focal ratios of these telescopes, along with the use of single, photographic-film size CCDs, allow them to probe large areas of galaxy haloes while reaching surface brightness levels ∼2–3 mag deeper (μ r ∼ 28 mag arcsec −2 ) than the classic photographic plate surveys (e.g. Palomar Observatory Sky Survey) and the available large-scale digital surveys (e.g. the Sloan Digital Sky Survey). Here, we use this amateur telescope discovery approach to report a faint, elongated galaxy projected on to the halo regions of NGC 253 in the Sculptor Group. With a distance of 3.5 Mpc, NGC 253 is one of the nearest large spirals, and has been well studied (e.g. Davidge 2010 ; Bailin et al. 2011 ; Greggio et al. 2014 ; Monachesi et al. 2015 ), but this object, which we call NGC 253-dw2, had been missed. 1 2 OBSERVATIONS We first noticed a candidate satellite galaxy in a visual inspection of several images of NGC 253 available on the internet that were taken by amateur astronomers: Alessandro Maggi using a Takahashi Epsilon 180ED astrograph (18-cm diameter at f /2.8) and Mike Sidonio using a 12-in f /3.8 Newtonian (see Fig. 1 ). In both cases, the pixel scale was coarse and it was not clear if the elongated feature was real or an artefact or reflection as often present in amateur images. Figure 1. Left: amateur images of NGC 253 and its satellite NGC 253-dw2. The grey-scale image is from the 12-in telescope luminance filter, with colour image of NGC 253 from the 0.5 m Black Bird Remote Observatory, and field of view of ∼11 × 10 (67 kpc × 60 kpc). North is up and east is left. The zoom-in on NGC 253-dw2 is from CHART32 and covers ∼8 kpc × 7 kpc. Right: Subaru/Suprime-Cam image, colourized using g and R c bands, and demonstrating that the satellite is composed of red, discrete stars. We investigated the nature of NGC 253-dw2 by follow-up observations using amateur and professional facilities as follows. First, deep imaging of the field centred on the dwarf candidate was collected remotely with the Chilean Advanced Robotic Telescope (CHART32), an 80-cm f /7 corrected Cassegrain telescope located at the Cerro Tololo Inter-American Observatory, Chile. An FLI PL-16803 CCD camera was used, with a pixel scale of 0.331 arcsec over a 22 arcmin × 22 arcmin field-of-view. Two overlapping sets of 20 × 1200 s individual image frames were obtained through a Baader luminance filter over several photometric nights between 2013 September and November. Each individual exposure was reduced following standard image processing procedures for dark subtraction, bias correction, and flat-fielding (Martínez-Delgado et al. 2010 ). The images were combined to create a final co-added image with a total exposure time of 48 000 s. Part of the resulting CHART32 image is shown as an inset in Fig. 1 (left-hand panel). The candidate object looks fairly regular and diffuse, like a nearby dwarf spheroidal (dSph) galaxy rather than a background galaxy or an instrumental artefact. It is also very

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion O O B-CelestialObject I-CelestialObject O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O B-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O B-Person I-Person O O B-Telescope I-Telescope I-Telescope I-Telescope O O O O O O B-Person I-Person O O B-Telescope I-Telescope I-Telescope I-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O B-CelestialObject I-CelestialObject O O O O O O B-Telescope I-Telescope O O O O O O B-CelestialObject I-CelestialObject O O B-Telescope I-Telescope I-Telescope I-Telescope I-Telescope I-Telescope O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O B-Instrument O O O O O O O O B-Telescope O O O B-Wavelength O B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope I-Telescope I-Telescope I-Telescope B-Telescope O O O O O O O O O O B-Observatory I-Observatory I-Observatory I-Observatory B-Location O B-Instrument I-Instrument I-Instrument I-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


The Gini coefficient is strongly dependent on the noise level of imaging data, and suffers from large uncertainties when signal-to-noise ratio (S/N) is not sufficiently high (Lisker 2008 ). For asymmetry A , noise contribution is estimated by measuring A on a nearby blank sky region with the same aperture. However, the noise correction for A overestimates the real noise contribution (see Figure 1 of Shi et al. 2009 ). Here, we present a detailed analysis on the noise effects in quantifying A , and introduce a revised correction for noise contamination. We construct a sample of model galaxies to test the morphological parameter A . The sample consists of 569 isolated galaxies from Wen et al. ( 2014 ) (see Section 3.2 for more details about model generation). An artificial image is obtained through combining a model galaxy image with a background noise image. The parameter A is measured from both the artificial image and the noise-free model image, following the definition given in Conselice ( 2003 ) aswhere I 0 is the intensity of the galaxy and I 180 is the -rotated intensity. The second term refers to the correction for noise contamination. A group of pixels are randomly selected from the background regions to form the background noise image. In the measurement, an aperture of 1.5 times the circular Petrosian aperture is adopted to estimate the noise contamination. Figure 12 presents comparison of the measure of A from noise-added and noise-free images for the 569 model galaxies. We find that noise contamination leads A to be systematically overestimated, and the significant scatter indicates the uncertainties of noise contribution—about 20% for a high-S/N galaxy, and up to 50% for a low-S/N galaxy (Shi et al. 2009 ). The noise correction introduced in Conselice ( 2003 ) overestimates the noise contamination and biases A to be smaller. This is because all background pixels within the Petrosian aperture are used to calculate the noise contamination. As discussed in next section, however, we argue that noise contamination is correlated with the number fraction of noise dominated pixels of a galaxy, indicating that only part of the noise contribution estimated by Equation ( 6 ) is real. Furthermore, the measured A from noise-added images is found to be lower than that from noise-free model images, in a few cases, even if no noise correction is adopted. This is because that noise dramatically changes the segmentation maps of the model galaxies. In our measurements, only pixels within 1.5 times the circular Petrosian aperture are counted to calculate A , and the extended structures of the model galaxies out of the aperture are ignored, leading to an underestimation in A . For a noise-free model galaxy image, all pixels associated with the galaxy are used to compute A . Figure 12. Comparison of asymmetry measurements from galaxy images, with and without noise. Asymmetry of the noise-free model image is marked as . For galaxy image with

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


TNG100 parent galaxy sample selection . Red dots show the positions of central disc galaxies in TNG100 with 10 10 ≤ M stell /M ⊙ ≤ 10 11 . Orange dots point to satellite disc galaxies in the same mass range; to avoid Virgo-like clusters, we require that satellite galaxies have no more than one massive () neighbour within 1 Mpc. Galaxies rejected on the basis of these environmental and morphological criteria are shown in black, for reference. In the background, the spatial distribution of all galaxies in TNG100 is shown in blue. In addition to this parent sample, we also defined smaller samples of stellar mass-matched TNG100 galaxies for each DNGS galaxy. This time we applied a more observer-friendly definition of stellar mass – specifically the integral of the stellar mass surface density profile. We denote this ‘observed’ stellar mass as M stell, obs . When calculating TNG100 stellar masses in this way, we only integrated the density profiles down to a floor of kpc −2 , as this corresponds to the typical depth of the DNGS observations (see Section 5.1 for more details). The physical radius corresponding to this surface density threshold varies between ∼20 and 70 kpc for the DNGS sample, although we note that this is an extrapolation (from a last observed point of kpc −2 ) in two of the eight galaxies. TNG100 galaxies exhibit an even larger variation in physical extent under this definition, ranging from ∼40 to 140 kpc. We can infer from these numbers that TNG100 galaxies are more extended than DNGS galaxies, and we will return to this idea in Sections 6 and 8.2 . As a consequence of the shape of the stellar mass function, if we were to simply select all TNG100 galaxies that fall within the observational errors (see Table 1 ), each mass-matched sample would remain strongly weighted towards low-mass galaxies by number. To alleviate this issue, we instead used rejection sampling (Press et al. 1992 ) to obtain a normal distribution of TNG100 galaxy stellar masses for each DNGS galaxy. We calculated the probability P ( M stell, obs ) of drawing each TNG100 stellar mass from a Gaussian distribution with a mean and standard deviation set by M stell, DNGS and , respectively, and accepted the first 50 TNG100 galaxies with P ( M stell, obs ) less than a random number drawn from the same distribution. We emphasize that, in addition to the definition of the mass-matched samples, all comparisons between observations and simulations were done using quantities measured from TNG100 galaxies (e.g. surface density profiles or stellar halo mass fractions) in a manner identical to the DNGS sample. When exploring parameter space that contains unobservable properties, however, we will occasionally use the ‘true’ stellar mass instead. In the following sections we will explicitly distinguish between the parent and mass-matched samples, and between ‘true’ and ‘observed’ stellar masses where applicable. 3 FROM STELLAR PARTICLES TO IMAGES The first step towards

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


with the power-law function. The fits included wavelength intervals that were free of BALs and ranged from approximately 1260–1350, 1370–1480, 1530–1800, and 1870–2500 Å. We integrated the P v BAL apparent optical depth profiles using the following equation, in Gaussian units: where f is the oscillator strength, λ is the rest wavelength, and τ( v ) is the apparent optical depth at a given velocity (Savage Sembach 1991 ). Rest wavelengths and oscillator strength values were taken from Morton ( 2003 ), and we treat the P v λλ1117,1128 doublet as a single line at λ = 1121 Å with an average oscillator strength of f = 0.705. For sources that showed non-variable P v BALs, we integrated τ( v ) in accordance with equation ( 1 ). For sources that showed variable P v BALs, we integrated the optical depth difference to generate lower limits for the change in P v column density. 4 RESULTS AND DISCUSSION 4.1 Absorption line variability We detect definite (category Y, see Section 3.1 ) variability from any BAL (i.e. from C iv , Si iv , or P v ) in 10 out of 71 BAL quasars in our sample (see Appendix A for notes on individual objects). Spectroscopic comparisons in our sample probe rest-frame time-scales between 0.5 d and 3.8 yr, and we measure BAL variability time-scales over ≤ 0.2–3.8 yr for our Y sources. Tentative (T) variations from any BAL are detected in 44 sources, and 17 objects exhibit no (N) BAL changes. Table 3 lists the associated ion, measured variability time-scale, LOS velocity of the variable region, and variability direction for each variable (Y) BAL in our sample. BALs not presented in Table 3 show no significant absorption line changes over the listed time-scales. For example, there are four cases of P v and/or Si iv BAL variations with no associated C iv BAL changes in the same time-scale comparison (see 013652 + 122501, 104059 + 055524, 104247 + 061521, and 0.5 yr for 122654−005430 in Table 3 ). We detect four cases of C iv BAL variability with non-variable P v absorption at similar velocities (see 2.4 yr for 122654−005430, 0.8 yr for 140532 + 022947, along with 2.0 and 0.8 yr for 221326 + 003846 in Table 3 ). There are five cases of C iv BAL changes with likely no associated P v absorption at similar velocities (see 102154 + 051646, 114548 + 393746, 2.4 and 0.8 yr for 122654−005430, and 2.4 yr for 140532 + 022947 in Table 3 ). In two cases (025042 + 003536 and 230721 + 011118; see Table 3 ), it is unclear if the C iv BAL variations are associated with P v absorption at the same velocity. Table 3. Variable BAL properties. Information listed for each BAL quasar includes (from left to right): ions associated with variable BALs, measured time-scales of BAL variability (upper limits that are limited by temporal sampling), LOS velocities corresponding to maximum flux changes within the BALs, and whether the BAL depths increased (+) or decreased (−). Multiple, distinct time-scales listed for the same ion are in chronological order.

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


also listed in Table 2 . The decay time-scale is in these cases of the order of or shorter than the decay time of the previous stages, meaning that the coalescence would supposedly happen promptly once the hard binary is formed. None the less, the hardening and inspiral time-scales we inferred in Table 2 are definitely longer than the ≈15 Myr found by Khan et al. ( 2016 ), who addressed the pairing of ∼10 8 M ⊙ MBHs in a massive early-type galaxy at z ≈ 3, which would become a BCG by z ≈ 0. The discrepancy in the time-scales has to be attributed to the large central density in their merging systems, which is nearly 10 5 M ⊙ pc −3 at 10 pc (their fig. 6), i.e. ∼100 times larger than in our case (see also the discussion in Khan et al. 2018 ). 13 Note that the system they explored is not a main-sequence galaxy as the one presented in this paper, but instead it is a more massive and relatively rare galaxy. For this reason, we expect the time-scales we obtain in this paper to be more representative for the bulk of the galaxy population. Note that the hardening and inspiral time-scales extrapolated for our system do not account for the effect of gas (which is expected to assist the orbital decay at scales larger than a pc, but could hinder it at smaller scales; Souza Lima et al. 2020 ), and the possibility that the fragmentation of a non-resolved circumnuclear disc could render even this smaller-scale decay very stochastic (Fiacconi et al. 2013 ; Souza Lima et al. 2017 ). If we neglect these complications, our estimates suggest that the whole pairing process could take as short as a few hundred Myr and probably less than a Gyr for the majority of the studied MBHs; that is, the MBH merger is likely going to occur at z = 5–3.5, except for the MBH that undergoes the bar-induced ejection. Concerning the fate of this latter object, one could wonder how likely this scattering event is. Even if our statistical sample is too limited to make strong statements here, it is worth mentioning that a test simulation with virtually the same initialization as the current one also showed evidence for a bar slingshot, suggesting that the event can be relatively common. 4.5 Caveats and limitations Our simulation has the important limitation that MBH accretion and feedback were not taken into account. However, it is reasonable to expect that feedback would render DF even less efficient by evacuating the gas mass around an MBH (see e.g. Park Bogdanović 2017 ; Souza Lima et al. 2017 ; del Valle Volonteri 2018 for a smaller scale analysis of this aspect). Each inspiralling MBH may also enhance its mass by accreting gas along the decay: in this respect, it is worth remembering that the MBH masses we adopted in the current run are relatively large for z ≳ 6, thus we do not expect this to represent a major issue. We also note that accretion on to MBHs may be used in future high-redshift surveys to sample offset or dual active galactic nuclei (e.g. Capelo et al. 2017 ; De

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


i.e. brighter quasars may live in a region of higher overdensities (e.g. see Guimarães et al. 2007 , and references therein). In order to check this effect, we devised a subsample of low and high luminosity. In the low- and high-luminosity bins, we have taken 25 lowest and 25 highest (∼29 per cent of the total sample) luminosity quasars of our sample. As can be seen from Fig. 7 , the excess pixel optical depth ratio is more pronounced for the subsample of higher luminosity with log L 912 > = 31.85 ergs s −1 Hz −1 as compared to the subsample of lower luminosity with log L 912 > = 31.12 ergs s −1 Hz −1 . The integrated value under the curve (e.g. see Fig. 7 ) between −6 ≤ r ≤ 0 Mpc is found to be higher by a factor of 3.70 ± 0.22 and 1.62 ± 0.15 w.r.t. the corresponding integrated value of curve for high- and low-luminosity subsamples, respectively. However, we do notice that higher luminosity bin has a higher median redshift of z em > = 4.06 in comparison to z em > = 3.85 for the lower luminosity bin (e.g. see grey shade). However, the above R τ ( r ) difference, especially in the −2 ≤ r ≤ 0 Mpc bins, cannot be merely explained by the redshift difference in these two subsamples. Figure 7. Left-hand panel : Same as right-hand panel of Fig. 6 , but for the extreme 25 low- and 25 high-luminosity quasars in our sample (e.g. see text in Section 4 ). The Lyman continuum luminosity was calculated using V -band magnitude (e.g. see Section 2.1 .) Right-hand panel : The plot shows radius versus flux (similar to Fig. 4 ) for the transmitted flux of the subsample of extreme 25 low- and 25 high-luminosity quasars. The transmitted flux of the control sample of IGM for the higher luminosity and lower luminosity quasars is shown in red-dashed and blue dot–dashed lines, respectively. Additionally, we also used our sample to check for any difference of density profile among radio-loud (RL) and radio-quiet (RQ) quasars (e.g. see Sopp Alexander 1991 ; Dunlop et al. 2003 ; Gopal-Krishna, Mangalam Wiita 2008 ; Retana-Montenegro Röttgering 2017 ) where the former is generally associated with the presence of jets. Such bimodality is quantified by a radio-loudness parameter ( i.e. ) defined as a ratio between the rest-frame flux densities at 5 GHz and 2500 Å (see also Ivezić et al. 2002 ; Kellermann et al. 2016 , and references therein), with its value ≥ 23 for RL sources as adopted by Ganguly et al. ( 2013 ). Out of the 85 quasars in our sample, 62 have information about its radio-loudness parameter with 12 being RL (i.e. 23) quasars and 50 being RQ (i.e. ) quasars (e.g. see Perrotta et al. 2016 ). We plot R τ ( r ) for these two sub-samples (i.e. RL and RQ quasars) as shown in Fig. 8 . From this figure, it is evident that their R τ ( r ) profile is quite similar in both sub-samples, though the sample size of RL quasars is small here (12 quasars). Here, we also note that the typical luminosity (median) among these two sub-samples is almost similar being 2.23 × 10 31

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


et al. ( 2006 ) and Kuwabara et al. ( 2009 ) in a numerical model best fitted to the measurements taken by the muon network at Earth (rigidities 50–100 GV) and was utilized to determine the orientation of the interplanetary FR. The diffusion–expansion approach was also implemented by Subramanian et al. ( 2009 ) and Arunbabu et al. ( 2013 ) in an analytical model and was compared to the GRAPES-3 muon telescope (rigidities 12–42 GV). These authors estimated the radial perpendicular diffusion coefficient to be of the order of 10 21 . However, it should be noted that their studies are adjusted to large events associated with a shock and observed at high particle rigidities. At rigidities of about 1 GV, Cane et al. ( 1995 ) estimated a diffusion coefficient of about 10 19 by utilizing spacecraft measurements and less energetic ejecta. Both are roughly in agreement with values obtained from the typical empirical expression used in numerical models (see Equations (23) and (24) in Potgieter 2013 ). Therefore, these studies outline a rough constraint on the diffusion coefficient used to model FR-associated FDs. Since both diffusion and expansion are processes that presumably start close to the Sun, FRs, that is, CME initial properties, need to be considered in the model. This ejecta-only FD model primarily describes FDs associated with ICMEs without a shock/sheath region, because a shock/sheath region presumably introduces an additional decrease via different physical mechanisms, but could also be applied to explain the ejecta part of an FD in two-step FDs. The aim of this study is to take these considerations into account in the diffusion–expansion model to improve our understanding on the cause, formation, and evolution of FDs. 2. Basic Diffusion Model First we consider an analytical FD model based on the perpendicular diffusion of GCRs into the FR, similar to Cane et al. ( 1995 ). In this basic diffusion model, the FR is regarded as a closed magnetic structure, rooted at the Sun, that is initially empty of GCRs (Figure 1 (a)). The FR is of cylindrical form (hereafter approximated by a long cylinder), it moves with constant velocity, and as it moves, it does not vary in shape or size (Figure 1 (b)). We note that the assumption of constant velocity is in general not valid, as it was shown that CMEs slower than the solar wind accelerate, whereas CMEs faster than the solar wind decelerate (e.g., Sheeley et al. 1999 ; Gopalswamy et al. 2000 ), which is attributed to the magnetohydrodynamical drag (see, e.g., Vršnak et al. 2013 ; Hess Zhang 2014 ; Sachdeva et al. 2015 , and references therein). However, since the acceleration/deceleration depends on the difference between the CME and solar wind speed, for a substantial subset of CMEs (and especially the slower ones that do not drive shocks), a constant velocity can be taken as a relatively fair approximation. We also note that the assumption of constant shape and size might not hold true, as it was

B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O B-CelestialObject B-EntityOfFutureInterest I-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-Telescope I-Telescope I-Telescope B-EntityOfFutureInterest I-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O B-CelestialObject O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O B-Model I-Model O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


distribution ranging from 0° to 10°. Asteroids which were initialized at the beginning of the simulation with two different eccentricity distributions depending on the simulation. The first is circular asteroids, and the second are asteroids with eccentricities chosen between 0.3 and 0.7. We emphasize that we are not attempting to reproduce realistic exo-debris discs in these systems (which would require a more detailed Yarkovsky model), but rather are placing bounds and observing trends. The evolution of most initially eccentric asteroids that we simulated are not shown, unless they provide a revealing physical trait. Asteroids which were initialized at the beginning of the simulation with orbital angles chosen from a random uniform distribution across their entire ranges. Yarkovsky prescriptions according to the following values of : Our choices for Models A–C arise from our intention to place bounds on the motion by considering only extreme cases. We approximate these extreme cases by focusing on and from the analytic limits in equation ( 25 ). In terms of semimajor axis, Model A pushes asteroids outwards, Model B pushes asteroids inwards, and Model C does not push them outwards or inwards. Alternatively, Models A and B have only a minor effect on asteroid inclination evolution, whereas Model C has a relatively large effect. We actually ran additional simulations with other combinations of entries, but found that they represent intermediate cases to Models A–C, supporting the analytics and our choices. 4 SIMULATION RESULTS The asteroids in our simulations are accelerated by three major effects: (i) mass-loss from the star, (ii) perturbations from the planet, and the (iii) radiation-driven Yarkovsky effect. 4 Mass-loss always pushes the asteroids away from the star (the orbital pericentre is always increasing, even in non-adiabatic motion; Veras et al. 2011 ), whereas the planet and the Yarkovsky effect may perturb the asteroids in either direction. Although both mass-loss and planets can increase e ast to unity (causing escape; e.g. Veras et al. 2011 ; Adams, Anderson Bloch 2013 ), Yarkovsky acceleration cannot. Veras et al. ( 2015 ) investigated the relative magnitudes of stellar mass-loss and the Yarkovsky effect, but did not include a planet nor run numerical simulations. The Yarkovsky drift varies in a complex manner, and is a function of all orbital elements, even in our simple approximation where the matrix elements of remain constant over time. However, equations ( 25 )–( 26 ) reveal that for small inclinations, the key parameters are and . Although the Yarkovsky acceleration drops roughly as , the acceleration increases linearly as a function of L ⋆ ( t ). The time dependence of L ⋆ ( t ) is, in turn, non-linear, and dominates changes in the Yarkovsky acceleration. Mass-loss is largely adiabatic within about 10 3 au (Veras et al. 2011 ), meaning that within this region it feeds back into the Yarkovsky acceleration only through an

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


the motivation for the selection of the volume for LASr. Next, we require a galaxy parent sample highly complete in terms of galaxies sufficiently massive to host an AGN, which can then be used to select AGN from. We will see that current local galaxy samples do not fulfil this criterion so that we have to assemble our own galaxy parent sample. Finally, we describe the assembly of the galaxy properties relevant for this work, namely the coordinates, redshifts, and distances, allowing us to find the MIR counterparts of the galactic nuclei and compute their luminosities. 2.1 Selection of the volume We wish to construct a highly complete census of SMBH growth in the local Universe. The choice of volume to be used for this purpose is motivated by several factors. In order to obtain a census that is representative for the whole AGN population, the volume needs to be representative of the larger scale, low redshift Universe. It is estimated that cosmological isotropy is reached for length scales of ∼200 h −1 Mpc with h = H 0 /100 km s −1 Mpc −1 and H 0 the Hubble constant (Sarkar, Pandey Khatri 2019 ). The volume should also be large enough to sample rarer AGN sub-populations in sufficient numbers to yield statistically robust conclusions on their relevance. Here particular emphasis should be on the high luminosity AGN regime because these may dominate the integrated black hole growth and AGN feedback (e.g. Aird et al. 2010 ; Fabian 2012 ). However, high-luminosity AGN have a low space density. For example, current estimates of the AGN luminosity function in X-rays, e.g. Aird et al. ( 2015 ), let us expect a space density of Mpc −3 for AGN with an intrinsic X-ray luminosity of , e.g. ∼20 objects within a sphere of 200 Mpc radius. On the other hand, the volume should be small enough so that the depth of the all-sky surveys, used to identify and characterize the AGN, is sufficient to probe the lower parts of the AGN luminosity range. This is particularly important in the X-rays where extinction is large for obscured AGN. For example, the final all-sky maps of eROSITA and ART-XC are expected to have depths of and at 2–10 keV, respectively (Merloni et al. 2012 ; Pavlinsky et al. 2018 ), which corresponds to a distance of 150–250 Mpc for an observed X-ray luminosity of . However, CT AGN are suppressed by easily a factor of 10 to ∼100 at these wavelengths. The MIR is much less affected by extinction, but sensitivity is the key restricting factor, i.e. the WISE all-sky maps have an average depth capable of detecting an AGN with a 12 luminosity up to a distance of 220 Mpc with ≥3σ in band 3 (W3∼11.6 mag; WISE documentation 1 ). Another factor to take into account is that the completeness of our parent sample of galaxies directly restricts the completeness of our AGN search. According to a recent estimate, our all-sky redshift completeness is only for galaxies with a redshift z 0.03 (Kulkarni, Perley Miller 2018 ), and the completeness is quickly

O O O O O O O O O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Model I-Model O B-Model I-Model B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O B-Instrument O B-Telescope O O O O O O O O B-Wavelength I-Wavelength O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength B-Formula I-Formula B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula B-Citation I-Citation I-Citation I-Citation O O O O O O


(Figure 4 ). Furthermore, we collected emission line fluxes of SLSN host galaxies from the literature (Lunnan et al. 2014 ; Leloudas et al. 2015 ; Perley et al. 2016 ; Chen et al. 2017a , 2017b ) and corrected for foreground and internal dust extinction given by the Balmer decrement. SLSN host galaxies are located predominantly in the high ionization region with log([O iii ]/H β ) > 0.5 for any given [N ii ]/H α . This region is populated by extreme emission line galaxies as Leloudas et al. ( 2015 ) pointed out. The positions of SN 2017egm and PTF 10uhf are in a distinct region of the BPT diagram to most other SLSN hosts. This may indicate that SLSNe extend out to large metallicities than previously believed, and may cover a similar region to gamma-ray burst (GRB) host galaxies (see Figure 8 in Krühler et al. 2015 ). Improved completeness of low-redshift SN samples should indicate if SN 2017egm (and PTF 10uhf) are outliers or at the extreme end of a continuous distribution. 3.4. Stellar Ages and Progenitor Masses of GRBs and SLSNe We used the EW of H α as a tracer of the stellar population age (e.g., Leloudas et al. 2011 ; Kuncarayakti et al. 2016 and references therein). In general, a higher EW H α corresponds to a younger age, though the relation between the EW and age is dependent on the star formation history, initial-mass function, metallicity, and binary or single stellar populations (e.g., Eldridge Stanway 2009 ). We collected the EWs of H α at the explosion sites of SLSNe and GRBs from IFU and resolved long-slit spectroscopy (for references see Table 1 ), and estimated the stellar population ages using consistent models. We applied the Binary Population and Spectral Synthesis (BPASS 11 11 http://bpass.auckland.ac.nz version 2.1 models (Stanway et al. 2016 ; Eldridge et al. 2017 ) in combination with the photoionization Code CLOUDY (e.g., Ferland et al. 2013 ). These models will be described in L. Xiao et al. (2017, in preparation), and have been used to study the ages of SNe in Xiao et al. ( 2017 ). Table 1 Physical Properties Inferred from IFU and Resolved Long-slit Spectroscopy at SLSN and GRB Explosion Sites Note. For consistency, we re-calculate the stellar population age using the BPASS model. References are: (a) this work, (b) Cikota et al. ( 2017 ), (c) Thöne et al. ( 2015 ), (d) Krühler et al. ( 2017 ) (GRB 980425/SN 1998bw), (e) Izzo et al. ( 2017b ) (GRB 100316D/SN 2010bh), (f) Thöne et al. ( 2014 ) (GRB 060505/SN-less), (g) Tanga et al. ( 2017 ) (GRB 111005A/SN-less). To calculate the ages of the stellar populations, we select models that have a [O/H] value closest to that measured at the explosion site using the O3N2 calibration (Table 1 ). For each of the SLSNe we then provide two ages, one assuming the stellar population is comprised of single stars only and the second of binary stars. We see that there is a significant difference in the stellar population ages that we derive depending on the BPASS model used. The

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O 2 and O 3 are also central to the design of instruments for other future ground- and space-based telescopes (Domagal-Goldman et al. 2014 ; Harman et al. 2015 ; Meadows 2017 ; Meadows et al. 2017 ). Here, we argue that O 2 and O 3 are reliable bioindicators under certain conditions. We outline what those conditions are, and discuss the secondary measurements and constraints necessary to demonstrate the presence of such conditions on another world. 2. False Positives in the Literature For the purposes of this paper, a “false positive” for life is defined as any abiotically derived O 2 concentration that exceeds that estimated to follow the GOE (Harman et al. 2015 ). If the low estimates by Planavsky et al. ( 2014 ) are correct, then that level is at or below 0.1% PAL. Possible mechanisms by which that abiotic O 2 level might be achieved have been recently reviewed by Meadows ( 2017 ) and Meadows et al. ( 2017 ). Broadly speaking, these scenarios can be divided into two categories: (1) false positives driven by changes in the redox budget of a planet’s combined atmosphere/ocean system (as defined in Catling Kasting 2017 , Ch. 8), and (2) false positives driven by photochemistry within the atmosphere. Examples of the redox-driven false positives include planets that experience substantial water loss because they are located inside the inner edge of the habitable zone (Kasting 1988 ; Kasting et al. 1993a ), or their host (M) stars are relatively bright during their pre-main sequence lifetimes (Ramirez Kaltenegger 2014 ; Luger Barnes 2015 ; Tian 2015 ), or they lack non-condensable gases like N 2 that help keep water vapor contained in the lower atmosphere (Wordsworth Pierrehumbert 2014 ). In each of these cases, hydrogen is irreversibly lost to space, oxidizing the atmosphere and oceans and, ultimately, the planet itself. The ultimate fate of this oxygen is uncertain but it could potentially be drawn down to undetectable concentrations by absorption into the mantle (Wordsworth et al. 2018 ). Other types of redox-driven false positives essentially correspond to hypothetical planetary scenarios that lack a volcanic source of reduced gases (e.g., Hu et al. 2012 ; Domagal-Goldman et al. 2014 ; Gao et al. 2015 ). If volcanic outgassing is assumed to be nearly zero, or the recombination of CO and O 2 is inefficient, or there are no surface sinks for O 2 , then O 2 can build up in the atmosphere. If reduced volcanic gas emissions are entirely neglected, O 2 can and must accumulate as H 2 O is photolyzed and the resulting hydrogen escapes to space. But we argue that a false positive driven by such low outgassing rates is unlikely if the planet is habitable, so that liquid water can facilitate reactions of O 2 with its crust, and if the planet remains volcanically active for long time periods, as the Earth has done. (We return to this last point in Section 6 .) The false positive scenario described by Hu et al. ( 2012 ) is more complicated in that it has

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


Plummer profile reads while the normalized projected number of stars for the same model is where φ( X ) is the angle corresponding to the effective circular section where we analyse the data (see Fig 1 ), and whose analytical expression for small cone apertures (i.e. R max ≪ 1 radian) is where R max is the maximum radius of the original cone search (usually two degrees) and d is the distance between the fitted centre and the centre from the original cone search (), set as the source centre on SIMBAD 2 by the automatic Gaia advanced query. The projected radius R is defined, in spherical trigonometry, as where () is the centre of the galactic object. The likelihood function is therefore written as Figure 1. Geometry of the centre estimation: The original cone search, centred in () is shown as the grey circle of radius R max , while the new fitted centre is (). The angles φ 1 and φ 2 represent the effective circular sections (of respective radii R 1 and R 2 ) where we consider circular symmetry. The distance between the two centres is labeled as d , and we consider this value to approach zero for the cone searches around the centres from the SIMBAD data base. We minimize with the differential_evolution routine from the scipy.optimize method and find the centres that best fit the data, later displaying them in Table C1 . For simplicity, since we expect the quantity d to approach zero, given the reliable previous measurements of the centres in SIMBAD, one can assume the case where , and thus derive Notably, for more general cases, the BALRoGO routine allows to use the more general representation of φ( X ), and thus to account for a more complicated expression for , presented in Appendix A . 2.2 Surface density The next step of our algorithm is to fit the surface density of the galactic object plus interlopers once again, using a maximum likelihood estimation (MLE), but this time with fixed centres from the previous step. It may seem as an unnecessary step given the previous one, but it actually allows the fitting routine to better explore the other parameters ranges like the scale radius and the interloper fraction, and thus derive more robust results. In this step, we also reduced the maximum projected radius whenever there was a parasite galactic object on the field or when the MW contamination was too intense, disturbing the fits. In this step, we not only tested Plummer profiles, but also Sérsic models (Sérsic 1963 , 1968 ) that can be useful for core-collapsed clusters such as NGC 6397, and the Kazantzidis model that is motivated from dynamical simulations of repeated tidal encounters (Kazantzidis et al. 2004 ). Equations ( 2 ), ( 6 ), and ( 7 ) remain valid for these two other models, while the normalized surface density and projected number of stars become for Sérsic, where is the lower incomplete gamma function and X = R / R e , R e being the effective projected radius. And for Kazantzidis, where K 0 and K 1 are modified Bessel functions of

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


at 200 pc. We retain the functional form of the Bovy model’s bulge, ρ( r ) = ρ s ( r / r 1 ) −α exp [−( r / r c ) 2 ], but with revised parameters α = 2.0, r c = 1.0 kpc, ρ s = 6.58 × 10 8 M ⊙ kpc −3 , and r 1 = 1 kpc. This yields a total bulge mass of 7.33 × 10 9 M ⊙ . The model roughly matches the observed circular velocity data collected in Sofue ( 2013 ), for both large and small radii. It does not match this data’s prominent peak at R ∼ 500 pc and subsequent decline out to 2.5 kpc, but Chemin, Renaud Soubiran ( 2015 ) argue that this feature is likely an artefact of perturbations from the Galactic bar. The axisymmetry of our potential is clearly an approximation, as orbits on scales of a few kpc are strongly affected by the bar. However, at smaller radii, the observed physical components are close to axisymmetric and the potential contours generated in physical models such as Bissantz, Englmaier Gerhard ( 2003 ) are more rounded. Thus, axisymmetric models continue to be used to study orbits near the Galactic centre (Molinari et al. 2011 ; Kruijssen et al. 2015 ; Perera et al. 2019 ), and we leave non-axisymmetric refinements to future work. We integrate orbits in this potential using the package galpy 3 (Bovy 2015 ). We assume Sgr A* lies fixed at the GC. We adopt a distance to Sgr A* of 8.175 kpc from Gravity Collaboration et al. ( 2019 ), and do not consider in the computation its small observed error. We first define a modified Galactic coordinate system ( l ′ , b ′ ), which uses a slight rotation around the Sun’s position to place Sgr A* exactly at l ′ = 0, b ′ = 0, then shift by the solar distance to obtain Galactocentric coordinates. We choose a solar motion in the Galactocentric frame of v X = −11.0 km s −1 , v Y = 248.5 km s −1 , v Z = 7.8 km s −1 that produces the observed PM of Sgr A*, μ α cos δ = −3.156 mas yr −1 and μ δ = −5.585 mas yr −1 (Reid Brunthaler 2020 ). We use a Galactocentric convention where X points from Sgr A* to the Sun. Fig. B1 shows orbits of the two clusters with a series of initial distances, using our best values of the PM. Orbits starting well on the near side of the GC are highly eccentric. The eccentricity first decreases with the starting distance, then increases again as the orbits become almost radial near the GC. About 20 pc further out, the orbits become retrograde. We note none of the orbits are circular. As noted in Stolte et al. ( 2008 ), circular orbits require , which implies X = ( v X / v Y ) Y , radius R = [1 + ( v X / v Y ) 2 ] 1/2 Y , and circular velocity . For Quintuplet, this implies a velocity V c = 177 ± 4 km s −1 at R = 48 ± 1 pc, where the uncertainties incorporate our estimated PM and RV errors. For Arches, it implies a velocity V c = 168 ± 7 km s −1 at R = 40 ± 2 pc. Both of these circular velocities are comfortably above those implied by our potential, which are 108 and 98 km s −1 , respectively, at these radii. They also lie well above the scatter of different observational

O O O O O O O O O O B-Model I-Model O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O B-Formula I-Formula I-Formula B-Formula I-Formula I-Formula I-Formula I-Formula B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O B-Model I-Model B-Citation I-Citation O O O B-CelestialObject I-CelestialObject O O O O B-CelestialObjectRegion O O O O O B-CelestialObject I-CelestialObject O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O B-CelestialObject O O O B-CelestialObject I-CelestialObject O O B-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O B-CelestialObject I-CelestialObject B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula B-Citation I-Citation I-Citation O O O O O O O O O O B-CelestialObject I-CelestialObject O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


by the region of the disk behind the inner rim. Detailed studies have indicated that the picture is somewhat more complicated, with intermediate-temperature components of uncertain origin (e.g., Fischer et al. 2011 ). For the purposes of this study, where we are taking a first look at time variability in the excess, we restrict ourselves to blackbody models of these three basic components, following McClure13 . Each component is defined by a characteristic blackbody temperature and solid angle. We fix the hot component temperature at 7000 K, which is characteristic of accretion shock emission (the exact value is not crucial here because we are seeing only the Rayleigh–Jeans tail). We also fix the cool component to a value of 600 K, which is roughly the equilibrium temperature for dust at the predicted location of the inner edge of the circumbinary disk around DQ Tau (∼2.5 a = 0.35 au). For the warm component, we allow the temperature to vary between 1000 and 1800 K (which spans the range of typical characteristic maximum dust temperatures in TTSs) in increments of 50 K. The solid angles (relative to the stellar value assuming R = 1.5 R ⊙ and d = 196 pc) are varied from 0 to 0.1 for the hot component, 10–50 for the warm component, and 50 to 300 in the cool component. For each set of parameters, the models for all three components are combined and then compared to the observed excess spectra, with the best fit determined via chi-squared minimization. The resulting best fits for each observed spectrum are shown in Figure 20 , with the associated parameters listed in Table 8 . Given the systematic uncertainties in the template matching, these values should be taken as indicative only; however, they provide a useful first look at the gross properties of the material in the inner regions of this system. The best-fit hot component solid angles range from zero at several epochs, where no discernible emission was detected, to 0.06, which is typical for weakly to moderately accreting TTSs. The cool component solid angles range from 90 to 260, roughly as expected for a puffed inner disk rim with a temperature of 600 K. If our assumption of a constant temperature is a reasonable approximation, the variation in solid angle may be indicative of a variable scale height of the inner edge of the putative circumbinary disk. There is a weak correlation with the warm component, but the origin of such a variation is unclear; it could simply be an artifact of our overly simplistic assumptions of the dust temperatures. However, it should be noted that this cooler dust emission is not as well-constrained as the other components because it contributes an appreciable fraction of the total emission only at the long-wavelength end of our spectra. Observations in the 5–10 μ m range are required to test the significance of any variations from this region. Figure 20. DQ Tau excess spectra shown in black, in order of observation time (left to right, top to bottom), with

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


the values. The values are taken from Dunlop et al. ( 1993 , 2003 ). 3.1. Evolution of the bolometric luminosity with time To demonstrate how luminous progenitors of UCDs could have been, we compute the bolometric luminosity, , as a function of time. The dependency is shown in Fig. 3 . The benchmark initial mass is . For the cases of the CAN, SAL, and vDC IMF, the values are proportional to . The MKDP IMF is a function of and therefore we plot also for . The main difference between different MKDP IMFs (for different ) is the slope of the luminosity as a function of time. For a more top-heavy IMF, the decrease of the luminosity with time is steeper. Fig. 4 Time evolution of for all IMFs considered (vDC, SAL, CAN, MKDP). We assume that the system is gas free and that neither stars nor remnants are leaving (the dashed lines show the change of the value if only certain fractions of remnants are kept). The upwards-pointing blue arrow demonstrates that if we would assume more massive remnants (e.g. due to implosion directly to a BH without a SN explosion), then this would lead to larger values of . The models are computed for the case of , however, results are mass independent. The only exception is the MKDP IMF, which depends on initial object mass, , and also contains a large fraction of mass in high mass stars, and is plotted for (, bottom to top) and different fractions of remnants retained (100%, 10%, 0%). Left panel : the evolution for [Fe/H] = 2. Right panel : the evolution for [Fe/H] = 0. The grey band indicates the span of the observed present-day values, approximately five to ten for the majority of UCDs ( Mieske et al. 2008 ; Dabringhausen et al. 2009 ). The scales are identical for both panels. There are several noticeable features in this figure: (i) for the MKDP IMF, UCDs with initial stellar mass are as bright as quasars ( Dunlop et al. 1993 , 2003 ; Souchay et al. 2015 ) for the first few yr. We use low-redshift quasars because for these we were able to find bolometric luminosities, but also absolute magnitudes in the and band. We note, however, that high redshift quasars show very comparable luminosities as shown for example by Mortlock et al. (2011) . This is mainly due to the presence of a large number of O and B stars () in the system. Due to stellar evolution and core-collapse supernova explosions, these UCDs will be variable on a timescale of months. As already suggested by Terlevich Boyle (1993) , such objects might be confused with quasars, especially for example in large photometric surveys. (ii) After less than a Myr, a strong degeneracy between the IMF and appears. That is, for different and different IMFs, similar luminosities comparable to those of observed UCDs occur. (iii) The metallicity is a second-order effect. Fig. 5 Values of the ratio as a function of for three different times . The case of the MKDP IMF is not constant since the MKDP IMF is a function of initial mass. The plotted curves assume all remnants are

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


found that Centaurs can produce HTCs, in particular they are trapped very often in the 1:6 MMR with Jupiter (energy x ≃ 0.058 au −1 ) which coincides with the clustering in the observed energy distribution of HTCs (Fig. 3 ). It is worth noting that our sample of observed Centaurs contains a few objects in retrograde orbits. To produce both the observed HTCs and JFCs, a flattened source is required but it should contain a small fraction of high-inclination and retrograde comets. A near-ecliptic, prograde population of Centaurs ( i ≲ 25°) will essentially lead to a near-Earth population of bodies with Tisserand parameters T J > 2, typical of JFCs (Levison Duncan 1997 ). It is not the purpose of this paper to discuss the ultimate origin of Centaurs, though we can say a few words. A flat source in the outer planetary region such as the Scattered Disk will essentially produce a population of Centaurs in prograde, low-inlination orbits (Di Sisto Brunini 2007 ), though it may be possible that some SDOs scattered outwards attain Oort cloud distances where galactic tides switch their orbits from prograde to retrograde (Levison et al. 2006 ). Other possibility is that some Centaurs come from the capture of Oort cloud comets in the outer planetary region as discussed by Emel'yanenko Bailey ( 1998 ) and Emel'yanenko, Asher Bailey ( 2005 ). In the end, some HTCs may come from the Oort cloud but through a different dynamical route that direct insertion of Oort cloud comets in the near-Earth or the Jupiter region. In order to check the results found for the simulated HTCs produced from the evolution of the Centaur sample, we also studied the dynamical evolution for 1 Myr to the past and to the future of 15 observed HTCs with q 1.3 au and energies 0.04 x 0.08 au −1 (orbital periods 44.2 P 125 yr). We confirm that HTCs do not diffuse randomly in a but tend to be captured in the 1:6 exterior resonance with Jupiter generating a concentration at x ∼ 0.058 au −1 . This peak is clearly shown in Fig. 17 which is a histogram of frequencies of the average 〈 a 〉 over periods of 500 yr. Figure 17. Frequency distribution of the time-average 〈 a 〉 (over 500 yr) for the observed sample of 15 HTCs with q 1.3 au and energies 0.04 x 0.08 au −1 (periods 44.2 P 125 yr) integrated over 10 6 yr in the past and in the future. Other remarkable feature is that even though we obtain about 4.7 per cent of LPCs that end up colliding with the Sun for a purely dynamical evolution, this percentage is practically null when we consider appropriate physical lifetimes ( N phys ( q = 1) ≲ 500 revolutions). The reason is that LPCs approach the Sun in a smooth way through a multi-step process, that takes hundreds to thousands revolutions, so it is very likely that such comets will disintegrate well before reaching sungrazing states. The inclination distribution of the old LPCs shows clear departures from randomness that can be described as a slight predominance of prograde orbits that is

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


O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O B-CelestialObjectRegion O O O B-Software O O O O O O O O O O B-Formula O B-Formula O O O O O B-CelestialObject O O O O O O O O O B-Formula O B-Formula O O O O O O O O O O O B-Wavelength O O O O O O O O O B-Telescope B-Model I-Model B-Formula I-Formula O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O B-CelestialObject O O O O O B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope B-Wavelength I-Wavelength O B-Telescope B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Tag B-Wavelength I-Wavelength O O O B-Telescope O O B-CelestialObject O B-CelestialObject O O O O B-Instrument I-Instrument I-Instrument I-Instrument B-Instrument O B-Instrument O B-Instrument I-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope B-EntityOfFutureInterest I-EntityOfFutureInterest O O B-URL O O B-Instrument O B-Instrument O O O O O O B-Software O B-Software O O O O O O O O O O O B-Instrument O O O O O B-Wavelength I-Wavelength I-Wavelength O B-Formula O O O O O O B-Wavelength O O O B-Wavelength I-Wavelength O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O B-Instrument O B-Instrument O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O


we study (i) a constant 29% contamination and (ii) the stellar mass and redshift-dependent [N ii ]/H α flux ratios predicted by our model (Equation ( 3 )). To derive the intrinsic H α LF using our model [N ii ] contamination (Φ model ), we start with the observed ([N ii ]+H α ) tot LF (Φ obs ( L )) measured by Colbert et al. ( 2013 ) at 0.9 z 1.5. We obtain this LF from their published H α LF (, , and α = −1.43) by dividing the luminosities by a factor of (1–0.29) to undo the constant total [N ii ] flux contamination fraction correction of 29%, which the authors applied. In the following, we treat Φ obs as the true observed LF. Importantly, this LF is not corrected for [N ii ] contamination and dust. Because of the evolution of the star-forming main sequence, Φ obs is redshift-dependent, but here we do not model this dependence across z = 1–2, as we are only interested in the effects of [N ii ] contamination and not the absolute number of galaxies. On the other hand, the stellar mass and redshift-dependent [N ii ] contamination correction will change the intrinsic H α LF across the redshift range studied here. To obtain Φ model , we choose an approach that only uses the measured ([N ii ]+H α ) tot luminosities as input and assumes the most likely underlying stellar mass distribution (robustly determined from other studies), from which we obtain the [N ii ] contamination from our model. This approach has the advantage that it enables an easy implementation and propagation of a variety of uncertainties into the final results. Furthermore, this method results in reliable intrinsic H α LFs even if the mass distribution is poorly measured due to the lack of sufficient multiwavelength data, as long as the selection function of the galaxy sample is known. Here we make use of the Schreiber et al. ( 2015 ) parameterization of the star-forming main sequence to derive the underlying stellar mass distribution (we comment below on possible shortcomings). We note that the choice of different parameterizations (e.g., Tomczak et al. 2016 ) should not change the following results. We start with a distribution of ([N ii ]+H α ) tot , which we sample from Φ obs . To obtain stellar masses for these galaxies, we use a “backward-engineering” technique. First, we convert the SFRs of the Schreiber et al. ( 2015 ) parameterization into H α luminosities using the Kennicutt ( 1998 ) prescription. Thereby, we include a dispersion of 0.3 dex measured on the SFR–versus–stellar mass main sequence. Second, we redden the H α luminosities according to the relation between A H α (H α extinction) and stellar mass robustly derived from the spectra of local galaxy samples in SDSS (Garn Best 2010 ). This relation holds for the WISPS sample at 0.8 z 1.5, as shown in Domínguez et al. ( 2013 ). Third, we add the contribution of [N ii ] to the H α luminosity by using our model. Finally, this translation between dust-reddened ([N ii ]+H α ) tot luminosities and stellar masses allows us

O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Formula I-Formula I-Formula O O O O O O O B-Wavelength I-Wavelength O B-TextGarbage I-TextGarbage O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O B-Wavelength I-Wavelength B-Wavelength I-Wavelength O O O O O O O O O O O O O O B-Survey B-Citation I-Citation I-Citation O O O O O O B-Dataset I-Dataset O B-Formula I-Formula I-Formula O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O


may be higher given that an unmeasurable component of light is lost during this period. No conclusion can or should be drawn from this point, which is presented only for the sake of completeness. 3.2 He <sc>i</sc> line 3.2.1 Equivalent width The equivalent widths of the He i line around the 2014 periastron are shown in Fig. 4 (b). The closed blue circles denote the equivalent width as measured by integrating from the base of the line, while the open green squares denote the measurement obtained from the Gaussian fit, relative to the continuum. Shown for comparison are the measurements around 2010 reported by Chernyakova et al. ( 2014 ) (red crosses). As with the Hα line, the He i line shows a general increase in the absolute equivalent width which peaks after periastron, though the growth is not as great. The variation in the strength of the line is consistent with the variability observed in the Hα line. 3.2.2 V/R In general, the violet component of the double peaked He i line is more dominant, as is seen in the equivalent width | W λ | of the violet component and the ratio of peaks of the violet to red (V/R) components. The V/R variation (Fig. 4 c) has been measured from the ratio of the heights of the Gaussian fits to the Violet and Red component of the He i line. The height is measured relative to the continuum and the error is given by the statistical error of the fit. Around the first disc plane crossing, there is a marked increase in the asymmetry of the line, while there is a decrease in V/R around periastron and a small increase in the red component around the second disc plane crossing. This clearly illustrates the asymmetry of the He i line and its variation around periastron. The V/R variation lies between 0.93 V/R 1.65 during the observed period. 4 DISCUSSION Around periastron the equivalent width of the Hα line smoothly increased to a maximum of −72.7 ± 0.7 around ∼τ + 13 d, after which it decreased to values consistent with the pre-periastron levels. The equivalent widths after ∼τ + 13 d are consistent with the previous periastron passage (Chernyakova et al. 2014 ) but appear to be consistently lower before this. This is clearly seen before periastron where the average equivalent width (and error) of the Hα line was −62.9 ± 3.1 Å in 2010, but −56.7 ± 0.6 Å in 2014. We interpret this as being due to variability in the Be star circumstellar disc which could well change from periastron to periastron. This may imply that the mass of the circumstellar disc was lower before the 2014 periastron passage (as compared to the 2010 periastron passage). Since the circumstellar disc influences the shock front around the pulsar, the differences in the circumstellar disc properties will be an important contributing factor to the variations in the multiwavelength emission observed around different periastra. There is also a marked change in the disc around the time of the first disc plane crossing (τ − 17.5 d), as is noted by the increase in the

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


not been identified due to the lack of counterparts in the radio/X-ray or GeV γ -ray bands (Aharonian et al. 2005 , 2008a ). Therefore, searching for the counterparts of these unidentified VHE sources in longer-wavelength bands is very helpful to identify and classify them. In the GeV band, more than 7 years of survey data from the Fermi Large Area Telescope ( Fermi -LAT) provides a good opportunity to hunt for the unidentified VHE sources. Indeed, several unidentified VHE sources have been detected with the Fermi -LAT data (Hui et al. 2016 ). HESS J1427−608 is one of the unidentified VHE sources discovered by the HESS Galactic Plane Survey (Aharonian et al. 2008a ). The TeV image shows that it is only slightly extended with a symmetric Gaussian function with a width of σ = 3′. This source is detected with an integral flux above 1 TeV of F γ (>1 TeV) = 4.0 × 10 −12 erg cm −2 s −1 and a power-law spectrum with an index of Γ = 2.16. No nearby SNR or pulsar was detected in the vicinity of HESS J1427−608 (Green 2014 ). The X-ray counterpart of it, Suzaku J1427−6051, was reported by Fujinaga et al. ( 2013 ). The X-ray spatial morphology is clearly extended with a Gaussian width of σ = 09 ± 01, and the spectrum is well fitted by a power law with an index of Γ = , implying nonthermal X-ray continuum emission. The unabsorbed flux in the 2–10 keV band is . Fujinaga et al. ( 2013 ) have discussed the possible nature of HESS J1427−608 as a PWN or nonthermal SNR. Each one can explain some of the observational facts but face difficulties. No radio counterpart was detected in the direction of HESS J1427−608. In the second Fermi -LAT catalog (2FGL; Nolan et al. 2012 ), a GeV source, 2FGL J1427.6−6048c, which is located in the vicinity of HESS J1427−608, was reported. However, their central positions differ moderately from each other. Furthermore, the power-law spectrum index of 2FGL J1427.6−6048c is Γ = 2.7 (Nolan et al. 2012 ), which cannot connect with the TeV spectrum of HESS J1427−608 well. It is very likely that 2FGL J1427.6−6048c is not associated with HESS J1427−608. Meanwhile, it should be noted that no source in the third Fermi -LAT source catalog (3FGL; Acero et al. 2015 ) is associated with 2FGL J1427.6−6048c. In this paper, we carry out a complete analysis of this region using more than 7 years of Fermi -LAT Pass 8 data to investigate the γ -ray emission of HESS J1427−608. In Section 2 , we describe the data analysis and results, including the spatial, spectral, and timing analyses. The possible nature of HESS J1427−608 based on the multiwavelength spectral energy distribution (SED) fitting is discussed in Section 3 , and the conclusion of this work is presented in Section 4 . 2. DATA ANALYSIS 2.1. Data Reduction The following analysis is performed using the latest Fermi -LAT Pass 8 data with the Source event class from 2008 August 4 (Mission Elapsed Time 239557418) to 2015 November 4 (Mission Elapsed Time 468288004). Considering the impact of

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


the dynamo action in astronomical bodies. We choose to work with periodic cuboid domains, because it allows us to study the dynamo properties of spatially periodic cellular flows. We vary the scale separation in the system through the reconstruction of the computational domain and the characteristic length-scale of the imposed velocity field. The first flow under consideration is the well-known ABC flow (named after Arnold, Beltrami Childress), recently reviewed by Galloway ( 2012 ). The second is a modulated version of the first, with imposed long-wavelength perturbation on the scale of the system. Such periodic flows are guaranteed to produce dynamo action for a wide range of finite values of R m (Roberts 1970 ). We study the kinematic dynamo action in domains of various aspect ratios, to examine the effect of changing the scale separation of the system as well as the effects of imposing a two-scale perturbed flow on the system in the kinematic regime. The first part (ABC flow) of the problem considered here has recently been investigated in a different way by Cameron Alexakis ( 2016 ), who carried out a theoretical study of kinematic dynamo using the Floquet formulation that was originally devised for the Mathieu equation (Whittaker Watson 1902 ). The authors adopted the concepts in Roberts ( 1970 ) to solve the induction equation in the presence of the ABC flow for arbitrary large-scale separations, showing a transition from a large- to small-scale dynamo through a change in the growth rate. The results from this analysis are in general agreement with the findings presented below as the scale separation becomes arbitrarily large. However, their paper does not include the results for Floquet waves with length-scales comparable to the size of the imposed flow, although Galanti, Sulem Pouquet ( 1992 ) noted that such eigenmodes play a crucial role in maintaining the dynamo for large R m . In this paper, we utilize a discrete wavenumber decomposition that is determined by the aspect ratio of the computational domain. This allows us to investigate the transition from a large- to small-scale dynamo with a special emphasis on the length-scale selection of the fastest growing eigenmode of magnetic field and focus on the comparison of the results from the classic ABC and the modulated perturbed flow cases. Our study is based on the results of numerical simulations using a pseudo-spectral method in a triply periodic domain and analytic estimates based on the scale-separation arguments. The choice of the imposed flows allows for the scenario wherein a large-scale dynamo would be obtained at the onset. We then vary magnetic diffusivity in order to study how the dynamo mechanism changes as we increase R m . There are two possibilities: (i) the large-scale structure is preserved due to either the large aspect ratio of the system or the imposed long-wavelength modulation; or (ii) the energy is passed from the large scales to the small scales as

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