O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Mission O O O O O O O O O O O O O O O O O O O B-Instrument O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation 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 B-Instrument O O O O O O O O O O O O O O B-Mission B-Instrument B-Telescope O B-Wavelength I-Wavelength O O B-Wavelength I-Wavelength O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-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 B-Mission O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation 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 O O B-Model I-Model B-Citation I-Citation O B-Citation I-Citation O O O O B-Software O B-Software I-Software O O B-Software O B-Citation I-Citation I-Citation 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 B-Citation I-Citation I-Citation I-Citation O O B-Instrument O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O B-Mission O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O B-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

Whilst a reasonable harmonic fit to the ESPaDOnS data can be achieved using this period, it does not produce an acceptable phasing of all available 〈 B z 〉 measurements. Figure 1. Photometric ( top ) and magnetic 〈 B z 〉 ( bottom ) measurements, phased with periods determined from (left to right) K2 photometry, all 〈 B z 〉 measurements, and all photometric measurements. 〈 B z 〉 measurements were obtained from ESPaDOnS by Shultz et al. ( 2018 ) and photopolarimetric data by Borra et al. ( 1983 , BLT83) and Bohlender et al. ( 1993 , BLT93). The solid and dashed curves show, respectively, the best second-order harmonic fit to the ESPaDOnS 〈 B z 〉 data and the 1σ fit uncertainty. Photometric data are from K2, SMEI, Hipparcos ( H p ), and Strömgren y photometry published by Sterken et al. ( 1995 , S95), Manfroid et al. ( 1995 , M95), and Pedersen Thomsen ( 1977 , P77). For clarity the K2 and SMEI data have been binned by phase, using bin sizes of 0.01 cycles. The mean magnitude of each data set was subtracted for display purposes. All of the periods obtained since the year 2000 are approximately consistent with one another; the two periods determined using photometric data obtained prior to the year 2000 are also consistent with one another. At the same time, the difference between the Bowman et al. ( 2018 ) and Catalano Leone ( 1996 ) periods, 0.00015 d, is almost eight times larger than the formal uncertainty in the Bowman et al. period (the less precise of the two). This suggests that the period may have changed. 3.2 Period analysis We now turn to a re-examination of the period analysis of the individual data sets; the results are summarized in Table 2 . Period analysis was performed using standard Lomb–Scargle statistics (Lomb 1976 ; Scargle 1982 ), utilizing both the idl program periodogram 4 and the period04 package (Lenz Breger 2005 ). The uncertainties were determined in the same manner as by Shultz et al. ( 2018 ), i.e. according to the analytic method described by Bloomfield ( 1976 ). Examining the ESPaDOnS data in isolation yields P rot = 0.97887(6) d, consistent within uncertainty with the K2 period (Bowman et al. 2018 ). The period determined from all available magnetic data (i.e. including the previously overlooked 〈 B z 〉 measurements of Borra et al. 1983 ) is 0.979855(5) d. The photometric and magnetic data are shown phased with this period in the middle panel of Fig. 1 . Phasing 〈 B z 〉 with this period and fitting the ESPaDOnS data with a second-order sinusoid yields a reduced χ 2 = 5, i.e. a poor fit. This period also does not provide a coherent phasing of the majority of the photometric data set. Notably, the variation in the phase-binned SMEI data almost completely disappears, likely because observations are being binned as though they were at the same phase when, in fact, they are not. We can also combine all available photometric data (shifted to the mean magnitude of each data set, as in Fig. 1 ), which yields P rot =


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ACKNOWLEDGEMENTS The authors thank an anonymous reviewer for comments and suggestions that strengthened our manuscript. NWCL gratefully acknowledges support from the American Museum of Natural History and the Richard Guilder Graduate School, specifically the Kalbfleisch Fellowship Program, as well as support from a National Science Foundation Award No. AST 11-09395.


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Lasota (2007) have updated this work, for a sample of ten CVs. The importance of this test was revived by Schreiber Gänsicke (2002) , who pointed out that the HST FGS parallax distance of SS Cyg, the archetypal dwarf nova, led to a revised mass transfer rate that placed this outbursting system in the stable region of the ( R out , Ṁ ) plane. This led to much hand-wringing ( Schreiber Lasota 2007 ; Smak 2010 ) until a radio VLBI parallax distance ( Miller-Jones et al. 2013 ), confirmed with Gaia ( Ramsay et al. 2017 ), firmly placed the system in the unstable region (as anticipated by Lasota 2008 ). Although there are dozens of CVs with relatively well-known binary parameters, a thorough investigation of this test has yet to be performed. Ramsay et al. (2017) proposed to test the DIM by taking the absolute magnitude at a specific stage of a dwarf nova outbursts (at the end of long outbursts or in stand-stills) to compare the derived mass accretion rate to the critical rate for the system, under the assumption that both should be nearly equal. Good agreement was found for the sample of a dozen CVs with distances in the Gaia first data release. Its main advantage is that the required optical magnitude is straightforward to extract from the light curves. However, a major drawback of this approach is that it relies on assumptions on how matter is transported in the disk because one needs to predict when the mass accretion rate happens to be equal to the critical rate during the outburst cycle. Hence, it is a much less fundamental and robust test of the basic premises of the DIM. Indeed, an important difficulty in using the fundamental test is that it requires extracting the average mass transfer rate from CV optical light curves, which in many cases are unevenly, inhomogeneously, and incompletely sampled. The situation is somewhat easier for X-ray binaries, for which the DIM also applies because X-ray monitors provide continuous coverage and X-rays provide a closer measure of the bolometric luminosity in those systems than optical magnitudes do for CVs, which in outburst emit primarily UV radiation. Coriat et al. (2012) were able to derive average mass accretion rates for ~50 X-ray binaries and showed that the DIM, modified to include X-ray irradiation ( van Paradijs 1996 ), separates consistently transients from steady systems. We carry out, for the first time on CVs, a similar analysis to that performed on X-ray binaries by Coriat et al. (2012) to test the fundamental prediction of the DIM: the separation of CVs into stable and unstable systems is determined by the orbital period (a proxy for disk size) of the binary and mass transfer rate from the companion. We use a subsample of the CV light curves gathered by Otulakowska-Hypka et al. (2016) . We consider all types of dwarf nova outbursts, including so-called super-outbursts that are not supposed to be described by the standard version of the DIM (see, e.g., Lasota 2001 , and references


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an antenna with cos 2 beam would have a maximum temperature at the LST when the Galactic center is at zenith. This also corresponds to the spectrum having the largest rms residual among the various mock spectra considered here. For various large-area samplings of the sky, we have thus demonstrated that the foreground component in a beam-averaged spectrum is adequately describable by an MS function. Thus for observations with a frequency-independent beam, MS functions can be used to separate foregrounds from the global EoR signal. We next discuss mathematical statistical detection based on MS-form modeling of foregrounds. 5. On the Detection of the Global Reionization Signal A mock observation of the radio sky as observed by a cos 2 beam is shown in Figures 14 . A GMOSS model for the sky has been adopted and CMB with a spectral distortion corresponding to generic global EoR has been added. We fit this mock observation of the sky spectrum with a function given by the sum of an MS function to model the foreground and a Planck spectrum to account for the undistorted CMB, as described by Equation ( 9 ). We use the downhill simplex (Nelder Mead 1965 ) optimization algorithm to iteratively fit this model to the synthetic spectrum, adopting a successive approximation strategy. The MS polynomial is expressed as a polynomial expansion about a frequency given by the parameter . The first iteration fits a function that has four parameters: the CMB temperature , the pivot frequency , and two coefficients that describe a single power law for the foreground. We successively include more terms using the optimized parameters from the previous iteration as initial guess and zero for the new coefficient introduced. The residuals on subtracting a model with a Planckian function and MS functions of degree 2, 5, 7, 8, 10, and 15 are also shown in Figure 14 . This may be compared to the residuals obtained above on fitting unconstrained polynomials to the same mock observation containing the EoR signal, which was shown in Figure 6 . As noted earlier, for the case where the foregrounds were modeled as unconstrained polynomials, the residual amplitude gets progressively lower with increasing polynomial order and there are additional turning points introduced. On the other hand, while using MS functions, the residual remains unchanged once the MS function encounters a shape that cannot be described as smooth and thenceforth increasing the order of the MS function no longer changes the residual. This would continue to be the case on fitting the spectrum with MS functions of arbitrarily higher order. The residual recovered on fitting the mock spectrum with such components that may accurately model the undistorted CMB and foreground appears qualitatively similar to the adopted global EoR signal, which was included in the simulation. We now proceed to quantify the confidence in signal detection and the likelihood of false positives. Figure 14. (a) Mock spectrum generated


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

of the CSM density profile and the forward shock evolution together determine the temporal behavior of the optically thin radio flux density. For s = 0 and , the flux density rises with time as once , the flux density evolution steepens to (visible as a kink in the model light curve of Figure 1 with cm −3 around 100 days after explosion; such a kink was also noted by Pérez-Torres et al. 2014 ). Meanwhile for s = 2, the optically thin scaling is when later, when bottoms out at unity, then . Therefore, the temporal evolution of the optically thin flux density can be used to estimate the density profile of the CSM. 4.5. Caveats and Complexities As discussed by Horesh et al. ( 2012 , 2013 ), the most significant uncertainty in converting radio luminosity to a density of the CSM is the efficiency of magnetic field acceleration, . In the case of uniform density CSM and optically thin synchrotron emission, the density derived from a given flux density will depend on as when , and when . For s = 2 and , we find , and when converges to unity then . In addition, as seen by comparing Figures 3 with 4 , and Figures 5 with 6 , the synchrotron emission becomes optically thin faster for lower values of . Figure 3. Each panel shows a set of radio light curve models at a distinct frequency (marked top left), assuming , , , , and s = 2. The model grids span a range of values () with spacing of 1 dex, with purple-blue models corresponding to low values and red models to high . Observed 3 σ upper limits at each frequency are overplotted as black triangles. Figure 4. Each panel shows a set of radio light curve models at a distinct frequency (marked top left), assuming a more conservative (compared to in Figure 3 ) and retaining , , , and s = 2. The model grid and color scheme represent the same range of values as in Figure 3 . Observed 3 σ upper limits at each frequency are overplotted as black triangles. Figure 5. Each panel shows a set of radio light curve models at a distinct frequency (marked top left), assuming , , , , and s = 0. The model grids span a range of n 0 values ( cm −3 ) with resolution of 1 dex, with purple-blue models corresponding to low n 0 values and red models to high n 0 . Observed 3 σ upper limits at each frequency are overplotted as black triangles. Figure 6. Each panel shows a set of radio light curve models at a distinct frequency (marked top left), assuming a more conservative (compared to in Figure 5 ) and retaining , , , and s = 0. The model grid and color scheme represent the same range of n 0 values as in Figure 5 . Observed 3 σ upper limits at each frequency are overplotted as black triangles. Radio light curve models are also affected by the assumed values of SN ejecta mass and explosion energy. If we take conservatively low values of and , we find forward shock velocities of and at t = 10 days since explosion for and , respectively. These blast wave velocities are high enough that synchrotron self absorption still dominates over


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version of the full table is available. Table 3 The Spectral Parameters Associated with the H β Emission Line Note. Column information is as follows: Column [1]: 4FGL name; Column [2]: redshift; Column [3]: log-scale continuum luminosity at 5100 Å; Column [4]: FWHM of H β line, in km s −1 ; and Column [5]: log-scale H β line luminosity, in erg s −1 . (This table is available in its entirety in machine-readable form.) Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available. Table 4 The Spectral Parameters Associated with the Mg ii Emission Line Note. Column information is as follows: Column [1]: 4FGL name; Column [2]: redshift; Column [3]: log-scale continuum luminosity at 3000 Å; Column [4]: FWHM of Mg ii line, in km s −1 ; and Column [5]: log-scale Mg ii line luminosity, in erg s −1 . (This table is available in its entirety in machine-readable form.) Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available. Table 5 The Spectral Parameters Associated with the C iv Emission Line Note. Column information is as follows: Column [1]: 4FGL name; Column [2]: redshift; Column [3]: log-scale continuum luminosity at 1350 Å; Column [4]: FWHM of C iv line, in km s −1 ; and Column [5]: log-scale C iv line luminosity, in erg s −1 . (This table is available in its entirety in machine-readable form.) Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available. 3.2. Absorption-line Spectrum The optical spectra of 346 γ -ray blazars show prominent absorption lines, e.g., the Ca HK doublet, primarily originating from the stellar population in the host galaxy. It has been shown in various works that the mass of the central black hole significantly correlates with the stellar velocity dispersion ( σ * , see Ferrarese Merritt 2000 ; Gültekin et al. 2009 ; Kormendy Ho 2013 ). Therefore, we have used the penalized PiXel Fitting tool ( pPXF ; Cappellari Emsellem 2004 ) to derive σ * for blazars present in the sample. This software works in pixel space and uses a maximum penalized likelihood approach to calculate the line-of-sight velocity distribution (LOSVD) from kinematic data (Merritt 1997 ). A large set of stellar population synthesis models (adopted from Vazdekis et al. 2010 ) with a spectral resolution of FWHM = 2.5 Å and the wavelength coverage of [3525, 7500] Å (Sánchez-Blázquez et al. 2006 ) was used in this work. The pPXF code first creates a template galaxy spectrum by convolving the stellar population models with the parameterized LOSVD. To mimic the nonthermal power-law contribution from the central nucleus, we further added a fourth-order Legendre polynomial to the model. The regions of bright emission lines were masked prior to the fitting. The model was then fitted on the rest-frame galaxy spectrum, and σ * and the


O O O O O O O B-Person I-Person O O O B-Person O B-Person O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Location B-Organization O O O B-Grant O O O B-Location B-Grant I-Grant I-Grant B-Grant B-Person O O O O O O B-Fellowship I-Fellowship I-Fellowship I-Fellowship O O O O O O B-Organization I-Organization O O O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility O O O O O O O B-Survey I-Survey I-Survey I-Survey I-Survey O O O O O B-Organization I-Organization I-Organization I-Organization O B-Location B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O O B-Survey O O O O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility O O B-Organization I-Organization I-Organization O B-Survey O O O B-URL O O O O O O O O O O B-Organization I-Organization I-Organization B-Organization O B-Telescope O B-URL O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-URL O O O O B-Organization O O O O O O O O O O O O O B-Collaboration I-Collaboration I-Collaboration


O O O O O O O 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 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 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 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 B-Telescope I-Telescope I-Telescope O B-Telescope I-Telescope I-Telescope B-Telescope O O O B-CelestialObject I-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject I-CelestialObject O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Observatory O O O O O O B-CelestialObject I-CelestialObject B-Citation I-Citation I-Citation I-Citation O B-Telescope I-Telescope I-Telescope I-Telescope O O O O O B-CelestialObject B-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Survey I-Survey I-Survey I-Survey I-Survey B-Citation I-Citation I-Citation I-Citation O O O O O O B-CelestialObject I-CelestialObject B-Citation I-Citation I-Citation I-Citation O B-Citation O B-Citation I-Citation I-Citation I-Citation O B-Telescope O B-Telescope I-Telescope I-Telescope O O O O B-CelestialRegion I-CelestialRegion O B-CelestialObject I-CelestialObject B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Observatory O O O B-CelestialObject I-CelestialObject I-CelestialObject B-Citation I-Citation I-Citation I-Citation O O O O B-CelestialObject I-CelestialObject B-Citation I-Citation I-Citation I-Citation O O O B-CelestialObject I-CelestialObject 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Mission O O O B-CelestialObject O O O O O O B-CelestialObject I-CelestialObject O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O

identified toward these positions. Column densities of this species are presented in Table 3 . Figure 5. Detected transitions of CH 3 NHCHO in the spectrum toward position MM1-nmf. The observed spectrum is plotted in black, with the synthetic spectrum overplotted in blue and the rest-frequency center of the transition is indicated by the red dotted line. The upper state energy of each transition is given in the top-left corner. At a number of positions a handful of spectral features are identified that can be assigned to NH 2 C(O)NH 2 . The most and clearest lines are identified toward position MM1-v, see Figure 6 , with at least three unblended lines. While these lines are not enough for a secure detection, a tentative identification can be claimed. The tentative and upper-limit column densities of NH 2 C(O)NH 2 are presented in Table 3 . Figure 6. Overview of NH 2 C(O)NH 2 spectral features toward position MM1-v. The observed spectrum is plotted in black, with the synthetic spectrum overplotted in blue and the rest-frequency center of the transition is indicated by the red dotted line. The upper state energy of each transition is given in the top-left corner. 4. Discussion 4.1. Chemical Comparisons To get a better understanding of the chemical processes leading to amides, it is useful to compare molecular ratios of the positions within NGC 6334I, but also with other inter- and circumstellar sources. In the following subsections molecular ratios with respect to NH 2 CHO are discussed. Comparisons are made with the following works: IRAM 30 m and Green Bank Telescope (GBT) single-dish observations of G + 0.693-0.027 (hereafter G + 0.693), a quiescent giant molecular cloud (Zeng et al. 2018 ; Jiménez-Serra et al. 2020 ); ALMA observations of the incipient hot corino Barnard B1b-S (Marcelino et al. 2018 ); Northern Extended Millimeter Array observations of the low-mass protostars SVS13A, NGC 1333-IRAS4A2, NGC 1333-IRAS2A(1) (Coutens et al. 2018 ; Belloche et al. 2020 ); ALMA Protostellar Interferometric Line Survey (Jørgensen et al. 2016 ) observations of the low-mass protostar IRAS 16293B (Coutens et al. 2016 , 2018 ; Ligterink et al. 2018a ); GBT and IRAM 30 m single-dish observations of the Galactic center source Sgr B2 (Hollis et al. 2006 ; Belloche et al. 2013 ); ALMA observations of the HMSFR Orion KL (Cernicharo et al. 2016 ); the high-mass star AFGL 4176 (Bøgelund et al. 2019a ); and of Sgr B2 (Belloche et al. 2017 , 2019 ). One has to be aware that precise knowledge of the source size or emitting area of a certain molecule is essential for ratio comparisons. In particular, single-dish telescopes do not have the spatial resolution to determine the source size and these are often assumed or estimated, potentially resulting in large column density errors. Finally, mass spectrometric measurements of the Rosetta mission to comet 67P/C-G are used to compare with a solar system object (Goesmann et al. 2015 ; Altwegg et al. 2017 ). 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Archive I-Archive I-Archive O O O O B-CelestialObject O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O

core. Figure 12 shows that such a quiescent gas environment barely affects the line ratios, as the difference in the line ratios calculated at the turbulence 0 and 150 km s −1 is very small. Figure 12. Line intensity ratio relative to w vs. log of hydrogen column density. Solid: no turbulence. Dashed: turbulence 150 km s −1 . Dotted: turbulence 500 km s −1 . We also plot the line ratios at the turbulence of 500 km s −1 . Such a high value of the turbulence is not applicable in our region of interest, but may apply for gas in other environments such as merging galaxy clusters (Cassano Brunetti 2005 ). Optical depth can be expressed as a product of column density ( N ), and absorption cross section ( α ν ):where α ν is inversely proportional to the total Doppler velocity.where is the downward transition probability, is the oscillator strength and other symbols have their usual meaning (Mihalas 1970 ). If the temperature is held constant, an increase in the turbulent velocity decreases α ν , which decreases the overall optical depth. Ideally, to achieve the same optical depth at zero and higher turbulent velocity, a higher column density should be required for the latter case. However, this outcome gets reversed due to line interlocking of x, y, and z with other ions (e.g., Fe 23+ , Cr 22+ , and Fe 22+ ; see Paper I ). The higher the turbulent velocity is, the higher the Doppler width of a line and the more pronounced the line interlocking effects will be. Total line-center optical depth will therefore increase with turbulent velocity rather than decrease, as Equation ( 3 ) suggests. 6.4. Interplay between Column Density and Metallicity Figure 13 shows the line ratios relative to w as contour plots by varying the hydrogen column density and metallicity. In the low-column-density limit, the line ratios are minimally affected by the change in metallicity. Figure 6 shows the effects of metallicity on the line ratios at the reported value of hydrogen column density by Hitomi Collaboration et al. ( 2018b ) (). The uncertainties in temperature and collision strengths from the sources mentioned previously contribute to the uncertainties in the line ratios (shown with the solid enclosed lines in Figure 6 ). At the reported hydrogen column density, x, y, and z are optically thin (Paper I ). Therefore, the line ratios are minimally affected with change in metallicity as these lines are still optically thin for the metallicity range (0 ≤ Z (solar) ≤ 5) shown in the figure. Figure 13. Left, middle, and right panels show x/w, y/w, and z/w as a function of hydrogen column density and metallicity, respectively. Hitomi Collaboration et al. ( 2018a ) use deprojected heavy element abundances relative to solar in the inner 150 kpc region from Chandra data archive for a spherically symmetric Perseus model. At a distance of 30–60 kpc from the central AGN of the Perseus core, the reported range in metallicity is ∼0.5–0.75 of solar (see Figure 7 in their paper). We


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This work is based on observations made with the NASA/ESA Hubble Space Telescope , obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 526555. These observations are associated with program #13364. R.C. acknowledges support from NSF grant 1517819. M.C. and M.T. acknowledge support from the INAF PRIN-SKA 2017 program 1.05.01.88.04. We thank Francesca Annibali for useful discussions. We also thank the referee for many useful comments that improved the paper. Facility: HST .


O O O O B-Person I-Person B-Person I-Person B-Person I-Person O B-Person I-Person O O O O O B-Person I-Person O B-Person I-Person O O O O O O O O O O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant B-Grant I-Grant B-Organization B-Location O O O O O O O B-ComputingFacility I-ComputingFacility O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility B-Observatory I-Observatory I-Observatory I-Observatory I-Observatory B-Person O O O O B-Grant I-Grant I-Grant I-Grant B-Grant O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-Grant I-Grant O B-Database I-Database O O O O O O O O O O O O O O O O O O O O O O B-Observatory I-Observatory I-Observatory I-Observatory O O O O O O O B-Organization I-Organization I-Organization I-Organization B-Organization O O B-Grant I-Grant I-Grant I-Grant I-Grant O B-Model O B-Model O O O O O B-Organization B-ComputingFacility I-ComputingFacility O O B-Organization I-Organization I-Organization I-Organization O B-Model B-Model O O B-Model O O O O O O O B-ComputingFacility I-ComputingFacility O B-ComputingFacility O O O O B-Organization O O B-Survey O O O O O B-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Survey O O O B-URL O B-Survey O O O O B-Collaboration I-Collaboration I-Collaboration O O O O O O B-Collaboration I-Collaboration O O B-Organization I-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration O B-Collaboration I-Collaboration I-Collaboration B-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration I-Collaboration I-Collaboration B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O B-Organization I-Organization

We are grateful to Francisco Prada, Risa Wechsler, Chiaki Hikage, and Surhud More for useful discussions. We acknowledge Yu Lu and Andrew Benson for useful discussions related to SAMs. This work was supported by World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan. Numerical computations were partly carried out on Cray XC30 at Center for Computational Astrophysics, National Astronomical Observatory of Japan. SS is supported by a Grant-in-Aid for Young Scientists (Start-up) from the Japan Society for the Promotion of Science (JSPS) (No. 25887012). The MultiDark Database used in this paper and the web application providing online access to it were constructed as part of the activities of the German Astrophysical Virtual Observatory as result of a collaboration between the Leibniz-Institute for Astrophysics Potsdam (AIP) and the Spanish MultiDark Consolider Project CSD2009-00064. The Bolshoi and MultiDark simulations were run on the NASA's Pleiades supercomputer at the NASA Ames Research Center. The MultiDark-Planck (MDPL) and the BigMD simulation suite have been performed in the Supermuc supercomputer at LRZ using time granted by PRACE. Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the U.S. Department of Energy Office of Science. The SDSS-III web site is http://www.sdss3.org/ . SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University.


O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O B-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 B-Wavelength B-Tag O O O O O O O O O O O B-Wavelength 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-CelestialObject O B-Citation I-Citation I-Citation I-Citation O O O O B-Wavelength O O O O O O O O O O O O O B-Wavelength 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 B-Wavelength O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O B-CelestialObject I-CelestialObject O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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-Identifier I-Identifier I-Identifier O O O O O O O O O O B-Software 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 B-Observatory O B-Telescope 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 B-Telescope O O B-CelestialObject I-CelestialObject O O O B-Wavelength O O O O O B-Wavelength O B-Wavelength I-Wavelength O O O O B-Telescope I-Telescope I-Telescope I-Telescope O O O O O O O O B-Wavelength O O O B-Wavelength O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O B-Wavelength O O O B-Survey 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-Survey B-Dataset I-Dataset I-Dataset I-Dataset O O B-Wavelength O O O O B-Wavelength O O O O O B-Wavelength O O O O O O O O O B-Wavelength O O B-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 B-Wavelength O O O B-Survey B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O B-Wavelength O B-Wavelength O O O B-Wavelength O B-Wavelength O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O B-Wavelength O O O O O O B-Wavelength O O O B-Wavelength O O O O O O O O O B-Wavelength O O O B-Wavelength O B-Wavelength O O O B-Wavelength O B-Wavelength O O O O O O B-Formula I-Formula I-Formula I-Formula O O B-Wavelength O O O O O O O O O O B-Wavelength O O O B-Wavelength O B-Wavelength O O O B-Wavelength O B-Wavelength O O 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 B-Citation I-Citation O O O O O B-Telescope B-Instrument 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 O O O O O O O O B-Instrument 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 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-Observatory B-Telescope O O B-Wavelength I-Wavelength O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O

all but one observation the exposure time was particularly low (i.e. 0.5–1 ks). We estimated the Bayesian 95 per cent upper limit (Kraft et al. ( 1991 ) to the source count rate from the observation with the longer exposure (4.2 ks, n. 4, obs ID 00087498001). It was equal to 0.0025 count s −1 . Using WebPIMMS, it converts into an observed (unabsorbed) 0.3–10 keV flux of ∼4 × 10 −13 erg cm −2 s −1 (∼7.6 × 10 −13 erg cm −2 s −1 ). We assumed the same spectral model as from the Swift / XRT observation n. 3. 3.4.3 Investigation at lower frequencies with archival data Halpern et al. ( 2007 ), using the precise Chandra localization of XTE J1829–098, individuated its probable infrared counterpart through images in the K and H bands as obtained with the MDM 2.4 m telescope on 2005 June 17. The measured magnitudes were H ∼ 13.9 and K ∼ 12.7, no measurement was obtained in the J band. Back in 2005, no additional infrared measurements were available from other infrared surveys, e.g. the UKIDSS survey started on 2005. Currently, we note that the infrared counterpart proposed by Halpern et al. ( 2007 ) has been also detected during the UKIDSS GPS data release 6 with magnitudes J = 16.147 ± 0.009, H = 14.064 ± 0.003, and K = 12.591 ± 0.002. If we use the reddening-free NIR diagnostic Q (Negueruela Schurch 2007 ) with the extinction law of Fitzpatrick ( 1999 ), we note that it has a Q value of –0.7 which is very typical of early-type OB stars. In particular, the negative value strongly indicates an infrared excess. Adopting the UKIDSS infrared magnitudes of such proposed counterpart, we can obtain a rough idea about its distance: if we assume a supergiant B0.5Ib star (with M V = −6.8 mag, V − K = −0.7 and V − J = −0.54), the source should be located at a distance d ∼ 18 kpc (with A V ∼ 21 mag). This implies a V magnitude fainter than V ∼ 30–31 mag. A main-sequence B0 star (assuming M V = −4 mag, V − K = −0.9 and V − J = −0.7), would imply a distance d ∼ 4.5 kpc (with A V ∼ 22 mag), while a giant B0 star (assuming M V = −5 mag, V − K = −0.8 and V − J = −0.7), would be located at about 8 kpc. 3.5 Search for periodicities We performed a timing analysis using the Lomb–Scargle method (Lomb 1976 ; Scargle 1982 ) of the long term INTEGRAL -IBIS and Swift -BAT light curves of the sources under study, in order to search for periodicities which could eventually be ascribed to their orbital periods. For all four sources, the long term IBIS/ISGRI ScW light curves (18–60 keV) cover the observational period from 2003 March to 2015 January. We applied standard optimum filtering in order to exclude poor quality data points which could eventually disrupt the periodic signal (see Goossens et al. 2013 and Sguera et al. 2007 for details). Periodicities were searched for in the range 1–100 d, but none were found. The public access Swift /BAT light curves (15–50 keV) on daily time-scale of all sources but IGR J12341–6143 were also searched for periodic signals in the range 2–250


O O O O O O O O O B-Organization I-Organization I-Organization B-Organization B-Mission I-Mission O B-URL O O O O B-Telescope B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-URL O O O O B-Survey I-Survey I-Survey I-Survey I-Survey O O O O O O O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization O O B-Database O B-Database I-Database O O O B-Organization B-Location I-Location O O O O O O O O O O O B-Person O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant B-Person O O O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization O O O O O O B-Grant I-Grant I-Grant I-Grant I-Grant O O B-Location B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Grant


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

Acknowledgements The authors would like to thank the referee Francisco-Shu Kitaura and Stefan Gottlöber for providing comments that helped clarified the paper as well as Sergey Pilipenko for very useful discussions. JS acknowledges support from the Astronomy ESFRI and Research Infrastructure Cluster ASTERICS project, funded by the European Commission under the Horizon 2020 Programme (GA 653477) as well as from the ‘l’Oréal-UNESCO Pour les femmes et la Science’ and the ‘Centre National d’études spatiales (CNES)’ postdoctoral fellowship programmes. ET was supported by ETAg grants IUT40-2, IUT26-2 and by EU through the ERDF CoE grant TK133. The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. ( http://www. gauss-centre.eu ) for providing computing time on the GCS Supercomputers SuperMUC at LRZ Munich and Jureca at JSC Juelich.


O O O O 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-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 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 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 B-Tag I-Tag B-Tag 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 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 B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


B-Instrument O O O O O B-Instrument O O B-CelestialObject I-CelestialObject O O B-Citation I-Citation I-Citation I-Citation B-Proposal I-Proposal O B-Person O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O B-Wavelength O O O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength I-Wavelength O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength I-Wavelength O O B-Instrument O O O O O O O B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O B-Instrument O O O O O O B-CelestialObject I-CelestialObject O O O O O O O B-Instrument B-Wavelength O B-Instrument B-ObservationalTechniques O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O B-Instrument 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 B-Wavelength O O O O O O O O B-CelestialObject I-CelestialObject O O B-Instrument O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O B-ObservationalTechniques O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument 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 B-ObservationalTechniques 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 B-Model I-Model I-Model O B-Citation I-Citation I-Citation I-Citation O O B-Formula I-Formula I-Formula I-Formula I-Formula B-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O B-Instrument O B-ObservationalTechniques I-ObservationalTechniques 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 O O O O O O O O O O O O O B-ObservationalTechniques O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument B-ObservationalTechniques O O O O O O O O O O O O O O B-Wavelength 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 B-Formula I-Formula I-Formula I-Formula I-Formula O O

SPHERE data We also re-reduced the SPHERE observations of HD 4113 published in Moutou et al. (2017) (Program 096.C-0249, PI: Moutou), taken on 2015-10-08. These observations were taken in IRDIFS-EXT mode following an observing strategy that is similar to our observationsas described above, and are summarized in Table 2 . The IRDIS data were taken in the K1-K2 mode ( λ K 1 = 2.1025 μ m, λ K 2 = 2.2255 μ m), while the IFS data cover a range of wavelengths from 0.97–1.66 μ m with an average spectral resolution of 34.5. These data include a maximum field rotation of 51 deg between coronagraphic frames. Our data reduction procedure was identical to that of the IRDIFS data described in the previous section. 4 Results 4.1 SPHERE 2016 high-contrast imaging data The source HD 4113C was detected at high significance in both IRDIS H2 and IRDIS SDI reductions, but was not recovered in the H3 filter, suggesting the presence of strong methane absorption. The measured relative photometry and astrometry are given in Table 3 , while the IRDIS PSF-subtracted images are shown in Fig. 2 . We adopt a lower limit on the contrast of 14.8 mag for the H3 filter, using the 3 σ contrast curve at the location of the H2 detection. Table 3 Measured astrometry and photometry of HD 4113C from the SPHERE observations. In the IFS data using PCA alone, no significant detection was found in any individual wavelength channel or in the mean taken over wavelength. After we applied SDI to the IFS data, we clearly detected the companion, with 14 of the wavelength channels showing an excess of flux above 1.5 σ significance at the location of the IRDIS detection. A weighted-mean image is shown in Fig. 2 . The data reduction for wavelengths below 1.02 μ m suffer from considerably more residual noise in the SDI+PCA reduction and are not included in the subsequent analysis. The measured contrast ratios from IFS and IRDIS were converted into apparent flux measurements through multiplication by a BT-NextGen spectral model ( Allard et al. 2012 ) with T eff = 5700 K, [Fe/H] = 0.3 dex and log g = 4.5, close to the values determined in Sect. 2 . The model spectrum was flux-scaled using the distance and radius of HD 4113A. The extracted spectrum is shown in Fig. 4 . 4.2 SPHERE archival high-contrast imaging data After processing the 2015 data, we were unable to unambiguously recover the companion HD 4113C in the IRDIS images. Close to the location of the 2016 detection, we find an excess of flux with 2–3 σ significance in the SDI reduction. However, because of the lower S/N, our reduction of the IRDIS data does not provide substantial constraints on the position or flux of the companion, and we have excluded it from the following analysis. In the IFS SDI reduction, we also find an excess of flux in wavelength channels corresponding to the J - and H -band peaks found in the2016 data, again with lower significance. We find six channels at which the companion is visible at S ∕ N > 4, and by


O O B-Survey I-Survey I-Survey O O O O O O O B-Telescope I-Telescope O B-Instrument I-Instrument I-Instrument I-Instrument I-Instrument B-Instrument O O O O O B-Organization I-Organization I-Organization O O B-Observatory I-Observatory I-Observatory O B-Dataset I-Dataset I-Dataset O O O O O O O B-Survey O B-Survey I-Survey O O B-Survey I-Survey I-Survey O B-Survey I-Survey I-Survey O O O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O O B-Grant O O O O O B-Survey I-Survey I-Survey O O B-URL O B-Survey O O O B-Location O O O O B-ObservationalTechniques O O O B-Telescope I-Telescope O B-Dataset I-Dataset I-Dataset O O O O O O O B-Survey O O B-Survey I-Survey I-Survey I-Survey I-Survey O O O O B-CelestialRegion I-CelestialRegion O O O O O O O O O O O B-Survey I-Survey B-Survey I-Survey B-Survey I-Survey B-Telescope B-Survey I-Survey B-Telescope B-Telescope O B-Wavelength O B-Wavelength O B-Survey O O O O B-Organization B-Location O B-Organization B-Location O B-Observatory O O O O O B-Survey O O B-URL O O O B-Person O O O B-Organization O B-Fellowship I-Fellowship I-Fellowship I-Fellowship O O O B-Organization I-Organization I-Organization I-Organization O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization O O B-Grant B-Person O O O O O B-Organization I-Organization I-Organization B-Fellowship I-Fellowship B-Fellowship B-Person O O O O O O B-Organization I-Organization I-Organization O O B-Fellowship I-Fellowship B-Fellowship O O B-Person I-Person I-Person O O O O O O O O

ACKNOWLEDGEMENTS The SAMI Galaxy Survey is based on observations made at the Anglo-Australian Telescope. The Sydney-AAO Multi-object Integral field spectrograph (SAMI) was developed jointly by the University of Sydney and the Australian Astronomical Observatory. The SAMI input catalogue is based on data taken from the SDSS, the GAMA Survey and the VST ATLAS Survey. The SAMI Galaxy Survey is funded by the Australian Research Council Centre of Excellence for All-sky Astrophysics (CAASTRO), through project number CE110001020, and other participating institutions. The SAMI Galaxy Survey website is http://sami-survey.org/ . GAMA is a joint European–Australasian project based around a spectroscopic campaign using the Anglo-Australian Telescope. The GAMA input catalogue is based on data taken from the SDSS and the UKIRT Infrared Deep Sky Survey. Complementary imaging of the GAMA regions is being obtained by a number of independent survey programmes including GALEX MIS, VST KiDS, VISTA VIKING, WISE, Herschel -ATLAS, GMRT ASKAP providing UV to radio coverage. GAMA is funded by the STFC (UK), the ARC (Australia), the AAO, and the participating institutions. The GAMA website is http://www.gama-survey.org/ . Support for AMM is provided by NASA through Hubble Fellowship grant HST-HF2-51377 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555. SMC acknowledges the support of an Australian Research Council Future Fellowship (FT100100457). MSO acknowledges the funding support from the Australian Research Council through a Future Fellowship (FT140100255). We thank Á. R. López-Sánchez for assisting in the proofreading of the paper.


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the stability of the orbits in the sense of keeping them within a well-defined section of the available orbital parameter space, Fig. 1 indicates that the eccentricity may eventually reach values that lead the aphelion closer to the Earth–Moon system, perhaps triggering an impact or an ejection from NEA parameter space. Conversely, a larger value of the eccentricity may lead to a shorter perihelion and an eventual collision with the Sun or an ejection from the Solar system or into its outskirts. In our case, the value of the aphelion distance, that oscillates between those of the semimajor axes of Venus and the Earth, can become as high as 1.02 au (see Fig. 6 , right-hand panel), opening the door to eventual impacts on our planet if one of the nodes reaches aphelion (see also Ribeiro et al. 2016 ). Members of the Atira population can eventually become impactors as a result of the complex orbital evolution discussed here and in the event of an impact, they will most probably come from out of the Sun’s glare. 3.3.2 Vatira evolution The evolution of 2019 AQ 3 shown in Fig. 1 initially leads to brief periods (in thick red/grey) in which the aphelion distance of 2019 AQ 3 , Q 0.718 au i.e. 2019 AQ 3 , an Atira, becomes a transient Vatira. This opens the door to transitions between the two dynamical classes. In fact, the dynamical context that keeps 2019 AQ 3 in a chaotic but relatively stable state may be effective in enabling a dynamical pathway to go from the Atira orbital realm into the Vatira one as shown by the evolution after about 3.5 Myr into the future. The progressive reduction in the value of the semimajor axis eventually leads to a transition from the Atira population into the Vatiras that avoid encounters with Venus altogether. Fig. 6 shows that transitions to and from the Vatira orbital realm are also possible well away from the nominal orbit. Our calculations show that a combination of secular evolution and eventual close encounters with Venus triggers the transitions. Atiras do not cross the orbit of the Earth–Moon system and Vatiras do not cross the orbit of Venus; both Atiras and Vatiras define disjoint subsets. Atiras can impact on Venus, Vatiras cannot; therefore and although the members of both dynamical classes interact with Venus, they do it quite differently. We may now argue that the distinctive dynamical property of putative, long-term stable Vatiras is that they must be virtually and dynamically detached from Venus. This implies a robust difference between the dynamical behaviour of hypothetically stable Atiras, such as those discussed by Ribeiro et al. ( 2016 ), and stable Vatiras. In general, Atiras may still experience close encounters with Venus, Vatiras cannot. When the Lidov–Kozai resonance is at work, in addition to avoiding close encounters with Venus at aphelion, close encounters with Mercury at perihelion are also reduced, but the orbit of Mercury is far more eccentric (0.21) and inclined (70) than that of