constraint is nearly same. So, we find that, different choices of the group prior p 0 ( z , Ω) cannot significantly affect the constraint of the Hubble constant. On the other hand, for LHVIK network with SBBH mergers, we find the error bars of H 0 are quite large in both cases. Figure 8. The posterior distributions of Hubble constant H 0 . The upper, middle, and lower panels show the results of for the LHVIK, LHVIKCA, CE2ETD network, respectively. The left-hand panels represent the cases of uniform window function w i = 1, and the right-hand panels represent the cases of w i proportion to the stellar mass of groups. In each panel, there are four lines. The green line is the result in the case of A and the blue one is that of B (see the main text for the details). Similarly, the red line is the result in the case of A, and the black line is that of B. Note that, green line overlaps with blue one, and red line overlaps with black one. For LHVIKCA network with SBBH mergers, we find that 44 events satisfy the criteria and are used for the parameter constraining. The posterior distributions of H 0 derived from this network are given in the middle left-hand panel of Fig. 8 , which are for both case of A and case of B. While for SBBH mergers, we find 21 events can be used for the parameter constraining, and the corresponding result is in the case of A and H 0 = 69.97 ± 0.86 km s −1 Mpc −1 in the case of B. Same to the cases of LHVIK network, we find that the effect of group prior p 0 ( z , Ω) is not significant. In comparison with the corresponding cases with LHVIK network, we find the uncertainties of H 0 are nearly five times smaller. Due to the contribution of the two 8-km detectors in the network, the localization ability for the individual event is significantly improved, which leads to two effects on the H 0 constraining: First, the uncertainties of the redshift distribution of the GW event is reduced. Secondly, the number of the GW events satisfying the criteria is increased. So, we conclude that, if the proposals of 8-km detectors can be realized in the near future, the capabilities of GW cosmological, based on the SBBHs as the standard sirens, will be greatly improved in the 2G detector era. Now, we turn to the 3G detector network CE2ETD. As anticipated, we find that the accuracies of H 0 are much better than that of the 2G detector networks. For mergers, 66 events can be used for the parameter constraining, which follow the result H 0 = 70.000 ± 0.008 km s −1 Mpc −1 for both cases with different prior choices. For SBBH mergers, the constraint of H 0 is 70.000 ± 0.018 km s −1 Mpc −1 , derived from 65 events, which satisfy the selection criteria. The posterior distributions in these cases are presented in the lower left-hand panel of Fig. 8 . We find that, even comparing with the results of 2G LHVIKCA detector network, the uncertainty of H 0 is reduced by a factor of 30. Nair, Bose Siani ( 2018 ) discussed a single ET’s accuracy of H 0

O O O O O O O O O O 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 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 B-EntityOfFutureInterest I-EntityOfFutureInterest I-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O B-Instrument B-Instrument B-Instrument I-Instrument O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 I-Instrument 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 B-Instrument I-Instrument O O O O O B-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 B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O B-EntityOfFutureInterest O O O O O O O O B-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 B-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 B-Instrument O O O O O O O O B-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 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-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 O B-Instrument I-Instrument I-Instrument I-Instrument O O O B-EntityOfFutureInterest I-EntityOfFutureInterest 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-EntityOfFutureInterest I-EntityOfFutureInterest


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values using least squares. Phase residuals of the cross-correlation spectrum are analysed and additive corrections to the a priori weights are computed on the basis of this analysis. The uncertainties of estimates of group delays are derived from uncertainties of fringe phases and additive weights corrections. The uncertainties of fringe phases depend on fringe amplitudes. The explicit expression can be found on page 233 of Thompson, Moran Swenson ( 2017 ), equation (6.63). Computation of total group delays and phase delay rates. The group delays and phase delay rates derived at the previous step are corrections to the a priori delays and phase delay rates used during correlation. The mathematical model of the a priori group delay and phase delay rate used by the correlator is expanded over polynomials of the fifth order at 2-min long intervals that cover the time range of a VLBI experiment. Using these coefficients, the a priori group delays and phase delay rates are computed to a common epoch within a scan for the event of arriving the wavefront at a reference station of a baseline. Using these a priori group delays and phase delay rates, the total group delays for that epoch are formed. 3.2 Astrometric analysis Total group delay is the main observable for astrometric analysis. During further analysis, the a priori model of group delay, more sophisticated than that used for correlation, is computed, and the differences between observed and theoretical path delays are formed. The partial derivatives of this model over source coordinates, station positions, the Earth ordination parameters, atmosphere path delay in zenith direction, and clock function are also computed. Then, corrections to those parameters are adjusted using least squares. The frequency set-up used for this campaign, selected due to hardware limitation (see as an example the set-up for v271i segment in Fig. 2 ) posed a challenge in data analysis. The Fourier transform over frequency over baselines with atca, ceduna, mopra in this example that uses LBDAR DAS has strong secondary maxima (see Fig. 6 ). The amplitude of the second maximum is 0.98, the third maximum 0.93, and the fourth maximum 0.83 with respect of the global maximum. Due to the noise in data and remaining instrumental phase distortion, the fringe-fitting process cannot reliably distinguish the primary and the secondary maxima, and as a result, group delay is determined with the ambiguity of N × 1/2.56 × 10 8 ≈ 3.9 ns, where N is a random integer number, typically in a range [−2,2]. Figure 6. The normalized fringe amplitude as a function of group delay between stations that had LBDAR recording system. The fringe amplitude is divided by the amplitude at the global maximum. At the first stage of the astrometric data analysis, we processed the so-called narrow-band group delays derived as an arithmetic mean of group delays computed over each IF independently and estimated source positions using least squares. The

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


0.18, respectively, for the 80 per cent/20 per cent train/test split (right-hand panels in Figs 4 and 5 ). Given more training data for the final model, these hyperparameters should deliver an appropriate model complexity that does not overfit the data. As before, I train 100 models with different random states to avoid being biased by the random components in the fitting process. Henceforth, I will report the median value of the predictions from the 100 models. In Fig. 7 , I compare input T e metallicities with those predicted by the MLP model from strong lines. The error bars show the 1σ standard deviations of the 100 predictions. In general, the spread in metallicity due to the random components in the fitting process is much smaller than the dispersion of the calibration. Fig. 7 suggests that the best MLP model performs reasonably well over a wide range of metallicity. Figure 7. Comparison between oxygen abundances from the best MLP model (Section 2.3.4) and the T e method. The data points are the working sample described in Section 2.1 . The error bars are the standard deviations of the 100 predictions from the 100 model realizations. The dashed line is the one-to-one line. 2.3.5 Feature sensitivity Extracting physical interpretation from neuron weights and biases is known to be difficult. However, it is worth investigating how sensitive different features are to the output to understand their importance to the network. The sensitivity analysis can be achieved by computing the partial derivative of the output with respect to the input features. Using the best MLP model, I perturb one feature at a time while keeping the other features unchanged and compute the changes in the output metallicity. The small perturbation is set to 3 per cent of the standard deviation of the input feature of the working sample. The response of the model to the perturbations is calculated for the entire working sample. Fig. 8 presents histograms of the resulting changes in the output metallicities in the form of a ‘violin’ plot. The top three features that the network output is most sensitive to are [S ii ]/[N ii ], [N ii ]/[O ii ], and [N ii ] (deviate most from zero). Interestingly, photoionization models have demonstrated that the [N ii ]/[O ii ] ratio is a good metallicity diagnostic (at above 0.2 solar) due to its insensitivity to ionization parameter (Kewley Dopita 2002 ; Dopita et al. 2013 ). The combination of [N ii ]/[S ii ] and [N ii ]/H α is also suggested by Dopita et al. ( 2016 ) to be an excellent diagnostic that is insensitive to ISM pressure and ionization parameter. The neural network appears to rely more heavily on features that are also important in diagnostics developed from photoionization models, despite that this information is not given a priori. This demonstrates the ability of the neural network to directly ‘learn’ from the data. Figure 8. Feature sensitivity of the best MLP model, as measured by perturbing one feature at a time and

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


gradually distorted until a singular point appears, where the derivative is discontinuous. Further increasing y , the singular point moves at different x positions, thus generating a discontinuity that is also in the derivative . Starting from the position y = 0 where the solution is regular, the singularity develops over a distance ( y ∼ 6), which is of the order of the typical wavelength. This singularity is found also for other values of z , indicating that a singular surface is present in the 3D structure of A z . At the singular surface the components B x and B y are discontinuous, therefore the surface represent a current sheet. In contrast, the component // is regular in the whole domain. In Figure 1 (bottom panel) the profiles of the magnetic field components and of are plotted as functions of x , for y = 6.13 and z = 0.78. The presence of the discontinuity is clearly visible, mainly in the B y profile. The profile of is remarkably constant, except for a dip localized at the singular point. In fact, the constancy of is guaranteed by Equation ( 1 ), while the smoothing procedure, which modifies the “ideal” solution mostly around the singular point, represents an additional element that does not allow the solution A z to exactly satisfy Equation ( 1 ). Figure 1. Case A. Top panel: profiles of as functions of x , for various values of y , and at z = 0.78. Bottom panel: profiles of B x , B y , B z , and as functions of x , at y = 6.13 and z = 0.78. To study a situation that is closer to the solar wind turbulence, in Case B we considered more complex forms for A x ( x , y , z ), A y ( x , y , z ), and a z ( x , z ) that have 3D power-law spectra (2D for a z ). For the evaluation of these quantities, we used a synthetic turbulence model (STM) introduced by Malara et al. ( 2016 ) and already employed in modeling magnetic turbulence (Pucci et al. 2016 ; Perri et al. 2017 ). The STM builds up a turbulent field as a superposition of localized fluctuations with different amplitudes at different logarithmically distributed spatial scales. The model can reproduce an anisotropic spectrum (Malara et al. 2016 ) that follows the critical-balance scaling law (Goldreich Sridhar 1995 ), where and l ⊥ are the perturbation scale lengths parallel and perpendicular to the mean magnetic field , respectively. Using the STM, we generated A x , A y and the boundary condition a z in the scale ranges π ≤ l ⊥ ≤ π /32, . On average, the amplitude of a fluctuation in the spectrum of the vector potential i th component scales as . For h = 1/3 the spectrum of the spatial derivatives of has a Kolmogorov index () in the perpendicular directions, while in the parallel direction. We choose the parallel direction along x , which is approximately the direction of (see below). The STM can also reproduce intermittency through a p -model technique (Meneveau Sreenivasan 1987 ); in the present case we used p = 0.5, corresponding to no intermittency. A more detailed description of

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


of Sgr in that area of the sky with mean velocities v r 130 and115kms 1 . The position of these peaks are compatible with the ones derived from the velocity distribution of the target stars. According to the classification provided by these models, the bulk of Sgr stars around v r 130kms 1 might belong to the trailing arm of that halo substructure while the less significant peak might correspond to the leading arm. The mean heliocentric distance predicted by PR10 for both wraps in this area of the sky is d 30kpc. On the other hand, LM10 predicts mean distances of d 21 and 28kpc for the leading and trailing arms, respectively. The expected two sections of the Sgr tidal stream along the line of sight to Whiting1 are evident in our spectroscopic results but not in the colourmagnitude diagram (CMD) shown in Fig. 1 . We analyse the distribution of target stars belonging to the Sgr components as a function of g by counting stars associated with the leading [160 v r (kms 1 )100] and trailing [90 v r (kms 1 )150] arms with a bin size of g 0.1. Fig. 3 shows the normalized distribution obtained for both populations and we are not able to determine a shift in the g band between the subsamples of target stars. This might indicate that the leading and trailing arms of Sgr are spatially coincident or have slightly different distances, making it difficult to distinguish the populations in the CMD. Therefore, our results are in good agreement with the predictions made by the PR10 model both for the position and the kinematics of the leading and trailing components of the Sgr tidal stream around Whiting1. Figure 3. Left-hand panel: CMD for stars beyond 10arcmin from the centre of Whiting1. The positions in the diagram of stars belonging to the Sgr trailing and leading wraps are indicated as orange stars and green triangles, respectively. The blue isochrone corresponds to a t 10Gyr and [Fe/H] 1.5 population. Right-hand panel: normalized distribution of stars belonging to both arms as a function of g in the range 19 g 23.5 and following the same colour code as in the left-hand panel. According to the PR10 classification, target stars with radial velocities around v r 120kms 1 might be associated with an old component of the leading arm of Sagittarius, accreted a long time ago (2Gyr). While the northern and southern trailing arms have been well characterized using different tracers such as RRLyrae, blue horizontal branch, sub-giant branch and red clump stars (e.g. Koposov etal. 2012 ; Belokurov etal. 2014 ), the southern leading arm predicted both by PR10 and LM10 , has remained undetected. This might be due to the coincidence of its projected path with that of the trailing arm or to its lower surface brightness. Only tentative detections have been reported using alternative tracers such as carbon stars, with distances and velocities consistent with our results along that line of sight (Huxor Grebel 2015 ). Alternatively, the group of stars with positive radial

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


the models relax during 200 T cr (about a Hubble time); the final snapshot was again rotated using the moments of the inertia tensor of the 80 per cent most tightly bound particles. These last systems (one for each model) were evolved during an additional interval of 300 T cr in order to verify their stability. For each of the two models, the snapshot corresponding to 100 T cr of this last evolution was the one used to study and classify the respective orbital contents; we call them E2af and E5af, respectively, for brevity. Fig. 1 shows the kinematic and structural characteristics of the E2af model. In this figure, the abscisae q stands for the ellipsoidal radius where a , b and c are the semi axes of the model, computed following the method of Dubinski Carlberg ( 1991 ), as adapted by Holley-Bockelmann et al. ( 2001 ); Q , on the other hand, is the same as q but projected on to the coordinate planes. The abscisae M ( r )/ M is the mass interior to radius r in units of the total mass of the model. The upper-left panel shows the density profile of the model, computed using ellipsoidal shells with constant axial ratios taken at the half-mass radius. As can be seen, the rotation has not substantially affected the cusp of the model (γ = −1.023 ± 0.020, computed from the densities of the 10 000 innermost particles binned in 100 intervals of distance to the centre). The upper-right panel shows the axial ratios, computed in shells each containing 3 per cent of the particles, previously sorted by energy. The ratios of the semi axes of the shell containing 81 per cent of the mass in its interior are b / a = 0.939 and c / a = 0.791, in good agreement with the values that correspond to the 80 per cent most tightly bound bodies ( b / a = 0.925, c / a = 0.823, T = 0.447), i.e. the parameters used in our previous works. Comparing these values with those of the original E2a model, we can see that the b / a ratio has increased, whereas the c / a ratio and the triaxiality have decreased. The bottom panels show the kinematical profiles, in which , where i is a Cartesian direction x , y or z in the left-hand panel, and r (radial) or t (tangential) direction in the right-hand panel. The anisotropy parameter . Fig. 2 shows the same characteristics but for the E5af model. Again, the cusp is well preserved (γ = −0.956 ± 0.023). In this case, for the same shell as before, b / a = 0.916, c / a = 0.602, while for the 80 per cent most tightly bound particles, b / a = 0.896, c / a = 0.641 and T = 0.335, i.e. both axial ratios have increased and the triaxiality decreased with respect to the E5a model. It might seem odd that rotation has not made the model flatter, but it should be recalled that the process that led from the non-rotating to the rotating model implied considerable changes in structure of the former. For example, about 30 per cent of the original particles were eliminated because they increased their energies beyond the established limits, and the a semi

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


flux toward the Lyman limit. The consequence of this is that at high redshift (), SLSNe-I have a characteristic red observer-frame color and long-duration light curves. The identification of SLSNe-I at requires information on the UV spectrum and evolution. As highlighted in Section 3.5 , data in this wavelength range are sparse, with only DES16C2nm, Gaia16apd, PS1-11bam, and DES15E2mlf having data that extend to . Figure 9 shows the luminosity and color evolution of SLSNe-I at maximum light inferred from these spectra as a function of redshift. The spectra have been normalized and adjusted to the peak magnitude and color of each event. These spectra are then redshifted between 0 and 4, and integrated through the DECam r and z passbands. Figure 9 shows the evolution in luminosity and color for these spectra, along with other events in the literature. Where required, K -corrections have been determined from the spectrum of Gaia16apd. The single-epoch 5 σ magnitude limits of the DES deep and shallow fields are shown along with those expected for LSST wide-field and deep-drilling fields (Scovacricchi et al. 2016 ; D. Scolnic 2017, private communication). These limits suggest that in a single epoch, DES can detect SLSNe-I that are spectroscopically similar to Gaia16apd and DES16C2nm, to z = 3.2 in z -band observations of its deep fields or z = 3.8 for objects that are spectroscopically similar to DES15E2mlf. For the LSST deep-drilling fields, the maximum redshifts in the z band are 3.5 for the DES16C2nm spectrum and 4.3 when considering the DES15E2mlf spectrum. Figure 9. Observer-frame evolution of SLSNe-I. Upper panel: the apparent r -band evolution of SLSNe-I as a function of redshift. DES16C2nm is shown as a purple star, with literature SLSNe-I in orange and the photometrically confirmed objects of Cooke et al. ( 2012 ) shown as black crosses. Values determined from the maximum-light spectrum of Gaia16apd, normalized to the peak magnitude of Gaia16apd, are shown in blue, with the corresponding DES16C2nm spectrum from VLT in red and DES15E2mlf in green. K -corrections for literature events have been determined using the Gaia16apd spectrum. The magnitude limits for the DES deep and shallow fields and LSST wide-field and deep-drilling fields are also shown. Second panel: as above, only for the z band. Third panel: the J -band evolution of SLSNe-I as a function of redshift. The magnitude limits for the Euclid and WFIRST shallow, medium, and deep surveys are also shown. Lower panel: the r − z color evolution of SLSNe-I as a function of redshift as inferred from the upper two panels. A horizontal line of mag highlights the difference between low () and high () redshift events. This analysis can be extended to the observer-frame NIR, where surveys such as Euclid (with 5 σ limiting magnitude per visit in the deep fields and an irregular cadence of 10 visits to each of the two fields in a 6-month observing window for 5 years; Inserra et al. 2018a )

O O O O O O O O O O O O O O B-TextGarbage 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 B-CelestialObject B-CelestialObject B-CelestialObject O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument 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 O O O O O O O O O O O B-CelestialObject O O O O O O O O B-Survey O O O O O O O O O O O B-Telescope 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 B-Survey O O O O O O O O B-CelestialObject O B-CelestialObject O B-Formula I-Formula I-Formula O B-Wavelength I-Wavelength O O O O O O B-Formula I-Formula I-Formula O O O O O O O B-CelestialObject O O B-Telescope O O O O O O O B-Wavelength I-Wavelength O O O O B-CelestialObject O O O O O O B-CelestialObject O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O B-CelestialObject 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 B-CelestialObject O O O O O O B-CelestialObject O O O O O O O B-CelestialObject O O B-Telescope O O O B-CelestialObject O O O O O O O O O O O O B-CelestialObject O O O O O O B-Survey O O O O O B-Telescope O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O B-Telescope O B-Telescope O O O O O O O O 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 O O O O O O B-TextGarbage O O B-TextGarbage O O O O O O O O O O B-Wavelength 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 B-Citation I-Citation I-Citation I-Citation O


; Livadiotis McComas 2012 , 2013b ; Livadiotis 2016 ). Therefore, the IBEX maps may be consistent with the radial trend in γ sw detected with NH -SWAP. If we find that γ sw behaves in a systematic way using Voyager 2 observations, we may be able to monitor γ sw with NH and forecast when NH will reach the termination shock or at least determine if the location of the termination shock is moving dramatically inward or outward. Many theoretical and simulation studies have explored how the process of the solar wind picking up interstellar material can heat the solar wind (Matthaeus et al. 1999 ; Smith et al. 2001 ; Isenberg et al. 2003 ; Adhikari et al. 2017 ; Zank et al. 2018 ). Given that when we account for the radial variation of γ sw , we are then able to obtain excellent agreement between the inferred slowing from the amount of pickup and the amount of observed slowing, we conclude our work provides further observational evidence that the solar wind picking up interstellar pickup ions likely plays a role in heating the solar wind and altering the T – n relationship with increasing radial distance. However, additional work combining simulations and data should be performed to determine exactly why the solar wind T – n relationship systematically varies in a way that produces a linear decrease in γ sw with increasing distance from the Sun. Possibly, solar wind turbulence or wave particle interactions generated by the pickup process heat the solar wind altering the T – n relationship with increasing radial distance. In the inner heliosphere compressions, shocks, and shears are strong, but in the outer heliosphere all of those are much weaker. Therefore, those are not likely to impact the changes in the T – n relationship to the degree that waves and turbulence related to the waves could in the outer heliosphere. Our solar wind polytropic index radial profile γ sw ( r ) for the outer heliosphere, our initial analysis of the evolution of the total polytropic index ( γ ) from the inner to outer heliosphere, and the total polytropic index ( γ ) in the heliosheath from IBEX provide substantial metrics for outer heliospheric simulations. This work will become more relevant as NH gets closer to the termination shock heading in the direction of the ribbon and higher-resolution maps of the ENA ribbon from the Interstellar Mapping and Acceleration Probe ( IMAP ) mission become available (McComas et al. 2018 ). Below, we summarize our main findings and conclusions. 1. In the outer heliosphere (21–43 au), we found the density radial profile to decrease at either nearly or slightly less than the spherical expansion rate. 2. As NH moves farther away from the Sun, we can assess if picking up of interstellar material hinders the expansion of the solar wind altering the solar wind density profile. 3. In the outer heliosphere (21–43 au), the temperature profile is well above what is expected for an adiabatic profile. 4. The relationship between the solar wind

O B-Citation I-Citation I-Citation O B-Citation O B-Citation I-Citation O O O B-Telescope O O O O O O O O O O O O O B-Mission B-Instrument O O O O O O O O O O O O B-Mission I-Mission O O O O O O O O O O B-Mission O O O B-Mission O O O O O O O O O O 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 O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O B-Model I-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest B-Model I-Model I-Model I-Model O O O O O O O O O O O O O O O O O O B-CelestialObject O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O O B-Model I-Model I-Model I-Model O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion 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 B-Model I-Model I-Model I-Model O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O B-EntityOfFutureInterest I-EntityOfFutureInterest B-Model I-Model I-Model I-Model I-Model I-Model I-Model I-Model I-Model O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O B-Model I-Model I-Model O O O O O B-CelestialObjectRegion O B-CelestialObjectRegion I-CelestialObjectRegion O O B-Model I-Model I-Model O O O O O B-CelestialObjectRegion O B-Instrument O O O O B-CelestialObjectRegion I-CelestialObjectRegion 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 B-CelestialObjectRegion I-CelestialObjectRegion O O B-Mission I-Mission I-Mission I-Mission I-Mission O B-Mission 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 B-Mission O O O O O B-CelestialObject O O O O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O B-EntityOfFutureInterest I-EntityOfFutureInterest 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 B-EntityOfFutureInterest I-EntityOfFutureInterest


lower. If the unknown energy is from dark energy, this implies the existence of inhomogeneity of the dark energy (de Putter et al. 2010 ; Blomqvist 2008 , 2010 ). Appendix A NPB Correction for Patches with Beam Convolution Fourier transform presumes that the signal is periodic such that the two ends are continuous; thus, when one deals with real data, it is inevitable to encounter jump discontinuity, which induces extra power in the power spectrum. Although the data are mostly discrete, the NPB effect nevertheless persists and should be taken into account as systematic error. A patch taken from a full-sky map has such an intrinsic effect, which is uncorrectable because NPB is part of the morphology. The effect, however, is further aggravated when there is beam convolution. As the statistics and comparisons in this paper are made between beam-convolved Planck data and simulations with the best-fit ΛCDM model (without beam convolution), it is necessary to study the effect because the power spectrum of a beam-convolved patch has more induced power than the smoothed power spectrum of the nonperiodic patch. To estimate the correction, we simulate 50 full-sky CMB maps and take 30 deg 2 patches centered at the equator (in total 600 patches). We take the central 20 deg 2 part directly from the 30 deg 2 patches and denote their mean power spectrum as . Then we use 5′ to convolve the 30 deg 2 patches and choose the central 20 deg 2 part, the mean power spectrum of which is denoted . The correction is therefore , where b is the beam transfer function. One finds that the extra power due to 5′ beam convolution is a rather smooth curve and can be best fitted to be ( μ K 2 ) from l ≥ 300. And for the 143 GHz band map with beam transfer function 730 (Adam et al. 2016a ) the correction for NPB is ( μ K 2 ). Appendix B XPS on the <italic>Planck</italic> Data Throughout the paper we use XPS on the Planck data: four CMB maps, the 143 GHz channel map, and the foreground-subtracted maps at 100, 143, and 217 GHz from the SEVEM method, to extract the peak position. The XPS is a quadratic estimator between two maps that can provide an unbiased estimate of the underlying power spectrum of the correlated signals and, at the same time, reduce the uncorrelated ones. We take from the Planck Legacy Archive the FULL MISSION RINGHALF1 and FULL MISSION RINGHALF2 maps for SMICA, NILC, SEVEM, Commander, and the 143 GHz map. Since the patches from RINGHALF1 (denoted α ) and RINGHALF2 (denoted β ) contain the same CMB signal but uncorrelated noise, we can employ the XPS on their Fourier modes and ,where ∗ denotes complex conjugate and the angle brackets denote average over all for integer k . However, as Chiang Chen ( 2011 , 2012 ) pointed out, lack of an ensemble and nonzero chance correlation with the so-called “uncorrelated” signal results in some residual from the XPS, which has the following relation:where and are the (uncorrelated) noise power spectrum from RINGHALF1 and

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 I-Citation O B-Citation O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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-Telescope 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 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 B-Formula I-Formula I-Formula O O O B-Wavelength I-Wavelength I-Wavelength O O B-Model I-Model I-Model I-Model B-Citation I-Citation I-Citation I-Citation O O O O B-Model O O O O O O O O O O O B-Tag O O O O O O O O O B-Telescope O O B-Wavelength O O B-Wavelength I-Wavelength O O O O O O O B-Wavelength B-Wavelength O B-Wavelength I-Wavelength 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-Archive I-Archive I-Archive O B-Dataset I-Dataset I-Dataset O B-Dataset I-Dataset I-Dataset O O B-Model B-Model B-Model B-Model O O B-Wavelength I-Wavelength O O O O O B-Dataset O O O O B-Dataset O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation 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 B-Dataset O


this work we do not see a wedge structure due to the incomplete treatment of instrumental frequency dependence. This will be addressed in future work. We have however included two theoretical lines relating to the wedge limit on all figures – a dashed line which assumes sources in the entire field of view (in our case 10 deg) will leak into the main field and an optimistic solid line which assumes only sources within the chosen central 4 deg (approximately the full width at half-maximum – FWHM – of the station beam) will affect the image. Further work on the contamination within the wedge is ongoing in the literature and as such recovery below the theoretical wedge line should be treated with caution. We refer to the combination of the noise, dirty foregrounds and dirty cosmological signal as the ‘total input signal’. We refer to the foreground model estimated by GMCA as the ‘reconstructed foregrounds’ and the difference between the reconstructed foregrounds and the total input signal as the ‘residuals’, which will contain the cosmological signal, noise and any foreground fitting errors. The foreground fitting errors can be defined as the difference between the simulated foregrounds and the reconstructed foregrounds and will contain any cosmological signal or noise which has been fitted as foregrounds as well as an absence of any foregrounds not modelled. 5 RESULTS Unless otherwise stated we present results for cylindrical power spectrum calculated over a 10 MHz bandwidth segment centred at 165 MHz, where the variance of the cosmological signal peaks in our simulation. This bandwidth is formed using an extended Blackmann–Nuttall window, though other windows are possible, as discussed in Section 5.1 . We 3D Fourier transform the data segment and bin the data according to the values of k perp , k los . The power at any particular k los , k perp , P ( k los , k perp ) = 〈δ( k los , k perp )δ*( k los , k perp )〉 is the average power of all the uv cells in the bin centring on k los , k perp . We choose to plot the ‘dimensionless’ power spectrum, , which has units of mK 2 throughout this paper: where V is the volume of the 10 MHz bandwidth in Mpc. We first construct cylindrical power spectrum for the different signal contributions in order to understand how the EoR window is constructed. In Fig. 1 , we see the Galactic synchrotron, Galactic free–free and unresolved extragalactic foregrounds while in Fig. 2 we see the dirty cosmological signal and dirty foregrounds (with all three foreground contributions summed). The action of the PSF can be clearly seen as a loss of power on scales above this (i.e. for k perp > 0.65 Mpc −1 ). Note that, since we are seeing power spectrum over a 10 MHz bandwidth only we do not see the evolution of the cosmological signal over redshift. We see clearly the area of k -space where the foregrounds appear to be at their strongest is at low k los , however, it should be noted that there is appreciable foreground

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


of the neck radius, a , determined by the numerical simulation and laboratory experiments. The spring constant increased almost linearly with neck radius, and the results from the numerical simulation (circles) and laboratory experiments (triangles and squares) were observed to overlap. Figure 6. Results of FEM simulation (circles) and laboratory experiments (triangles and cubes) for compression. The solid line denotes the semianalytical formula (Equation ( 4 )). Triangles and cubes are determined using the data between 90 to 95 and 40 to 90 N, respectively. The error bars of laboratory experiments are the standard deviation of three samples. The upper curve is from SU17 . The inverse triangle is the FEM simulation result for the a = R cylinder (without shrinkage due to sintering). Two sets of laboratory experiment results are shown in Figure 6 ; the difference between these sets is the force range used to determine the spring constant. Figure 7 displays the applied force as a function of displacement as measured in the laboratory experiment. This relationship was not linear, particularly for small forces; thus, the spring constant is dependent on the range of the applied force. In contrast, the FEM simulation was based on a linear response. The spring constant at the commencement of the compression was small compared to that at a large compressive force. There are two possible causes for this nonlinear behavior. First, the misalignment of the two end planes led to a nonlinear behavior because the force required to enable deformation until perfect fitting to the autograph was small compared to the force required after the perfect fitting. Second, if there is a bump on the end surface, the compression force changes at the commencement of compression. Figure 7. An example of a laboratory experiment result. At the beginning, the force increases nonlinearly, and then increases almost linearly after reaching 20 N. The neck shape was adopted from the second curve from the bottom in Figure 2 . The spring constant was determined using the data in the linear region of the force-displacement curve. For comparison, two ranges of the compression force were used; 40–90 and 90–95 N. Although there was a considerable scatter in the data, the results from the laboratory experiments were consistent with the numerical simulation results. The maximum radius in Figure 6 is 2.375 mm, corresponding to the original radius of the sphere prior to sintering. However, this radius was not realized by sintering, because the volume of the sphere decreased as a result of sintering. The maximum radius () following sintering was . The solid curve in Figure 6 is the model in SU17 . In contrast to the experimental and numerical results, the spring constant of the model increased as the neck radius decreased. In this model, the deformable region was restricted to the neck between the spheres, and the length of the neck decreased with the neck radius. As a result, 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 B-Model I-Model 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 B-Citation O O O O O O B-Model I-Model 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


mergers might be detectable for longer (e.g. through stellar streams, bright cores) than gas-poor galaxies. CO surveys of protocluster and identically selected field galaxies would allow one to compare the gas mass fractions of these two populations. Protocluster galaxies might be expected to have higher gas fractions due to efficient supply of pristine intergalactic gas through filamentary accretion, but this is a picture yet to be empirically tested. Lyα blobs are generally found in high- z protoclusters and indicate the presence of large volumes of cold gas around forming galaxies. Fakhouri Ma ( 2009 ) examined the role of environment on the halo merger rate in N -body simulations, using the friend-of-friends group finder (Davis et al. 1985 ) within the millennium simulation (Springel, Matteo Hernquist 2005 ) to trace the merger histories of dark matter sub-haloes out to z = 2. A key finding was a correlation between environment and merger rate, such that sub-haloes in the densest environments underwent merger rates 2–2.5 times higher than those in the lowest density regions. With the caveat that galaxies are biased tracers of the matter field, it is reasonable to assume that there will be a similar trend for the galaxies themselves. It is interesting that the level of enhancement of the merger rate found by Fakhouri Ma ( 2009 ) in the simulations is broadly in agreement with the enhancement we find for SSA22. Our analysis traces the rest-frame ultraviolet emission which is very sensitive to dust obscuration; for example, extended/clumpy star-forming regions could be hidden and the merger fraction understated, or a clumpy dust distribution could lead to very high extinction to certain stellar populations, giving the stellar emission overall a clumpy morphology, that could possibly be misinterpreted as a merger. We do not expect the use of rest-frame UV observations to lead to a significant bias in our interpretation unless there is a significant difference between the obscuration properties of galaxies in the protocluster and the field, since we have applied an identical analysis to both. Nevertheless, we are now obtaining near-infrared HST -WFC3 observations that will allow us to repeat our analysis based on the morphology of the rest-frame optical flux. Similarly, we have ALMA follow-up observations of LBGs along the ‘merger sequence’ in SSA22 that will allow us to directly detect the thermal emission from cold dust responsible for extinction in the ultraviolet/optical light. Our result is marginal mainly due to small number statistics, which dominate the size of the uncertainties on our merger fractions. This arises from the lack of a complete LBG catalogue covering the whole SSA22 field and sparse HST coverage of SSA22. It would be useful to extend our analysis to additional protoclusters and fields at a similar redshift to overcome the potential issues of small number statistics and cosmic variance, but high- z protoclusters are

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 I-Model O O B-Model I-Model I-Model B-Citation I-Citation I-Citation I-Citation 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 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 B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O B-CelestialObject 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 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 B-Telescope B-Instrument O O O O O O O O O O O O O O O O O O O O O B-Observatory 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-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-CelestialObject O O O B-Telescope 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


SNe roughly match the required luminosity and timescale, but we would not expect their progenitors to explode two years later as SNe Ia (Bildsten et al. 2007 ). The fast-declining light curves of SNe Ibn also indicate that very little 56 Ni is produced in the explosion (Foley et al. 2007 ; Pastorello et al. 2008a ), which may challenge white dwarf explosion models. One way of avoiding these issues is to allow PS1-12sk and SN 2006jc to come from different types of stars. SNe Ibn would then be a mixed class, with some low- and some high-mass progenitors. This could potentially explain some of the spectral diversity we see among SNe Ibn (Hosseinzadeh et al. 2017b ). The five spectra that we have of PS1-12sk look almost identical to spectra of SN 2006jc, 12 12 SN 2006jc was discovered after peak, so the phases of these spectra are not well constrained. but perhaps any explosion into helium-rich CSM would look the same. This situation would be analogous to the discovery that some events initially classified as SNe IIn are actually the explosions of white dwarfs with hydrogen-rich CSM (now called SNe Ia-CSM; Dilday et al. 2012 ; Silverman et al. 2013 ). In fact, this may be the reason that events classified as SNe IIn are less correlated with star formation than other classes of core-collapse SNe (Anderson et al. 2012 ; Habergham et al. 2014 ), despite some having luminous progenitor detections. 5. Summary and Conclusions We have presented a very deep limit on the star formation rate at the site of the SN Ibn PS1-12sk, nominally ruling out a massive star origin. We present three alternative proposals for how this SN could have occurred in such a unique environment. 1. The progenitor of PS1-12sk was a massive star ejected or tidally stripped from a nearby ultra-compact dwarf galaxy. 2. The progenitor of PS1-12sk was a rare massive star in a region with a very low star formation rate. 3. The progenitor of PS1-12sk was a low-mass star. Our result only deepens the mystery surrounding PS1-12sk, in that none of these possibilities is fully satisfactory in explaining the origins of SNe Ibn. Given that there is not much more data to collect on this particular event, the resolution will likely come from a statistical study of SN Ibn host galaxies. Although this is currently the only SN Ibn discovered in a non-star-forming environment, we still suffer from a small sample size of only tens of events. Current and future large-scale surveys will be much better suited to find these rare, fast-evolving transients, allowing us to better understand the statistical properties of their host environments. Appendix A Extinction Sanders et al. ( 2013 , p. 4) claimed that “the SED of [PS1-12sk] is not consistent with significant reddening given reasonable assumptions about the photospheric temperature” and neglect extinction throughout their analysis. However, as an additional check, we calculate an upper limit on the host galaxy extinction based on the nondetection of

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


find (their Table 1, with ). On the other hand, Hoang et al. ( 2018 ) find much higher merger fractions of up to for their nominal GC model, which are higher than the merger fractions of Petrovich Antonini ( 2017 ) and our merger fraction by 2 orders of magnitude. This large difference can be ascribed to different initial conditions. About half of the binaries in Hoang et al. ( 2018 ) merge due the gravitational wave emission only (i.e., even in the absence of the torque of the MBH). Moreover, Hoang et al. ( 2018 ) considered binaries much closer to the MBH ( to (∼10 −2 )) for which the octupole-order terms are important, in contrast to our simulations. The merger rate predicted by Hoang et al. ( 2018 ) is ∼1–, which is one (two) order(s) of magnitude larger than our GC rate estimate without VRR assuming a top-heavy (canonical) IMF. This can be ascribed to the following. 1. The merger fraction adopted by Hoang et al. ( 2018 ) is , which is 0.15/0.005 = 30 times larger than our adopted fraction. 2. The “conversion” factor from the merger fraction to the rate adopted by Hoang et al. ( 2018 ) is . We assumed a “conversion” factor of and for the canonical and top-heavy IMFs, respectively. These two points combined explain the different merger rates. In calculating their rates, Hoang et al. ( 2018 ) assumed that there exists a steady-state population of BH–BH binaries in the central 0.1 pc, with a number of corresponding to a merger rate of . This requires replenishment of the BH–BH binaries on a timescale of 100 Myr, which would be consistent with in situ star formation in a disk of massive O/B stars close to the MBH (e.g., Bartko et al. 2009 ). In our rate calculation, we assumed a global influx of compact objects, which is more appropriate in our situation given that we considered a binary population at larger distances from the MBH. VanLandingham et al. ( 2016 ) were the first to consider the combined effects of VRR and LK evolution by means of hybrid N -body methods. Due to computational limitations, the MBH masses were limited to up to . VanLandingham et al. ( 2016 ) found high merger fractions in their simulations. This is consistent with our results, in the sense that we find that the enhancement due to VRR is most significant for low MBH masses. More quantitatively, VanLandingham et al. ( 2016 ) found a merger fraction of in their simulation with (10k stars). This is very similar to our merger fraction of for the case and γ = 2 (adding the semisecular and non-semisecular fractions). This apparent agreement may be fortuitous, however, given that we did not consider a number of potentially important effects (see Section 6.1 ). In particular, DF is an important process in the simulations of VanLandingham et al. ( 2016 ); prior to their merger, most merging binaries sink inwards to the MBH. DF could therefore be important for bringing a binary from a regime with , where LK–VRR coupling is unimportant, to a region in which , where LK–VRR

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


the test set, where the training set builds the model, and the testing set evaluates the model's performance. In principle, the predictor performs better with a larger fraction of training data. On the other hand, the performance statistic will have greater variance if there is less testing data (Kohavi 1995 ). To strike a balance, we have tried changing the ratios of our training and testing sets from 50:50 to 90:10, and we verify that the XGBoost performs the best in both AUROCC and f1-score with a 70:30 split. To avoid over-fitting, we adopt an early stopping in XGBoost after five training iterations that do not yield any improvements. To control the balance of positive and negative weights, we set the scale _ pos _ weight = 28.7, which is given by the ratio between the number of negative and positive instances (4705/164; see Section 2.3 ). 3.3. Feature Selection Feature selection is an important process in machine learning that strongly influences the performance of the model. Feature selection is a procedure of selecting a subset of relevant features for model construction. In general, proper feature selection can increase the efficiency by reducing the training duration, enhancing generalization by reducing over-fitting, and improving the prediction performance (see Chen Guestrin 2016 ; An et al. 2019 ). A trained XGBoost model will automatically calculate feature importance and provide the feature importance scores. In this work, we first trained the XGBoost model based on the training data set and selected features by sorting feature importance scores calculated from the trained model. We then iteratively trained the model based on the selected subset of features until the point of best performance. We verified that both f1-score and AUROCC increase with the number of selected features until we use up all 79 features. Therefore, we did not reduce the number of feature vectors in this work. Considering the limitations of our computational resources, we repeated this procedure 10 times by using a different combination of training and test data sets in each iteration and estimated the average feature importance score from these 10 realizations. The top five important features in our sample are: K , ([3.6]−[4.5]), ( K − [4.5]), ([3.6]–[5.8]), and ( H − K ), which are similar to those photometric wave bands used by Chen et al. ( 2016 ; Optical-Infrared Triple Color: ( z − K ), ( K − [3.6]), and ([3.6]–[4.5])) and An et al. ( 2019 ; ( z − K ), ( J − K ), ( K − [3.6]), and ([3.6]–[4.5])). The top five important features in our sample can be associated to fundamental physical properties. The K -band flux roughly maps to the stellar mass, while the SMGs appear to be red and occupy a relatively well-defined region in near-infrared color–color space (see also Chen et al. 2016 ; An et al. 2019 ). 3.4. Tuning the Hyper-parameters The hyper-parameters are a set of parameters that define the machine-learning algorithm as a mathematical formula. 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 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 B-Model 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 B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O B-Model O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength O B-Wavelength O B-Wavelength B-Wavelength O O B-Wavelength O B-Wavelength O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O B-Wavelength O O O B-Wavelength O B-Wavelength O O B-Wavelength O B-Wavelength O B-Wavelength O B-Citation I-Citation I-Citation I-Citation I-Citation O O B-Wavelength O B-Wavelength O O B-Wavelength O B-Wavelength O O B-Wavelength O B-Wavelength O B-Wavelength 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 B-Wavelength O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O


site at a coronal location at or above the looptop. Having said that, we note that some spectral evolution of the electrons injected at the looptop along with the pitch-angle distribution can still affect the exact delay values, while the field inclination is taken into account within our 3D model. We checked that an SHS evolution of the injected nonthermal electron spectrum, where the spectral index varies by a few percent, while the electrons are beamed along the magnetic field can reduce the TOF distance by a factor of two as needed. However, such a model does not contain any population of nonthermal electrons reflected back to the coronal portion of the flaring loop(s) needed to account for the microwave emission. From this, we conclude that an electron beam with a modest angular scatter, rather than an ideal field-aligned beam, is responsible for the observed deviation of the loop half-length from the estimated TOF distance. Such an angular distribution is capable of reducing their “effective” speed along the magnetic field typically by a factor of 1.5–3. As we noted above, some angular spread is also required to supply a population of the upward-reflected electrons needed to interpret the microwave data. However, an isotropic angular distribution does not look likely given that it assumes a rather large pitch angle of the majority of streaming electrons and, thus, efficient trapping, which is not observed. Thus, the data favor an anisotropic beam-like distribution of the accelerated electrons with a modest opening angle of 30°–40°. The mirror ratio m = 3 in Loop II of our 3D model; thus, the electrons launched downward at the pitch-angle θ ≲ 35° will not be reflected at the footpoint and, thus, will not contribute to the trapping. The mean parallel velocity for the electrons launched at the looptop at θ = 35° is . Electrons with θ ≳ 35° will be reflected and will contribute to the brightness peaks observed at 5.7 GHz from the LF–loop. The observed delay of 70 ms between 5.7 GHz peaks and 102.2–293.5 keV emission peaks, both produced by presumably 400 keV electrons, places the 5.7 GHz source at a distance ∼5 Mm from the mirror points at the bases of loop II. Microwave emission at 17 and 34 GHz delayed by 120 ms requires an additional time for the electrons to be transported from Loop II to Loop I and, perhaps, additional time for trapping in Loop I. Thus, the time delays are naturally consistent with the identified magnetic configuration of the flare and the TPP model in which the particles are injected at the looptop of Loop II and then propagate to produce the observed variety of the HXR and microwave components. 3.2. Accelerated Electron Population In Section 2.4 we determined the HXR spectrum of subpeaks to be a single power-law with the indexes about 2.4. This spectrum is injected during a subpeak in addition to a preexisting population of nonthermal electrons responsible for a gradual (background) component of the burst.

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


β > 1 where L max remains irrelevant. Thus, equation ( 4 ) reduces to EE detection probability: Perley et al. ( 2009 ) caution that many non-EE short bursts are faint, and the presence of an extended emission might have gone undetected resulting in their classification as non-EE bursts. Norris et al. ( 2010 ), who did a detailed study on the sensitivity of BAT to extended emission conclude that BAT should be able to detect extended emission to intensities ∼10 −2 counts cm −2 s −1 , however it is only seen up to around ∼0.005 counts cm −2 s −1 indicating a true absence of EE in some bursts. Going by the latter, one does not necessarily have to incorporate an additional EE detection probability. However, we take a conservative stand and try to account for a possible selection bias against the detection of the faint extended emission component. The redshift-dependent EE detection probability should involve the luminosity function of extended emission, but with the limited sample it is difficult to arrive at the same. Therefore, we considered a single constant luminosity for extended emission. This approximation is simplistic, given the two orders of magnitude spread in EE luminosity (see Fig. 3 ). For the threshold of BAT, we used ε BAT = 0.005 counts cm −2 s −1 , motivated by the typical average fluxes EE is seen in BAT as mentioned by Norris et al. ( 2010 ). Thus, equation ( 4 ), in this particular case, reduces to as, P () becomes a step function, H ( L EE − 4π d L () 2 ε BAT ) which is zero if L EE 4π d L () 2 ε BAT and unity otherwise. We ran our simulations for two values of L EE around the average luminosity of the six bursts (1.5 × 10 56 counts s −1 ), L EE = 10 56 , and 2 × 10 56 counts s −1 resulting in a max of 1.8 and 2.53, respectively. The results we obtain from these are nearly identical. Figure 3. Average luminosity of the EE component, from the data presented in Norris et al. ( 2010 ). Pen symbol is GRB 090510A. The error bars on other bursts are smaller than the symbol. One of our weak-EE bursts, 080123, is not a part of the data of Norris et al. ( 2010 ). We included GRB160410 following the GCN report by Sakamoto et al. ( 2016 ). We used a det = 0.16 sq cm to convert numbers from Sakamoto et al. ( 2016 ) and calculated the average luminosity. It can be seen that L EE varies by around two orders of magnitude. For our analysis we fixed values near the mean of these bursts (dotted and dash–dotted lines). The yellow solid line is the threshold, . We also considered a P () = 1 throughout, i.e. BAT does not miss any EE component due to sensitivity issues. Throughout this paper, we have used a standard cosmological model with H 0 = 71 km s −1 Mpc −1 , Ω m = 0.3, and Ω λ = 0.7. 4 ANALYSIS AND RESULTS In this section, we describe our analysis of the redshift distribution for both EE and non-EE bursts, and compare the parameters focusing mostly on the delay time distribution function. We begin by giving a detailed account of how we set up

B-Formula I-Formula I-Formula 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-Telescope 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O B-Telescope 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 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 B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O B-CelestialObject O O B-Dataset I-Dataset O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula 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 B-TextGarbage I-TextGarbage O O O O B-Formula I-Formula I-Formula I-Formula 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 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 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


component of this line and the corresponding tomogram are presented in Fig. 8 . Meanwhile, the same line is treated as an absorption feature on the right-hand side. The emission component of the line basically repeats the pattern observed in H α. The observed trailed spectrum is faint, but the program picks up the signal correctly, reflecting it in the reconstructed spectrum. The low-velocity component definitely dominates, and hence a compact spot materializes close to the L1 point, in contrast with the diffuse appearance in the H α case. The HVC is hardly traceable in the observed trailed spectra, but apparently some emission comes from here too. Hence, a coma-like extension in the velocity map is visible 5 SYSTEM PARAMETERS The average mass of WDs in CVs above the period gap is M WD ( P orb > 3 h) = 0.86(20) M ⊙ (Zorotovic et al. 2011 ). For simplicity, we adopted M WD = 0.8 M ⊙ . Taking into account the semi-empirical relation of secondary type versus orbital period, we expect a secondary with a mass of M 2 ≈ 0.3 M ⊙ and spectral type of M3V–M4V (Knigge 2006 ). The expected mass ratio and separations are q ≡ M 2 / M WD ≈ 0.4 and a = 1.23 R ⊙ , respectively. The accretion-disc truncation radius 4 is R ⊙ . The corresponding primary, secondary, and L1 orbital velocities are 117, 292, and 129 km s −1 , respectively (see Fig. 9 ). Figure 9. A geometric model of BG Tri. The centre of mass (x) and corresponding Lagrangian points are marked. Velocities of the L1 point, the disc outflow area (green), and the WD are denoted. The LVC, which is emitted from the irradiated hemisphere of the secondary star, has a velocity exceeding that of the L1 point and less than the orbital velocity of the star. There are numerous flux measurements of BG Tri available in the public domain. We fetched all available data from VizieR 5 (Ochsenbein, Bauer Marcout 2000 ). We revised the available data, since some measurements are erroneous (e.g. the SDSS data are not correct because the object is too bright), and compiled those that passed scrutiny in Table 2 . Selected data are plotted using circles in the bottom panel of Fig. 10 , after the interstellar reddening correction of E ( B − V ) = 0.03 (Green et al. 2015 ). Using the Gaia distance of d = 334(8) pc, we can calculate the luminosity of different components. In particular, even a hot 50 kK white dwarf will have a negligible contribution to the optical flux. A secondary M3–4 V Roche lobe filling star has some insignificant influence in the IR. A comparison of the observed fluxes with those expected from different components confirms that the flux in the entire wavelength range is formed mostly by the accretion disc. The dashed lines in the bottom panel of Fig. 10 indicate a simple accretion-disc spectrum as a composition of multiple blackbodies, from concentric rings with a corresponding distribution of temperatures throughout the stationary optically thick disc (La Dous 1989 ). Since the observed flux would

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the MOS 1, MOS 2, and pn data with the xspec model const*phabs ( cemekl ) (see text for details). 2.4 RGS data Note that the same multitemperature model used for the EPIC spectral fit provides an adequate description of the RGS spectra when fixing all the parameters of the model to those derived above but adjusting consistently the model normalizations. In particular, inspecting Fig. 5 (where the best fit is superimposed to the RGS1 and RGS2 data re-binned in order to have at least a significance of 10σ per bin), one can note the existence of the O VIII Ly α emission line at ≃ 0.65 keV, and emission lines in the energy range 0.56–0.57 keV (21.6–22.1 ) possibly associated with the He-like transitions of O VII , i.e. the resonance line r (corresponding to the transitions between the n = 2 shell and the n = 1 ground state), and the intercombination ( i ) and the forbidden ( f ) lines. In this respect, as shown by Porquet Dubau ( 2000 ) the relative emission strength of the r, i , and f lines is a good indicator of the physical conditions of density and temperature of the gas. Figure 5. The best-fitting model superimposed on the RGS 1 (red) and RGS 2 (black) data. Note the presence a strong O VIII Ly α line at 18.96 and the O VII He-like triplet. In order to have a measure of the line fluxes, we followed the phenomenological spectral analysis method described in Nucita et al. ( 2010 ) and references therein. In particular, the unbinned RGS spectra are divided in intervals of 100 channels wide and Gaussians are fitted to all the identified emission lines. For each (single) emission line the centroid energy is free to vary and, when triplets are identified, the relative distance between the central energies was frozen to the value predicted by atomic physics. The local continuum was always modelled as a power law with a fixed photon index Γ = 1 and normalization free to vary. Since we are dealing with the unbinned spectra, we estimated the goodness of the fit by using the C-statistic (see Cash 1979 ). We further consider the line (or triplet) detected at confidence level when, repeating the fit with the continuum only, we obtained a change in the C-statistic value (Δ C ) by at least 2.3. The result of this analysis (see also Table 2 ) showed that the O VII resonance line is much more weaker than the intercombination line so that ionization processes may occur in the medium (Porquet Dubau 2000 ). This is also clear when using the standard line ratios R = f / i, L = r / i , and G = ( f + i )/ r as standard diagnostic. In particular, as clear from table 2, the large (small) values of the G ( R ) ratio imply photoionization and, since R decreases with increasing values of the electron density n e , a lower limit on the electron density of ≃10 11 cm −3 (Porquet Dubau 2000 ). Table 1. Spectral parameters for the best-fitting model ( const * phabs *( cemekl ) in xspec , see text for details). We also give the 0.3–10 keV absorbed and unabsorbed fluxes.

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


the 2 level in the Y and J bands, consistent with the measured magnitudes in the HST /WFC3 imaging. To determine the photometry and colour of the Pop III/DCBH candidate, we measured photometry on the ground-based imaging centred on the position of component A using small circular apertures of 1.2arcsec in diameter. We also measured the photometry in larger apertures of 2arcsec in diameter to compare directly with the results of S15 , and using a diameter of 3arcsec to provide a more appropriate measure of the total flux. The larger apertures were centred on the peak of the Y J UltraVISTA image, which is offset by 0.35arcsec to the north-west of component A (the stamps shown in Fig. 1 are centred on this position). The results are shown in Table 1 . All photometry was corrected to total magnitudes assuming a point-source correction. 2 S15 found a strong excess in the J -band photometry for CR7 using the UltraVISTA DR2 data, when the continuum level was derived from fitting to the Y , H and K s bands. The observed offset of m AB 0.4 0.13mag was interpreted as the contribution to the measured photometry from the spectroscopically observed He ii emission line. Converting the J -band excess into an estimated rest-frame equivalent width, S15 inferred an equivalent width of EW 0 80 20 for the He ii line. Table 1. The measured photometry for CR7 utilizing deeper near-infrared data from UltraVISTA DR3 and mid-infrared imaging from the SPLASH survey. The upper part of the table shows the available HST and Spitzer photometry. For the full object photometry, labelled as component Full, the photometry was measured in 3-arcsec-diameter circular apertures on the HST /WFC3 data, and the Spitzer /IRAC photometry was obtained using a deconfusion analysis based on the UltraVISTA K s -band data. The lower part of the table shows the ground-based photometry measured in 1.2-, 2.0- and 3-arcsec-diameter circular apertures. Note that the aperture photometry has been corrected to total assuming a point-source correction. The final row of the table reproduces the photometry and value as measured in S15 . Using the deeper near-infrared imaging now available, we find a smaller J -band excess than that determined in S15 , with for the 1.2-arcsec-diameter measurement. Here, the continuum level was determined from the best-fitting Bruzual Charlot ( 2003 ) SED to the Y , H , K s and [3.6] bands with the redshift fixed to z 6.6 (as shown in Fig. 2 ). If, instead, the continuum level in the J band is determined from a power-law fit to the Y , H and K s bands, we find an excess of . An offset of 0.2mag was also found using the two larger aperture measurements, and the results are unchanged if point spread function (PSF) homogenized images are used. To understand the differences between our results and those of S15 , we compared photometric catalogues from the older DR2 data used by S15 to those from the DR3 data. In the four bands, we find no significant zero-point offset

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2015 ). Although the SED of these CDs presents several overlapping features with a ‘normal’ SED of TDs, it would be misleading to treat them in a similar way. For instance, the implications for the presence of another star in the star--disc system entails an incorrect measurement of the luminosity and temperature, which translates into inaccurate age and mass estimates. This is the case of Coku Tau/4 and CS Cha that were originally described as TDs (Forrest et al. 2004 ; Espaillat et al. 2007 ), but eventually were presented as CDs (Guenther et al. 2007 ; Ireland Kraus 2008 ). This misclassification would be reflected in the estimation of birthplaces and time-scales for formation of sub-stellar companions (brown dwarfs) and/or planetary systems, and the demographic properties of these populations (e.g. Najita, Andrews Muzerolle 2015 ). Therefore, determining a more accurate relative picture of the lifetime of TDs and CDs requires a comprehensive survey capable of resolving close binaries ( ≲ 30 au) and measuring their frequency in objects previously classified as TDs through their SEDs. Although the open gap in the inner region of the disc might have different physical origins, in this paper we seek to identify if the dispersion of the primordial material in the inner region of the disc is a result of the tidal interaction between a close binary system and the disc. At small separations, detecting faint companions orbiting bright stars, that in addition, are surrounded by dusty material, can be challenging due to the high contrast between the companion and the primary star. However, observations of objects at early ages provide favourable IR contrast ratios for the detection of so far unresolved faint companions because of their intrinsically higher luminosity (Δ K 5 mag). We use the Non-Redundant Mask interferometry (NRM) technique and NIRC2 instrument located at the Keck II telescope, which offers a solution to reach angular resolutions with the necessary contrast and is resistant to speckle noise in the image by measuring a self-calibrating quantity known as closure phase (e.g. Martinache 2011 ). In order to achieve a higher accuracy in the detection limits of our data, the NRM completeness as a function of position and contrast utilizes a combination of a MonteCarlo Integration approach, giving a random sample of artificial binary stars, and Bayesian Inference , which uses prior probability density functions of the binary orbital parameters. We have restricted the selection of objects to regions with an age of ∼1–3 Myr and within a distance of about 220 pc. Taurus-Aurigae, IC348 region (Perseus) and Ophiucus star-forming regions satisfy these criteria (Loinard et al. 2008 ; Wilking, Gagné Allen 2008 ). This article is arranged as follows. In Section 2 , we present the motivation for the sample selection, description of observations together with the data analysis and a review of the target properties such as distance to the star-forming

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