sample into three metallicity bins ([Fe/H] −1.5, −1.5 [Fe/H] −0.7, and [Fe/H] > −0.7) and plot the difference between CaT based and literature [Ca/H] as a function of half-mass relaxation time for each bin in Fig. 26 . For the low-metallicity bin, Kendall’s test provides weak evidence (τ = 0.26 and p = 0.07) for a correlation. Using pymc3 , we fit a significant slope () and find that a linear relationship is favoured over a constant value (ΔBIC = 9.2) for 24 GCs in the low-metallicity bin. The nuclear remnant NGC 5139 appears to be a significant outlier from the low-metallicity GC relationship. For both the 20 GCs in the intermediate-metallicity bin and the eight GCs in the high-metallicity bin, Kendall’s test provides no evidence (τ = 0.18, p = 0.27 and τ = 0.00, p = 1.0, respectively) for a correlation. The pymc3 fits finds an insignificant slope for the intermediate-metallicity subsample (), but a marginally significant slope for the metal-rich subsample (). Neither subsample shows strong evidence that a linear relationship is preferred over a constant value (ΔBIC = −5.7 and 2.3, respectively). A significant relationship between the CaT and the half-mass relaxation time only at low metallicity is consistent with the behaviour of the CaT with the slope of the stellar mass function. For both the mass function slope and the relaxation time relations, the relationship for all GCs in our sample is driven by the low-metallicity GCs. Figure 26. Differences between literature and our CaT-based [Ca/H] as a function of the half-mass radius relaxation time. From top to bottom, we show the difference for GCs with [Fe/H] −1.5, −1.5 [Fe/H] −0.7, and [Fe/H] −0.7. The black line in the top panel shows our fitted relationship between Δ[Ca/H] and the relaxation time for the lowest metallicity GCs. The colours, shapes, and size of the points are the same as in Fig. 18 . Since the slope of the mass function and the relaxation time are anticorrelated, the relaxation time increases from right to left to match the trend seen between the CaT and the mass function slope. As in Fig. 19 , the dashed line shows Δ[Ca/H] = 0, while the dotted lines show Δ[Ca/H] = ±0.1. The lowest metallicity GCs with longer relaxation times show stronger CaT strengths than GCs with shorter relaxation times and the same metallicity. However, intermediate- and high-metallicity GCs show no relationship between CaT strength and relaxation time at fixed metallicity. The observed qualitative behaviour of the CaT with the stellar mass function slope and metallicity is consistent with the predictions of stellar population synthesis models. The Vazdekis et al. ( 2003 , 2012 ) models predict that the slope of the relationship between the CaT strength and the slope of the stellar mass function as a strong function of metallicity, with a strong anticorrelation between the two at low metallicities, little or no mass function dependence at intermediate metallicities and a strong correlation at solar


and one, two, or three Faraday-thin components, each with a contribution to the polarized emission as given in equation ( 4 ), approximated to be independent of frequency over our band. We did not fit for any models with Faraday-thick components, as LOFAR HBA is minimally sensitive to these: from equation ( 3c ), the maximum scale recoverable is φ max-scale = 0.46 rad m −2 , so any polarized source with Faraday thickness exceeding this would not be properly recovered, although the edges in its Faraday spectrum might be visible if they were sufficiently sharp (Van Eck et al. 2017 ). In order to evaluate the quality of the fits across the knot and the lobe we calculate for each pair of models the Bayes factor, K , which is given by where each model M i is defined in terms of parameters θ i , is assigned a prior Pr(θ i | M i ), fits the data with likelihood Pr( D |θ i , M i ), and is supported by Bayesian evidence Pr( D | M i ). Following Kass Raftery ( 1995 ), we evaluate the Bayes factor based on the derived value 2ln K : a positive value supports model 2, constituting weak (values 2), positive (2–6), strong (6–10), or very strong (>10) evidence. Negative values of 2ln K , similarly, support model 1. Fig. 15 shows the results for the model with one Faraday-thin source. The evidence of the models with two or three Faraday-thin sources is less than the evidence for all other tested models and so is not shown. Fig. 15(a) shows the Faraday depth found for the one-source model for each pixel, where it is favoured over the null hypothesis with K > 1. Fig. 15(b) shows 2ln K > 2, where white to blue (2ln K > 2) indicates support for the one-source model and red (2ln K 2) indicates support for the null hypothesis. We find an average Faraday depth in the knot of −50.8 rad m −2 . Despite the fact that there is a significant polarized region detected at 5σ in the Faraday spectrum of the lobe, only 10 pixels are detected in the lobe with the presence of a source favoured over the null hypothesis with K > 1. The average Faraday depth of these pixels is −53.6 rad m −2 , in agreement with that measured from the Faraday spectra, with a standard deviation of 0.7 rad m −2 . The difference of 2.8 rad m −2 between the Faraday depths in the knot and the lobe is significant against this uncertainty. Figure 15. Results of the QU fitting. (a) shows the Faraday depth of the component found for a single Faraday-thin screen plus instrumental polarization. (b) The Bayes factor when comparing the fits for a single thin screen plus instrumental polarization with just instrumental polarization. Red indicates support for the null hypothesis while blue indicates support for the single Faraday-thin screen. White indicates inconclusive. There are small variations in Faraday depth of order Δφ ∼ 0.2 rad m −2 . Fig. 16 shows the distribution of the Faraday depths in the knot. The variance in the Faraday depth is rad 2 m −4 . If the variation in Faraday depth is due solely to


estimate of 5.36 ± 0.30 kpc was obtained by Thompson et al. ( 2001 ) from the detached eclipsing binary OGLEGC 17 (Kaluzny et al. 1996 ). A once challenging aspect of using Gaia parallaxes from the earlier DR2 release (Gaia Collaboration et al. 2018a ) to directly measure the parallax of ω Cen was the systematic uncertainty related to the parallax offset found by Lindegren et al. ( 2018 ), and which has been demonstrated to vary with source color, magnitude, and position (e.g., Arenou et al. 2018 ; Riess et al. 2018 ; Zinn et al. 2019 ). The DR2 offset was calibrated from quasars, which are bluer than the bulk of ω Cen stars and only cover a small fraction of their magnitude range. The DR2 parallax estimates for ω Cen by Gaia Collaboration et al. ( 2018b ) and by Shao Li ( 2019 ) are 0.1237 ± 0.0011 and 0.1368 ± 0.0015 mas, respectively, and are substantially smaller than other determinations, presumably because the parallax offset estimated by Lindegren et al. ( 2018 ) on the basis of quasar data is much smaller than the values found for brighter stars (Arenou et al. 2018 ; Riess et al. 2018 ; Zinn et al. 2019 ). Our own analysis of the DR2 parallax data for stars in ω Cen revealed a large trend of parallax with star magnitude and color, leaving us to conclude that a parallax from DR2 was not reliable without further characterization of its parallax offset. Thanks to the great improvement realized in EDR3, such a measurement is now feasible, and we exclude the DR2 parallax-based estimates from further consideration. Both ground-based and HST observations have shown that ω Cen has a complex structure, with many separate color–magnitude sequences (Bellini et al. 2009 , 2010 , 2017 ) that can have different structural (Bellini et al. 2017 , 2018 ; Calamida et al. 2017 ) and metallicity (Milone et al. 2017 ; Zennaro et al. 2019 ) properties, including an unusually broad range in helium abundance for a globular cluster. We would not expect this large range to influence the peak of the TRGB in the I -band as the mean helium abundance in ω Cen is not much affected by the high and low sub populations, and the TRGB is known to be quite insensitive to star formation and chemical abundance in general (McQuinn et al. 2019 ). The complex kinematic structure of ω Cen does not affect its parallax measurement, but needs to be taken into account in kinematics-based distance measurements (Watkins et al. 2015 ; Baumgardt et al. 2019 ). It is also worth recognizing that the distribution of abundances in the halos of galaxies where TRGB is often measured is largely unknown making comparisons difficult; it is not unlikely that the multiple populations of ω Cen could more closely resemble the complexity of a galaxy’s stellar halo than a simpler, single-population system. 5.2. Comparison with the TRGB Calibration Anchored to 47 Tuc The determination of the parallax to a globular cluster as massive as ω Cen represents a milestone of distance measurements and


2003 ) and have been called “GRB-SNe” (see Hjorth Bloom 2012 ; Woosley Bloom 2006 ; Cano et al. 2017 , and references therein). While most GRB-SNe are Type Ic-BL, not all SNe Ic-BL are associated with GRBs. The most luminous SNe Ic are Type Ic superluminous supernovae (SLSNe; Quimby et al. 2011 ; Gal-Yam 2012 ); their peak luminosities are erg s −1 (Gal-Yam 2012 ), tens of times greater than those of ordinary SNe. In this paper, we study a very luminous SN Ic, SN 2011kl, which is associated with an ultralong ( s) GRB 111209A (see, e.g., Golenetskii et al. 2011 ; Palmer et al. 2011 ; Gendre et al. 2013 ; Stratta et al. 2013 ; Gompertz Fruchter 2017 ) at redshift z = 0.677 (Vreeswijk et al. 2011 ). By using WMAP ΛCDM cosmology (Spergel et al. 2003 ) and adopting km s −1 Mpc −1 , , and , Kann et al. ( 2016 ) derived a luminosity distance ( D L ) of 4076.5 Mpc for GRB 111209A/SN 2011kl. With a peak luminosity erg s −1 (Kann et al. 2016 ), 8 8 Greiner et al. ( 2015 ) found a slightly lower peak luminosity ( erg s −1 ) since they ignored the near-infrared contribution. SN 2011kl is the most luminous GRB-SN yet detected and is significantly more luminous than all other GRB-SNe, whose average peak luminosity is erg s −1 with a standard deviation of erg s −1 (Cano et al. 2017 ). The time of peak brightness of SN 2011kl is ∼14 days, slightly larger than the average (13.0 days with a standard deviation of 2.7 days; Cano et al. 2017 ) of other GRB-SNe. The peak luminosity of SN 2011kl is comparable to that of some not-quite-superluminous “SLSNe” (e.g., PTF11rks, PTF10hgi, iPTF15esb, iPTF16bad, and PS15br) and commensurate with the SN-SLSN gap transients observed by Arcavi et al. ( 2016 ); moreover, Liu et al. ( 2017c ) pointed out that the spectrum of SN 2011kl is very different from those of GRB-SNe, but consistent with that of SLSNe. So, the energy sources powering its LC might be similar to those powering the SLSN LCs instead of the ordinary SNe Ic. The most popular prevailing models for explaining SLSNe are the magnetar model (Maeda et al. 2007 ; Kasen Bildsten 2010 ; Woosley 2010 ; Chatzopoulos et al. 2012 , 2013 ; Inserra et al. 2013 ; Chen et al. 2015 ; Wang et al. 2015a , 2016b ; Dai et al. 2016 ; Moriya et al. 2017 ) and the ejecta plus circumstellar medium (CSM) interaction model (Chevalier 1982 ; Chevalier Fransson 1994 ; Chugai Danziger 1994 ; Chatzopoulos et al. 2012 , 2013 ; Liu et al. 2017a ). 9 9 Almost all SLSNe (except maybe pair-instability SLSNe—e.g., SN 2007bi Gal-Yam et al. 2009 ; but see Dessart et al. 2012 and Nicholl et al. 2013 ) cannot be explained by the radioactive heating model (Quimby et al. 2011 ; Inserra et al. 2013 ; Nicholl et al. 2013 , 2014 ). Some SLSNe I exhibiting late-time rebrightening and H α emission lines (Yan et al. 2015 , 2017 ) might be powered by a hybrid model containing contributions from magnetars and ejecta-CSM interaction (Wang et al. 2016c ). There have been several papers modeling the LCs of SN


index increases and the energy distribution becomes steeper, limiting the number of higher energy electrons. This leads to spectra becoming more ‘thermal’ in shape, with the peak generated from the non-thermal particles flattening out. This is seen in the spectra of Fig. 10 compared to the Z LOS spectra from Fig. 7 . At earlier times, the peaks are similar, with the power-law index not increasing noticeably until later times where the system relaxes to a thermal state much faster than when the index was a constant value. The addition of an increasing power-law index therefore results in the spectral peak being reduced faster and pushed to lower frequencies as the contribution of higher energy particles is reduced. 3.2.2 Distribution along the loop The distribution of non-thermal particles within the loop is defined by equation ( 2 ). As described in Section 2.2 , l is the distance from the loop top to one footpoint, or the loop half length. The factor that controls the distribution within the loop, s , is initially set as this half loop length. As is seen in Fig. 4 the density is always highest at the apex of the loop, dropping off to a minimum at the footpoints. The parameter s was varied to investigate the effect on spectra of different spreads in non-thermal electrons within the loop. The results from using two values of s are shown in Fig. 11 . The top two panels show the spectra along the Z LOS for s parameter values of 0.3 times the half loop length (same as the Z LOS spectra in Fig. 7 ) and 1.5 times the half loop length. Figure 11. Spectra along the Z LOS resulting from changing the non-thermal electron density spatial distribution (top two plots). Two different configurations ( s = 0.3 and 1.5) are considered over the seven time-steps. The results for s = 1.0 are seen in the Z LOS spectra of Fig. 7 . Bottom images are 3D visualization of sample flux tube field lines at 4112 s and their electron distributions. Colour bar units are cm −3 . Also shown in Fig. 11 is a 3D visualization of these two different distributions along the field lines (and throughout the total flux tube) at 4112 s (bottom two panels of Fig. 11 ). For a smaller value of s , the particles are more constrained to the loop top, while a larger s value leads to a more even distribution from the apex down towards the foot points. The point of highest non-thermal density is found in the s = 0.3 plot as the total mass is conserved before the time decay component is added (equation 4 ). For the more compact distribution ( s = 0.3), in Fig. 11 it is clear the system relaxes to a thermal state quicker than for the more extended distribution of electrons and has a lower peak flux overall. However, the peak in emission occurs at 1790 s, later than the 169 s seen for the other distributions and LOSs. Overall, however, the pattern of the spectral evolution is similar. After the peak flux is reached, the decay of the non-thermal particles leads to the decrease in peak flux


density and, through a gradient descent, iterate in small steps until the solution has converged. The total electron density is given by the sum of the free electrons from hydrogen, helium, and metals. We approximate this using only the first 30 elements, as others are too scarce to contribute significantly:where Z is the atomic number, A Z is the fractional abundance of element number Z , k is the ionization stage ranging from singly to fully ionized (e.g., k = 2 corresponds to doubly ionized), and Y k is the fractional population of ionization stage k of element Z . For trace elements, we solve for the ionization fractions Y k either using an equilibrium calculation that is a function of temperature or by solving a continuity equation for nonequilibrium ionization states, as detailed in, e.g., Bradshaw Mason ( 2003a , 2003b ). The nonequilibrium solver can be used with all, some, or none of the elements, as determined by the user and appropriate for the study at hand. The code makes an initial guess for the H ii fraction, calculates the rate coefficients, solves Equations ( 1 ) and ( 16 ) for the level populations, and then recalculates the total electron density. The process iterates in small steps until the electron density has converged within a defined relative tolerance (default of 10 −6 ). 2.5. Radiative Losses In previous versions of HYDRAD, the hydrogen and electron densities were essentially equal in the corona (with only a small correction for trace elements), so that the optically thin radiative losses E R (erg s −1 cm −3 ) were approximated by setting n e = n H . We drop that approximation now and use the more accuratewhere is the sum of the emissivity over all ions and all transitions for each ion (more precisely, all in the current version of CHIANTI; Del Zanna et al. 2015 ), and the minus sign indicates that the energy is lost from the system. The loss function Λ also depends on the ionization fractions and therefore also utilizes a nonequilibrium ionization calculation when desired. In the chromosphere, we calculate radiative losses following the prescription of Carlsson Leenaarts ( 2012 ), which calculates the loss of energy from hydrogen, calcium, and magnesium. We now use the ionization fraction of hydrogen determined by the above prescription in this calculation. 2.6. Performance The calculation of the NLTE level populations is a significant computational task. A few simple tests with various parameters have found that the code slows by a factor of 10–20 compared to previous versions. To offset these losses, HYDRAD has been recently parallelized with OpenMP. In Figure 3 , we briefly show a timing test of the code. We have run an example simulation of electron beam heating (see the next section) with energy flux F 0 = 3 × 10 9 erg s −1 cm −2 for 10 s of heating. The simulations were only run for 100 s of simulation time. The timing of the simulation run with the older version of the chromosphere is shown in red, compared


by observations of polarised optical radiation. However, polarization signatures are only detected in a limited number of sources, and at present there is no compelling evidence for a simple obscuring torus geometry, possibly suggesting a more complex picture (see the recent review by Netzer 2015 , and references therein). The different AGN obscuration models discussed so far may be broadly divided into two categories: static and dynamical. For instance, analytic calculations suggest that the vertical support for a geometrically thick obscuring torus can be provided by infrared radiation pressure (Krolik 2007 ). The different nature of smooth and clumpy dust tori in different AGN luminosity regimes has been analysed by Hönig Beckert ( 2007 ). Circulation of gas leading to the development of radiation-driven ‘fountains’ has also been proposed as a possible mechanism for the formation of the obscuring torus (Wada 2012 ). The detailed evolution of dusty gas clouds illuminated by the central AGN has been followed through 3D radiation hydrodynamic (RHD) simulations (Namekata, Umemura Hasegawa 2014 ); while the dynamics of dusty gas subject to anisotropic disc emission, X-ray heating, and reprocessed IR radiation, has also been analysed via axisymmetric RHD simulations (Namekata Umemura 2016 ). Another class of models consider the obscuring toroidal structure as supported by winds driven by IR radiation pressure, due to the relatively high opacity of dust in the infrared (Dorodnitsyn, Bisnovatyi-Kogan Kallman 2011 ). A further refinement of the model based on multi-dimensional RHD simulations confirms that the geometrically thick obscuration on pc-scales can indeed be provided by outflows driven by IR radiation pressure on dust (Dorodnitsyn, Kallman Bisnovatyi-Kogan 2012 ). On the other hand, 3D time-dependent RHD simulations of dusty tori suggest that UV radiation pressure on dust can drive powerful winds with considerable mass loss rates (Chan Krolik 2016 ). The most recent multidimensional simulations of dusty gas acceleration in star-forming galaxies suggest that dusty clouds are able to survive longer when accelerated by radiation pressure rather than entrained in a hot outflow (Zhang et al. 2018 ). Here, we envisage a simple picture in which AGN radiative feedback, driven by radiation pressure on dust, strongly affects the distribution of dusty gas in the host galaxy. We assume a spherical shell geometry throughout the paper, while we separately discuss the case of anisotropic emission from the accretion disc in Section 5 . Our results are in agreement with the observational data based on the 70 month Swift /BAT AGN catalogue, which is the most complete sample of X-ray selected AGNs, with measured N H and λ values, currently available. This suggests that our model assumptions are reasonable and sufficient for the purpose of comparison with X-ray observations. In summary, the overall picture is entirely consistent with AGN radiation pressure


IRIS detected quasi-periodic fluctuations in the relative Doppler velocities of the C i , Si iv , and O iv lines from its pointing position about 40′′ east of the EIS slit's position, within the same ribbon. This may be because IRIS observed that portion of the ribbon to undergo quasi-periodic fluctuations before the onset of explosive chromospheric evaporation, when the amplitudes of velocity fluctuations may simply have been more readily detected. Other contributing factors may be that IRIS has higher spectral resolution, and spatial resolution nearly 10 times better than that of EIS. The IRIS observations revealed, however, that quasi-periodic fluctuations in the redshifted relative Doppler velocities were not as pronounced as those in the intensities (Brosius Daw 2015 ). The observed O iv , Mg vi , Mg vii , Si vii , Fe xiv , and Fe xvi fluctuations provide evidence for quasi-periodic energy injections into the chromosphere (at the location of the flare ribbon observed by EIS) by accelerated, nonthermal particles. This is similar to the conclusion drawn by Brosius Daw ( 2015 ) regarding fluctuations in C i , Si iv , and O iv at the location of the flare ribbon observed by IRIS , all of which occurred before the appearance of Fe xxi . In that work, each episode was thought of as a failed flare because no emission at temperatures characteristic of flares (Fe xxi emission) was produced. The quasi-periodic injections of nonthermal beam particles could be produced by MHD oscillations in a magnetic trap at the site of the initial flare energy release (by reconnection). In this scenario (Zaitsev Stepanov 1982 ), MHD oscillations in the trap are generated by the impulsive energy release itself, and modulate the periodic escape of particles therefrom. Alternatively, the injections could be driven by MHD oscillations in a nearby, nonflaring magnetic loop (Nakariakov et al. 2006 ). In this scenario, the oscillating loop perturbs the plasma external to the loop, which produces variations of the electric current density in the flaring region. These induce plasma micro-instabilities and, hence, anomalous resistivity in the flaring region, which can quasi-periodically trigger the magnetic reconnection events that accelerate nonthermal particles. Yet again, the injections could be supplied by quasi-periodic particle acceleration episodes during dynamic magnetic reconnection in a large-scale current sheet dominated by repeated formation of magnetic islands (Kliem et al. 2000 ). In this scenario, particles are presumably accelerated by DC electric fields near the reconnection X points. Recently, Guidoni et al. ( 2016 ) extended the approach of Drake et al. ( 2010 ; see also Karpen et al. 2012 ) to investigate electron acceleration in sunward-moving magnetic islands (plasmoids) formed by spatially and temporally variable reconnection in a flare current sheet. Their 2.5D simulations of an eruptive flare revealed that energy gains in a single island


estimated using the total luminosity derived from spectral energy distribution fitting. Traditionally, MYSOs have been found to have luminosities similar to those of OB stars. Spectral types have rarely been determined directly in MYSOs, and not at all in the case of RMS MYSOs. Previously, Kendall, de Wit Yun ( 2003 ) observed H -band spectra of three MYSOs, IRAS 171753544, IRAS 174412910 and IRAS 180791756 at intermediate resolution ( R 5000). They found photospheric absorption lines in IRAS 180791756 and IRAS 171753544, and assigned spectral types of B3V and O7-8V, respectively, to these two objects. Most of our MYSOs show strong, broad H i emission, due to a stellar wind (see also Section 4.3 ). However, two of the objects in this sample (G015.128800.6717 and G034.050000.2977_A) display absorption in the Br10, Br11 and Br12 lines. There are also hints of absorption in Br and Pa, alongside the dominant emission in these two objects. The RMS survey quotes G015.1288 as having L bol =13000 L . This corresponds to a spectral type of B0.5 for a zero-age MS star, using the values from Straizys Kuriliene ( 1981 ). The absorption profiles in the H band of G015.1288 were compared with spectra of normal stars from the surveys of Hanson etal. ( 2005 ) and Meyer etal. ( 1998 ). A spectral type of F or later would be hard to reconcile with the MYSO data, as F stars have a large number of metal lines. In addition, early O spectral types do not match either, as their Brackett lines are weaker and narrower than observed for G015. Late O and B1-5 stars show a He i line at 1.70 m, at comparable or higher strength than the hydrogen absorption lines, and is not present here. We note that the NIR spectral surveys of Hanson etal. ( 2005 ) and Meyer etal. ( 1998 ) do not have complete spectral and luminosity type coverage. The only B-type sample spectra available are those for B1, B5 and B8. Therefore, given the presence and absence of diagnostic absorption lines, a spectral type later than B5 and earlier than A9 would be expected for G015.1288. However, the Br10-12 absorption in the B5-A9 stars is much stronger than observed for G015.1288. It is possible that a significant amount of excess could veil the H i absorption to a comparable level to our observations. This is illustrated in Fig. 2 , which zooms in on the Brackett lines in the H -band spectra of a number of normal B8-A7 stars with added excess continuum emission. Overplotted on these are the GNIRS data for G015.1288. A B8 star with added excess does not match the observed H i profiles, as the lines in this star are considerably narrower than in G015.1288. In addition, the He i line is still strong enough to be observed. The A0Ib profiles match the observations in strength, but are narrower. An A0V star has broader wings in the Brackett lines than G015.1288. In the absence of more observational MS star spectra to compare our data with, we conclude that G015.1288 has the spectrum of an early A giant or


by disk emission, even in the optical/near-IR, and changes at optical/near-IR wavelengths would reflect changes in the superheated disk rather than the central protostar. FU Ori ( D = 450–500 pc; Hartmann Kenyon 1996 ) is a wide (05) binary system consisting of a outbursting young stellar object modeled as a 0.3 M ⊙ with a 0.04 M ⊙ circumstellar disk (Zhu et al. 2007 ) at an A V of ∼1.8 (Zhu et al. 2010 ) and a more massive young companion ( M > 0.5 M ⊙ ; Reipurth Aspin 2004 ; Wang et al. 2004 ; Hales et al. 2015 ). The companion (FU Ori S) is at 227 au projected separation (Pueyo et al. 2012 ) at an A V of 10 ± 2 (Pueyo et al. 2012 ). In this work, we present new mid-IR photometry and spectroscopy of FU Ori obtained with the Stratospheric Observatory for Infrared Astronomy (SOFIA) in 2016, and we compare with previous observations with the Spitzer Space Telescope in 2004. We find that the continuum flux density at wavelengths shorter than 8 μ m (arising from the hot inner disk) has decreased by 12%–14%, dominating the change in bolometric luminosity. The continuum at wavelengths greater than 10 μ m has decreased only 7% within uncertainties. Additionally, we find that the H 2 O vapor absorption resulting from the superheated disk photosphere remains present. Finally, we note no significant changes in the 10 μ m silicate emission feature, which shows no evidence of crystallinity. Taken together, these observations suggest that the decrease in viscous dissipation energy over this period has occurred predominantly in the innermost section of the disk, which is changing rapidly. 2. OBSERVATIONS 2.1. SOFIA-FORCAST Spectroscopy We observed FU Ori with the Faint Object infraRed CAmera for the SOFIA Telescope (FORCAST; Herter et al. 2012 ) on board the SOFIA (Young et al. 2012 ) on two separate flights (on 2016 February 4 and 18, flights 272 and 279, respectively); see Table 1 for the Observing Log. The observations were performed in C2N (two-position chop with nod) mode, using the slit, and the NMC (nod-match-chop) pattern in which the chops and nod are in the same direction and have the same amplitude. In each case, an off-source calibrator was selected from an ensemble of observations from cycles 2–4, using the observation closest in zenith angle and altitude to the science target (A. Helton 2016, private communication). We did not use dithering. The FORCAST grism was used in three spectral bands, G063 (∼5–8 μ m), G111 (∼9–13 μ m), and G227 (∼18–25 μ m), from 5 to 25 μ m to achieve a spectral resolving power of R ∼ 200. The achieved signal-to-noise ratios (S/Ns) for the individual grism segments were 30 (G063, measured from 5.7 to 6.3 μ m), 46 (G111, measured from 11 to 12 μ m), and 22 (G227, measured from 21 to 26 μ m). The total observation time was 12,904 s (3.58 hr), including imaging, which totaled approximately 0.33 hr (see below). Table 1 Observing Log Notes. Observations were performed over two different flights, 272 (2016 February 04) and


et al. ( 2018 ) and Stiele Kong ( 2018 ), but due to sparser observations, the correlation is not as tight as seen in this work. The trend observed by Mereminskiy et al. ( 2018 ) resembles the correlation observed for GRS 1915+105 (Shaposhnikov Titarchuk 2007 ). Such correlation has been previously observed in several BHBs (Vignarca et al. 2003 ) and provides a tight link between the QPO and the hard-component emission. In that work, the correlation was found on time-scales of minutes in GRS 1915+105 and on scales of days-months for other transient BHBs. Here, we follow the QPO over 5 d. Fürst et al. ( 2016 ) also observe an extremely tight correlation of the QPO centroid frequency and power-law index in GX 339–4 in the frequency range of 0.6–1 Hz and Γ of 1.66–1.8. The authors estimate the mass of the BH using a scaling relation provided by Shaposhnikov Titarchuk ( 2007 ). The typical evolution of the outburst of a transient BHB is described best in the HID, where a counterclockwise path is followed. In the right ‘vertical’ branch, corresponding to the LHS, the flux increases, the power-law index is well correlated with it and the frequencies of the timing features, although no peaked QPO is usually observed, also increase (see Motta, Belloni Homan 2009 ; Motta et al. 2011 ). Since the spectrum gradually softens, this branch is not really vertical. In the top ‘horizontal’ branch, the spectrum softens further, with the power-law index Γ increasing in absolute value. The flux usually continues to increase, although not as fast as before, and the QPO frequency is correlated with both flux and Γ. Given the shape of the PDS and the values of the power-law index, our observations are clearly on the HIMS branch. As described before, usually both the LHS and HIMS branches see a correlation between frequencies of variability components, the flux, and the power-law index. In our AstroSat data, we see the absence of a correlation with flux, although in the NICER data following our observation this correlation is present. This clearly shows that the QPO frequency is related to the energy spectral shape and not to the flux in either of the two main components. In a thermal-Comptonization scenario, the index of the hard component steepens as the population of electrons cools due to the increase in soft photon input (see e.g. Motta et al. 2009 ). However, from Fig. 4 we can see that this is not the case here, as the secular increase in disc flux is not followed by Γ. Another parameter that determines Γ is the optical depth of the cloud τ 0 : for a spherical cloud and input photon energy much lower than the temperature of the electron cloud kT e , we have , where (Sunyaev Truemper 1979 ; Sunyaev Titarchuk 1980 ). Therefore in order to keep Γ from varying when the cloud temperature decreases is to increase τ 0 in a very specific way. Fluctuations in this relation could in principle give rise to the observed fluctuations in Γ, but it would be very ad hoc.


well as for the PSF models, which are mandatory for the subsequent modeling. Excluding variance maps from our modeling process would lead to an underestimation of errors, since the flux contribution of the central point source is significantly higher than that of the sky. We create 2D two-component models of our objects utilizing the same PSFMC algorithm 8 8 See https://github.com/mmechtley/psfMC for additional information, examples, and documentation. (Mechtley 2014 ) as described and used in Mechtley et al. ( 2016 ). We use a point-source model and a Sérsic profile to simultaneously fit the central AGN component and underlying host galaxy respectively. Although the host galaxies may not be perfectly described by a Sérsic profile, it is a sufficient approximation, as we can determine potential asymmetries or tidal features. Furthermore, the advantage of using this two-component approach is twofold: First we ensure that the contributing flux of the central source is not overestimated and avoid an eventual PSF oversubtraction. Second, we also keep the computational time needed for the fits within reasonable limits. Contrary to most of the tools adopted to fit galaxies in 2D, our algorithm allows the user to input a prior probability distribution for the fitted model parameters of the different components, e.g., position in x and y , total magnitude, Sérsic index, position angle, etc. As a result, posterior probability distributions of all the fitted parameters with the corresponding covariances are produced. Additionally, the algorithm does not assume an error-free PSF, but implements the respective PSF variance maps during the convolution process. To that end, we deploy the HST focus model (Cox Niemi 2011 ) to determine for each source the time-dependent telescope focus and find the best matching PSF within our PSF library. For the actual fit we mask and exclude neighboring galaxies, whose central flux peaks do not coincide with the central source in the respective images. The resulting point-source component is then subtracted from the HST /WFC3 image to remove the AGN, and just display the host galaxy beneath. In Figure 2 we show from left to right for one of our 21 AGN sources the original, drizzled HST /WFC3 image, the convolved point-source model, and the point-source-subtracted model showing the host galaxy, once with the original sampling, and once smoothed by a σ = 2px Gaussian. All four images are shown in the same arcsinh scaling. Comparable plots for the remaining 20 AGNs are shown in Appendix A . Figure 2. Different steps of our AGN/host galaxy modeling process shown for one sample source: in the first column we show the original, processed HST /WFC3 image, the second column displays the PSF convolved point-source model, and the third and fourth columns show the host galaxy after point-source subtraction with the original sampling and smoothed by a σ = 2px Gaussian, respectively. This particular source is one of the five AGN host


locations of the clusters on the sky are used to correct the individual distances for the inclination of the disc, thereby obtaining a more accurate absolute distance for the LMC. By doing so, we obtain an estimate of the distance to the centre of the LMC that is more accurate by accounting for the geometry of the galaxy. This process is outlined in van der Marel Cioni ( 2001 ) and Grocholski et al. ( 2007 ), and also presented in the equations ( 2 ) through ( 5 ) below. The distance to the LMC centre is denoted by D 0 . D is the distance to any location on the disc plane; in our case, this is the distance to each cluster. We assume the LMC disc to be inclined to the plane of the sky by the angle i around an axis at the position angle θ. θ is measured anticlockwise from the west; to align with usual astronomical convention, Θ is defined the position angle from the north (Θ = θ – 90). These values are adopted from van der Marel Cioni ( 2001 ); we note that Grocholski et al. ( 2007 ) explored a variety of geometries from other past works, finding differences in the resulting distance of ≲0.2 kpc for varying i and Θ. The right ascension and declination are referred to, respectively, by α and δ in the equations below, To calculate the distance to the LMC centre (D 0 above), it is necessary to calculate ρ and sin (φ − θ). The former is calculated as in equation ( 3 ): Via a typical trigonometric expansion, sin (φ − θ) may be determined as sin (φ − θ) = sin (φ) cos (θ) – cos (φ) sin (θ). These components are detailed in equations ( 4 ) and ( 5 ): Through these equations, we determine an average, error-weighted distance modulus to the LMC centre of D 0 = 18.20 ± 0.06, equivalent to 46.42 ± 0.45 kpc. However, NGC 1841 is a clear outlier in these data, lying more than 3σ from the mean D 0 distance to the LMC centre, leading to several possibilities. One interpretation of these results suggests that NGC 1841 may not be a member of the LMC disc or may have been pulled out of the LMC disc (Grocholski et al. 2007 ). Another view is that an uncertain estimate of the reddening could be affecting the distance measurement; if the reddening of NGC 1841 is doubled from E ( B − V ) = 0.18, it is brought into agreement with the LMC mean distance. Regardless of the reason(s) for the discrepancy, we remove NGC 1841 as an anomaly and continue determining the distance to the LMC centre. Leaving out the extreme outlier of NGC 1841, the error-weighted mean is 18.41 ± 0.04 (48.29 ± 0.38 kpc). This is within the range of the result from Section 4.1 from the HB analysis, as seen in Fig. 9 , where the subdwarf distances and the subdwarf distances adjusted for the LMC geometry are compared to those derived from the HB analysis. The subdwarf distances tend to be shorter by 0.14 mag on average than those of the HB analysis; the adjusted subdwarf distances are also shorter than the HB distances by 0.12 (leaving NGC 1841 out). The offset appears to be consistent regardless of


of residuals on a cluster by cluster basis when compared to the grid of Kroupa IMF clusters. This increase in scatter is especially noticeable in mass, and originates from the M 3 degeneracy described above. As the mass of the cluster and its IMF slope are highly dependent on each other, the wide scatter in mass is further reflected in the inaccurate values inferred for 3 . Indeed, given the flat and broad posterior PDFs for the IMF slope, the medians of 3 have no physical meaning and simply reflect the median of the prior on 3 [in this case, a flat distribution between 3 (3.0, 1.5)]. Figure 12. Comparisons of the medians of the inferred posterior PDFs for all physical parameters to the true values adopted when simulating the mock clusters. Results for individual clusters are shown with crosses, while the median residuals and the corresponding 10th and 90th percentiles are shown with solid points. We plot analysis including broad-band photometry alone with (red, circles) and without (purple, diamonds) a variable IMF. We also show results of the variable IMF case when including H (blue, squares). Points are shifted along the x -axis for visualization purposes, with the leftmost point situated at the true x -axis value. Given this result, it is clear that obtaining refined constraints on the upper-end slope of the IMF requires a different approach. It is readily apparent that the ability to apply a prior to the cluster mass that is independent of the broad-band photometry may prove very useful in analysis such as this. Independent constraints on the masses of clusters that may then be used as priors may come, for instance, from dynamical measurements (e.g. Ho Filippenko 1996 ; Gerhard 2000 ). The era of 30m telescopes will make such measurements more feasible. To illustrate this point in more quantitative terms, we present in Fig. 13 a study of the accuracy with which 3 can be recovered as a function of the width of a prior on the mass. Results of three choices of IMF are presented, when leaving the mass unconstrained, and when applying a top-hat prior with width 0.5, 0.2 and 0.05 dex about the target cluster mass, for both broad-band filters only and broad-band filters combined with H. This analysis shows that, as expected, the medians of the PDFs on 3 converge to the true value as the precision with which the mass is constrained increases. Due to the difference between logarithmic intervals in mass and the linear scale in the IMF upper-end exponent, there is a weak scaling of 3 with the prior width, with the underlying values being recovered to within 3 0.2 when the mass is constrained to better than 10percent. However, more realistic constraints on the mass (to within a factor of 2), for instance via dynamical measurements, appear to be useful to rule out extreme variations in the IMF upper-end slope through multiwavelength broad-band photometry, given the assumptions of our model. The inclusion of H results in a wider scatter towards zero for


of neutron-rich nuclei are required in r -process simulations, and most of these nuclei lie far beyond the experimentally known region. Theoretical predictions of the properties of these neutron-rich nuclei have large uncertainties, which can further interplay with the astrophysical uncertainties. This makes it even more difficult to address the issues of the r -process. Nuclear masses are extremely important for r -process simulations, as they are needed to extract the reaction energies that go into the calculations of all involved nuclear reaction rates. During recent decades, great achievements in nuclear mass measurements have been made thanks to the development of radioactive ion beam facilities, and about 2500 nuclear masses have been measured to date (Wang et al. 2012 , 2017 , 2021 ). Nevertheless, the masses of a large number of neutron-rich nuclei relevant to the r -process remain unmeasured and cannot be reached in the foreseeable future, due to the difficulties in production, separation, and detection. Therefore, reliable theoretical predictions for nuclear masses are imperative at present. However, an accurate prediction of nuclear masses is still a great challenge for nuclear theory due to the difficulties in understanding nuclear interactions and quantum many-body systems. Tremendous efforts have been made in improving the prediction of nuclear masses and, currently, the rms deviations between theoretical mass models (Pearson et al. 1996 ; Koura et al. 2005 ; Zuker 2008 ; Goriely et al. 2009 ; Wang et al. 2014 ; Möller et al. 2016 ) and the available experimental data reach about 0.5 MeV. The rms deviations are further reduced to about 0.2 MeV by employing machine learning approaches (e.g., Wang Liu 2011 ; Niu et al. 2013 ; Utama et al. 2016 ; Neufcourt et al. 2018 ; Niu Liang 2018 ; Wu Zhao 2020 ). However, different mass models predict very different masses when moving to the region of neutron-rich nuclei and, thus, lead to obviously different abundances of nuclei in the r -process nucleosynthesis simulations (e.g., Wanajo et al. 2004 ; Sun et al. 2008 ; Farouqi et al. 2010 ; Arcones Martínez-Pinedo 2011 ; Martin et al. 2016 ; Li et al. 2019 ; Zhao Zhang 2019 ). Therefore, it is important to address how the nuclear mass uncertainties limit our knowledge of the r -process (e.g., Sun et al. 2008 ; Farouqi et al. 2010 ; Arcones Martínez-Pinedo 2011 ; Brett et al. 2012 ; Xu et al. 2013 ; Aprahamian et al. 2014 ; Martin et al. 2016 ; Mendoza-Temis et al. 2016 ; Mumpower et al. 2016 ; Li et al. 2019 ; Sprouse et al. 2020b ). Addressing the impact of mass uncertainties on r -process abundances is useful to deepen our understanding of the r -process in the present stage. For instance, can we identify the dominant r -process site with current uncertainty (e.g., Mumpower et al. 2015c ; Martin et al. 2016 )? Can we understand the origin of the rare-earth peak (e.g., Surman et al. 1997 ; Goriely et al. 2013 )? To what extent can we


= 6.50 a 0 and along R and φ for θ = 75° is given. These cuts show that the R stretch coordinate is strongly coupled with θ and φ . Finally, it is worth noting that this interaction potential is strongly anisotropic especially along the R , θ and φ coordinates. This strong anisotropy is expected to lead to significant values for the collisional rates of the HNS rotational (de)-excitation by He. Figure 2. Two-dimensional contour plots of the 3D HNS–He PES along the R and θ coordinates for fixed φ = 0°, 90° and 180°. We give also the cuts along the angular coordinates and along R and φ for θ = 75°. Energies are in cm −1 . Black (red) contour lines represent repulsive (attractive) interaction energies. Table 1. Equilibrium geometries and energies of the minimal structures of HNS–He 3D-PES for φ = 0°, φ = 90° and φ = 180°. 3 DYNAMICAL CALCULATION DETAILS We consider the collision between an asymmetric top molecule (HNS) with He atom. The rotational Hamiltonian of the HNS molecule is given by where I α (α = x , y , z ) are the principal moments of inertia with respect to the principal axes of inertia (Gx), (Gy) and (Gz) of HNS. (G,x,y,z) is the body-fixed reference related to the space-fixed reference (G,X,Y,Z) by the Euler angles. I x , I y and I z are related to the rotational constants according to , and . The total angular momentum of the molecule is such that . D J , D JK and D K are first-order centrifugal distortion corrections. The rotational wave function | j τ m 〉 of an asymmetric top can be defined by three quantum numbers j , τ , m and can be expressed as a linear combination of the rotational wave functions | j τ m 〉 of a symmetric top molecule such as (Townes Schawlow 1955 ): where, j, k and m denote the rotational quantum number, its projection along the molecular z -axis and its projection along the space-fixed Z -axis, respectively. τ is the pseudo-quantum number that varies between − j and j . The rotational levels of an asymmetric top molecule are conventionally labelled (adopted hereafter) where K a and K c are the projection of the rotational angular momentum along the axis of symmetry in case of prolate and oblate symmetric tops limits being related to τ through τ = K a − K c . The rotational energy levels, of HNS, are deduced from the ab initio rotational and distortional constants calculated by Ben Yaghlane et al. ( 2014 ) at the CCSD(T)-F12/cc-pVQZ-F12 level of theory which are A e = 0.63583, B e = 0.61585, C e = 19.59885, D J = 9.11 × 10 −7 , D K = 4.68 × 10 −5 , D JK = 5.30 × 10 −3 (all values are in cm −1 ). The precision of these rotational parameters should be better than ∼0.3% according to theoretical benchmarks and their comparison to experimental data dealing with sulphur compounds (see for instance Cazzoli, Puzzarini Gauss 2014 ). All data represent predictions that can help for the identification of this molecule. For scattering calculations, only the first 29 levels of HNS molecule are considered. This corresponds


and the observation ID are given in each plot. The soft and hard LCs (left panel), HR plot (middle panel), and the DCF plot between the soft and hard bands (right panel) of 1ES 0347−121 are shown in Figure 3 . No significant spectral change is seen from the HR plot. We checked for variations quantitatively using a standard χ 2 test,where x i is the HR value, σ i is its corresponding error, and is the mean HR value. We considered a variation in the HR to be significant only if χ 2 > χ 2 99, ν , where ν is the number of degrees of freedom (DoF) and the significance level is 0.99. These results are given for all these blazars in Table 4 , where we see that for each source , so no significant spectral variations were detected. Figure 3. Soft (3–10 keV, denoted by red filled circles) and hard (10–79 keV, denoted by black filled circles) LCs (left panels), hardness ratios (middle panels), and the discrete correlation functions between soft and hard LCs (right panels) of the blazars 1ES 0347−121, 1ES 0414+009, RGB J0710+591,1ES 1101−232, 1ES 1218+304, and H 2356−309. The source names and observation IDs are given in the left panels. Table 4 Test of Temporal Variation of HR The DCF plot is flat, which, in the presence of significant variations, would indicate no correlation between the two energy bands, but since no variations are detectable this type of DCF is expected. 4.2. 1ES 0414+009 The TeV blazar 1ES 0414+009 ( α 2000 = 04 h 16 m 530; δ 2000 = +01°05′20′′) is an HBL at z = 0.287 (Halpern et al. 1991 ). It was first detected in X-rays with the High Energy Astronomy Observatory ( HEAO 1 A-1) (Ulmer et al. 1980 ) and was classified as a BL Lac object by Ulmer et al. ( 1983 ). It was observed above 200 GeV by VERITAS with source flux equal to (5.2 ± 1.1 stat ± 2.6 sys ) × 10 −12 photons cm −2 s −1 (Aliu et al. 2012 ). 1ES 0414+009 was observed with NuSTAR on 2015 November 25 with a good exposure time of 34.16 ks. The 3–79 keV LC of 1ES 0414+009 is shown in Figure 1 . The data are both noisy and sparse, resulting in no significant IDV detection, which is consistent with the value of fractional variance given in Table 2 . Consequently, the ACF plot, given in Figure 2 , does not show any hint of variability timescale. The soft and hard LCs of 1ES 0414+009 are plotted in the left panel of Figure 3 . The HR plot in the middle panel of that figure reveals no significant spectral variations (also see Table 4 ) and the DCF plot shown in the right panel of Figure 3 again is flat. 4.3. RGB J0710+591 The high-frequency-peaked BL Lacertae object RGB J0710+591 ( α 2000 = 07 h 10 m 264; δ 2000 = +59°09′00′′) is located at a redshift of z = 0.125 (Giommi et al. 1991 ) and also was first detected by HEAO A-1 (Wood et al. 1984 ). It was detected with VERITAS with the integral flux (above 300 GeV) recorded to be (3.9 ± 0.8) × 10 −12 cm −2 s −1 (Acciari et al. 2010 ). NuSTAR observed RGB J0710+591 on 2015 September 1 for 26.48 ks. As seen from the LC in Figure 1 the


dynamo than precession. We must point out that this conclusion is valid only at this Ekman number. At a smaller Ekman number, the precessing flow is more complex, which favors the onset of the dynamo, and this conclusion may not hold any longer (we leave the large-scale simulations at smaller Ekman numbers for other researchers who will be interested in the result of this work). The comparison between Figures 1 (a) and 2 (a) suggests that not only the mean poloidal kinetic energy but also the fluctuation amplitude of the precessing flow are much higher than those of the convective flow. This implies that the precessional instabilities are more vigorous than the convective instabilities in the two successful dynamos. The dominant azimuthal mode in the convective flow is m = 3 (Table 1 ), indicating a shorter length scale than the dominant spin-over mode m = 1 in the precessing flow. Figure 2 (b) shows the time evolution of the magnetic energy. Compared to Figure 1 (b), the magnetic energy of the convection dynamo becomes noticeable at the time ≈5000, which is much later than the time ≈400 of the precession dynamo. It is not surprising that the magnetic energy of the convection dynamo is also much lower than that of the precession dynamo (Table 1 ) because of the lower Rm of the former. Figure 2. Convection dynamo at . Here, we show the time evolution of the poloidal kinetic energy (a) and the magnetic energy (b). After studying the dynamos driven by precession alone and by convection alone, we study the combined effect of precession and convection. In the above two dynamos, the dynamo driven by precession alone cannot be maintained at Po = −0.2 and the dynamo driven by convection alone cannot be maintained at . We test whether the preceission-convection dynamo can be maintained at Po = −0.2 and . This dynamo works! It indicates that the combined effect of precession and convection can indeed facilitate the onset of the dynamo. As we discussed, the conventional Ra differs by more than one million, which indicates that precession greatly helps the onset of the convection dynamo. Moreover, it is interesting that the Rm = 677 of the precession-convection dynamo is lower than the Rm = 694 of the failed precession dynamo, as shown in Table 1 . This suggests that the combination of precession and convection has some non-trivial effect and triggers the dynamo action at a lower Rm of the pure precession dynamo. This non-trivial effect probably arises from the resonance of precessional instability and convective instability. Figure 3 shows the time evolution of this precession-convection dynamo and its time-averaged values are listed in Table 1 . Although the of the precession-convection dynamo is lower than the of the convection dynamo, the Nu of the former is higher (Table 1 ). This is because the poloidal flow driven by precession contributes more to heat transfer than convection, i.e., of the precessing flow at Po = −0.2 is already much higher than


reproduced with a two-component photometric model that consists of a PN-poor inner halo with a de Vaucouleurs profile and a PN-rich exponential outer component. Relying solely on the information from surface photometry, we were unable to constrain the scale radius of the exponential profile. We constrained the shape of the exponential profile using the information from resolved stellar populations. Harris et al. (2007a) and Lee Jang (2016) published number-density profiles of MR and MP RGB stellar populations in the halo of M 105. We combined the information from these studies to infer that the density distribution of the most MP stars ([M/H] −1.0) follows an exponential profile with a central surface brightness of μ 0 = 27.7 ± 0.1 mag arcsec −2 and a scale radius of r h = 258 ± 2′′ (Sect. 5 ). Using the information from the RGB populations, we constructed a two-component photometric model, where the two components were weighted by their α -parameter values. In the PN-poor inner halo, the light distribution is dominated by intermediate-metallicity ( − 1.0 ≤ [M/H] −0.5) and MR ([M/H] ≥ −0.5) stars, while in the PN-rich outer halo the MP stars dominate the light distribution. The α -parameter values of the two components are as follows: for the inner PN-poor component, and for the outer PN-rich component. We find a difference of a factor of seven in the α -parameter values of the inner versus outer components, implying that the luminosity-specific PN number of the stellar population that traces the old and MP halo at large radii is seven times higher. We interpret the high α -parameter value and the steep faint-end PNLF slope as tell-tale signs of an additional old and MP stellar population whose contribution towards the overall light distribution increases at large radii. This interpretation is corroborated by the results of Harris et al. (2007a) and Lee Jang (2016) based on resolved stellar populations. While in earlier works ( Longobardi et al. 2013 ; Hartke et al. 2017 ) this association was made mostly by inference, we are now able to directly establish the link between the high α -parameter value, the steep PNLF slope, and the increase in the old and MP stellar population in the outer regions of M 105 (identified by Harris et al. 2007a ). The data of Harris et al. (2007a) clearly ruled out a single chemical evolution sequence for the entire halo stellar population and instead suggested a multi-stage evolutionary model. For the outer MP halo, two different scenarios were proposed: Harris et al. (2007a) argued that the MP halo was built up from pristine gas and that star-formation therein was truncated early, at the time of cosmological reionisation. In contrast, Lee Jang (2016) proposed a formation dominated by dissipationless mergers and accretion. The scenario by Harris et al. (2007a) implies that the faint MP halo reached the current extension out to 40−50 kpc at high redshift, which is at odds with the observed slow growth of the


data to analyse them together with our CO ( J = 3−2) observations. BD+30 3639 was the source with the best complementary CO ( J = 2−1) data, given the size of the source and the beam size of the CO ( J = 2−1) observations. A discussion of the use of these diagnostic plots is presented for different molecules in the Appendix of van der Tak et al. (2007) . Linear molecules, such as CO, are density probes at low densities, while at higher densities, the line ratios are more sensitive to temperature. However, with no other information than a single line ratio (such as our case), it is only possible to provide lower limits to density and temperature. Table 4 Size, distance, and morphology of PNe with CO emission. References. (1) Cahn et al. (1992) , (2) Robinson et al. (1992) , (3) Groenewegen et al. (2012) , (4) Frew (2008) , (5) Sahai et al. (2007) , (6) Acker et al. (1992) , (7) Tajitsu Tamura (1998) , and (8) Guzmán et al. (2006) . In Fig. 2 we show the diagnostic plot for the CO ( J = 3−2) to CO ( J = 2−1) intensity ratio, assuming 2.73 K as the background temperature and a line width of 50 km s −1 . The plot shows the results for a column density of 1 × 10 16 cm −2 , but we find that the CO line ratio is not very sensitive to column density within the range 3 × 10 15 cm −2 to ~4 × 10 16 cm −2 . The plotted ratios corresponded to the observed values for BD+30 3639 (1.6), NGC 3132 (1.3), IC 4406, and M2-9 (0.7, for the last two). However, for the latter three sources, the measured ratios are only lower limits because of different CO ( J = 2−1) and CO ( J = 3−2) beam sizes (the former larger than the latter) and the source size (larger than both beam sizes). The CO intensity ratio constrains a lower limit to the H 2 volume density, n H 2 > 10 3 –10 3.7 cm −3 , and kinetic temperature, T kin > 10–35 K. The highest lower limit values are given for IC 4406 and M2-9. 3.6 Correlation with H2 We would like to probe the relationship between the detection of CO and H 2 . We compared our sample with the sample analysed by Kastner et al. (1996) , whose study was made by imaging the molecular hydrogen emission ( λ = 2.122 μ m) using the near-infrared cryogenic optical bench mounted at Kitt Peak National Observatory, from the National Optical Astronomy Observatories. They observed 60 PNe and detected H 2 in 23 of them. When compared with out sample, 9 objects are in common. Of these 9 objects, 4 were detected in H 2 , and all are also detected in CO as part of our survey. The objects are NGC 3132, IC 4406, PN M2-9, and BD+30 3639. The remaining objects (five) were not detected in H 2 and are they detected here in CO either. These PNe are PN M3-2, PN MyCn18, NGC 6778, NGC 6790, and HD 193538. Although the overlap between PANDORA and the H 2 survey of Kastner et al. (1996) is small, we find a clear correlation between the detection of CO and the detection of H 2 . Fig. 2 Results from the LVG analysis of the CO lines. The curves represent the


is in good agreement with the correlation coefficient measured from the 545 and 857GHz dust maps in the Planck Sky Model (dashed lines). Dust is more than 99percent correlated between these frequencies. In the Planck 2013 analysis of cosmological parameters, the following simple parameteric model for the dust power spectrum was adopted: The parameters , c and are fixed by matching to the mask-differenced dust power spectra. Given the universality of the dust power spectrum, neither the choice of frequency nor mask sizes are critical in fixing these parameters. Using the 857GHz mask 40mask 25 spectrum, we find 0.387, c 162.9 and 0.168, so that asymptotically . This dependence at high multipoles is compatible with previous high-resolution measurements of the dust power spectrum in high Galactic latitude cirrus clouds, C 2.7 0.1 (Miville-Deschnes, Lagache Puget 2002 ; Miville-Deschnes etal. 2010 ), although our mask-differenced results consistently give slopes at the shallower end of this range. For a given mask, the dust power in the spectrum is specified by the parameter . For the values of , c and given above, is the dust power at multipole 10. The solid black lines in Fig. 4 show the model of equation ( 4 ) compared to the mask 40mask 25 and mask 50mask 25 spectra for the 353, 545 and 857GHz spectra. The model provides a reasonably good fit but one can see evidence for an excess at 500. We have therefore fit the dust spectra to a slightly more complicated fitting function: where B , 2 , 2 , c 2 , 2 and are parameters that we fit to the 857857 mask 50mask 25 spectrum. The best-fitting parameters are B 0.74, 2 0.19, 0.58, c 2 543.1, 2 11.6 and 0.07. We normalize the template at 10, so that the dust amplitudes derived using the templates of equations ( 5 ) and ( 4 ) can be compared directly. The best-fitting template of equation( 5 ) is shown by the red lines in Fig. 4 . Equation ( 5 ) provides a better fit to both the mask 40mask 25 and mask 50mask 25 spectra than equation ( 4 ), capturing the small excess at 500. Unless otherwise stated, we use the template shape of equation ( 5 ) in our baseline analysis. In summary, using mask-differenced spectra to isolate the contribution from Galactic dust, we find that the dust power spectrum has a nearly universal shape independent of frequency and sky fraction up to mask 60. For larger sky fractions, we see relatively small departures from universality that depends on the point source mask and are most likely associated with the anisotropy of the point source masks at low Galactic latitudes. The shape of the dust power spectrum is modelled accurately by the fitting function of equation( 5 ), which provides a template shape used in our likelihood analysis. We have verified that the dust power spectra are almost perfectly correlated over the frequency range 353857GHz. We therefore solve for three dust amplitudes, , and in our likelihood analysis assuming that the dust power spectrum is completely


It can be seen that it agrees well with the other methods tested. The three methods, whilst not in exact concurrence, are in good agreement. Thus, to separate spirals and ellipticals in our sample, we use the parameter, both because it gives the intermediate values for fraction of spirals and ellipticals, and because it is more reliable and less computationally expensive when computed for a very large number of galaxies. We also present numerical results from our tests using g r band luminosity as the divide between spiral and elliptical galaxies, with a cut defined by equation ( A1 ) (Figs A2 and A3 ). Figure A2. Similar to Fig. A1 , but here galaxies are split based on the cutoff in g r band luminosity from equation ( A1 ). Figure A3. Distribution of ETGs in the R plane, as in Fig. 3 , but using g r luminosity, rather than as the cutoff between spirals and ellipticals. We find a smaller number of ellipticals by the same selection criteria, roughly half those in the ATLAS 3D survey, and a similar distribution, with a slightly higher fraction of highly elongated or fast-spinning galaxies compared to that found with a cutoff. We also experimented with making a cutoff between star-forming and quiescent galaxies based on their magnitude in the g and r bands. Galaxies for which g r is large are redder with little star formation and these quiescent galaxies are often ellipticals, whilst smaller g r colours characterize bluer, star-forming galaxies, which in observational surveys correspond well with the population of spirals (Kormendy 2016 ). We define a cut between star-forming galaxies as those below the line and quiescent galaxies as those above, motivated by the distribution of the whole sample of galaxies in Illustris (Vogelsberger etal. 2014 ). The luminosities are found by summing the individual luminosity of all stellar particles in the galaxy. The fraction of quiescent to star-forming galaxies, by mass, is in line with observations (Muzzin etal. 2013 ) over the whole mass range examined (down to haloes with stellar mass of 10 10 M ). Fig. A3 is a comparison with the galaxy population found in the ATLAS 3D survey, as presented in Section 3.1 using a cutoff defined by . We find less galaxies classified as ellipticals in the same volume, roughly half the previous number, with a wider spread in the distribution. There are more, faster spinning galaxies included though still few as rapidly rotating as in the ATLAS 3D survey. The population of high-mass galaxies is essentially unchanged, still with particularly elongated high-mass SRs as mentioned in Section 3.1 . Fig. A2 shows the stellar mass function derived using a colour cut. Whilst the results are more in line with the observed stellar mass function at low masses, we believe that this is due to the dependence of both on galaxy mass, rather than any strong link between luminosity and kinematic behaviour. Bottrell etal. ( 2017 ) performed similar analysis on carefully constructed mock


also been recently reported in HH 212 in the inner 100 au with a detection of CH 3 CHO and deuterated water HDO (Codella et al. 2016 , 2018 ). Now at higher resolution, we find CH 3 CHO to reside in the disk atmosphere. Moreover, we also detect 8 other organic molecules (H 2 CCO, t-HCOOH, CH 3 OH, CH 2 DOH, 13 CH 3 OH, CH 2 DCN, HCOOCH 3 , and CH 3 CH 2 OH) in the disk atmosphere, with an excitation temperature of ∼150 ± 50 K. Adding 3 other organic molecules (D 2 CO, CH 3 SH and NH 2 CHO) from Lee et al. ( 2017c ), we have 12 organic molecules, with 9 of them being COMs, detected in the disk atmosphere. These results indicate that the hot corino in HH 212 is actually a warm atmosphere of the disk. 4.2. Formation of Organic Molecules We can study the formation of the organic molecules in the disk atmosphere by comparing their abundances to those estimated in the hot corinos around other Class 0 low-mass protostars. The abundance of CH 3 CHO, which is commonly observed in hot corinos, is estimated here to be 3.9 × 10 −9 in HH 212, similar to those found in other hot corinos, e.g., 5.8 × 10 −9 in IRAS 16293-2422B (Jørgensen et al. 2016 ), 2.4 × 10 −9 in B335 (Imai et al. 2016 ), and 4.2 × 10 −9 in NGC 1333 IRAS4A2 (López-Sepulcre et al. 2017 ). To facilitate comparison, we calculate and compare the abundances of the organic molecules relative to CH 3 CHO. Figure 4 shows the comparison of the relative abundances of seven organic molecules (excluding deuterated species and 13 C isotopologue) to those in IRAS 16293-2422B (Jørgensen et al. 2018 ), B335 (Imai et al. 2016 ), and NGC 1333 IRAS4A2 (López-Sepulcre et al. 2017 ). In this comparison, CH 3 SH is excluded because of no reliable measurement of this molecule in other hot corinos to compare with. Interestingly, the relative abundances of most molecules here in HH 212 are similar to those in other hot corinos to within a factor of few, suggesting that the formation of these molecules in the disk atmosphere could be similar to that in other hot corinos. Notice that the abundance of CH 3 SH here is also consistent with that predicted in the hot corino, which can be as high as 5 × 10 −8 (Majumdar et al. 2016 ). Moreover, the abundances here are also similar to those seen in the Class I corino SVS13-A (Bianchi et al. 2019 ) and to those seen in Comet Lovejoy, which shows similar abundances to IRAS 16293-2422B (Biver et al. 2015 ). Figure 4. Comparison of the abundances of organic molecules in the HH 212 disk atmosphere with those in the hot corinos around other low-mass protostars. As shown in Table 2 , our measurements have an uncertainty of about 50%. As discussed in Lee et al. ( 2017c ), the high degree of deuteration in methanol (with [CH 2 DOH]/[CH 3 OH] ∼0.12) and the detection of doubly deuterated formaldehyde suggest that the methanol and formaldehyde in the disk atmosphere are originally formed on icy grains and later desorbed (evaporated) into gas phase due to the heating possibly by


x min in our research. Figure 1. Cumulative distributions of fluence, peak counts, rise time and duration for 4U 1728-34. The best-fitting results are shown by the red lines. The best-fitting parameters are given in each panel. Based on the criteria proposed by Aschwanden ( 2011 , 2014 ), which are the statistical independence of events, non-linear growth phase, random rise times and power-law distribution of these observed parameters, type I X-ray bursts can be explained by a SOC process. The SOC theory predicts that subsystems self-organize, owing to some driving force, to a critical state, at which a slight perturbation can cause a chain reaction of any size within the system (Bak, Tang Wiesenfeld 1987 ). The SOC theory also predicts a power-law distribution for the waiting times (Aschwanden 2011 ; Marković Gros 2014 ). The WTD has been widely discussed in astrophysics (Wheatland, Sturrock McTiernan 1998 ; Aschwanden McTiernan 2010 ; Wang Dai 2013 ; Li et al. 2014 ; Wang et al. 2015 ; Guidorzi et al. 2015 ; Wang Yu 2017 ). In the SOC theory, the WTD is usually described as a (non-)stationary Poisson process. The probability function is expressed by (Wheatland et al. 1998 ) where Δ t is the waiting time, T is the period and λ( t ) is the burst occurrence rate. Below, we model the occurrence rate λ. We propose that the burst rate can be modelled by λ( t ) ∝ t −γ . The reason is given below. Type I X-ray bursts are induced by a thin-shell instability. In LMXBs, the accreted H/He fuel accumulates on the stellar surface and forms a shell. The typical time for nuclear energy release is τ N ∝ Δ M / L N , where Δ M is the mass of the shell and L N is the nuclear energy generation rate (Hōshi 1968 ; Joss 1977 ). In the quiescent stage, L N remains almost unchanged. The energy will be diffused in a typical time τ d ∝ Δ M 2 , which also depends on the stellar temperature and the opacity of the shell (Hōshi 1968 ; Ayasli Joss 1982 ). The condition for triggering a burst is τ N /τ d = Δ M crit /Δ M ≤ 1, where the critical shell mass Δ M crit is obtained by τ N = τ d (Hōshi 1968 ; Ayasli Joss 1982 ). Alternative descriptions of this critical condition are also used (Fujimoto et al. 1981 , 1987 ; Narayan Heyl 2003 ). We assume that Δ M = Δ M crit happens at a typical time t 0 . When the shell grows thick enough at a time T , any perturbation affects the stellar hydrostatic structure significantly and leads to stable nuclear burning (Schwarzschild Harm 1965 ). Therefore, a burst can be triggered only in a time range t 0 ≤ t T . Since these time-scales are mainly determined by the shell mass, it is plausible to assume that the occurrence rate also mainly depends on the shell mass. Because the accreted mass is proportional to time, we can adopt for the burst rate The occurrence rate is taken as λ = 0 when t t 0 . We put all the time-dependent effects into the power-law index γ, which contains the dependence on shell mass and the possible time evolution of


(above 500 km) and 4 K at 200 km. Each observation was modeled independently and results for all five emission lines were combined using the technique provided in Nixon et al. ( 2008a ) Section 4 . A systematic error in the CO line intensity of 2% (Rothman et al. 2013 ) was also added to the measurement error. The best-fitting abundance for CO was found to be 49.6 1.8 ppm, which is consistent with and more accurate than previous measurements. Retrieved vertical temperature profiles from CO models were then used as fixed temperature profiles for modeling of the less abundant CO isotopologues ( 13 CO, C 18 O, and C 17 O.) For each isotopologue transition, the retrieved temperature profile which was closest in time to that observation was used as the fixed temperature profile with errors from that temperature retrieval propagated into the isotopologue retrieval. For a priori abundances, we assumed terrestrial isotopic ratios of 89.3 for 12 C/ 13 C, 498.8 for 16 O/ 18 O, and 2680.6 for 16 O/ 17 O (Lodders 2003 ). Best-fitting models of CO isotopologues were found using the same modeling procedures as CO (aside from the fixed temperature profile) and are presented in Figure 2 . The combined best-fitting 12 C/ 13 C ratio of 89.9 3.4 is consistent with similar studies of other molecules (Courtin et al. 2011 ; Mandt et al. 2012 ; Nixon et al. 2012 ), suggesting no significant carbon fractionation occurred during CO formation. Best-fitting ratios of 16 O/ 18 O and 16 O/ 17 O are 486 22 and 2917 359, respectively. Although the C 18 O (2–1) peak appears slightly under-fitted, the spectral residuals (model minus observation) for this transition indicate an optimal fit given the noise. The mixing ratios for C 18 O, derived independently from the J = 3–2 and J = 2–1 transitions, are consistent within the observational errors. Figure 2. Top: spatially integrated spectra of 13 CO with best-fitting models overlaid. Bottom: spatially integrated spectra of C 18 O and C 17 O (3–2) with best-fitting models overlaid. C 18 O (2–1) and C 17 O (3–2) are each combinations of two observations taken close in time to each other, while C 18 O (3–2) is a combination of three observations. Observations were combined in CASA before deconvolution. Additional systematic errors that have not been quantified in the final error estimate could exist. Sources of systematic errors include our assumption that Titan has the same temperature profile at all locations in our disc-averaged calculation, as well as our assumption that the Voigt profile is correct. Additional errors could exist in the line-broadening coefficients and temperature-dependence exponent used in the line database (Rothman et al. 2013 ), which could alter the line strength and shape. An accurate estimation of these systematic errors is difficult and beyond the scope of this paper, but these possible sources are mentioned for completeness. Our results constitute the most accurate determinations of atmospheric


stars increases rapidly toward fainter magnitudes. The relative fractions are a combinations of the intrinsic distribution of different types of sources, whereby the density of Galactic stars increases toward the disk of the Milky Way, while the distribution of extragalactic sources does not depend on the Milky Way structure, but all sources are affected by the Milky Way dust, which is mostly confined to a thin disk. The reddening therefore depends on the line of sight toward the sources going through more or less of the dust disk. This effect was dramatically illustrated by Figure 2 (bottom) of Bianchi et al. ( 2011a ): the “V-shape” region devoided of UV-source counts in their figure is essentially a direct image of the dust disk. It is also visible, though less evident, in Figure 6 . Figure 6. Top: number of sources per square degree detected in NUV (left) and in FUV (right), as a whole (circles) or by magnitude ranges (dots). Values are shown for every 5° latitude strip. Bottom: fraction of FUV detections over NUV detections (left), and fraction of sources with FUV–NUV 0.5 (middle), and 0.0 (right) among the FUV detections (no error cuts, but sources in the footprint of extended objects have been excluded from the counts). While the faint sources (largely extragalactic) dominate the total samples, the FUV-detected sources are mostly bright stars. We recall that, for average Galactic dust, the UV extinction is similar in FUV and NUV, and much higher in both bands than at optical wavelengths (Table 1 and Bianchi 2011 ). In Figure 6 we plot the density of NUV and of FUV sources in GUVcat_AIS (top plot) as a whole and divided by NUV magnitude ranges; the plots show that the sources fainter than NUV_mag = 21mag dominate the sample, despite AIS being the shallowest survey, and especially in the NUV, where extragalactic objects are more prominent. The bottom panels show the fraction of FUV detections over NUV detections, again as a function of Galactic latitude, and among these, the hot and very hot sources (FUV_mag-NUV_mag ≤ 0.5 and ≤0.0 respectively). Such UV color cuts correspond to different stellar for different types of stars (Bianchi 2009 ), but roughly hotter than ∼15,000 K. Some QSOs may intrude on these FUV–NUV color cuts, as shown by Bianchi et al. ( 2009 ): these affect the faint sources most. The different behavior of relative source densities in Figure 6 reflects the fact that brighter samples (and hotter samples) are dominated by Galactic stars, which are more numerous in the Milky Way disk (see, e.g., Bianchi et al. ( 2011a )). 8.2. Summary of Suggestions and Caveats for Using the Catalog To conclude, we distill here, in terms of practical advice for users, the relevant information on the catalogs presented in this paper. 1. GUVcat_AIS contains unique measurements of all sources from AIS observations with both FUV and NUV detectors exposed. Duplicate measurements are removed in the main catalog, however, a version called


dicarboxylic acid (Hollauer et al. 2001 ). The aforementioned study assigned the ν (C=O) + δ (COH) combination band to 1630 cm −1 . Assignment of the remaining newly emerging bands was accomplished using a study on the literature infrared spectra of the three benzene dicarboxylic acids (Arenas Marcos 1980 ). However, it is to be noted that two broad peaks, at 1776 cm −1 and 1793 cm −1 , in the spectrum at 8 K did not correspond to a single carrier. Rather, the bands were assigned to a combination of carbonyl stretches from the various carboxylic acid species in the ice. 3.1.2. Quantitative Analysis From the peak assignments in Section 3.1.1 , the column density changes throughout the irradiation can be determined for the two reactants, benzene and carbon dioxide, along with the irradiation-induced products. For carbon dioxide, the temporal development of the ν 1 + ν 3 and 2 ν 2 + ν 3 of CO 2 and the ν 3 of 13 CO 2 was monitored to quantify the carbon dioxide molecules destroyed. Exploiting the integrated absorption coefficients of the three previously mentioned bands, 1.4 × 10 −18 cm molecule −1 for the ν 1 + ν 3 of CO 2 , 4.5 × 10 −19 cm molecule −1 for the 2 ν 2 + ν 3 of CO 2 , and 7.8 × 10 −17 cm molecule −1 for the ν 3 of 13 CO 2 , we found that (1.9 ± 0.9) × 10 16 molecule cm −2 of carbon dioxide was destroyed over the course of the hour-long irradiation. Corresponding to the diminishing carbon dioxide column density were new bands assigned to carbon dioxide and carbon trioxide. The development of the two new carbon oxides was monitored using the fundamental band of carbon monoxide, assigned to 2141 cm −1 , and the ν 1 of carbon trioxide, assigned to 2044 cm −1 . Using a previously published work on the irradiation of carbon dioxide ices (Bennett et al. 2004 ), we found that the integrated absorption coefficients of the two previously mentioned carbon monoxide and carbon trioxide bands to be 1.1 × 10 −17 cm molecule −1 and 3.1 × 10 −17 cm molecule −1 , respectively. Utilizing this information, we determined that following irradiation with energetic electrons, the total increase in column density of carbon monoxide was (1.1 ± 0.1) × 10 16 molecule cm −2 , while the total increase of carbon trioxide was (7.9 ± 0.3) × 10 14 molecule cm −2 . The total column density of newly formed low-mass carbon species was therefore (1.2 ± 0.1) × 10 16 molecule cm −2 , i.e., 64 ± 3% of the total carbon dioxide destroyed was converted to carbon monoxide and trioxide. The difference between this value and the total quantity of carbon dioxide destroyed was therefore the amount reacted to form benzene carboxylic acids, i.e., (6.8 ± 1.0) × 10 15 molecule cm −2 . The destruction of benzene was monitored by the development of its ν 11 band at 690 cm −1 , with an integrated absorption coefficient of 1.5 × 10 −18 cm molecule −1 (Zhou et al. 2010 ). Comparing the initial column density of benzene with the column density following irradiation, we found that (4.4 ±


at 3 s resolution. Magnetic field data is provided by the MFI instrument (Lepping et al. 1995 ) and density and velocity data by the 3DP instrument (Lin et al. 1995 ) measured during a stationary slow stream. The start time of the interval is 12:00 2000 April 4 and stop time is 16:00 of 2000 April 6. During this interval the solar wind speed remained about 300 km s −1 . As it is seen from Fig. 1 , λ 0.03 except for very small τ. We suggest that this enhancement at the small scales is probably due to measurement uncertainties (which are known strongly affecting plasma parameters at high frequencies Kasper et al. 2006 ; Gogoberidze et al. 2012 ) rather than indicating a real enhancement of compressible perturbations. To support this suggestion, we present another important characteristic of compressible/non-Alfvénic perturbations (Tu Marsch 1995 ; Bruno Carbone 2013 ) by dashed line in Fig. 1 . As can be seen λ m is approximately constant and does not increase with decreasing time-scale. Figure 1. The ratio of dimensionless rms amplitudes (solid line) and (dashed line, see the text for details) as a function of time-scale for a stationary stream of the slow solar wind. The above consideration suggests that the thermal-speed spectra reported by Safrankova et al. ( 2016 ) are in fact the pseudo-thermal spectra dominated by the magnetic fluctuations rather than the temperature fluctuations. This conclusion is supported by the fact that the level of spectra reported by Safrankova et al. ( 2016 ) cannot be caused lonely by the temperature fluctuations. Indeed, the spectrum of the (pseudo-)thermal speed in their fig. 1(b) is only about three times lower than the spectrum of the bulk speed driven by Alfvén waves (their fig. 1a), whereas the authentic temperature fluctuations should be at least one order less energetic (Goldsein Siscoe 1972 ; Tu et al. 1991 ; Tu Marsch 1995 ). To be more specific, let us utilize the straightforward expression relating the bulk velocity fluctuations δ V Bn measured by Safrankova et al. ( 2016 ) and magnetic fluctuations due to Alfvén waves. By means of ( 34 ), we can eliminate from ( 31 ) thus arriving to the following estimation for the velocity spectra ratio: With reasonable values T 0∥ / T 0⊥ ∼ 0.5 or T 0∥ / T 0⊥ ∼ 1.8 and , ( 35 ) easily explains the modest ratio ≳ 1/3 between 〈|δ V Tn | 2 〉 B and deduced from figs 1(a) and (b) by Safrankova et al. ( 2016 ). With autentic temperature perturbations this ratio would be at least one order less (Goldsein Siscoe 1972 ; Tu et al. 1991 ; Tu Marsch 1995 ). 4 DISCUSSION AND CONCLUSIONS We have shown that the nature of 'temperature fluctuations' derived from the currents of Faraday cup(s) is strongly affected by the temperature anisotropy. If the temperature anisotropy is close to zero, then the derived 'temperature fluctuations' are dominated by the perturbations of real temperature (thermal speed). However, when the temperature anisotropy is finite, as is typical


parameter in N -body simulations. Numerous studies have argued that minimizing the scatter in certain statistical descriptions of the matter field (i.e. power spectrum or two-point correlation function) among an ensemble of N -body realizations requires a softening length ε that is at least as large as the mean inter-particle separation l = L box / N 1/3 (e.g. Melott et al. 1997 ; Splinter et al. 1998 ; Romeo et al. 2008 ; Joyce, Marcos Baertschiger 2009 ). Here, L box is the (periodic) box size of the cosmological simulation and N is the total number of particles used. Most cosmological simulations, though, are run with much smaller softening lengths, typically of the order of ε/ l ∼ 0.01–0.02. For example, the Millennium simulation (Springel et al. 2005 ) has ε/ l ∼ 0.022, while the MDPL and SMDPL simulations of Klypin et al. ( 2016 ) adopt ε/ l ∼ 0.019 and ε/ l ∼ 0.014, respectively. Whether such simulations produce reliable results on scales below the (comoving) mean inter-particle separation is still a matter of fierce, ongoing debate (see e.g. Knebe et al. 2000 ; Melott 2007 ; Joyce et al. 2009 ; Power et al. 2016 ; Benhaiem, Joyce Sylos Labini 2017 , and references therein). Several studies have focused on the optimal softening length for simulating individual objects (i.e. individual DM haloes or galaxies). For example, Dehnen ( 2001 ), extending studies by Merritt ( 1996 ) and Athanassoula et al. ( 2000 ), suggests that one should aim to minimize force errors. This can be achieved by optimizing the softening length such that it simultaneously minimizes the force bias (which increases with increasing ε) and the force noise (which decreases with increasing ε). Based on such considerations, Dehnen ( 2001 ) advocates that a collisionless system with a Hernquist ( 1990 ) density profile (which has the same r −1 -cusp as a NFW profile) should be simulated with a Plummer softening , where r 0 is the scale radius of the Hernquist (or NFW) profile and N 5 = N /10 5 with N the number of particles used to model the system in question. Power et al. ( 2003 ) use a different criterion to optimize the softening length: by minimizing the impact of two-body effects on the (central) density profiles of virialized DM haloes in cosmological simulations, they advocate a much larger softening length of , where c is the NFW halo concentration parameter. Note that both of these criteria have the optimal softening length depend on the size of the system as well as the number of particles that is used to represent the system. If we adopt a concentration–mass relation of the form c ∝ M −0.1 (e.g. Dutton Macciò 2014 ) and use that the virial radii of DM haloes scale according to r vir ∝ M 1/3 ∝ N 1/3 , we find that the optimal softening length depends on halo mass according to ε opt ∝ M α , with α = +0.2 and −0.17 for the criteria of Dehnen and Power et al., respectively. This scaling is sufficiently weak so that the softening is close to optimal for haloes


of the inner binary progressively suppresses the effect. This is because a in decreases, bringing down the ratio in equation ( 38 ). The exact point at which K-L becomes effective also depends on the mass ratio of the intruder with respect to the inner binary, and on the eccentricities of the inner versus the outer binary. Note that as e in increases, the ratio decreases. Therefore, the K-L mechanism might eventually self-regulate itself: as it grows the inner binary more eccentric, it also makes relativistic precession more effective. The condition might therefore not be satisfied any longer, thus suppressing the K-L effect and eventually altering the overall dynamics of the system. Although our investigation is similar in spirit to that of Hoffman Loeb ( 2007 ), the above discussion highlights the importance of the differences in the two implementations. In particular, Hoffman Loeb ( 2007 ) did not include 1PN and 2PN relativistic precession in their equations. This might significantly alter the overall statistical properties of merging binaries (e.g. eccentricities, coalescence time-scales) because, as we just discussed, the conditions for triggering K-L resonances, and thus the general dynamics of the system, are different. Moreover, our treatment of the hardening in the stellar background is more accurate, since it also reproduces the eccentricity evolution in the hardening phase. This is important because (i), it affects the triggering point of K-L cycles (equation 38 ), and (ii), it has a strong impact on the stability of the hierarchical triplet and on the probability of close encounters leading to chaotic behaviour. 5.2 Astrophysical implications The main aim of this paper is to present and validate the code, and a thorough analysis of the dynamics of MBH triplets is deferred to forthcoming papers of the series we planned. Still, the few cases examined here already provide some interesting astrophysical insights that we briefly outline in the following. In all our simulations, two of the MBHs (not necessarily those originally forming the inner binary) coalesce in less than 1Gyr from the start of the dynamical friction phase of the intruder. Therefore, triple interactions might provide a viable channel to merge MBH binaries in massive, low-density galaxies, where hardening against the stellar and gaseous background might act on a time-scale of several Gyr (Khan et al. 2011 ; Sesana Khan 2015 ; Vasiliev et al. 2015 ). At least a fraction of massive elliptical galaxies, which host the most massive binaries targeted by PTAs, might realistically undergo multiple mergers at z ≲1 (see Gerosa Sesana 2015 , and references therein). If the typical coalescence time-scale of the formed MBHBs is several Gyr, then the occurrence of a second merger will bring in an intruder, typically leading to coalescence on a much shorter time-scale. Triple interactions might therefore be an important channel for merging very massive, gas-poor low-redshift


the LG (e.g. see updates to McConnachie 2012 ). While environmental effects (e.g. efficient destruction of satellites, dwarfdwarf mergers, stellar stripping) could alleviate some tension, these mechanisms do not appear efficient enough to resolve the discrepancy (e.g. Kirby etal. 2013 ; Deason etal. 2014 ; Garrison-Kimmel etal. 2017 ). Furthermore, the overabundance of LG dwarfs is not limited to the faintest UFDs, as it is known to persist in the classical dwarf regime (Boylan-Kolchin etal. 2015 ), which is thought to be observationally complete (e.g. Koposov etal. 2008 ). Even more challenges arise if (i) the faint end of the UVLF approaches 2.4 (i.e. many more faint galaxies); and/or (ii) such low-mass galaxies have a low star formation duty cycle (e.g. 10percent; Wyithe etal. 2014 ). In the latter case, 90percent of the haloes would be in the off state at any given time, and thus have reduced UV luminosities. Effectively, this results in higher luminosity galaxies hosted in even lower mass haloes, assuming a canonical SHM. 3.2 Minimizing the flux contribution of ultra-faint dwarfs Up to this point, we have considered the consequences of extrapolating a Schechter UVLF into the regime of UFDs. However, several numerical simulations of galaxy formation predict a turnover in the UVLF, decreasing the predicted number of very faint galaxies in the early Universe (e.g. Jaacks etal. 2013 ; OShea etal. 2015 ; Gnedin 2016 ; Liu etal. 2016 ; Ocvirk etal. 2016 ; Yue etal. 2016 ; Finlator etal. 2017 ). Although details vary, the common threads among these simulations are that not all low-mass haloes necessarily host a galaxy and that baryonic effects internal to the galaxies (e.g. supernova feedback, radiation pressure) can significantly affect galaxy formation in low-mass haloes. Alternately, a turnover in the high- z UVLF is consistent with models that suppress or eliminate small-scale structure (e.g. warm dark matter; Schultz etal. 2014 ; Dayal etal. 2015 ). A broken luminosity function at high z is also necessary in order to avoid dramatically overproducing UFDs and even classical dwarfs in the LG (Boylan-Kolchin etal. 2014 , 2015 ). Fig. 4 illustrates the effects of two plausible UVLF turnovers. For simplicity, we focus only on the z 7 case and adopt analytic UVLFs that turn over from Jaacks etal. ( 2013 ) and Boylan-Kolchin etal. ( 2015 ). The UVLF from the latter study has 2 for M UV 13 and 1.2 for M UV 13 and is designed to reproduce z 0 LG dwarf galaxy counts. We have tuned the UVLF from Jaacks etal. ( 2013 ) to match that of Boylan-Kolchin etal. ( 2015 ). Figure 4. Top panel: a comparison between the UVLFs at z 7 with and without turnovers. The steep UVLF (black; 2) is from Finkelstein etal. ( 2015 ), while the other curves show models from Boylan-Kolchin etal. ( 2015 , orange) and Jaacks etal. ( 2013 , magenta). Bottom panel: the fraction of UV flux at z 7 for each of the UVLFs shown in the top panel, when integrated to M min 3.1. A break or


counter rotation was produced in the first place, the formation of retrograde accretion discs has also been proposed to explain the long-term evolution of spin periods in X-ray binaries ( Nelson et al. 1997 ; Christodoulou et al. 2017 ). However, for the time window 2010–2015 we can only speculate for the evolution of Ṁ due to lack of observational coverage and because of the high absorption of the X-ray spectrum (see Fig. 3 of C18). Nevertheless, the P and Ṗ measurements during the 2014 Chandra observation are consistent with the constant Ṁ assumption (see Fig. 3 ), supporting our finding that the decrease of the observed flux between 2010 and 2015 is only due to high absorption. If Ṁ during that period was two orders of magnitude lower than after 2015 then it is possible that there was no NS spin reversal. In this case the NS spin period should have been larger than a few hundred seconds prior to the SN 2010da event. In general there are multiple ways to maintain the necessary Ṁ to fuel ULXPs. For systems fueled by Roche Lobe (RL) overflow, the accretion flow carries the angular momentum of the orbit. It is therefore implausible for an accretion disc to switch between retrograde and prograde rotation ( Chakrabarty et al. 1997 ), and any change between retrograde and prograde rotation of the NS disc system needs to be due to a change in the direction of the NS rotation. Therefore, for NGC 300 ULX1 it is more plausible that the accretion mechanism was drastically altered during the SN 2010da event, prior to which the NS could have been fueled via wind accretion. A possible explanation for such a phase transition to occur can be an episode of thermal-timescale mass transfer ( King et al. 2001 ). In that case the donor star has a radiative envelope and fills its RL as it expands across the Hertzsprung gap after the wind-fed X-ray phase ends. However, RL overflow is not the only way to explain such high accretion rates. Supergiant systems and luminous blue variables (LBV) can also exhibit mass loss rates in excess of 10 −6 M ⊙ yr −1 ( Smith 2014 ), and therefore for a binary system in a moderately close orbit the compact object can capture enough matter to sustain super-Eddington accretion. An LBV is also most probable according to Binder et al. (2016) while other authors have deemed this classification inconclusive ( Lau et al. 2016 ; Villar et al. 2016 ). We note that many of the arguments used in the classification of the system were based on the decay of the X-ray flux observed after the SN 2010da event. However, the decay in the X-ray flux was most likely a result of rapid increase in X-ray absorption (C18). 4. Conclusions We have studied the spin period evolution of NGC 300 ULX1, the most extreme spin-up NS powered by an accretion disc. We derived precise measurements of P and Ṗ for different epochs, and applied theoretical models of accretion theory in order to estimate the magnetic field strength of the NS. Even though many of the models


in Sect. 3.2 . We did not identify any significant gas contamination from other species in any of our spectra. Second, we selected the lines with intensities above a defined threshold (ten times the noise level). We summarize the results in Table 4 . We find that the number of U I lines differs considerably for different lamps (e.g. in the lamp 0127 we find a factor of 1.8 more lines than in the lamp 0120). The number of U II , Ne I, and Ne II lines is essentially constant. Table 4. Number of confirmed isolated U and Ne lines with S/N higher than ten found in the 12 U–Ne spectra for NIR wavelengths. The last column contains the average of the U line intensity normalized to the average of its line intensity in the 12 spectra ( I U ). We looked for the confirmed lines that can be found in all of the 12 spectra to systematically analyse the difference between the 12 lamps. In total, we detected 222 U I and 104 Ne I lines in the spectra of all lamps. We normalized the 12 spectra to the sum of the Ne lines intensities averaged in each spectrum. Then we divided the line intensity of each U line by the average line intensity of this line in the 12 spectra. Last, we calculated the average of the normalized line intensity of the 222 U I lines (named I U in Table 4 ) for each lamp. In Fig. 8 we plot the normalized line intensity of the common U I lines in the NIR spectral range for seven HCLs (for readability reasons). The dashed lines represent I U for each HCL. From Fig. 8 and Table 4 it can clearly be seen that I U varies significantly between the lamps. Lamps with the lowest U line intensities are HKH0120 and HKH0122. Lamps with the highest U line intensities are HKH0127 and HKH131. The maximum U line intensity difference is 88% (with respect to the minimum value), measured between lamps HKH0127 and HKH0120. Fig. 8. Coloured dots represent the normalized line intensity of 222 U I lines for each HCL in the spectral range from 1000 to 1700 nm. Dashed coloured lines indicate of each lamp (i.e. average of the 222 U I normalized line intensity). For readability reasons we plot only seven of the 12 HCLs. A possible explanation for the observed behaviour of the HCLs could be a different geometry of the lamps or in the light-fibre coupling efficiency, as seen in Huke et al. (2016) . This could affect the gas-metal intensity ratio. Another explanation could be that the metal line intensities are very sensitive to the internal pressure of the buffer gas ( Crosswhite et al. 1955 ). Therefore, even small changes in pressure from lamp to lamp would have an effect on the metal line intensity. We conclude that HCLs can show noticeable differences in number and intensity of metal lines even if they are manufactured in a single batch. 7. U line list We concluded in Sect. 4 that U cathode lamps are more suitable for wavelength calibrators than Th lamps from 500 to 1700 nm. To use HCLs as wavelength calibrators for high precision RV spectrographs, the wavelength of the