint γ-ray and GW detections (red crosses) from a simulation of SJPL model with θ 0 = 0.1 and δ = 4.5. Top and bottom panels show results for an effective GW horizon distance of 107 and 220 Mpc, respectively. The median distance of future joint detection events is ≈150 Mpc and correspondingly the median GRB luminosity is 7 × 10 48 ergs −1 ≫ L GRB170817 . The fact that GRB170817 is an atypical event of the sample of expected joint prompt and GW detections is also illustrated in Fig. 4 , where we present the expected L γ − θ obs distributions of joint detections for two models of prompt emission given a detection horizon of 220Mpc. For both models, the properties of GRB170817 (blue crosses) are not representative of the sample. Only and of the simulated events (jointly detected in γ-rays and GWs) in the CL and SJPL models, respectively, is found to have 0.25 ≤ θ obs ≤ 0.45 and 5 × 10 46 ≤ L γ ≤ 4.8 × 10 47 erg s −1 . The shape of the observed two-dimensional distributions is driven by the emission model, since the emission is typically dominated by material that is radiating within its 1/Γ beaming cone from the observer. A differentiation between the underlying emission models would require a sufficiently large number of joint GW and GRB detections (see also Section 5 ). Figure 3. Distances and observation angles for mergers detected in GW alone (yellow circles) and for mergers with joint GW and γ-ray detections (red crosses). We present the distribution with a detection horizon of 107 Mpc (top), corresponding to the effective detection horizon for GW170817 or 220 Mpc (bottom), suitable for future events. The inferred values for GRB170817 are shown with a blue symbol. The maximum distance at which it could have been observed in γ-rays is depicted by the vertical dashed line. Results are shown for an SJPL model with θ 0 = 0.1 and δ = 4.5. Figure 4. Two-dimensional distributions of observation angles and γ-ray luminosities for different structure models assuming a joint prompt GRB and GW detection. The location of GRB170817 on these plots is marked with blue crosses that denote the 1σ error in luminosity (Zhang et al. 2018 ) and observation angle (Mooley et al. 2018b ). 4 THE COCOON EMISSION We estimate here the thermal energy stored in the cocoon, the fraction of it radiated in γ-rays at breakout and the cooling emission signature arising when the thermal cocoon eventually becomes optically transparent. The latter corresponds to a ∼ hours long ultraviolet (UV) signal, that may be detectable, provided sufficiently rapid localization of the NS merger. The peak thermal energy stored in the cocoon (as a function of time) is found by Duffell et al. ( 2018 ). As mentioned above, here we assume that the that the injected opening angle is equal to the opening angle after breakout. Rewriting equations (10) and (21) in Duffell et al. ( 2018 ) in a slightly different form, we obtain: where erg and E j is the beaming


The author appreciates the referee's valuable advices to improve the quality of the present paper.


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

inclination, i , must be specified during the starspot modelling and line profile recovery. The stellar radius cannot generally be measured directly from observation, which means that i is not generally known. We performed a 2 search for a range of stellar axial inclinations, i rec , to determine the effect of an incorrectly determined axial inclination. A minimum 2 is always attained at the simulated combination of v sin i and P rot , irrespective of adopted axial inclination for 30 i rec 90. These parameters are therefore effectively independent of the choice of i rec . However, for the trial i rec values, only 2percent r.m.s. variation in was seen, with no discernible trend in 2 versus i rec in the 3090 range above the scatter. Thus, although the simulated inclination of i 60 cannot be recovered for v sin i = 5km s 1 , this does not preclude identification of v sin i and P rot , which are correctly recovered at all trial i rec values. A robustly determined rotation period, P rot and v sin i still enable i to be estimated for an assumed stellar radius. The typical 10percent uncertainty for M dwarf estimates of R (Stassun etal. 2012 ; Williams etal. 2015 ) will dominate uncertainty in the axial inclination determination. For instance, uncertainties of 10percent in sin i yield , , , and (upper limits at 75 and 90 arise from requiring sin i 1). For RV sim data using i 60 and N obs = 60, Fig. 3 (right) shows the FAP for RV corr data points using i 3090 (in 15 steps). In fact, there is a tendency towards improved FAPs when using higher inclinations (i.e. i rec = 75 and 90) for recovery. This is likely related to the lack of resolution elements, when instrumental resolution and stellar v sin i are of comparable magnitude. 4 SENSITIVITIES As every object and data set combination is unique, a full exploration of parameter space is beyond the scope of this paper. Nevertheless, a more complete picture of the range of sensitivities can be gained by exploring the S/N and v sin i values that are expected empirically. Fig. 5 shows the reduction in starspot noise achieved, = sim / corr (where sim and corr are the r.m.s. for the RV sim and RV corr data points), as a function of v sin i for the simulated S/N ratios. The lowest values of are found for Model 2, where 1. Again, this is due to an inability to recover the small spots, and in some combinations, the noise may be marginally increased by5percent. The procedure is most efficient for v sin i 5 km s 1 , where a maximum 8.6 is achieved. At v sin i 1km s 1 , the efficiency is generally lower, as fitting distortions below the instrumental resolution is less effective. For v sin i 10km s 1 , although starspot distortions are modelled well, the broader lines due to higher v sin i limit the efficiency of the procedure by increasing the RV uncertainties. Figure 5. Starspot noise reduction factor, , as a function of v sin i for S/N = 2000, 5000 and 10000 (bottom to top). For projected equatorial rotation


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

We thank to Dr John Pye for very useful comments. KB is grateful the Paul Scherrer Institute and ETH Zurich, Switzerland, where some of the early work for this paper was done. TL is supported by an Science and Technology Facilities Council studentship. PW is supported by an Science and Technology Facilities Council consolidated grant (ST/L000733/1).


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

of the system or the effects of anisotropic line emission, are subsumed into the constant f . Thus, f is expected to be different for every individual AGN, but should be approximately constant for every emission line in a given AGN assuming similar geometries and dynamics of the line-emitting gas. In every case where the lags from multiple emission lines can be measured in a single object, it is found that , as expected from Equation ( 1 ), suggesting that this is the case (Peterson Wandel 1999 , 2000 ; Kollatschny 2003 ; Peterson et al. 2004 ; Bentz et al. 2010b ). It is worth reminding the reader that the scale factor f depends on which parameter is used to characterize the emission-line width, as we discuss in Section 4 . The scaling factor f can be determined for an AGN if there is an independent measurement of the black hole mass. Unfortunately, there are few cases where the black hole radius of influence is large enough that either stellar or gas dynamical modeling can also be used. At the present time, there are stellar dynamical masses (Davies et al. 2006 ; Onken et al. 2014 ) and gas dynamical masses (Hicks Malkan 2008 ) for NGC 3227 and NGC 4151; these are useful for comparison purposes, but it would be unwise to attempt to calibrate the entire reverberation-based mass scale on only two objects. Instead, one of the well-known correlations between central black hole mass and properties of the host galaxies can be used. The first of these to be used to calibrate the AGN black hole mass scale was the correlation between black hole mass and host galaxy luminosity (Magorrian et al. 1998 ) by Laor ( 1998 ). More recently, calibration of the AGN black hole mass scale has been based on the strong correlation between the black hole mass and the velocity dispersion of host-galaxy bulge, the M BH – σ * relationship, which applies to both quiescent (Ferrarese Merritt 2000 ; Gebhardt et al. 2000a ; Tremaine et al. 2002 ; Gültekin et al. 2009 ; McConnell et al. 2011 ; McConnell Ma 2013 ) and active galaxies (Gebhardt et al. 2000b ; Ferrarese et al. 2001 ; Nelson et al. 2004 ; Onken et al. 2004 ; Dasyra et al. 2007 ; Woo et al. 2010 , 2015 ; Graham et al. 2011 ; Park et al. 2012 ; Grier et al. 2013a ; Batiste et al. 2017 ). With σ * measurements now available for ∼30 AGNs from the reverberation-mapping database (Woo et al. 2015 ), an ensemble average can be computed by comparing the predicted masses from the M BH – σ * relationship with the observed VPs, using the line dispersion to characterize the line width. Using this prescription, black hole masses have been measured for ∼60 AGNs using reverberation mapping (see Bentz Katz 2015 for an up-to-date compilation). An important result from reverberation mapping is the observed “ R – L ” relationship between the size of the BLR and the AGN luminosity (Wandel et al. 1999 ; Kaspi et al. 2000 , 2005 ; Bentz et al. 2006b , 2009a , 2013 ). This R – L relationship allows us to bypass


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

period (10,000–14,000 days in the MHD case), the large-scale magnetic field does not show any polarity reversal. We note that the polarity reversal is seen around 4500 and 8000 days. Figure 1. 3D volume rendering of the perturbation of the specific entropy multiplied by the background density for the (a) HD and (b) MHD cases are shown. A corresponding movie for panel (b) is available online. The animation continues for seven seconds covering 40 days of the global convection. The turbulent nature of the thermal convection is clearly seen in the animation. (An animation of this figure is available.) Figures 2 (a) and (c) show the streamline of the mass flux of the meridional flow for the HD and MHD cases, respectively, where includes the radial and latitudinal components of the velocity. The meridional flow in the HD case (Figure 2 (a)) shows a north-south aligned feature around the tangential cylinder. The overall flow pattern is counterclockwise (clockwise) in the northern (southern) hemisphere. In the MHD case (Figure 2 (c)), we see a clockwise (counterclockwise) meridional flow cell around the base of the convection zone in the northern (southern) hemisphere. Figures 2 (b) and (d) show the angular velocity for the HD and MHD cases, respectively. Because of the strong Lorentz force of the dynamo-generated magnetic field, the shear of the differential rotation, i.e., ΔΩ, decreased in the MHD case (see the difference in the color bar). In addition, the polar region is accelerated as well as the equator in the HD case. This feature is frequently seen in hydrodynamic calculations (Miesch et al. 2000 ; Gastine et al. 2012 ). The most important difference between the HD and MHD case concerns the Taylor–Proudman balance. In the HD case, the contour lines of the angular velocity are almost parallel to the rotational axis (Figure 2 (b)). This indicates that the HD case is in the Taylor–Proudman state. In contrast, the angular velocity in the MHD case shows significant deviation from the Taylor–Proudman state. This indicates that some terms in Equation ( 1 ) are balanced with the Coriolis force term. Figure 2. Panels (a) and (c) show the streamline of the meridional flow for the HD and MHD cases, respectively. The solid and dashed lines show the clockwise and counterclockwise flows, respectively. The angular velocity, Ω/(2 π ), is shown for the HD and MHD cases in panels (b) and (d), respectively, where Ω = v φ / λ + Ω 0 . To investigate the force balance on the meridional plane, we transpose Equation ( 1 ) as where is ignored, because the calculation is already in a statistically steady state. Figure 3 shows the balance in the MHD case. Minor contributions from the advection term ADV and the Lorentz force MAG around the top boundary are seen in Figures 3 (b) and (d), but the Coriolis force (COR, Figure 3 (a)) is mainly balanced with the baroclinic term, i.e., the entropy gradient (BAR, Figure 3 (c)). Although the difference in the differential


O O O O O O O O B-Survey O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O B-Wavelength 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 B-Wavelength O O O O O O O O O O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-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 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 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 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-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-Citation I-Citation I-Citation 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 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

NVSS object. We restrict our samples to the SDSS–NVSS quasars with a matching radius of 15 arcsec in order to consider the selection effect by the matching radius. This sub-sample contains 6081 radio-loud objects. The relation between and with the matching radius of 15 arcsec is given aswith a scatter of 0.54. The Spearman rank correlation gives , with a p -value of . Therefore, the correlation between disk luminosity and jet power still statistically exists. The jet production efficiency is given as . 5.4. Effect of the Radio-loudness Cut At , radio-loud quasars are also referred to as radio-intermediate quasars (Falcke et al. 1996 ). Most of them are likely to be FR-I type radio quasars. Figure 9 shows the correlation between and of the SDSS–NVSS detected quasars but having . The dashed line represents . 3083 quasars are included. The regression line, shown by the solid line, is given aswith a scatter of 0.38. The Spearman rank correlation gives , with a p -value of . There is still a positive correlation between disk luminosity and jet power in radio quasars. Based on the jet production efficiency arguments above, here we have . By selecting sources at , a slightly higher jet production efficiency is expected but is still consistent with that at at the 1 σ level. Figure 9. Same as Figure 4 , but at . Figure 10 shows the estimated jet production efficiency as a function of the limiting radio-loudness. As we select high jet power objects by setting high , the jet production efficiency gradually increases with . However, even at , is still at an order of 0.1. Figure 10. Jet production efficiency as a function of the limiting radio-loudness The 1 σ statistical uncertainty of the data is also shown. 5.5. Comparison with Blazar Studies The relation between the disk and jet has been also investigated using blazar spectral fitting studies (e.g., Celotti Ghisellini 2008 ; Ghisellini et al. 2014 ; Inoue Tanaka 2016 ). Differing from our radio quasar studies, blazar studies enable us to compare accretion with jet outflow at the same epoch. Multi-wavelength observations from the radio band to gamma-rays allow us to study overall SED and physical parameters of jets via spectral fitting. A spectrum of a blazar is composed of two emission components: the low-energy component is synchrotron radiation and the other one is an inverse Compton component targeting synchrotron radiation (e.g., Jones et al. 1974 ; Maraschi et al. 1992 ) and/or an external radiation field (e.g., Dermer Schlickeiser 1993 ; Sikora et al. 1994 ). Generally, blazar spectral fitting studies predict large jet production efficiencies (e.g., Celotti Ghisellini 2008 ; Ghisellini et al. 2014 ; Inoue Tanaka 2016 ), while our results show . Such a difference has also been recently reported by Pjanka et al. ( 2016 ) using published blazar samples. Here, the jet power estimates based on blazar spectral fittings strongly rely on the assumptions on the pair fraction and the electron minimum


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

several tens of percent at high optical depths. An accurate calculation of the dichroic optical depth requires the full solution of the intensity profile along the path. In the general case of a dichroic medium, the radiative transfer equation becomes a set of four coupled first-order differential equations with varying coefficients, and a closed expression for the dichroic optical depth cannot be derived. However, the exact solution corresponding to a medium with uniform grain alignment can be used to find the full solution in an elegant way without any further numerical integration. There is no benefit in using τ ext , τ tot , or any other approximation instead of the dichroic optical depth to calculate the next interaction location in a Monte Carlo radiative transfer simulation. Our results have implications for Monte Carlo radiative transfer coders that wish to incorporate the attenuation by elongated dust grains. If scattering polarisation by spherical grains already adds some complexity to Monte Carlo radiative transfer codes, dealing with non-spherical grains increases this complexity to a new level. Compared to spherical grains, the scattering process is significantly more complex. The scattering properties of spherical grains are fully described by just the albedo and the scattering phase function; for elongated grains, a full 4 × 4 scattering matrix comes into play ( Mishchenko et al. 2000 ), and the random determination of a new propagation direction after a scattering event is not trivial ( Wolf et al. 2002 ; Whitney Wolff 2002 ; Lucas 2003 ). A related complexity concerns the amount of data that needs to be stored and accessed. Each of the elements of the extinction matrix and the scattering matrix is not only dependent on grain material, size, and wavelength, but also on shape and incidence angle. Moreover, each element of the scattering matrix needs to be discretised on the unit sphere. Finally, the process of dichroic extinction adds yet another level of complexity, and the results in this paper show that this also affects the random generation of the next interaction location. So far, only a limited number of Monte Carlo radiative transfer codes have attempted to actually calculate dichroic attenuation by non-spherical aligned grains 4 . Wolf et al. (2002) were the first to include non-spherical aligned grains in their Monte Carlo radiative transfer calculations. They presented multiple light scattering calculations and demonstrated that the incorporation of elongated grains is important to explain the circular polarisation of light. They discussed the concepts of dichroism and birefringence, but they did not include these effects in the simulations they presented. Whitney Wolff (2002) presented a Monte Carlo code that models the effects of scattering and dichroic absorption by aligned grains in circumstellar environments. While their code is presented for general geometries, they only discussed models with a uniform grain