reduce the in equation ( 60 ). Thus, it can achieve arbitrary precision by increasing the bit length. However, the round off error will also propagate and accumulate through the extrapolation table in Table 1 . As the order of the GBS extrapolation increases, the round off will accumulate faster and faster. Thus the additional mantissa bits becomes less and less efficient in increasing the integration accuracy. Therefore, reducing the round off error in GBS extrapolation is also important in order to achieve the same precision with less mantissa bits and less CPU time. 3.1.1 Improvement on GBS extrapolation In the BS extrapolation, higher order methods can be obtained from lower order methods by extrapolation, as described in equation ( 52 ). However, the round off error will also propagate and accumulate through the extrapolation table. If the round off error from the base integration method is ε, −ε, ε, ... in the first column, then the round off error propagation with the extensively used step sequence n i = 2 i suggested by Deuflhard ( 1983 ) will behave as in Table 2 . As shown in the table, T 8, 8 with 16th order precision magnified the round off error to become 100 times larger. Thus, we will lose at least 2 significant digits from the extrapolation. This becomes more problematic for higher order extrapolations, as required by arbitrary precision integration methods with extremely low tolerance. Table 2. Round off error propagation in the Bulirsch–Stoer extrapolation with step sequence n i = 2 i . To reduce the round off error in the extrapolation process, there are two fine-tunings that can be performed on the extrapolations. The first is a step sequence choice. The step sequences n i = 1, 2, 3, 5, 8, 12, 17, 25, 36, 51, 73, ...(Fukushima 1996 ) is better than the extensively used sequence n i = 2 i , where the extrapolation coefficient reduces the round-off error propagation. Table 3 shows the error propagation with the new step sequence. We see that it performs much better than the original sequence suggested by Deuflhard ( 1983 ). Table 3. Round off error propagation with optimal step sequence in the BS extrapolation. The second method to reduce the round off error in the extrapolation process is to extrapolate the raw increment dξ of the integration instead of the integrated result ξ. Since the GBS extrapolation is linear, it is possible to do the following Because the raw increment dξ is usually tiny compared to the integrated results, the round of error in the first column of Table 1 is ∼eps × |dξ| instead of ∼eps × |ξ|. Then, the round off error accumulated from the extrapolation table will be smaller than the error accumulated from the direct extrapolation. We note, however, that the initial Δ T i , 1 should be the raw increment evaluated from the basic integrator, not from the subtraction of T i , 1 ( H ) − T i , 1 (0). The close value subtraction will introduce additional round off errors and will significantly degrade the


ACKNOWLEDGEMENTS We thank Elisabeth Krause and Fabian Schmidt for their useful discussions. This work was in part supported by Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (JSPS) Promotion of Science (No. 23340061, 26610058, 15H03654, and 17H01131), Ministry of Education, Culture, Sports, Science and Technology (MEXT) Grant-in-Aid for Scientific Research on Innovative Areas (No. 15H05887, 15H05893, 15K21733, and 15H05892), JSPS Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers, and Japan Science and Technology Agency (JST) CREST Grant Number JPMJCR1414. Numerical computations were in part carried out on Cray XC30 at Centre for Computational Astrophysics, National Astronomical Observatory of Japan.


decrement, the flattest BLR decrements (lowest-ratio) are similar to the narrow-line decrement; i.e. the lower envelope is a 45-deg line parallel to the reddening vector. The null hypothesis, that the minimum BLR decrement is independent of the NLR decrement (see for example, Fig. 2 , panel VI), is excluded at a probability p = 0.002. There is a lack of AGNs with NLR decrements steeper than the BLR decrement. Points to the right of the 45-deg line are consistent with measuring errors. Only one point lies more than two standard deviations to the lower right of the red line. For the majority of AGNs, the BLR decrement is steeper than the NLR decrement. There is no significant difference in the median NLR decrement for the AGNs with very steep BLR Balmer decrements compared with those with very flat BLR Balmer decrements. These results are consistent with the earlier findings of De Zotti Gaskell ( 1985 ) and Glikman et al. ( 2007 ). De Zotti Gaskell ( 1985 ) found that Balmer decrements for nearby AGNs were steeper for the broad lines than the narrow lines, and Glikman et al. ( 2007 ) found that, for the FIRST–2MASS red quasar survey, broad lines seem to be reddened more than the sum of broad and narrow lines. Our results strongly imply that: the dust that reddens the NLR also reddens the BLR, but most of the dust reddening the BLR lies between the BLR and the NLR. The dust causing the common reddening of both the NLR and BLR could be associated with the NLR or it could be dust in the host galaxy. De Zotti Gaskell ( 1985 ) studied nuclear continuum colours and both broad- and narrow-line Balmer decrements of nearby AGNs as a function of the orientation of the host galaxy. They found that for more highly inclined disc galaxies, the nuclear colours were redder and the Balmer decrements steeper. Since the axis of symmetry of an AGN is not necessarily aligned with the rotation axis of the galaxy (see for example, Tohline Osterbrock 1982 ; Valtonen 1983 ; Battye Browne 2009 ), the greater nuclear reddening of inclined galaxies must be due in part simply to dust in the plane of the galaxy. 4 THE RELATIVE STRENGTH OF [O <sc>iii</sc>] VERSUS THE BLR REDDENING As noted above, intervening dust not only causes reddening, but also extinction. If the dust is located between the NLR and the BLR, we would expect higher extinction of the BLR and AD to make [O iii ] stronger relative to the BLR and the continuum. 4.1 Selection of objects [O iii ] λ5007 is the strongest narrow line in the optical and the Balmer lines are the strongest broad lines. Therefore, a very large number of measurements are potentially available in the Sloan Digital Sky Survey (SDSS). Dong et al. ( 2008 ) have carefully measured Hα/Hβ ratios after subtraction of narrow lines and Fe ii , etc. Comparison of their ratios with the simple Gaussian fits of the SDSS pipeline reveals quite a few very discrepant measurements in the SDSS data base and that the difference between the Dong et al. (


Acknowledgements IRIS is a NASA Small Explorer mission developed and operated by LMSAL, with mission operations executed at NASA Ames Research Center and major contributions to downlink communications funded by the Norwegian Space Centre through a European Space Agency PRODEX contract. The Solar Dynamics Observatory (SDO) data that we used are provided courtesy of NASA/SDO and the Atmospheric Imaging Assembly and Helioseismic and Magnetic Imager science teams. The authorsthank the anonymous referee for suggestions. We thank Y. Chen, Z.J. Ning, Y. Li, and L.P. Yang for valuable discussions. The work at Peking University is supported by NSFC under contracts 41574168, 41231069, 41274172, 41474148, 41421003. LM Yan is supported by National Postdoctoral Program for Innovative Talents (grant BX201600159). J.S. H.E. is also supported by “National Youth Talent Support Program” of China. L.D. Xia is supported by NSFC under contracts 41274178 and 41474150.


model. This is partially caused by the inner region of the circumbinary disk ( ), which is thinned out by the gravitational forces of the two stars (e.g., Avramenko et al. 2017 ). However, this effect only occurs if the separation between the two stellar components is on the order of . A smaller separation would lead to a behavior that is similar to circumstellar disks around a single star. If the separation is significantly larger, the dust and gas around the binary can no longer be described with a single circumbinary disk. In circumstellar disks with a single star, the inner region has the highest density and usually the highest magnetic field strength (see Fig. 1 in Sect. 5.4 ; Flock et al. 2017 ). Therefore, as mentioned in Sect. 6.3 , circumbinary disks lack a significant fraction of circularly polarized emission if the inner high magnetic field region is missing. In addition, the different directions of circulation of the toroidal magnetic field decrease the circularly polarized emission from regions with similar velocities relative to the observer if not spatially resolved. Furthermore, the estimation of the LOS magnetic field strength from circumstellar disks with a single star is dominated by the inner region characterized by high magnetic field strength. In contrast, a Zeeman observation of a circumbinary disk is able to provide information about the magnetic field farther out in the disk if the requirements for such an observation are fulfilled. However, this requires that a significant part of its innermost region be depleted by the gravitational forces of both stellar components. 7. Conclusions We studied the requirements to observe the Zeeman splitting of the CN lines in circumstellar disks and their dependence on selected disk parameters. Such observations can be used to resolve degeneracies and obtain complementary information about the magnetic field if combined with polarimetric continuum observations. However, this is only applicable, if the polarimetric continuum observations are mainly caused by elongated aligned dust grains. In particular, we evaluated whether Zeeman observations of circumstellar disks should be performed spatially resolved or unresolved. With spatially resolved Zeeman observations, the strength and structure of the magnetic field in the LOS direction can be reconstructed for most regions in circumstellar disks. Only the region close to the star cannot be traced. However, the required sensitivity (, if ) is far beyond the capabilities of recent and upcoming instruments/observatories. For spatially unresolved Zeeman observations, we obtained different results. Under the assumption of Keplerian rotation and a toroidal structure of the magnetic field, two independent average magnetic field strengths can be obtained from the circularly polarized fraction. These average values are sensitive to changes in the strength and structure of the magnetic field inside the disk. In addition, they can be used to


leads to the inclusion of a number of RGB stars that are located close to the selection boundary, while retaining the color selection in ( m F435W − m F555W ) will still lead to rejection of RC stars. The RGB sample resulting from this updated selection run includes 207 stars. We repeated all of our subsequent analysis and found a new C index value of 0.063 mag, which is almost the same as our initial result, C index = 0.062 mag. We therefore conclude that the potential loss of a small number of genuine RGB stars by our initial selection method does not significantly influence our measurement of the cluster’s RGB broadening, nor our final results. 4. Discussion Our results show that the artificial stellar population is characterized by a similar dispersion in C F336W,F435W,F814W as the observed RGB sequence of NGC 1783. This demonstrates that the photometric uncertainties fully account for the RGB’s broadening in NGC 1783. The color index used, C F336W,F435W,F814W , is sensitive to the stellar N and He abundances, which are two of the most representative elements that exhibit large abundance variations in star clusters (Gratton et al. 2004 ). The consistency of the observed RGB’s width with that defined by our artificial SSP therefore indicates that our RGB sample is best represented by single-valued N and He abundances. There are a small number of outliers in the observed RGB distribution, in particular two stars at the far left (see the top panel of Figure 6 ). These objects are unlikely statistical fluctuations, given that they deviate by >5 σ from the Gaussian peak. Alternatively, they might be field stars that have not been properly removed by our field star decontamination algorithm. If they were cluster members, they would need to have unrealistically extreme metallicities. Note that these two data points appear both in the scatter diagram in the top panel of Figure 6 and in the observed histogram in the figure’s bottom panel. We suspect that these two stars might result from stochasticity in the field’s RGB sample (see Figure 5 ), rather than from random effects associated with our field star decontamination. We explored whether these objects might be binary systems instead. If we assume that the primary components ( M 1 ) of such binary systems are genuine RGB stars, the secondary components ( M 2 ) must have lower masses. We tested the appearance of binary systems with different mass ratios, M 2 / M 1 . For very low-mass companions, the change in color is almost negligible, while for equal-mass binaries no color difference is expected, compared with the single-star case. The top panel of Figure 6 includes binary sequences for M 2 / M 1 = 0.7, 0.8, and 0.9. It is clear that the outliers at the far left cannot be binary systems. An intermediate-age cluster with an age of 1.8 Gyr and a mass of 1.8 × 10 5 M ⊙ , NGC 1783 is comparably as massive as other star clusters that show clear evidence of MSPs (e.g., Martocchia et al. 2018 ). If


Acknowledgements We would like to thank John Helly for technical assistance during the course of this work and Spoorthy Raman for reading the manuscript and providing useful suggestions for improving the text. This work was supported by the Science and Technology Facilities Council [ST/L00075X/1]. This work used the DiRAC Data Centric system at Durham University, operated by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility ( www.dirac.ac.uk ). This equipment was funded by BIS National E-infrastructure capital grant ST/K00042X/1, STFC capital grant ST/H008519/1, and STFC DiRAC Operations grant ST/K003267/1 and Durham University. DiRAC is part of the National E-Infrastructure.


which both β and IRX have been measured (Capak et al. 2015 ), but the galaxies with from Capak et al. ( 2015 ) and the galaxy presented by Watson et al. ( 2015 ) lie outside the region spanned by the simulated galaxies. Because our simulations and theirs cover disjoint regions of parameter space in terms of redshift and mass, it is not possible to make detailed comparisons between our results and theirs. However, their results highlight the potential importance of dust destruction for accurately predicting the UV properties of simulated galaxies and provide motivation for future studies that include more complex treatments of dust production, growth, and destruction. 9. Implications for Observations Our simulation results suggest that there is not a tight relation between IRX and β that applies to all galaxies at all redshifts. The simulated galaxies tend to lie near the M99 relation, which was determined based on observations of galaxies in the local universe. However, during merger-induced starbursts, even the galaxies can depart significantly from the relation: because IRX increases significantly but β is almost unaffected, the merger-induced starbursts, such as that shown in Figure 3 , tend to lie above the M99 relation. The simulations—of both disk galaxies and mergers—deviate more significantly from the M99 relation: even when they are not undergoing starbursts, they tend to lie above the relation. These results are consistent with observational works that have demonstrated that some classes of galaxies deviate significantly from the M99 relation. As already discussed above, observed DSFGs tend to lie above the M99 relation and do not exhibit any relationship between IRX and β (e.g., Bell et al. 2002 ; Goldader et al. 2002 ; Howell et al. 2010 ; Casey et al. 2014 ). Conversely, some galaxies lie significantly below the M99 relation (i.e., have lower IRX than expected from the relation given their β ). This was demonstrated for the lensed galaxies cB58 at (Pettini et al. 2000 ) and the Cosmic Eye (Smail et al. 2007 ) at . Similarly, Reddy et al. ( 2012 ) found that young systems (age Myr) at lie below the M99 relation. Moreover, we have demonstrated that the dust composition—specifically the strength of the 2175 Å feature—can have a very dramatic effect on the UV slope. Consequently, extrapolation of the locally calibrated relation to regimes for which it is not observationally constrained may be problematic if, e.g., the dust composition of high-redshift galaxies is significantly different from that of galaxies. How the strength of the UV bump varies with galaxy properties and redshift is still poorly understood, but there are some useful observational constraints. The commonly employed Calzetti et al. ( 1994 ) attenuation law, which was defined based on observations of local-universe starburst galaxies, does not exhibit a UV bump. Based on a study of ∼10,000 star-forming galaxies, Battisti et al. ( 2016 ) derived an average attenuation


configuration. 6. Formation of Molecular Gas Due to Jet–ISM Interactions? Figures 10 – 12 display that a wall structure is clearly seen toward the locus of the extension of the precession axis of the SS 433 jets, in which the column density of H i increased precipitously. Enhanced CO emissions are also found to be nicely associated with the wall structure seen in H i emission. MC G40.331−4.302 has the H i counterpart, which displays more extended arc-like structure nearly perpendicular to the precession axis of the SS 433 jets (Figure 12 ). The positional coincidence between G40.331−4.302 and the precession axis of SS 433, as well as their coincident kinematic features, strongly suggests the physical connection between them (see Sections 4 and 5 ). We obtain that the column density, N H = N (H i ) + 2 × N (H 2 ), is about 2.1 × 10 21 cm −2 for the cloud G40.331−4.302, which corresponds to A V ≈ 1.1 mag assuming N H ≈ 1.9 × 10 21 cm −2 mag −1 × A V . At the column density, the molecules are shielded from UV radiation, and self-shielding allows significant H 2 molecules to exist. The total mass of the main concentration of the cloud is ∼3 × 10 3 M ⊙ within a radius of ∼66 (Table 1 ). The molecular fraction / N H is about 0.87, suggesting that the dominant of the gas in the cloud is in molecular form. Table 1 Properties of Gas toward G39.315−1.155 and G40.331−4.302 Notes. a The area of the emission with I (CO)>5 K km s −1 for G39.315−1.155 and I (H i )>130 K km s −1 and I (CO)>2.5 K km s −1 for G40.331−4.302. b The effective radius is calculated from (Area/3.14) 0.5 . c The mean intensity of the H i (70–90 km s −1 ) and CO (73–88 km s −1 ) emission. d The column density of the atomic and molecular gas is calculated from 1.823 × 10 18 × I mean (H i ) and 2 × 10 20 × I mean (CO), respectively. See the text. e Parameter d 4.9 is the distance to the cloud in units of 4.9 kpc (see Section 4 ). f The volume density of the atomic and molecular gas is calculated from the mass and the effective radius of the emission. The virial mass exceeds the total mass of the cloud by more than one order of magnitude, indicating that the cloud is in a gravitationally unbound state. The fragmented subclouds (e.g., with a size of ∼1 pc) in MC G40.331−4.302 may dissipate on a timescale of several Myr (sound crossing time) without other support. Alternatively, the MC may be confined by an external pressure of ≳4.4 × 10 4 K cm −3 (e.g., ρ (H i ) σ 2 (H i )) when the magnetic pressure and the self-gravity are negligible. We emphasize that G40.331−4.302 is the only detected MC within the range of l = 349–451, −51 ≲ b ≲ −30, and V LSR ≳ 70 km s −1 . It indicates that such an MC is located about 370 pc below the Galactic plane, where a kinematic distance of 4.9 kpc is adopted. However, the MCs within the solar circle are concentrated in the Galactic plane with a Gaussian FWHM of ∼90–100 pc (e.g., see Section 4.5 and Figure 6 in Heyer Dame 2015 ). This suggests that


This work was partially supported by NASA grants ATP12-0139 and ATP13-0077. We thank Alessandra Buonanno, Francesc Ferrer, Ted Jacobson, Henric Krawczynski, Tzvi Piran, Laleh Sadeghian, and Joe Silk for helpful comments and discussion.


The research of E.C. and J.C.W. is supported by NASA grant HST-AR-13276.002-A. E.C. thanks the Enrico Fermi Institute for its support via the Enrico Fermi Fellowship.


a stronger field provides more magnetic energy to damp. We fit the slopes of this “big trend” for all the curves by appropriately removing a few points far away from this “big trend” and taking the average of these slopes. Interestingly, both viscous and magnetic dissipations obey an identical scaling law:The dashed lines in Figures 5 (b) and (c) denote this scaling law. This scaling law for the relation of the two dissipations and magnetic fields reveals that there exists self-similarity for the magnetic effect on dynamical tide. Figure 5. (a) Kinetic energy, (b) viscous dissipation, and (c) magnetic dissipation vs. S 2 at various ω. Pm = 1.0. The two dashed lines denote the scaling law ∝ S 2 . 3.2. Investigation of Pm In this subsection we investigate Pm . Similar to Figure 2 , Figure 6 shows viscous dissipation, magnetic dissipation, total dissipation, and the ratio of magnetic to viscous dissipations versus tidal frequency at various Pm with S 2 fixed to be 0.1, namely in a strong field regime. The first three subfigures show that for all the tidal frequencies, a larger Pm leads to higher viscous dissipation and lower magnetic dissipation but total dissipation is almost independent of Pm . This is reasonable because Pm is the ratio of viscosity to magnetic diffusivity (see Equation ( 9 )) but it cannot influence the total diffusivity. More interestingly, Figure 6 (d) shows that magnetic dissipation wins out over viscous dissipation for and this ratio is approximately equal to Pm −1 . In the astrophysical situation Pm is very small, and it can be inferred that magnetic dissipation dominates over viscous dissipation with a moderate or stronger magnetic field. Note again that with a very weak field, e.g., S ≤ 10 −4 , viscous dissipation wins out over magnetic dissipation even at a small Pm , e.g., (Lin Ogilvie 2018 ). Figure 6. (a) Viscous dissipation, (b) magnetic dissipation, (c) total dissipation, and (d) ratio of magnetic to viscous dissipations vs. tidal frequency at various Pm . . To find the scaling laws for Pm , we plot the two dissipations versus Pm as shown in Figure 7 . The dependence on Pm looks more regular than the dependence on S in Figure 5 because the field strength influences the resonant frequencies, whereas diffusivities cannot. By taking the average of the slopes for different tidal frequencies, we obtain the scaling lawsThe dashed lines in Figures 7 (a) and (b) denote these two scaling laws. The ratio of magnetic to viscous dissipations is indeed close to Pm −1 , as shown in Figure 6 (d). Note that our parameter regime is not the real regime, e.g., E and Pm are not too small, so these scaling laws might not be realistic. Lacking knowledge of the physical properties in stars and planets, we do not know the real parameters, and even estimating the order of magnitude is not convincing. These scaling laws obtained in the moderate parameter regime at least give us some qualitative evidence that a moderate or stronger


different from those of normal SNe, and the study of the immediate environment of these events can provide important information on physical properties of their progenitors which so far have remained undetected. Fig. 1 Left panel : Pan-STARRS -band image of NGC 3191 with the PMAS (blue squares) and the MaNGA fields of view (red hexagon) superposed. Right panel : map of the H ii regions obtained with the code described in the text and applied to the PMAS cubes. The SLSN 2017egm position is marked with a red cross in both panels. The levels of the isophotes, from the outermost to the innermost, are 21.86, 21.11, 20.66, 20.22, and 19.91 mag/arcsec. Indeed, several studies of SLSN host galaxy samples have revealed significant differences in the properties of Type I and Type II hosts ( Leloudas et al. 2015 ; Perley et al. 2016 ; Lunnan et al. 2014 ; Schulze et al. 2016 ). Type I hosts are usually star-forming (SF) dwarf galaxies with low metallicities at the extreme end of the distribution in the Baldwin-Philips-Terlevich (BPT; Baldwin et al. 1981 ) diagram and likely even more extreme than gamma-ray burst (GRB) hosts (see e.g. Leloudas et al. 2015 ; Schulze et al. 2016 ; but see also Lunnan et al. 2014 ). In addition, they have been found in very young stellar populations, indicating that Type I SLSNe might be the first and most massive stars to end in a SN explosion after the onset of a new starburst episode in their galaxy or HII region ( Thöne et al. 2015 ). Type II hosts seem to be more metal rich and within the bulk of emission-line galaxies in the SDSS. At higher redshifts, Type I SLSN hosts evolve in line with the most star-forming galaxies towards higher-mass galaxies with higher absolute star formation rates (SFRs), but still seem to show a metallicity cut-off at 0.4 solar and a tendency towards low-mass hosts ( Schulze et al. 2016 ). In this paper, we present integral field unit (IFU) spectroscopic data of NGC 3191, the host galaxy of SN 2017egm, a Type I SLSN discovered by the Gaia satellite ( Delgado et al. 2017 ) on May 23, 2017. Detailed analysis of its early optical spectra revealed its Type I SLSN nature ( Dong et al. 2017 ; Nicholl et al. 2017 ). The SLSN reached its optical maximum on June 20, 2017, with an absolute magnitude of mag. As pointed out in Nicholl et al. (2017) , Bose et al. (2017) , and Chen et al. (2017b) , the host seems to be the first Type I host with super-solar metallicity. In this work, we analyse the properties of different regions in the host galaxy, and in the SLSN location, providing a more detailed analysis of the metallicity and the star formation rate distributions around the SLSN environment and several other H ii regions. Resolved spectral modelling across the host galaxy gives us important clues to the different underlying stellar populations, their ages, and their metallicities, allowing us a more detailed insight into this apparently very peculiar SLSN-I environment. 2. Observations We observed the


Fig. 12 shows a time frame of each of the gasoline2 simulations compared to the gas surface density data of Corbelli et al. ( 2014 ) in the bottom right. Best fits were found via a combination of by eye and an automated routine using a structural similarity index (SSIM; built into python ’s scipy module) of images of the gas surface density. The simulated disc is first inclined at the orientation of M33, then rotated in increments to assess the suitability of different phase angles. These images are smoothed over a scale of 2 kpc to leave only the strongest features. The SSIM is then calculated for each time-stamp and phase angle (Δ t = 10 My, Δ θ = 10° using the time domain of 0.5–1.0 Gyr, resulting in 1800 images for each calculation). The best fitting of these low-resolution comparisons are then shown in Fig. 12 , now at their natural resolution. Figure 12. Best-fitting gasoline2 models compared to M33 gas distribution (lower right). In Fig. 12 we show one of the better-fitting snapshots of each simulation, orientated in the same manner as the observed M33. Certain features like the arms shown in Fig. 8 are seen in some of these models, with accompanying inter-arm voids. The lowest feedback model displays some very similar features; the upper-right arm structure, the irregularly shaped arm north-west of the centre, and the straight-arm segment in the edge of disc to the south-east. The nature of dynamic spiral features such as these allows for spiral arms that are less regular than the assumed fixed log-spiral features used by density wave-like potentials (Grand, Kawata Cropper 2012 ; Baba, Saitoh Wada 2013 ). Cavities in the gas seen in M33 are a simple result of inter-arm voids. However, the gas does not display the same smaller scale features, like the irregular patchy features seen in the inter-arms of M33. The 5 per cent feedback model shows a more disrupted spiral structure. Similar small arm features are seen as previously, though now the increased feedback stunts their growth considerably. This appears one of the poorer matches to the observational data, with both the feedback cavities and inter-arm regions too small to provide a good match for M33. The remaining higher feedback models provide a good match to the general structure of M33, though neither is a precise match. The 20 per cent model is very effective at creating large ISM cavities, much like the sphNG models, though this comes at the expense of creating very few strong arm features. The cavities in the 20 per cent model may even be too large and numerous, with the disc perhaps showing too great a degree of fragmentation compared to M33. The 10 per cent feedback model is a good middle ground, creating a handful of large cavities but also managing to maintain some elongated arm features. We found that many of the snapshots not shown here produced certain features very well, while missing others entirely. Enough realizations could feasibly eventually produce every feature


ACKNOWLEDGEMENTS We thank the referee for going through the manuscript carefully and providing constructive comments, which improved the manuscript. All the observers of the 2-m HCT (operated by the Indian Institute of Astrophysics), who kindly provided part of their observing time for observations of the supernova, are gratefully acknowledged. We thank Takashi Hattori, Ji Hoon Kim and the staff at the Subaru Telescope for their excellent support of observations under S15A-078 (PI: K. Maeda). We thank Professor David Branch for clarifying some of the issues related to the spectrum synthesis code syn++ . We also thank Dr Kuntal Mishra for providing us with the code for fitting the bolometric light-curve. This research has been supported in part by the DST-JSPS grant DST/INT/JSPS/P-211/2016, the Grant-in-Aid for Scientific Research of JSPS (15H02075, 16H02168, 26400222, 26800100) and MEXT (25103515, 15H00788), and by the World Premier International Research Center Initiative, MEXT, Japan. This work has made use of the public data in the Swift data archive and the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration (NASA).


panel), 95701-01-03-00 ( km, middle panel), and 91701-01-52-01 ( km, bottom panel), respectively. 3.2. Spectral Parameters The spectral fitting results are presented in Figure 5 . The unabsorbed power-law luminosity ( L PL ) and the disk luminosity increase simultaneously with the total luminosity ( L 3–30 keV ). The apparent inner disk radius ( R in ) is related to the disk normalization as , where D 10 is the distance in units of 10 kpc. Here we adopt the inclination angle θ = 66° (Fender et al. 1999 ), a color correction factor f = 1.9 (Neilsen et al. 2011 ), and a distance of 8.6 kpc (Reid et al. 2014 ) in the calculation. There are two branches shown in the diagrams of L 3–30 keV − R in and L 3–30 keV − kT : (1) The inner disk remains at a small radius ( R in ≤ 70 km, hereafter S branch), kT increases with the X-ray luminosity, and the X-ray emissions are fainter and softer (larger Γ). (2) The majority of data (189 out of 233) draw the other branch (L branch), the apparent inner edge of disk recedes, and the temperature increases slowly at high luminosity. Meanwhile, the photon index (Γ) of the nonthermal component is anticorrelated with the X-ray luminosity. Figure 5. Correlations between the spectral parameters and distribution of the reduced χ 2 with the fitting model of diskbb + powerlaw (right bottom panel). Open squares and filled cycles correspond to the data with R in being smaller and larger than 70 km, respectively. All parameters are plotted with their 1 σ errors. Intriguingly, there are the positive correlations between T rec , R in , and the X-ray luminosity as well. Additionally, T rec has an even tighter correlation with the power-law luminosity. Since the uncertainty on T rec is much larger than on L 3–30 keV , we carry out a power-law fit to the relation by taking the error on T rec into account, yielding an index of n = 1.10 ± 0.10. Meanwhile, T rec is proportional to . It is worth noting that the change of apparent inner disk radius can be interpreted as a varying color correction factor without moving the intrinsic inner disk radius (e.g., Merloni et al. 2000 ; Zoghbi et al. 2016 ). In order to check this scenario, we model the disk component with diskpn (Gierliński et al. 1999 ), in which the disk normalization is linked to the color correction factor: . The inner disk radius is fixed to the bottom limit 6 R g , although it is much smaller due to high spinning rate (McClintock et al. 2006 ). In addition, the power-law model is replaced by a physical Comptonization model ( tbabs*(diskpn + comptt) in XSPEC). We tie the seed temperature ( kT seed ) to the disk temperature and fix the plasma temperature to 50 keV because it cannot be constrained by our data. The data in the S branch are relatively soft, and the model described above cannot provide an adequate fit to them unless the kT seed varies freely and becomes hotter than the disk temperature; however, it is inconsistent. Henceforth, we only fit the data in the L


one is a delta-function type in logarithmic scale given by where corresponds to the amplitude at the peak wavenumber k p , and another is a power-law type given by where is the amplitude at the normalization wavenumber k n . In this Letter, we set the normalization scale as k n = 1 Mpc −1 . First, we focus on the delta function type for the power spectrum. By substituting equation ( 8 ) into equation ( 3 ) with equation ( 7 ), we obtain the injected energy fraction to the CMB energy by the decaying PMFs as where a function of k p , is explicitly given by When k p is much larger than k D ( z i ) (> k D ( z μ )), the energy injection due to the decay of the PMFs becomes efficient before the BBN era. On the other hand, when k p is much smaller than k D ( z μ ), the energy injection from the PMFs occurs during the CMB distortion era. We focus on the case where the energy injection from the decaying of the PMFs is efficient after the BBN era and before the CMB distortion era, that is, the case where k p is set between the two decaying scales k D ( z i ) and k D ( z μ ). For such a case, we can approximately take (see Miyamoto et al. 2014 ). Combining equa-tion ( 2 ) and equation ( 10 ) yields a constraint on PMFs in the k p - plane. We present our new result obtained from magnetic reheating as a red line in Fig. 1 . Figure 1. The upper bound on the amplitude of the delta-function type for the power spectrum as a function of k p from the magnetic reheating. The limits from the BBN (Kawasaki Kusakabe 2012 ) and CMB distortions (Jedamzik et al. 2000 ) in blue and magenta lines, respectively, are shown in the same plot. For comparison, we plot limits from the BBN and CMB distortions in magenta and blue lines, respectively. We can see that our magnetic reheating constraint gives a tight limit on the PMFs on small sales from to 10 8 Mpc −1 . Next, we consider the power-law type of the power spectrum defined in equation ( 9 ). By using equation ( 3 ) with equation ( 7 ), we obtain Here, we focus on the magnetic reheating due to the fast-magnetosonic mode given in equation ( 5 ). In Fig. 2 , we plot a limit for the amplitude of the power-law type as a function of the spectral tilt n B in a red line. Figure 2. The upper bound on the amplitude of the power-law type for the power spectrum as the function of n B from the magnetic reheating of the fast-magnetosonic mode (red) and Alfvén-magnetosonic mode (blue). The constraint from the Planck (Planck Collaboration XIX 2016 ) is also shown. Note that n B = −3.0 corresponds to the scale-invariant power spectrum. We find that blue-tilted spectrum is strongly constrained compared with the scale-invariant spectrum ( n B = −3.0). It is shown that the causal mechanism of PMF generation predicts only a blue spectrum with n B ≥ 2 (Durrer Caprini 2003 ). Therefore, the constraint on the blue-tilted spectrum is suggestive for such a causal mechanism. So far we have considered the case that the Alfvén and


given in Table 1 . Positive time lag hints that the radio emission precedes the X-ray emission but the lag is consistent with zero within Gaussian dispersion. Table 1. Best-fitting parameters of the Gaussian function fitted to the DCF in Fig. 3 according to equation ( 4 ). A is the amplitude of the Gaussian, T is the time-lag, and represents the width. The error in brackets of time-lag T represent the fit errors. Although using a conservative approach, the error on time-lag is given by the Gaussian width, . To further analyse the data, we work with the detrended light curves. The fractional variability amplitude of the radio frequencies is and that of the X-ray is . The normalized detrended flux for both the radio and X-ray emission (normalized with respect to the maximum flux density in their respective light curves) are shown in the top panel of Fig. 4 and a zoom-in of the same for the 5 h simultaneous observations is shown in the bottom panel of Fig. 4 . There is variability with varying amplitude. Qualitatively, the variability at both radio frequencies seems to coincide with the variability in the X-rays (see Fig. 4 ). We perform the cross-correlation analysis using the simultaneous X-ray and radio data of the detrended light curves. Fig. 5(a) shows the cross-correlation between the two radio bands. The DCF peaks at around zero time lag with a coefficient of 0.30 ± 0.04. There is also a correlation at negative time lag of 2.0 ± 0.1 h and positive time lag of 1.7 ± 0.1 h with DCF coefficients of 0.10 ± 0.04 and 0.13 ± 0.04, respectively. These secondary peaks hint at a possible periodicity in the radio data. The cross-correlation between the detrended radio and X-ray data is shown in Fig. 5(b) . The DCF of radio band with X-ray peaks around zero lag with a coefficient of 0.36 ± 0.10. The same DCF pattern is also evident when we correlate the X-ray data with the two independent radio bands (Figs 5c and d ). The DCF of both radio bands with X-ray peaks around zero lag with a coefficient of 0.45 ± 0.10 and 0.42 ± 0.10 for 13–15.5 GHz/0.3–10 keV and 15.5–18 GHz/0.3–10 keV, respectively. Figure 4. Detrended and normalized light curves for comparison. Top: For the entire duration of the observations of about 11 h with 13–15.5 GHz, 15.5–18 GHz, and 0.3–10 keV represented by the red circles, the black squares, and the blue diamonds, respectively. Bottom: Zoom-in of the light curves only for the simultaneous radio and X-ray observations of 5 h. Figure 5. Discrete cross-correlation of detrended light curves of (a) 15.5–18 and 13–15.5 GHz with secondary peaks representing possible periodicity, (b) 13–18 GHz/0.3–10 keV, (c) 13–15.5 GHz/0.3–10 keV, and (d) 15.5–18 GHz/0.3–10 keV. All correlations peak around zero time-lag. The blue-dotted line represents correlation coefficient of zero. As mentioned earlier, the radio and X-ray light curves show variability. The 5 h simultaneous observations of radio and X-ray data do not reveal significant features in


The authors thank Rik Van Lieshout for fruitful discussions and an anonymous referee for an insightful review. Q.K. acknowledges funding from STFC via the Institute of Astronomy, Cambridge, consolidated grant. P.T. dedicates this paper to the memory of André Brahic.


( M *) or the cumulative number density of massive galaxies () over 0.4 z 1.0 (even after accounting for the Eddington bias using the forward-modeling method). In this section, we further investigate the evolution of the SMFs derived using specific sets of M * measurements. We first consider how the SMF changes based on different assumptions for the SFH. In Figure 8 , we show galaxy SMFs derived using stellar masses from different SFHs, including the effects of bursts. It is clear that the effects of SFH, at least among the set of stellar mass estimates used here, on the SMF are minor. In Figure 11 , we illustrate this by comparing the SMFs based on FSPS models with bursts () with those with no bursts (). While there is a slight (≲0.1 dex) increase in characteristic mass derived from SFHs that allow bursts, this falls within the range of uncertainties, and we do not consider it significant. In both cases where we measure the SMF from stellar masses with SFHs that allow and disallow bursts, we find that the characteristic mass shows little evolution from z = 0.4 to 1.5. In Figure 12 , we show the cumulative comoving number density of massive galaxies () derived using stellar masses with different SFHs. In both cases, we normalize the results to the measurement at z = 0.4. Over 0.4 z 1.0, the normalized comoving number density of massive galaxies is approximately constant regardless of SFH. Similarly, the number densities drop by ≲0.3 dex from z = 1.0 to z = 1.5 relative to that at z = 0.4 if we use stellar masses from SFHs that allow bursts. We conclude that the systematic uncertainties arising from the choice of SFH contribute 0.1 dex to the error budget in the growth of the characteristic stellar mass of massive galaxies, which we determined from the combined assumption-average mass function. 6.3. Dependence on SPS Models In Figure 9 we evaluate how three choices for the stellar population models underlying iSEDfit M * estimates impact the derived SMFs and constraints on the growth of massive galaxies. In all cases, we compare only models with smoothly varying SFHs (e.g., no bursts). We show again the FSPS SMF in the left panel. We compare these to the SMFs based on Bruzual Charlot ( 2003 ) masses (, middle panel) and Maraston ( 2005 ) masses (, right panel). The different SPS models lead to different trends in terms of the redshift of the evolution of both the characteristic mass ( M *) of the SMF and comoving number density of galaxies with stellar mass >10 11 M ⊙ . There are competing claims as to the ability of the treatment of TP-AGB stars in the Maraston ( 2005 ) models to reproduce the colors of galaxies and star clusters. Kriek et al. ( 2010 ) found that the Maraston ( 2005 ) models could not simultaneously reproduce the rest-frame optical and near-IR portions of galaxy SEDs. Similarly, Conroy Gunn ( 2010a ) showed that the Maraston ( 2005 ) models produce redder colors at intermediate ages inconsistent with the colors of star


We thank Tobi Heinemann, Ben Chandran, Phil Isenberg, and, in particular, Matt Kunz for fruitful discussions. E.Q. is supported in part by NASA HTP grant NNX11AJ37G, NSF grant AST-1333682, a Simons Investigator award from the Simons Foundation, the David and Lucile Packard Foundation, and the Thomas Alison Schneider Chair in Physics. M.R. thanks support from the Chilean Comisión Nacional de Investigación Científica y Tecnológica (CONICYT; Proyecto Fondecyt Iniciación No. 11121145). D.V. is supported in part by NASA HTP grant NNX11AJ37G and NASA grant NNX12AB27G.


is much shorter than the dynamical time-scale of the system: To test this, we integrate equation ( A14 ) for Δ t = t 1 − t 0 = 1, and leave the rest of the parameters unchanged with respect to the fully adiabatic case shown in the left-hand panel of Fig. A3 . The right-hand panel of Fig. A3 shows the numerical solution in this case (solid black line). It is apparent that when the change in potential is impulsive, the solution to equation ( A14 ) obtained by numerical integration is no longer sensible, which confirms that we can no longer use the ansatz ( A9 ). Instead we need to resort to the arguments summarized in Appendix A1 and derived in Pontzen Governato ( 2012 ). A solution based on the latter is shown in the right-hand panel of Fig. A3 as a red dashed line. We caution the reader that a specific choice of phase underlies this solution, in particular one that maximizes the growth of the amplitude. APPENDIX B: STABILITY OF HALOES SIMULATED IN EQUILIBRIUM In order to assess the intrinsic differences between the adiabatic and impulsive core formation scenarios, we need to ensure that numerical artefacts are well under control in the central regions of the halo where core formation takes place. In particular, we want to ensure that two effects are negligible on the time-scales of our simulations within the region of interest for our work: (i) the growth of numerical errors coming from the initial set-up of a DM halo in equilibrium, and (ii) the development of collisionless relaxation due to particle discreteness. In order to assess the magnitude of these two effects, we look at the stability of the halo set-up in equilibrium in a self-consistent way in Section 3.1 (referred to as the equilibrium case throughout this work). Regarding (i) above, the method we have used (developed in Kazantzidis et al. 2004 ) has been used and tested extensively and we can be confident that numerical errors are under control as long as the amount of simulation particles sampled in the central region is large enough, which is connected to (ii), the issue of particle discreteness. Regarding collisionless relaxation, the relaxation time-scale is given by (Binney Tremaine 1987 ): where N is the number of collisionless particles and t cross is the crossing time. To ensure that an N -body representation of a DM halo does not suffer from gravitational two-body relaxation, the relaxation time needs to be longer than the simulation time. In order to achieve that, we need to avoid very large accelerations arising due to close encounters between simulation particles. Choosing an appropriate softening length ensures this (Power et al. 2003 ). In particular, by demanding that the maximal gravitational force due to two-body encounters (equal to the maximum stochastic softened force) is smaller than the minimum mean field force in the simulation (which occurs at the virial radius), we get From this, it follows that a lower limit to the softening length required to


will require not only a large number of telescopes but many person-hours to plan observations and process the data. Citizen astronomers, citizen science, and educational outreach offer an excellent opportunity to support future space missions. Given the brightness of the host stars of planets found by TESS , even modestly sized telescopes can be used to re-observe these systems, reducing the errors on their ephemerides. The ability of small ground-based telescopes to contribute to exoplanet science is well known (e.g. Kabath et al. 2019 ). The Next Generation Transit Survey (NGTS; Wheatley et al. 2018 ) has shown that sub-millimag precision is achievable by simultaneously observing the same transit with many identical small telescopes and combining data. Using such methods could expand the number of exoplanets that are observable from the ground. Here we present a project to refine the ephemerides of eight exoplanets using a fully robotic telescope network, observations from citizen astronomers, and data from TESS ; a significant portion of the work has been completed by high school students via the Original Research By Young Twinkle Students (ORBYTS) programme. 2 OUTREACH AND CITIZEN SCIENCE PROJECTS The observations and analysis presented here have been achieved via engagement with several citizen science and outreach initiatives and a brief description of each of these is given below. 2.1 Original Research By Young Twinkle Students ORBYTS is an educational programme in which secondary school pupils work on original research linked to the Twinkle Space Mission under the tuition of PhD students and other young scientists (McKemmish et al. 2017a ; Sousa-Silva et al. 2018 ). The ORBYTS programme has been run since 2012 and is jointly managed by Blue Skies Space Ltd. (BSSL) and University College London (UCL). The Twinkle Space Mission 1 is a new, fast-track satellite designed for launch by 2024 and has been conceived for providing faster access to space-based spectroscopic data. While the satellite will also survey Solar system objects (Edwards et al. 2019a , b ), a key science case for Twinkle is the characterization of a population of extrasolar planets via transit and eclipse spectroscopy (Edwards et al. 2019c ). ORBYTS offers school pupils the chance to enrich our understanding of these new worlds by improving our knowledge of the molecules they are made of, their orbits, and their physical properties. This provides a unique opportunity for pupils to undertake cutting-edge science, which has a meaningful impact on a future space mission. To achieve this, ORBYTS partners dynamic, passionate science researchers with secondary schools, where, through fortnightly school visits over an academic year, the researcher teaches the students undergraduate-level physics. The goal of every partnership is that school students will have the opportunity to use this new knowledge to contribute towards publishable research. Pupils get hands on


simple power-law component does not achieve a formally acceptable fit to either spectrum. The fit to the lower-sensitivity spectrum from Obs. 1 measured a power-law index of , but only achieved (where ν is the number of degrees of freedom in the fit). The spectrum of Obs. 2 is steeper, with in this simple fit, and a very fit statistic result owing to the improved S/N: . These simple fits are shown in Figure 2 . The data/model ratio from each fit shows residuals that are consistent with disk reflection, including Fe K emission and a Compton back-scattering excess peaking in the 20–30 keV range. The ratio from Obs. 2 is consistent with blurred reflection from an inner disk that extends close to the black hole, similar to the features observed in the low/hard state of GRS 1915+105 (see Miller et al. 2013a ). Figure 2. NuSTAR spectra of GS 1354−645, fit with a fiducial power-law continuum. The FPMA is shown in black, the FPMB is shown in red, and the model for the FPMA is shown in blue. The data in each panel have been rebinned for visual clarity. Left: the spectrum of Obs. 1 is shown. Right: the spectrum of Obs. 2 is shown. This ratio reveals evidence of strong, broadened reflection consistent with illumination of the inner accretion disk. We next considered fits with relxill (version 0.4c; Garcia et al. 2013 ; Dauser et al. 2014 ). This model includes the power law that illuminates the disk and also incorporates a Kerr blurring function to translate from the frame of the accretion disk to the frame of the observer. It is this function that measures the strong Doppler shifts and gravitational redshifts imprinted on the reflection spectrum. Spin is measured directly using relxill , within the bounds . The inclination of the inner disk—not necessarily the same as the binary system—is also measured directly. For these parameters, values obtained in fits to Obs. 2 were assumed in fits to Obs. 1, owing to its lower sensitivity. Relxill also allows the inner disk to deviate from the ISCO for a given spin parameter, so we also allowed the parameter R in to vary (the model has a hard upper limit of ) in fits to both observations. The emissivity of the disk is described as a broken power law in radius (e.g., ), giving three parameters: q in , q out , and R break . Any corona with an energetic profile defined by the underlying potential and linked to the disk is likely to have a time-averaged emissivity that falls with radius, so we require in fits to both observations. The limited sensitivity of Obs. 1 does not permit more detail to be discerned, so we simply fixed , obviating the meaning of R break . For Obs. 2, however, additional constraints can be imposed based on theoretical and observational expectations. Wilkins Fabian ( 2012 ) have calculated the emissivity profiles expected for idealized point source scenarios, including a “lamp-post” geometry. All calculations assume a disk that extends to the ISCO. The predicted profiles are complex and a


of 90%–100% completeness, while the remainder (12%) lies in the region of 50%–90% completeness. To place an upper limit on the impact of selection biases, we adopt the lower limits of 90% and 50% on the completeness in these two regions of the R eff – H 160 plane, assign weights 2.0 (i.e., 1/0.5) and 1.1 (i.e., 1/0.9) to the galaxies in our sample in these regions, and then recompute the R eff – R 200 c relations. For R 200 c ≳ 100 kpc, we find negligible corrections to the median R eff – R 200 c relations, while for R 200 c ≲ 100 kpc, we find corrections below 0.1 dex for all galaxy types and redshifts 0 z 3. We conclude from this exercise that selection biases are likely to be subdominant sources of uncertainty in our R eff – R 200 c relations. Based on this assessment of uncertainties, most of the results of this paper appear to be robust. In particular, there is a strong, approximately linear correlation between the sizes of galaxies and their dark matter halos over the full range of redshifts examined here, 0 z 3. The coefficient of proportionality is larger for late-type galaxies than for early-type galaxies, which follow roughly parallel sequences, except possibly at the highest redshifts. For late-type galaxies, the observed R eff – R 200 c relation is generally consistent with simple models in which galactic disks grow with the same specific angular momentum as their dark matter halos. There is some evidence for a slowdown in disk growth at z 0.5, but the apparent deviation from the J / M equality line is only ∼0.2 dex. We have plotted and examined the R eff – R 200 c relations at all redshifts (0 z 3) for all four SMHM relations to determine whether or not they support the four main results discussed in Section 4 . The outcome of this test is recorded in Table 2 by a T (for true) or F (for false) for each combination of SMHM relation and result. All of the entries are Ts. Table 2 therefore reinforces our conclusion that the main scientific results of this study are robust relative to discrepancies among the SMHM relations (because of the weak dependence of R 200 c on M 200 c ). Table 2 Verification of Main Results 6. Discussion We have found that the sizes of galaxies are proportional on average to the sizes of their dark matter halos over a wide range of galaxy and halo masses and over the entire redshift range 0 z 3 studied here: R eff = αR 200 c with α ≈ 0.03. In particular, we confirm the basic relation found by Kravtsov ( 2013 ) at z = 0 with only minor adjustment, some of which is related to the difference between 2D half-light radii and 3D half-mass radii. There is some curvature at the upper end of our overall R eff – R 200 c relation, which is due to the larger abundance and smaller average size of early-type galaxies compared with late-type galaxies of the same stellar mass. Indeed, we find that early- and late-type galaxies follow distinct, roughly parallel R eff – R 200 c relations offset by a factor of ∼2 for the


panel d shows the period from cosine fitting, panels e, f, g present the amplitude, the phase, and the spectral power from the cosine fitting, and panel h shows the H α intensity. 3.2.1. Periods We detect oscillatory motions with periods between 5 and 80 min (Fig. 2 c). The shorter periods (5 to 40 min) have a local significance level of around 99%; they last only two to four times their periods and are visible in small areas. It would be interesting to find out where and when they occur, but this is beyond the scope of this study. Here, we concentrate our work on the long periods between 40 and 80 min which were already detected in Paper I. We find that the prominence does not oscillate as a block at these long periods. We identify four main oscillatory areas with a high spectral power (see Fig. 2 g and Table 1 ). We select these four areas with high spectral power and overplot their contours on all the panels of Fig. 2 . For each area, we calculate the mean value of the oscillatory parameters (see Table 1 ). The value of the spectral power in relative units is around 40. The mean oscillation period for areas A1 and A2 is close to 65 min with the two methods (Scargle and cosine fit methods). For area A3 we obtain a value of 45 min. We exclude area A4 from further analysis because of the non-uniform pattern in period, amplitude, and phase distribution, which is a hint of the bad fit of the cosine curve due to high noise. Additionally, the periods calculated using the two methods are significantly different. We may note that a similar period value of 65 min is commonly observed for longitudinal oscillations in prominences ( Luna et al. 2018 ). In areas A1, A2, and A3, the period is nearly uniform (Fig. 2 c). The mean amplitude of the oscillations is between 0.70 km s −1 and 1.43 km s −1 , values larger than the estimation of the error bars. However, higher amplitude values are present in the selected areas, reaching locally 3 km s −1 (Fig. 2 e). We notice another region with even higher amplitude located near the pixel coordinates ( x = 40, y = 150), but the signal has a relatively low spectral power value and is too small to be treated as an oscillating feature. Table 1. Mean oscillatory parameters calculated for areas with the highest spectral power (see Fig. 2 ). 3.2.2. Phase Fitted phase is presented in Fig. 2 f. In areas A2 and A3 at the bottom of the prominence the phase has the same value in each area. Additionally, in each of these two regions the period values are very similar (see Figs. 2 c and d), and the spectral power reaches local peaks (see Fig. 2 g). On the contrary, in area A1 the period and amplitude are similar but the phase does not have a uniform value; it shows a continuous transition between − π and 0 radians. This may be interpreted as the passage of a wavefront of a MHD wave ( Schmieder et al. 2013 ; Ofman et al. 2015 ). The colour gradient gives the direction of the propagation of the wave in the POS. This is


accurately. Accounting for the large equivalent widths of the Hβ lines, we use a 600 s integration time for broad-line (i.e. narrow-band) observations. Figure 2. The SDSS-BOSS spectrum for Target-10. The transmission curve for the Hα filter used to measure the flux contained within the Hβ line is shown in orange and the SDSS i -band filter is shown in green. The region between 6820 and 6960 Å used to determine the median rest-frame L 5100 for the SDSS spectrum is shown in grey. Top: The whole spectrum. Bottom: The region between 6400 and 7000 Å which contains both the broad Hβ line and the region used to measure the rest-frame L 5100 . Our targets span a range of redshifts between 0.350 and 0.398. Therefore, for each source, we use the appropriate Hα photometric filter for which the redshifted Hβ line dominates. For Target-10, we use the Hα-6566 Å narrow-band filter. As seen in Table 1 , we obtain the largest number of acceptable exposures with SDSS-J144645.44+625304.0 (referred to as Target-10 hereafter). Indeed, Target-10 is the only QSO for which we have obtained a baseline of observations longer than the recommended 3 t H β (1 + z ) needed to recover a lag. Thus, in what follows, we only discuss the analysis of Target-10 and defer the rest to a future work. Table 1. Our pre-observation targets selected based on their luminosity, redshift, and visibility. t Hβ (1 + z ) is expected observed-frame lag derived from the Bentz et al. ( 2013 ) t rest – L 5100 relation, where L 5100 is estimated from the SDSS spectrum. We quote the length of time each target is visible and the baseline of the observations in units of days and expected observed-frame lag. 2.3 Ensemble photometry and flux calibration In order to estimate lags between the BLR and the continuum-emitting region of the QSO, we must first calibrate the i -band and Hα photometric magnitudes to a common magnitude system. We are then required to calibrate our i -band photometry using the known SDSS DR12 AB magnitudes of sources in the observed field. We calibrate Hα photometry by propagating available SDSS spectra through the transmission curve for the same narrow-band Hα filter (6566 Å) used to observe the Hβ line in Target-10, accounting for the fibre aperture. We perform aperture photometry using source extractor (Bertin Arnouts 1996 ) to estimate Petrosian magnitudes (Petrosian 1976 ; Graham et al. 2005 ) for each detected source in the field for both i -band and Hα exposures. We use Petrosian magnitudes in order to calibrate each exposure to the SDSS catalogue and to easily avoid the effects of differing seeing between our observations without modelling the point spread function (PSF). We consider only those sources which have SDSS clean = True and source extractor flags = 0 for use as reference sources. We can then apply a similar ensemble photometry method to that detailed by Honeycutt ( 1992 ), on the i -band exposures and calibrate those instrumental magnitudes to the SDSS


J.A.l.R. acknowledges support from NASA grants NNX14AF43G and NNX14AJ53G. J.A.l.R. and G.M.W. were also supported by NASA grant NNX15AI65G. G.P.Z. was supported by NASA grants NNX08AJ33G, Subaward 37102-2, NNX09AG70G, NNX09AG63G, NNX09AJ79G, NNG05EC85C, Subcontract A991132BT, NNX09AP74A, NNX10AE46G, NNX09AW45G, and NSF grant ATM-0904007. This work was also supported in part by a UAH IIDR award to G.P.Z. O.K. was supported by RFBR grants no. 14-02-00769 and no. 16-02-00479.


Acknowledgments We thank the anonymous referee for their comments. MJM acknowledges the support of a UK Science and Technology Facilities Council (STFC) funded PhD. SPL and VSD are supported by STFC grant ST/J001589/1. TRM and EB are supported by the STFC grant ST/L000733/1. VSD and TRM acknowledge the support of the Leverhulme Trust for the operation of ULTRASPEC at the TNT. Support for this work was provided by NASA through Hubble Fellowship grant HST-HF2-51357.001-A. The research leading to these results has received funding from the European Research Council under the European Unions Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement n. 320964 (WDTracer). The results presented are based on observations made with the WHT , operated at the Spanish Observatorio del Roque de Los Muchachos of the Instituto de Astrofsica de Canarias by the Isaac Newton Group, as well as the TNT, operated at the Thai National Observatory by the National Astronomical Research Institute of Thailand. This research has made use of NASAs Astrophysics Data System Bibliographic Services.


ACKNOWLEDGEMENTS This work was supported by the European Research Council under the European Commission’s Seventh Framework Programme (FP7/2007-2013 grant agreement no. 339248). The calculations discussed in this paper were performed on the DiRAC complexity system, operated by the University of Leicester IT Services, which forms part of the STFC DiRAC HPC Facility ( www.dirac.ac.uk ), and the University of Exeter Supercomputer, Isca. The former equipment was funded by BIS National E-Infrastructure capital grant ST/K000373/1 and STFC DiRAC Operations grants ST/K0003259/1 and ST/M006948/1. DiRAC is part of the National E-Infrastructure.


We acknowledge support from the Knud Højgaard Foundation, the Villum Foundation (Project No. 13164), the Danish National Research Foundation (DNRF91), the Deutsche Forschungsgemeinschaft under the Excellence Cluster Universe (Grant No. EXC 153), and the European Union under the Innovative Training Network “Elusives” (Grant No. H2020-MSCA-ITN-2015/674896) and under the ERC Advanced Grant No. 341157-COCO2CASA. We thank the Institute for Nuclear Theory at the University of Washington for hospitality and the DOE for partial support during early stages of this work.


The authors acknowledge support from NewCompstar, COST Action MP 1304. R.O. Gomes and S. Schramm acknowledge support from HIC for FAIR. This work was also partially supported by grant No. BEX 14116/13-8 of the PDSE CAPES and Science without Borders programs, which are an initiative of the Brazilian government.


We thank the referee for making very helpful comments and suggestions.


Acknowledgements We thank the anonymous referee for his/her useful comments and suggestions. L.M. acknowledges support from “Proyecto interno” of the Universidad Andres Bello. P.B. acknowledges financial support from the Scientific Council of Observatoire de Paris and from the action fédératrice “Exploitation Gaia”. S.V. gratefully acknowledges the support provided by Fondecytreg. n. 1170518.


We warmly thank our anonymous referee whose comments significantly improved this paper. The authors would like to thank Carolyn Doherty, Simon Campbell, Luca Casagrande and Warrick Ball for useful discussions. We also thank David Nataf and Alessio Mucciarelli for providing us with their data tables. GCA would like to thank the staff at MoCA for their help and support through the duration of his PhD part of the research leading to the presented results has received funding from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no. 338251 (StellarAges). VD'O is partially supported by an ARC grant (Super Science Fellow 2011). RPC is supported by the Swedish Research Council (grants 2012-2254 and 2012-5807). RJS is a recipient of a Sofja Kovalevskaja Award from the Alexander von Humboldt Foundation, by ARC DP1095368 and Discovery Grant. This work was supported in part by ARC DP1095368 and Discovery Grant DP120101815 (PI: J. Lattanzio) at Monash University, Clayton, Australia.


Acknowledgement We thank Patrick Dufour and Simon Coutu for sharing with us a poster presented at the EUROWD-21 workshop in Austin 2018. We have used their results in the belief that they are public. Only very recently we realized that this paper is not available in the public archive of the conference. We acknowledge that Coutu et al. (2018) was the first paper to determine carbon abundances for DQ using Gaia data. Our current study was motivated by their results. This work was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001, Conselho Nacional de Desenvolvimento Científico e Tecnológico - Brasil (CNPq), and Fundação de Amparo à Pesquisa do Rio Grande do Sul (FAPERGS) – Brasil. This research has made use of NASA’s Astrophysics Data System Bibliographic Services, the SIMBAD database, operated at CDS, Strasbourg, France, the NIST and VALD atomic databases, and public data from the Sloan Digital Sky Survey and the Gaia Mission.


The authors thank Judd Bowman, Adam Lidz, Rennan Barkana, Anastasia Fialkov, and Jordan Mirocha for useful discussions, along with Florian Bolgar for correcting several numerical errors. Calculations in this work were performed using the Colossus library (Diemer 2017 ). A.E.W.’s contribution was supported by an appointment to the NASA Postdoctoral Program at the California Institute of Technology Jet Propulsion Laboratory. Part of the research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. R.A.M. was supported by the NASA Solar System Exploration Virtual Institute cooperative agreement 80ARC017M0006.


This research was supported under the Australian Research Council's Discovery Projects funding scheme (project number DP 120102393). We acknowledge the AAVSO network of variable star observers for providing the optical light curves of SS Cyg. JCAM-J is the recipient of an Australian Research Council Future Fellowship (FT140101082). GRS acknowledges funding from an NSERC Discovery Grant. DA acknowledges support from the Royal Society. KLP acknowledges support from the UK Space Agency. This work was supported by the Spanish Ministerio de Economá y Competitividad (MINECO) under grant AYA2013-47447-C3-1-P (SM). This work has made use of NASA's Astrophysics Data System. This research made use of APLpy, an open-source plotting package for python hosted at http://aplpy.github.com . The International Centre for Radio Astronomy Research is a joint venture between Curtin University and the University of Western Australia, funded by the state government of Western Australia and the joint venture partners. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. The Westerbork Synthesis Radio Telescope is operated by the ASTRON (Netherlands Institute for Radio Astronomy) with support from the Netherlands Foundation for Scientific Research (NWO). The European VLBI Network is a joint facility of independent European, African, Asian and North American radio astronomy institutes. This research has made use of data and/or software provided by the High Energy Astrophysics Science Archive Research Center (HEASARC), which is a service of the Astrophysics Science Division at NASA/GSFC and the High Energy Astrophysics Division of the Smithsonian Astrophysical Observatory.


Acknowledgements The authors wish to acknowledge the contribution of Henk Spruit, who visited Monash University as part of the Monash Centre for Astrophysics Distinguished Visitor Program in 2014. This project was partly supported by the European Research Council through ERC Advanced Grant No. 320478–TOFU.


positions, which are greatly improved by refining PECs using experimentally measured line positions, this is seldom true for the line intensities, for which DM and TDM curves are usually best computed ab initio (Tennyson 2014 ). The line intensities, which are directly based on the ab initio DMCs, often suffer from the numerical noise, especially those from the overtone transitions (Medvedev et al. 2016 ). In order to reduce this noise, it was sufficient to apply a dipole moment cut-off of 10 −8 D to the vibrational transition matrix elements, see e.g. Yurchenko et al. ( 2018c ). When computing these matrix elements, the original ab initio X – X and A – X (T)DMCs were mapped on the duo grid using the standard cubic spline interpolation technique. The final spectroscopic model in the form of the duo input file is provided as part of the supplementary data to this paper and can be also found at www.exomol.com . This also includes our fitting set of experimental frequencies. A sample of the refinement to the data of Ramsay ( 1952 ) for the X 2 Π – A 2 Σ + system is shown in Table 2 . The Obs. − Calc. values of the fit are comparable to the actual experimental measurement uncertainty. Although these may seem from the outset to be of much lower accuracy compared to previous ExoMol line lists for non-transition metal-containing diatomics, given that in the regime of ≈30 000 cm −1 an uncertainty of 0.5 cm −1 corresponds to a resolution R of ≈60 000, which is within the realms of high-spectral resolution methods of characterizing exoplanet atmospheres (Snellen 2004 ; de Kok et al. 2014 ). For all isotopologues of SH-type ( 33 SH, 34 SH, 36 SH), we use the same empirical model (PECs, SOCs, EAMCs, SRCs, and BOBCs) developed for 32 SH. When solving the Schrödinger equation, the mass of sulphur is replaced by the nuclear mass of the corresponding isotope. For the isotopologue 32 SD, however, this approach usually leads to too large discrepancies with the experimental line positions. We have therefore refined the 32 SH model by fitting to the experimental line positions of 32 SD from the A – X band, which were taken from the same sources listed in Table 1 . Ideally, this refinement should be only applied to the BOB-correction. However, due to the lack of the experimental data on the X 2 Π state for SD, we could not build an accurate and self-consistent model without including other curves into the fit. We have therefore varied the parameters of PEC( A ), PEC ( B ), BOBC ( X ), BOBC ( A ), SRC ( X ), and SRC ( A ) by fitting to the SD line positions from Ramsay ( 1952 ), Johns Ramsay ( 1961 ), and Pathak Palmer ( 1969 ). All other curves were fixed to the those from the spectroscopic model of 32 SH, including PEC( X ), SOC ( X ), SOC( X – A ), SOC( X – B ), SOC( A – B ), EAMC( X – A ), and EAMC( A – B ). The rms error of this fit to the A – X line positions if SD is 0.4 cm −1 . The spectroscopic model for SD is included in the supplementary material as a


The authors would like to thank Daniel Gifford and Doron Lemze for helpfully answering questions regarding the caustic technique and useful comments. We also thank the anonymous referee for constructive comments which helped to improve the work. The Dark Cosmology Centre is funded by the Danish National Research Foundation. RW acknowledges support through the Porat Postdoctoral Fellowship.


in this limit. is given bywhere n , a , e , i are a resonant eKBO’s mean motion, semimajor axis, eccentricity, and inclination (relative to HP’s orbit plane), is the planet’s semi-minor axis, and c is a numerical coefficient whose asymptotic value is ∼5.8 for a ≪ a ′ ( c will be larger for a approaching a ′). For numerical estimates we adopt e ′ = 0.2 and c = 8. We find that for m ′ = 10 M ⊕ , the small amplitude oscillation periods for the four eKBOs are 0.6–0.94 Gyr, a factor of a few smaller than the age of the solar system. We conclude that 10 M ⊕ is approximately the minimum mass necessary to maintain periodic orbits of the third kind for the four eKBOs. 2.3. Planet’s Current Location in Its Orbit Each resonant eKBO constrains the longitude of HP because the critical resonant angle must librate about either 0° or 180°. For illustration, consider the libration of about 180° for Sedna’s 3/2 resonant orbit. Given that Sedna is presently near its perihelion, λ ≈ π , the planet can be in proximity to one of three longitudes: 60°, 180°, or 300° from Sedna’s longitude of perihelion, π . The trace of the resonant orbit in the rotating frame (Figure 2 ) shows that libration of φ would allow the planet to be located as far as ∼54° from these longitudes. This means that only three small zones of ±6° around each of three locations, π , and are excluded for the planet’s present location. For e ′ = 0.2, we find that the excluded zone is a little larger, ±75 around each of the same three locations. However, such geometric estimates of exclusion zones do not account for the planet’s gravity. To account for this, we computed surfaces of section for the circular planar restricted three body problem for several values of the planet mass in the range of 10 −6 –10 −3 M ⊙ , for the neighborhood of the 3/2, 5/2, 3/1, and 4/1 MMRs and the extreme eccentricities of the four eKBOs (0.85, 0.87, 0.85 and 0.7, respectively). Figure 4 shows a sample of these for planet mass 3 × 10 −5 M ⊙ (approximately 10 M ⊕ ). From these surfaces of section, we determine the range of excluded longitudes of the planet by measuring the complement of the large libration zones of the 3/2 and 5/2 MMRs. We also conservatively exclude a small range, ±5°, around the homoclinic points of the 3/1 and 4/1 resonant eKBOs. Figure 5 shows our estimates of the excluded zones, projected on the sky, for a planet of mass 3 × 10 −5 M ⊙ ; we plot a representative case of the planet’s low inclination orbit (in green) and also a representative case of its high inclination orbit (in red). (Note that a range of orbital planes near each of these representative cases is allowed by our calculations.) We find that approximately half of the ecliptic longitudes are excluded in both cases; the excluded zone is not contiguous. Figure 4. Surfaces of section for the circular planar restricted three body problem, for mass ratio , and Jacobi constant values as indicated. These are phase space portraits in the


is of similar order to earlier UV-based measurements (∼1 M ⊙ yr −1 ; Shull et al. 2009 ; Lehner Howk 2011 ; R17 ), but higher than radio-based measurements derived from large 21 cm HVCs (≈0.08 M ⊙ yr −1 ; Putman et al. 2012 ) and higher than the flow rates derived for individual clouds like Complex C (≈0.1 M ⊙ yr −1 ; Wakker et al. 1999 ; Collins et al. 2003 ; Shull et al. 2011 ). This makes sense because most HVC mass is in ionized HVCs (Lehner Howk 2011 ). The ratio of the UV inflow rate to the 21 cm inflow rate quantifies the relative mass in ionized and neutral gas. Our inflow rate calculations indicate (H ii )/ N (H i ), equivalent to a mean HVC ionization fraction f H II = N (H ii )/ N (H i +H ii ) = 0.87. This is higher than the mean ionization fraction reported in large 21 cm HVCs such as Complex C and Complex A because such large clouds are atypical; most HVCs are ionized and not detected at 21 cm (Shull et al. 2009 ; Lehner Howk 2011 ; R17 ). For comparison with the HVC mass flow rates, the intermediate-velocity mass flow rates are of interest. These can be derived from optical observations of Ca ii and Na i absorption (Ben Behkti et al. 2012 ). The Ca ii and Na i doublets are much less saturated than UV resonance lines, particularly at intermediate velocities, resulting in cleaner measurements. Ben Behkti et al. ( 2012 ) report a population of Ca ii IVCs with a sky covering factor of ≈30%, a mean v GSR = −42 km s −1 , and an associated N (H i ) distribution peaking near log N (H i ) ≈ 19. Combining these numbers with a typical IVC distance of 2 kpc (Richter et al. 2017 ) we derive an H i mass flow rate of ≈0.04 M ⊙ yr −1 in these Ca ii IVCs. If a similar ionization correction N (H ii )/ N (H i ) = 6.6 applies to IVCs as to HVCs, then IVCs represent a total mass flow rate of ≈0.27 M ⊙ yr −1 , comparable to the HVC flow rate (this similarity occurs because the larger column densities of IVCs are compensated by their smaller velocities and distances). To fully explore this, a more thorough investigation of the IVC mass flow rates using UV data would be worthwhile, including a distinction into inflow and outflow and detailed ionization modeling. We emphasize that the HVC mass flow rates derived in this paper are effectively instantaneous , as they represent the mass flux contained in HVCs observed at the current epoch. Hydrodynamic simulations (Heitsch Putman 2009 ; Armillotta et al. 2017 ) show that HVC lifetimes are typically a few 100 Myr depending on HVC mass and the density contrast with the surrounding hot medium, after which the clouds will become disrupted and evaporated by coronal interactions. Caution should therefore be used in integrating our mass flow rates over long timescales to calculate the total mass delivered in and out of the disk, as the gas will change phase over time via evaporation and subsequent condensation (e.g., Fraternali 2017 ; Voit et al. 2019 ). Finally, we can use our HVC mass outflow rate measurement to


ACKNOWLEDGEMENTS FEM and EEM acknowledge support from National Science Foundation (NSF) award AST-1313029. Part of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration (NASA). EEM acknowledges support from the Jet Propulsion Laboratory Exoplanetary Science Initiative and the NASA NExSS Program. KL was supported by grant AST-1208239 from the NSF. We thank the staff of CTIO and the Blanco 4-m telescope in particular for their help and hospitality during the 2013 and 2015 observing runs. We thank Frank Valdes and Robert Gruendl for their help understanding the DECam community pipeline and calibration of photometry and astrometry. The Center for Exoplanets and Habitable Worlds is supported by the Pennsylvania State University, the Eberly College of Science, and the Pennsylvania Space Grant Consortium. We thank the anonymous referee for a very thorough report which significantly improved the paper.


The authors would like to thank Alan Calder for many fruitful discussions and exchanges. Part of the software used in this work was developed by the DOE-supported ASC/Alliances Center for Astrophysical Thermonuclear Flashes at the University of Chicago. This work has been partially supported by the Spanish MINECO grant AYA2014–59084–P, by the E.U. FEDER funds, by the AGAUR/Generalitat de Catalunya grant SGR0038/2014, and by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics. We also acknowledge the Barcelona Supercomputing Center for a generous allocation of time at the MareNostrum supercomputer.


ACKNOWLEDGEMENTS We thank an anonymous referee for stimulating comments and Elisabeta Lusso and Gabriele Ghisellini for sharing results of previous publications. The data collected by the WEBT collaboration are stored in the WEBT archive at the Osservatorio Astrofisico di Torino – INAF ( http://www.oato.inaf.it/blazars/webt/ ); for questions regarding their availability, please contact the WEBT President Massimo Villata ( massimo.villata@inaf.it ). This publication uses data obtained at Metsähovi Radio Observatory, operated by Aalto University in Finland. We acknowledge financial contribution from the agreement ASI-INAF n.2017-14-H.0 and from the contract PRIN-SKA-CTA-INAF 2016. PR and SV acknowledge contract ASI-INAF I/004/11/0. We acknowledge support by Bulgarian National Science Programme ‘Young Scientists and Postdoctoral Students 2019’, Bulgarian National Science Fund under grant DN18-10/2017 and National RI Roadmap Projects DO1-157/28.08.2018 and DO1-153/28.08.2018 of the Ministry of Education and Science of the Republic of Bulgaria. GD and OV gratefully acknowledge the observing grant support from the Institute of Astronomy and Rozhen National Astronomical Observatory, Bulgarian Academy of Sciences via bilateral joint research project ‘Study of ICRF radio-sources and fast variable astronomical objects’ (head – G.Damljanovic). This work is a part of the Projects No. 176011 (‘Dynamics and Kinematics of Celestial Bodies and Systems’), No. 176004 (‘Stellar Physics’), and No. 176021 (‘Visible and Invisible Matter in Nearby Galaxies: Theory and Observations’) supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia. This research was partially supported by the Bulgarian National Science Fund of the Ministry of Education and Science under grants DN 08-1/2016, DN 18-13/2017, and KP-06-H28/3 (2018). The Skinakas Observatory is a collaborative project of the University of Crete, the Foundation for Research and Technology – Hellas, and the Max-Planck-Institut für Extraterrestrische Physik. The St Petersburg University team acknowledges support from Russian Science Foundation grant no. 17-12-01029. The Abastumani team acknowledges financial support by the Shota Rustaveli National Science Foundation under contract FR/217950/16. This work was partly supported by the National Science Fund of the Ministry of Education and Science of Bulgaria under grant DN 08-20/2016, and by funds of the project RD-08-37/2019 of the University of Shumen. The Astronomical Observatory of the Autonomous Region of the Aosta Valley (OAVdA) is managed by the Fondazione Clément Fillietroz-ONLUS, which is supported by the Regional Government of the Aosta Valley, the Town Municipality of Nus and the ‘Unité des Communes valdôtaines Mont-Émilius’. The research at the OAVdA was partially funded by two ‘ Research and Education’ grants from Fondazione CRT. This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.


We thank Y. Qian and P. Banerjee for help with the torch network code. DK is supported in part by a Department of Energy Office of Nuclear Physics Early Career Award, and by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Divisions of Nuclear Physics, of the US Department of Energy under contract no. DE-AC02-05CH11231. RF was supported by NSF Division of Astronomical Sciences collaborative research grant AST-1206097, and a UC Office of the President grant. BDM gratefully acknowledges support from the NSF grant AST-1410950 and the Alfred P. Sloan Foundation. This work was supported in part by NSF grant no. PHYS-1066293 and the hospitality of the Aspen Center for Physics. The software used in this work was in part developed by the DOE NNSA-ASC OASCR Flash Center at the University of Chicago. We are grateful for computing time made available by the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the US Department of Energy under contract no. DE-AC02-05CH11231. Computations were performed using Carver and Hopper .


the behaviour of emission lines at 0.913 keV (Ne ix ) and 1.02 keV (Ne x ) with the pulse phase. We summarize the results as follows: Light curve obtained using the EPIC -pn data during its current spin-up phase showed dips. Unlike other flaring sources like LMC X–4 and SMC X−1, it is interesting to notice a broad dip in the light curve soon after the decay of a large flare. This feature is similar to that observed in the bursting pulsar, GRO J1744−28. The light curve of GRO J1744−28 showed the presence of a dip and recovery period following each outburst (see e.g. Giles et al. 1996 ) and the X-ray spectrum of GRO J1744−28 showed no significant change going from quiescence to outburst (Cannizzo 1996 ). The same authors proposed that the outbursts observed in the bursting pulsar could be due to Lightman–Eardley instability (Lightman Eardley 1974 ) in the accretion disc and the material that is evacuated on to the pulsar during an accretion event is replenished by material flowing in from further out; hence, the dip and recovery in the light curve following an outburst. After performing intensity-resolved spectroscopy of 4U 1626−67, we found that overall there is no change in the shape of shape of the spectrum (see Fig. 9 ) except that the continuum and line parameters follow an increasing trend with intensity. Therefore, it is plausible that a similar mechanism might be responsible for the presence of flares and sharp dips in the light curve of 4U 1626−67. A QPO feature around 3 mHz is observed in the PDS. This feature has been observed for the first time using X-ray data of current spin-up phase. The feature at 3 mHz also shows strong energy dependence. The feature is sharp at low energies as flares dominate at low energies. The energy dependence of fractional rms amplitude of a QPO has been used as a tool to understand the physical origin of the QPO (see e.g. Gilfanov, Revnivtsev Molkov 2003 ; Cabanac et al. 2010 ; Mukherjee Bhattacharyya 2012 ). The fractional rms amplitude of a 3 mHz QPO observed in 4U 1626−67 showed an increase up to 5 keV and thereafter its value saturates (probably due to lower count rates at higher energies). Therefore, it seems that fluctuations in the blackbody component could be a plausible cause of the observed mHz QPO in 4U 1626−67. We found that the pulse profile shape below 2 keV is different from that seen during spin-down phase of 4U 1626−67 (Fig. 4 ). Moreover, during its spin-up phase, pulse profiles below 2 keV are quite different from that seen above 2 keV (Fig. 3 ). A possible explanation to these observations is changes in the emission diagram of the accretion column. During the low-luminosity phase (spin-down) of 4U 1626−67, the emission of the accretion column is concentrated in a beam, oriented along the magnetic field axis while during the high-luminosity phase (spin-up) the emission diagram changed to the fan beam pattern (Basko Sunyaev 1975 ). Soft X-ray emission (below 2 keV) is attributed to


We thank Arash Bahramian, Nate Bastian, Robert Mathieu, Wolfram Kollatschny, Stan Lai, and Mark Gieles for helpful discussions. BG, SD, SK and PMW acknowledge support from the German Ministry for Education and Science (BMBF Verbundforschung) through grants 05A14MGA, 05A17MGA, 05A14BAC, and 05A17BAA. AA is supported by the Carl Tryggers Foundation for Scientific Research through the grant CTS 17:113. SK gratefully acknowledges funding from a European Research Council consolidator grant (ERC-CoG-646928- Multi-Pop). JB acknowledges support by FCT/MCTES through national funds by grant UID/FIS/04434/2019 and through Investigador FCT Contract No. IF/01654/2014/CP1215/CT0003. This research is supported by the German Research Foundation (DFG) with grants DR 281/35-1 and KA 4537/2-1. Based on observations made with ESO Telescopes at the La Silla Paranal Observatory under programme IDs 094.D-0142, 095.D-0629, 096.D-0175, 097.D-0295, 098.D-0148, 0100.D-0161, 0101.D-0268, 0102.D-0270, and 0103.D-0204. Based on observations made with the NASA/ESA Hubble Space Telescope, obtained from the data archive at the Space Telescope Science Institute. STScI is operated by the Association of Universities for Research in Astronomy, Inc. under NASA contract NAS 5-26555. Supporting data for this article is available at: http://musegc.uni-goettingen.de .


). Stars and SPH particles were coupled by direct point-to-point interaction, without any approximation for the gravitational field. Finally, we corrected the gas positions and velocity according to Eq. ( A.4 ) by recalculating the accelerations and the energy rates at the new stage n + 1. Appendix B: Technical features B.1. Neighbor search and acceleration updating Before we employed it to compute gravitational interactions, the tree grid was also used to support the operations related to the nearest-neighbor search. To calculate the density and the smoothing length, each i th particle starts with a first-guess value of h i and makes a tree walk by adopting an opening criterion that is slightly different from Eqs. ( 20 ) and ( 21 ). Given a generic particle of index i, in order to find the other points enclosed in its SPH kernel support, we checked for each cube the overlap with a sphere of radius 2 h i centered onto the point r i = ( x i , y i , z i ). A box is opened only if the following three conditions are valid: where ( x A , y A , z A ) are the coordinates of the geometrical center of the cube and D L is its side length. The tree walk continues by opening the further cubes according to the last rule, until the single particles are reached and the neighborhood is thus determined. At the end of the walk, a temporary value of density ρ i is calculated. If the number of encountered neighbors differs from the expected number (and the difference exceeds the tolerance number), h i is updated according to Eq. ( 5 ). Then, a new tree walk is performed, and a new value for the density is computed. The tree walk and the h i , ρ i updating are executed cyclically until the number of neighbors converges on the desired value. During the tree walk, the various quantities P i , Ω i , ζ i , f , ∇ ⋅ v i , and ∇ × v i are computed at the same time together with the density. After this preliminary phase, the acceleration a and the thermal energy rate can be computed by performing a further tree walk for each particle. During the walk, the hydrodynamics contribution to the acceleration and the gravity field are computed at the same time. For each box, before Eq. ( 20 ) (or Eq. ( 21 )) is applied, the code primarily checks Eq. ( B.1 ) to distinguish cubes that might contain some neighbor particles for the SPH interpolation. If this is satisfied, the box is opened, otherwise the particles inside will not contribute at all to hydrodynamics. After this primary check, the algorithm performs a secondary control by applying the opening criterion of Eq. ( 20 ) (or Eq. ( 21 )) to decide whether the multipole approximation can be applied to the Newtonian field. As a result, practically, a generic i th particle will interact with its local SPH neighborhood following Eqs. ( 7 ) and ( 8 ), experiencing the Newtonian force through a direct particle-to-particle interaction. The remaining particles that lie outside the SPH domain contribute to the accelerations with or


B ), which can be used not only to capture complicated patterns between variables and to keep a good balance between bias and variance, but also to identify the most important variables that explain model predictions. We address the second problem by using a linear dimension reduction algorithm, the principal component analysis (PCA; see Appendix A ), which can effectively reduce the dimension of the halo AH and the galaxy SFH and yet retain large amounts of information of the histories for the empirical modelling. Finally, we address the third problem by building a deep model that incorporates components of both dimension reduction and ensemble regressor and classifier. Each component in the model is motivated physically and can be optimized separately. This approach makes the model capable of dealing with complex patterns in parameter space, and yet transparent to interpret. The ensemble regressor and linear dimension reduction method has already been used to study the relationship among halo properties in Chen et al. ( 2020 ). Here, we extend it to studying the galaxy–halo connection. As the first in a series, this paper focuses on central galaxies in dark matter haloes. We identify important ingredients that should be included in an empirical model, and demonstrate the limit such a model can reach in describing the stellar masses and SFHs of individual galaxies. Our model is built on the inferences from two hydrodynamic simulations, the Illustris-TNG (e.g. Nelson et al. 2019 ) and EAGLE (e.g. The EAGLE team 2017 ). This paper is organized as follows. In Section 2 , we describe the simulation data we use, and define the halo properties and samples used in our analysis. In Section 3 , we use both the GBDT and PCA to study the relations of galaxy stellar mass and SFR with halo properties for both star-forming galaxies and quenched galaxies. We also identify halo properties that cause a galaxy to quench. In Section 4 , we build an empirical model that predicts the SFH of galaxies in dark matter haloes, testing its performance in several steps. We summarize and discuss our results in Section 5 . 2 THE DATA 2.1 The Illustris-TNG and EAGLE simulations The Illustris-TNG simulation (Marinacci et al. 2018 ; Naiman et al. 2018 ; Nelson et al. 2018 , 2019 ; Springel et al. 2018 ; Pillepich et al. 2018b ) is a suite of cosmological, hydrodynamical simulations implemented with the moving-mesh code Arepo (Springel 2010 ). The cosmological parameters are taken from the Planck 2015 results (Planck Collaboration XIII 2015 ): Hubble constant with h = 0.6774, cosmological constant Ω Λ,0 = 0.6911, matter density Ω M,0 = 0.3089, baryon density Ω B,0 = 0.0486, and initial power spectrum with normalization σ 8 = 0.8159 and index n s = 0.9667. The simulated physical processes for galaxy formation include gas cooling, star formation, stellar feedback, metal enrichment, black hole feedback, and so on. The details can be found in the two method papers, Weinberger


We want to thank Chris Carilli for assistance on the simulations of the ngVLA observations and for providing us with the ngVLA antenna position files, and Giovanni Dipierro for helpful comments on the manuscript. This work was supported in part by the ngVLA Community Studies program, coordinated by the National Radio Astronomy Observatory, which is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. A.I. and L.R. acknowledge support from NSF grant No. AST-1535809. A.I., S.L., and H.L. acknowledge the support from the Center for Space and Earth Sciences at LANL, and H.L. acknowledges the support from the LANL/LDRD program. ALMA is a partnership of ESO (representing its member states), NSF (USA), and NINS (Japan), together with NRC (Canada) and NSC and ASIAA (Taiwan) and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO, and NAOJ. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.