baryon fraction. Once M g is specified, the gas density is normalized such that, 2.3 Ionization balance In this paper, we consider models that may represent the most metal-poor DLAs currently known. Given the presumably minimal level of recent star formation in these systems, it is reasonable to assume that the local sources of ionizing photons are sub-dominant relative to the extragalactic background. In what follows, we have therefore assumed that the surface of the most metal-poor DLAs is illuminated solely by the Haardt Madau ( 2012 ) ultraviolet/X-ray background radiation from quasars and galaxies with intensity J 0 (ν). We also explore simple power-law models for the ionizing background, which are equivalent to the ‘ table power law slope α ’ command within cloudy , where f (ν) ∝ ν α . We assume that the distributions of gas and dark matter are spherically symmetric. Under this assumption, gas at a distance r from the centre of a dark matter halo is irradiated by background photons from all directions. The radiation field is therefore attenuated by a different amount depending on the density distribution of the gas along a given direction. If J 0 (ν) represents the unattenuated radiation field at a frequency ν, and 2πsin (θ)dθ/4π is the fraction of sky with an optical depth τ(ν, r , θ), then the intensity of the radiation field at a distance r from the centre of the cloud is given by where μ = cos θ, and i corresponds to every element/ion stage that we consider in this work. Unfortunately, our calculations are computationally too demanding to include every ionization stage for all elements with atomic number 30 (unlike cloudy ). We have therefore incorporated only the most abundant metals that are commonly observed in metal-poor DLAs, including H i , D i , He i , He ii , C i –C iv , N i –N iv , O i –O iv , Mg i –Mg iv , and Si i –Si iv . We have adopted the photoionization cross-section, σ i (ν), of each element using the compilation by Verner et al. ( 1996 ). At a distance r from the centre of the halo, the column density of species i in the direction θ can be calculated by integrating the volume density of species i, n i ( R ), from a radial distance r to the virial radius 2 (i.e. integrate along the path defined by the dashed line in Fig. 1 ): where equation ( 12 ) is used for 0 ≤ θ ≤ π/2 and equation ( 13 ) is used for π/2 θ ≤ π. The rate of primary ionizing photons at a given radius from the cloud centre of each species is then where h ν i is the ionization energy 3 of ion i . Each radiation field considered in this work is finely interpolated around the ionization energy of each ion to ensure numerical accuracy in the integrations. Figure 1. The coordinate system used to calculate the angular dependence of the column density of each species at a given radial coordinate (see equations 12 and 13 ). The rate of collisional ionization, Γ ci ( T ), is incorporated in our models using the Dere ( 2007 ) rate calculations.


range of 60–80 kpc. Similar numbers have been found by Zhang et al. ( 2019 ) from the analysis of about 300 galaxy clusters at redshift 0.2 z 0.3. These authors described the BCG+ICL radial profile by using a triple Sérsic model and found a dominant core in the innermost 10 kpc, a bulge between 30 and 100 kpc and the ICL that dominates the distribution beyond 200 kpc, but already outside 100 kpc the profile transitions from the BCG to the ICL. They suggested that this transition is a potential cut between the two components, in good agreement with Pillepich et al. ( 2018 ) who noticed that simulated halos more massive than 5 × 10 14 M ⊙ have more ICL mass outside 100 kpc than within. All the values of the transition radius, i.e., the radius at which the ICL starts to become the dominant component, reported above are comparable with the range predicted by our model. We stress again that a wide range of possible values of R transition is preferable to a narrow one for the reasons discussed above. It strongly depends on the morphology of the BCG, on the amount of ICL with respect to the other components, and on the dynamical state of clusters, which reflects the merging history of the BCG+ICL system and thus its evolution with time. 5. Conclusions Following the analysis done in our recent paper (Contini Gu 2020 ), we have further improved our model by assuming that the radial mass distribution of a BCG+ICL system can be described by the sum of three profiles: a Jaffe profile for the bulge, an exponential disk, and a modified NFW for the ICL. We have taken advantage of a wide sample of simulated galaxy groups and clusters from our state-of-the-art semianalytic model to study the innermost ∼100 kpc of BCG+ICL systems. Unlike the model used in our previous study, the new one offers the opportunity to go below 100 kpc since bulge and disk are treated separately. The main goals of this study were to confirm that our model can reproduce several observed relations between the stellar mass at a given radius and the total BCG+ICL/halo mass, at different redshift and, give an idea of where the transition between the BCG and the ICL happens, i.e., when the ICL component starts to dominate the total distribution. In light of the analysis done and the overall discussion, we conclude the following: 1. The radial mass distribution of a BCG+ICL system can be described by the sum of three profiles: a Jaffe profile for the bulge, an exponential disk, and an NFW-like profile for the ICL. The model can reproduce several observed scaling relations between the BCG+ICL stellar mass within a given aperture and the BCG+ICL/halo mass, at different redshift with an overall precision below 0.05 dex at z = 0 and 0.3 dex at z ≳ 0.5 along the wide stellar mass/halo mass ranges probed. 2. In good agreement with recent observational studies, our model predicts that R transition , i.e., the radius at which the radial distribution of BCG+ICL systems transitions from the BCG to the


; Boylan-Kolchin etal. 2012 ), and rotation curves (van der Marel Kallivayalil 2014 ). 2.4 Likelihood from <italic>V</italic>max distributions Here, we summarize the statistical method for comparing the observational and simulated V max distributions. It is identical to that of Jiang van den Bosch ( 2015 ) except where noted below. The goal is to determine the probability that the Milky Way satellite V max function can be drawn from the distribution of simulated functions. We will establish the statistical scatter between the simulated V max functions, and calculate the mean deviation between the measured Milky Way V max function and the simulated systems. The size of the measured V max function deviation relative to the size of the scatter will tell us about how readily the Milky Way V max function is realized in each of our models. The first step is to define the variation within the set of V max for a given halo mass-dark matter modelgalaxy formation model combination. The n most massive satellites of the i th simulated halo are selected, and their values of V max are sorted into descending order. The V max distribution is then { V i , 1 , V i , 2 , V i , 3 V i , n }; here we have omitted the max subscript for clarity. We can define the difference between this i th halo distribution with respect to the j th halo distribution thus: and if there are N realizations of the model in question, the mean Q for the i th distribution, , is Similarly, if we substitute the i th simulated V max distribution to instead be { V MW, 1 , V MW, 2 , V MW, 3 V MW, n }, i.e. the observed V max distribution of the Milky Way satellites, then we obtain Q MW : The probability that a V max function with Q MW could be drawn from the parent distribution is then P ( Q MW ), where P is the cumulative distribution of . We expand on the method described above to describe how we select satellites. The luminosities calculated for the satellites enable us to take account of the fact that the brightest satellites, for which the velocity dispersions have been measured with the highest precision, need not necessarily reside in the most massive haloes. Therefore, we consider two options for selecting our top n satellites to be matched to observations: (i) select the n brightest V -band satellites and (ii) select the n highest V max satellites. We compare the results from these two approaches in Section 3.1.3 . 2.5 Sterile neutrino matter power spectra In addition to CDM, we consider keV-scale, resonantly produced sterile neutrino dark matter. The latter constitutes part of a larger particle physics model called the neutrino minimal standard model (MSM), which explains neutrino oscillations and baryogenesis in addition to yielding a dark matter candidate, see Boyarsky, Ruchayskiy Shaposhnikov ( 2009 ) for a review. The keV sterile neutrino behaves like WDM, in that it free streams out of small perturbations in the early Universe. The resulting matter power spectrum


of galaxies with high SFRs/luminosities to the CSFRD/total IR luminosity decreases much flatter. This discrepancy reflects the tension between the SFRFs of the EAGLE reference model and IR constraints. The later imply larger number densities of objects with SFR ∼ 10–100 M ⊙ yr −1 (Section 4.1 ) at z 2, and the disagreement with the L100N1504-Ref run increases with time. In Section 6 we will see the important role that feedback plays on keeping the number of these extremely high star-forming objects low at these redshifts. 5 THE CONTRIBUTION OF HALOES WITH DIFFERENT MASSES TO THE SFRF AND CSFRD In this section we present the contribution of haloes with various masses to the CSFRD (Fig. 4 ), the number density of haloes of different masses at different redshifts (Fig. 5 ) and their contribution on the SFRF (Fig. 6 ) in the EAGLE L100N1504-Ref run. Figure 4. CSFRD contribution of haloes with different masses in EAGLE. Below redshift 5 objects with masses M halo = 10 11–12 M ⊙ dominate through their high efficiencies besides their low numbers (Fig. 5 ). Figure 5. Left-hand panel: evolution of the number of haloes with different masses in the L100N1504-Ref. Haloes with low masses are numerous even at high redshift while higher mass objects (e.g. M halo ∼ 10 11–13 M ⊙ ) form with high rate up to redshift z ∼ 1.5. Right-hand panel: percentage of star-forming haloes at different masses. Haloes with M halo ∼ 10 11–12 M ⊙ are typically star forming at all redshift. Figure 6. The contribution of dark matter haloes to the SFRF (black stars) for redshifts z ∼ 8.0 (top left-hand panel), z ∼ 4.0 (top right-hand panel), z ∼ 2.0 (bottom left-hand panel) and z ∼ 0.1 (bottom right-hand panel). Galaxies with SFR ≥ 1 M ⊙ yr −1 reside in large haloes M halo ∼ 10 11–12 M ⊙ even at z ∼ 4.0. These haloes represent only ∼1 per cent of the total star-forming population at this era. In the local Universe the number of massive haloes M halo ≥ 10 11 M ⊙ is significantly higher than that of z ∼ 4. They dominate almost entirely the SFRF at SFR ≥ 0.1 M ⊙ yr −1 . Behroozi, Wechsler Conroy ( 2013 ) and Moster, Naab White ( 2013 ) argued that haloes near 10 12 M ⊙ are the most efficient at forming stars at all redshifts with the baryon conversion efficiency ( M ⋆ / M baryon ) dropping rapidly at both higher and lower masses. In addition, the stellar to halo mass ratio also peaks at 10 12 M ⊙ (Behroozi et al. 2013 ). However, in the paradigm of hierarchical structure formation, small haloes form earlier than larger ones, which need some time to emerge. In Fig. 4 we see that at z ≥ 5 the CSFRD is dominated by relatively small haloes of mass M halo = 10 9–10 M ⊙ . 5 The left-hand panel of Fig. 5 reveals that the number of objects of this mass interval is high. In addition, the right-hand panel of the same figure, where we present the percentage of star-forming haloes at different masses (i.e. n haloes, SFR > 0 / n haloes, total ), shows that a large percentage (>50 per


10 and 15 per cent, respectively. Figure 2. Distribution of the resultant distance uncertainties of the catalogued PGCCs. In Fig. 3 , we compare our newly derived extinction distances with the kinematic values deduced by Zhang et al. ( 2018 ). In general, the newly estimated extinction distances differ significantly from the kinematic ones. Amongst the sample objects, 10 clumps have similar kinematic distances ( d Z18 ∼ 0.46 kpc), as they all have similar radial velocities (8.0 or 3.0 km s −1 ). However, their directly measured extinction distances range from 0.21 to 0.51 kpc. It is quite possible that the peculiar and non-circular motions of the clumps may have significantly affected the calculation of their kinematic distances (Liszt Burton 1981 ; Gómez 2006 ; Reid et al. 2009 ). For some PGCCs, such as G176.17-02.10 and G177.14-01.21, the differences between the two sets of distances are very large. The kinematic distance probabilities of those clumps derived with the Bayesian Distance Calculator (see table 1 of Zhang et al. 2018 ) are very small (less than 0.5), indicating that those kinematic distances are poorly constrained. Figure 3. Comparison of our extinction distances with their kinematic values from Zhang et al. ( 2018 ). In the left-hand panel, the black dash line denoting complete equality is used to guide the eyes. 5 DISCUSSION The improved distance estimates allow us to revise some of the distance-dependent physical properties of the cores of the PGCCs, such as their radii, masses, and the virial parameters. We update those physical parameters by simply rescaling the results of Zhang et al. ( 2018 ). For example, effective radius R eff of a Planck core is proportional to distance d , R eff ∝ d . Thus the revised radius is evaluated as Similarly, the revised mass M ′ is given by We note that these updates also lead to changes of other parameters, such as the virial parameter, which is given by Fig. 4 plots the space distribution of these 61 PGCCs in the X – Y space with both the original kinematic distances and our updated distances, where the distance changes are indicated. According to the formula (3) and (4), we present the changes of these physical quantities in Fig. 5 . From the histograms in the left-hand panel of Fig. 5 , we find that on the whole the radii and masses calculated with the new extinction distances tend to be smaller than those of Zhang et al. ( 2018 ), by respectively ∼ 17.9 and 32.6 per cent. This leads us to conclude that to understand the local molecular structures, accurate distances are necessary. We use an MCMC algorithm to fit the mass–radius relation for both sets of distances. The new distances yield a slope of 1.95 ± 0.09, comparable to 1.93 ± 0.09 obtained with the kinematic distances. In spite of the significant changes, the slope is largely unaffected. The result is understandable, considering that a change in the distance measurement leads to changes in both mass and size estimates. Since the


of all bodies to zero. We also fixed the orbital period of the planet–moon barycenter to 287.378949 days (the best fit from TK18 ). We elected not to vary the period of the planet–moon barycenter because it is poorly constrained from a single transit observation. A longer period would cause a longer transit duration for the planet, but this could equivalently result from a smaller impact parameter, a larger star, or a massive moon that significantly perturbs the planetary orbit. We used the following priors: the stellar radius was normally distributed, R * ∼ N (1.81, 0.17) R ⊙ (see the next section). The planet radius was uniform from 8 to 14 R ⊕ . The planet transit time was uniform over the timespan of the observations, and inclination was uniform from 0° to 90°. The planet mass was log-normally distributed, M p ∼ 10 2.5±0.5 M ⊕ , based on the expectation for Jupiter-radius objects from Ning et al. ( 2018 ). For the moon model, we allowed the transit time to vary uniformly over the entire visit. The moon period was uniform between 1.6 and 260 days. These limits span the duration of the HST observations (so there is one possible moon occultation event), to the orbit at 0.5 the Hill radius, based on the stability limit for prograde moon orbits (Domingos et al. 2006 ). The Hill radius calculation assumed that the planet and stellar masses are 1 M Jup and 1.37 M ⊙ . The moon mass varied uniformly from 0 to 30 M ⊕ . The longitude of the ascending node was also uniform from 0° to 360°. The moon inclination was uniform from 0° to 90°, and was defined relative to the line of sight. We assigned zero prior probability to scenarios where the moon did not transit or experienced a grazing transit. We made this choice to put an upper limit on the radius of a fully transiting moon; for grazing transits or non-transits the moon radius could be arbitrarily large. 3.1.1. Stellar Parameters For both the moon and no-moon scenarios, we used a quadratic stellar limb-darkening law and fixed the coefficients to the prediction for a 5700 K, solar metallicity PHOENIX model from Espinoza Jordán ( 2015 ); u 1 , u 2 = [0.216, 0.183]. We estimated the host star parameters using the Gaia second data release (DR2) parallax (Gaia Collaboration et al. 2016 , 2018 ) along with UBV photometry from Everett et al. ( 2012 ) and JHK photometry from the Two Micron All-Sky Survey (Skrutskie et al. 2006 ). We employed the isochrone python package (Morton 2015 ) with the Dartmouth isochrone grid (Dotter et al. 2008 ) to obtain posterior constraints on the stellar parameters. The resulting parameters indicate that Kepler-1625 has stellar mass M ⊙ , radius R ⊙ , and age Gyr. In our analysis, we fixed the stellar mass to the best-fit value (1.37 M ⊙ ), and used a Gaussian prior on the radius, R * ∼ N (1.81, 0.17). 3.2. Instrument Systematics Model There are two systematic trends in the data. One is the orbit-long ramp, attributed to charge traps in the detector filling up over the orbit


results, the most important one being that due to the photoelectric charging. This is further illustrated below. Two typical runs, though limited to 100 grains for each a value and with integration times of only 0.1 Myr for clarity, are illustrated in Figs. 4 and 5 . The spread of the orbits into broom-like structures is entirely due to the turbulence; if v turb is set equal to 0 the orbits collapse to a single vertical line. It is obvious from these figures that the choice of initial conditions for the velocity is important for the orbits, although the fraction of grains falling into the star as a function of grain radius is not as dependent on these conditions. Fig. 4. The orbits of grains over 10 5 yr, from a point indicated by an “ x ” in black along the z axis at a distance of 10 4 AU from the star (which is at the origin of the coordinate system), and with different grain radii a as indicated by the different colours. The dust grains were given an initial velocity identical to the gas free-fall velocity. The turbulent mean speed was set to 0.1 km s −1 . We note that the scales of the x and y axes are different from that of the z axis. Fig. 5. The orbits of grains over 10 5 yr, from a point indicated by an “ x ” in white along the z axis at a distance of 10 4 AU from the star (which is at the origin of the coordinate system), and with different grain radii a as indicated by the different colours. The initial velocity of the dust grains was set to zero. The turbulent mean speed was set to 0.1 km s −1 . We note that the scales of the x and y axes are different from that of the z axis. The main results of these numerical experiments are displayed in Fig. 6 . Here we have plotted a quantity called “the defect”, D ( a ), of the run, as a function of a for different choices of the defining parameters. D ( a ) measures the fraction of grains that leave the proto-solar cloud as a result of the radiative cleansing. It is defined as where N l is the number of dust grains lost inside 100 AU, and N 0 is the corresponding number lost in a run with identical parameters with the exception that the stellar luminosity L is set equal to zero. In this way, we try to correct for the fact that even at zero luminosity some of the gas may depart at high turbulence speeds from the stellar neighbourhood. It is seen from the figure that the variation of D with a is smoothed when v turb increases, from a very steep change when a passes the limiting value in Eq. ( 9 ) for small turbulence, to a less steep variation. We also note that an increased inflow of gas decreases the deficit at a given a , as does a change of the initial condition from v ( r 0 )=0 to setting v ( r 0 ) equal to the free fall velocity of the gas flow. Also, the coulomb forces diminish D but not drastically so. None of these effects is unexpected. Obviously, these variations of the deficit with the different parameters are not very dramatic: the conclusions concerning the cleansing effects in


of the blended line intensities of Fe xiii and Fe xii in the analysis of EIS spectra, we applied the same method to the Fe xvii line complex around λ 204.6 Å in the LHD spectra to unblend the Fe xiii and xii line intensities. The results are summarized in Figure 5 . The time evolution of the electron density for low-temperature LHD peripheral plasmas is plotted in Figure 5 (a), where the electron density ( n e ) is estimated to be log n e (cm −3 ) ∼ 10.5–11.8 after the NBI controls, slightly higher in the later phases of discharge. The estimated electron densities are somewhat lower than those measured by Thomson scattering at t = 4.3 s and t = 4.9 s (see Figure 2 of Murakami et al. 2014 ), but these line intensity ratios of Fe xii and xiii are located in the range that is close to the high-density limit, and the apparent large difference in the absolute n e values derived from Fe xii and Fe xiii does not affect the estimation of the blended Fe xiii/xii line intensities much, and therefore is negliglible in the following analysis results. Figure 5. (a) Electron densities for the LHD plasma plottted against time since the discharge of shot 107,802. The line types are the same as in Figure 4 (b). (b) Reduced Fe xvii line ratios by unblending the contributions of the Fe xii and xiii lines. The horizontal thin dotted line indicates the line intensity ratio averaged at the eight epochs in discharge 107,802. Error bars show photon noise ranges only. We take this contribution of the Fe xiii emissions to the emission line intensity at 204.6 Å into account and plot the Fe xvii λ 204.6/ λ 254.8 ratios against time after the start of discharge in Figure 5 (b). No lines are assumed to be blended in the Fe xvii λ 254.8 line, and a common electron density is assumed for the Fe xii/xiii emitting plasmas. The measured ratio is reduced to 20%–30% as a result of subtracting the Fe xiii line contribution, and the average value (∼1.12) is very close to the theoretically predicted constant vlaue of ∼1.1, although the temporal variation, henceforth, the temperature dependence of the line ratios, could not be completely eliminated in this analysis. The average value at the four epochs ( t = 4.8–5.4 s) is rather close to ∼1.3, when the line complexes at 204.6 Å are the strongest and the electron temperatures are the lowest during the discharge. 4. Discussion and Summary The Fe xvii line intensity ratios obtained from the solar active region in Section 2.3 and the LHD experiment are plotted against electron temperature in Figure 6 , in which the revised sensitivity proposed by Del Zanna ( 2013 ) is adopted for the EIS radiometric calibration. The LHD experimental results clearly show that the Fe xvii line branching ratio of λ 204.6/ λ 254.8 is close to the theoretical value of ∼1.1, which means that the revised in-orbit EIS sensitivity calibration (Del Zanna 2013 ; Warren et al. 2014 ) makes the solar data consistent with the laboratory data. The apparent


with the yellow shades. The light-gray shades represent the 3 σ noise levels. The dark-gray shades present the wavelength range of bright sky lines and bad pixels. Left: HETDEX Fiber positions atop the broadband images taken with CFHT/MegaCam or HST/WFC3. The red, blue, green, and yellow circles present the positions and the sky coverage of the fibers used for the measurements of the LAE spectra. Figure 17. Same as Figure 11 , but for the H i radial profile around LAE1–4 in the the extreme QSO overdensity EGS–QO1 (red circles). The blue and black circles are the H i radial profiles of LAEs in the blank fields: the blue circles are the remaining 22 EGS LAEs that reside outside of the EGS–QO1 (i.e., EGS outside), and the black circles are the COSMOS LAEs. A significant H i transmission underdensity is identified around LAE1–4, which is similar to the one around the QSOs in EGS–QO1 (Figure 15 ). We find that one of the four LAEs, LAE4, shows triple-continuum components over the scale of a 10 pkpc radius circle on the HST F814W/F160W images of the EGS, indicative of a triple merging system (middle/bottom panels of Figure 18 ). LAE4 is located at (R.A., decl.) = (14:19:13.02, +52:49:11.2) near the center of the ionized bubble of EGS–QO1 (bottom panel of Figure 13 ). The average Ly α redshift of LAE4 over the HETDEX fibers is , and the total Ly α luminosity over the fibers is erg s −1 . The top panel of Figure 18 presents the spectrum of LAE4, summed over the fibers, which is the same as the one in Figure 16 . The spectrum of LAE4 has a broad Ly α emission line whose FWHM is ∼1100 km s −1 (about 3 times broader than the instrumental resolution), possibly suggesting a type I AGN (e.g., Kakuma et al. in preparation). 24 24 Other AGN features of high-ionization emission lines, C iv and He ii , are not detected in the LAE4 spectrum shown in Figure 16 . This is probably because the LAE4 is optically faint (∼25 mag) and its metal lines are too faint to be identified. The bottom panel of Figure 18 presents the positions and the sky coverage of the fibers used for the measurements of the LAE4 Ly α redshift and total luminosity and indicates that three fibers cover the triple-continuum components with the blue, green, and yellow circles. The spectra of these three fibers are shown on the right-hand side in Figure 18 . All of the three fiber spectra of the blue, green, and yellow circles have Ly α emission lines at , suggesting that the three objects probably reside at the same redshift. Moreover, these three fiber spectra have broad Ly α emission lines with an FWHM of ∼1000 km s −1 . Although each of these fibers does not separately cover one of the triple-continuum components, whose blending due to the HET image quality and large fiber diameter may produce apparent broad lines, these broad Ly α emission lines found in the different positions over the triple-continuum components imply that the LAE4 system could be a merging type I AGN doublet or


Figure 8. Galaxy stellar mass function at z = 0 for simulations with different black hole feedback parameters, including (i) no feedback (grey), (ii) v out = 10 3 km s −1 and (blue; fiducial simulation), (iii) v out = 10 4 km s −1 and (green), and (iv) v out = 10 3 km s −1 and (red). Error bars show cosmic variance estimates computed as the standard deviation over the eight sub-octants of the simulated volume. Black points connected by a dashed line show the observed stellar mass function from Baldry et al. ( 2012 ). Quasar mode feedback alone is not sufficient to reproduce the observed galaxy mass function, either at low or high masses. 4.4 Mass dependence of black hole feedback effects Fig. 9 shows in more detail how the effects of black hole feedback depend on galaxy stellar mass. We cross-match galaxies between simulations based on the unique ID of the particles they contain at z = 0. Each galaxy is matched to the galaxy that contains the largest number of common star particles, which we use to compute the stellar mass of galaxies in simulations with black hole feedback relative to the no-feedback simulation. Figure 9. Mass-dependent effects of galaxy-scale black hole feedback. Left: ratio of the stellar mass of galaxies at z = 0 in simulations including black hole feedback to the stellar mass of the corresponding galaxies in the no-feedback simulation as a function of stellar mass. Different colours indicate simulations with different outflow velocity and momentum flux. Solid lines and shaded regions indicate median and 10 per cent–90 per cent percentile ranges. Right: same as left for black hole masses. Black hole feedback appears to be more effective in galaxies with mass M ⋆ ∼ 10 10 M ⊙ for outflows with velocity v out = 10 3 km s −1 , while the mass suppression efficiency increases to higher mass galaxies for simulations with v out = 10 4 km s −1 . The overall effect of feedback on the growth of black holes and galaxies is qualitatively similar. Black hole feedback in our simulations with v out = 10 3 km s −1 is more effective at suppressing star formation and black hole growth in galaxies in the mass range M ⋆ ≈ 10 9 –10 11 M ⊙ at z = 0. This trend with M ⋆ , already present at z = 2, suggests that black holes in lower mass galaxies have not coupled enough energy to affect their host galaxies from the time of seeding down to z = 0 (which may be sensitive to our seed model), while outflows with v out = 10 3 km s −1 may not be sufficient to unbind gas in galaxies at the highest masses. With the same momentum flux and v out = 10 4 km s −1 , the results are similar at low M * but the mass suppression efficiency keeps increasing towards high masses, giving a ∼60 per cent reduction of the stellar mass of galaxies with M ⋆ ≳ 10 11.5 M ⊙ by z = 0. As expected, our simulation with v out = 10 3 km s −1 and yields the strongest suppression of stellar growth at all masses, but the efficiency follows a trend with M ⋆ similar to that of the


rays, and calibrate the absolute flux to reduce the raw SAMI observations (Allen et al. 2015 ). Each galaxy field was observed in a set of approximately seven 30 minute exposures that are aligned together by fitting the galaxy position within each hexabundle with a two-dimensional Gaussian and fitting a simple empirical model describing the telescope offset and atmospheric refraction to the centroids. The exposures are then combined to produce a spectral cube with regular 05 spaxels, with a median seeing of 21. More details for Data Release 1 and Data Release 2 reduction can be found in Green et al. ( 2018 ) and Scott et al. ( 2018 ), respectively. 2.2. Sample Selection The GAMA group sample includes all galaxy associations with two or more members, so to ensure the robustness of our group sample, we first select all SAMI observed galaxies that belong to GAMA halos with at least five members to ensure that they have a robustly estimated velocity dispersion (Robotham et al. 2011 ). Moreover, only galaxies classified as cluster members by Owers et al. ( 2017 ) are taken as cluster galaxies. This gives us an initial sample of 574 galaxies (out of a potential 2502 observed by GAMA) in 205 groups in the GAMA regions and 861 galaxies in eight clusters. Stellar population measurements are compromised for 100 galaxies because nearby galaxies or stars affect their observation (van de Sande et al. 2017 ). In addition, we also exclude three more galaxies whose g − i colors suggest contamination from other objects in the field of view and eight galaxies whose annuli do not reflect the shape of their isophotes and/or the central bin is not well aligned with the peak of their flux map (since they could lead to a biased gradient). In this paper, we are particularly interested in whether the evolution of central and satellite galaxies has an environmental dependence. We focus on the passive central galaxies to ensure a like-to-like comparison in determining how their central and satellite status affects their stellar population gradients. We use the SAMI spectroscopic classifications presented in Owers et al. ( 2019 ) to select a homogeneous sample. The galaxies are classified as star-forming, passive, or H δ -strong using the absorption and emission line properties of each SAMI spectrum. We select 843 passive galaxies; of these, 98 are central and 745 are satellite galaxies (Figure 1 ). Figure 1. Distribution of g − i color with stellar mass as a function of galaxy classification for the galaxies included in SAMI v0.11. Unselected passive galaxies are shown as green crosses. Galaxies selected in the final sample are shown as red crosses, and nonpassive galaxies are shown as black crosses. The dotted line is the stellar mass cut at ; galaxies below this mass are excluded from the final sample. To ensure the stellar population measurements we use are reliable, we exclude all galaxies with masses less than , owing to the low signal-to-noise ratio (S/N) and


while the dark matter distribution in the interior of the halo hardly changes at low redshift (Prada et al. 2006 ; Diemand, Kuhlen Madau 2007 ; Cuesta et al. 2008 ). Recently More, Diemer Kravtsov ( 2015 ) proposed that the best physically based definition of halo radius is the ‘splashback radius’ R sp ≈ 2 R 200m , where there is typically a sharp drop in the density; using this definition, there is actually more halo mass increase than for R vir , R 200m , or R 200c . What is actually relevant to star formation of the central galaxy in the halo is the amount of gas that enters the halo and eventually reaches its central regions. Wetzel Nagai ( 2015 ) have used adaptive refinement tree (ART) hydrodynamic galaxy simulations with a best resolution of about 0.5 kpc to show that infalling gas decouples from dark matter starting at about 2 R 200m and roughly tracks the growth of M 200m . Thus, they argue that pseudo-evolution is relevant to the accretion of dark matter, but not to that of gas. Further evidence that the gas falling into the central regions of haloes roughly tracks the halo MAR is provided by Dekel et al. ( 2013 ), who used a suite of ART hydrodynamic zoom-in galaxy simulations with M vir /10 12 M ⊙ = 0.1 to 2 at z = 2 and best resolution of 35 pc, and found that the gas inflow rate is proportional to the halo MAR, with about half the gas penetrating to 0.1 R vir at redshifts from z = 4 to 2, and with the fraction increasing from z = 2 to 1. Analysis of a subsequent suite of ART hydrodynamic zoom-in galaxy simulations with better resolution and feedback showed that these simulated star-forming galaxies grow stellar mass at the same rate as the specific halo mass increase (Tacchella et al. 2015 ; Zolotov et al. 2015 ). A similar result has been reported in González-Samaniego et al. ( 2014 ) for galaxies formed in haloes of . Star-forming galaxies are known to show a tight dependence of SFR on stellar mass, which is known as the ‘main sequence’ of galaxy formation (Daddi et al. 2007 ; Elbaz et al. 2007 ; Noeske et al. 2007 ; Salim et al. 2007 ), in analogy with the tight dependence on stellar mass of the properties of stars on the stellar main sequence. Dark matter haloes also have an MAR that is roughly proportional to their mass, and we show in Section 2.1 of this paper that the dispersion of the halo MAR at a given halo mass is 0.3 to 0.4 dex, similar to the dispersion of the SFR on the main sequence. It was this equality that originally motivates us to examine more closely the connection between mass accretion and star formation. Our analysis is limited to the connection between distinct haloes and central galaxies only. One reason is that subhaloes lose mass via tidal stripping, resulting in negative values of accretion rates (see e.g. van den Bosch, Tormen Giocoli 2005 ). Satellite galaxies are also affected in other ways by their proximity to central galaxies. Therefore, studying the connection between subhalo mass accretion


in our model to reproduce the free–free continuum spectrum flattening near 2 mm and the surface brightness depression at the center in the continuum and mm-RRL maps. We estimate average electron temperatures of T e ~ 8000–11 000 K and densities in the range n e ≈ 10 7 –10 6 cm −3 in the ionized core of MWC 922. A density radial law n e ∝ r −2.7 , and a smooth variation with the latitude (decreasing from the disk outer boundary to the poles) is inferred. The density radial law could be slightly shallower than adopted, as suggested by the H39 α cubes, which show that the emission from this transition arises at slightly larger distances from the center than predicted by our model. We deduce a mass-loss rate of the fast bipolar wind of Ṁ fast ~ few × 10 −6 M ⊙ yr −1 . Assuming that a slow wind is also present at intermediate latitudes (i.e., bridging the ionized surface of the rotating disk and the fast bipolar wind), we obtain a mass-loss rate of Ṁ slow ~ few × 10 −7 M ⊙ yr −1 . The dynamical age of the winds traced by our observations is a few decades at most, with the innermost layers of the fast wind (at ~29–51 au) ejected just ~1.5–2.6 yr ago. The total ionized mass deduced from the free–free continuum emission at millimeter wavelengths is M H II ~ 2 × M ⊙ . The dominant mass component in the close environment of MWC 922 is probably that probed by the ~160 K dust millimeter continuum emission, from which we deduce ~ 8 M ⊙ . In Sect. 5 we discuss the evolutionary status of MWC 922 from different perspectives and provide a number of arguments that favor a post-main sequence stage. We believe that MWC 922 could be a ~15 M ⊙ blue giant (with T eff ~ 20–30 kK and L ⋆ ~ 5.9 × 10 4 L ⊙ ) located at d ~ 3 kpc that has recently left the main sequence (~10 Myr ago) and is probably undergoing a phase of mass exchange with an unseen companion. Appendix A Additional figures The Band 3and Band 6 continuum emission maps of MWC 922 obtained with 15 and 30 mas-resolution, respectively,are shown in Fig. A.1 . We note the X-shaped morphology, reminiscent of that of the near-IR andmid-IR nebulosities around MWC 922 (Sect. 1 ). The predictions from our model, which is described in Sect. 4 and is schematically represented in Fig. 6 , are shown in Fig. A.2 with the same angular resolution. The equatorial plane of the disk is oriented along PA ~ 45°. The velocity-channel maps of the H30 α and H39 α lines towards MWC 922 are presented in Figs. A.3 and A.4 , respectively. In Fig. A.5 a summary of the observational results for the weak non- α mm-RRLs detected in MWC 922 together with our model predictions is offered. In Figs. A.6 and A.7 we summarize the comparison between data and model for the H30 α and H39 α transitions with super-resolution (15 and 30 mas, respectively). For H30 α , we also display the predictions given by a model where rotation has been suppressed in the fast wind to show that when there is no rotation of the fast wind, the peaks of the red- and


on the Reynolds number. We select the dependence appropriate for spherical grains. For better comparison of the coupling between dust particles with a certain size and the disk gas, the dimensionless Stokes number is defined asParticles with Stokes number of unity come to match the gas velocity in one local orbital period. For a wide range of gas densities, submicrometer dust grains have and hence come quickly to rest in the gas reference frame. The dust scale height ( h d ) in a turbulent protoplanetary nebula can be calculated following Dubrulle et al. ( 1995 ) and Youdin Lithwick ( 2007 ):For tightly coupled particles with , h d ≈ h g , and we approximate the dust scale height by that of the gas at t = 0. To model the dust size distribution at t = 0, we adopt a grain-size distribution with an MRN (Mathis et al. 1977 ) power-law index, , where N ( a ) da is the number of dust particles of radii between . We consider that dust grains already grow beyond the ISM size in the molecular cloud phase (Suttner Yorke 2001 ) and adopt the maximum and minimum sizes of the dust size distribution at t = 0 as a max = 1.0 μ m and a min = 0.1 μ m. To begin our grain growth and settling simulation, we make two assumptions: 1. Gas and dust of all sizes are dynamically coupled and well mixed at t = 0, with (this will not be true at later times); 2. The dust to gas mass ratio is η = 0.01, similar to the ISM. 3. Dust Evolution Model The main objective of this work is to obtain the disk temperature profile, which is controlled by the dust opacity. To simulate dust evolution, we introduce a hybrid model in which the collisional dust growth is implemented through a weighted Monte Carlo method along with a Lagrangian Monte Carlo prescription for vertical settling and diffusion. 3.1. Collision Model The outcome of a modeled collision between two dust particles in a protoplanetary environment has many possibilities according to laboratory experiments. On the experimental side, Güttler et al. ( 2010 ) presented 19 possible collisional outcomes for particles with various mass ratios, speeds, and porosities. However, it is prohibitively computationally expensive to include all possibilities in a global disk model. For simplicity, we adopt a collisional model that includes only sticking and fragmentation. We treat collisions as a binary process, identifying the smaller mass as the projectile and the bigger mass as the target . The collision outcome is determined by the relative velocity (see Section 3.2 for a description of our velocity computation). If the particles collide with a velocity less than a threshold velocity v frag , they stick and form a new particle with mass . When , the collision results in fragmentation. As particles grow by sticking, their eddy-crossing times drop, leading to lower coupling with the gas and higher collision speeds (Ormel Cuzzi 2007 ). When the collision speed reaches v frag , instead of sticking, both particles fragment. For such an


of solids, α tur . The previous work assumed α acc = α tur . We will show that Drift-BKR and Diff-BKR of silicate grains are the most essential factor for the occurrence of the runaway pile-up of silicate grains and that of icy pebbles is also resulted in by Diff-BKR. The ratio between α tur and α acc controls relative importance between the runaway pile-up of silicate grains inside the snow line and that of icy pebbles outside the snow line. We map the parameter regions of F p/g and α tur ∕ α acc for GI (runaway pile-up) of silicate grains, GI of icy pebbles and SI of the icy pebbles. In Sect. 2 , we describe our basic set-ups of numerical appro- aches. In Sect. 3 , we present our numerical results. In Sect. 4 , we discuss the results. In Sect. 5 , we summarize our paper. 2 Numerical methods In this section, we discuss our numerical methods and models. 2.1 Gas disk model In this paper, we use classical α -accretion disk model ( Shakura Sunyaev 1973 ; Lynden-Bell Pringle 1974 ) where the surface density of the gas is expressed as a function of the gas accretion rate Ṁ gas and the effective viscosity ν acc as and ν acc is written using the sound speed c s , the Keplerian orbital frequency Ω and the dimensionless effective viscous parameter α acc given as The above equation assumes a steady state of the background gas. When the gas accretion is dominated by the viscous diffusion, α acc equals the dimensionless turbulence parameter α tur . In contrast, when the gas accretion is regulated by the disk wind-driven accretion ( Bai et al. 2016 ; Suzuki et al. 2016 ), generally α acc is larger than α tur ( Armitage et al. 2013 ; Hasegawa et al. 2017 ). The isothermal sound speed of the gas is written as where k B is the Boltzmann constant, μ gas is the molecular weight of the gas and T is the temperature of the gas. In this paper, the temperature profile is fixed as We note that our disk is somewhat a hot disk but we chose this profile so that we can directly compare with the previous work ( Schoonenberg Ormel 2017 ). Under the above conditions, the gas scale height is written as The midplane gas density is . In this paper, we assume that the above gas profile is unchanged through the simulation and thus μ gas = 2.34 m proton , where m proton is the proton mass. The accretion velocity of the gas v gas is written as where a negative value indicates radial drift to the central star. 2.2 Radial motions of solids and vapor In this work, we describe a pebble as the mixture of many micron-sized silicate grains covered by water ice that is also used in the previous paper (see “many-seeds pebble model” in Schoonenberg Ormel 2017 and the models used by Saito Sirono 2011 and Ida Guillot 2016 ). In our one-dimensional calculation, we adopt the single-size approximation ( Ormel 2014 ; Sato et al. 2016 ) where the pebble size is represented by a single size depending on the radial distance r , and solve the system integrated over the vertical direction of the disk


ocean with a depth of 50 m everywhere; no continent is considered. Sea ice is allowed to form when the surface temperature is below the freezing point (271.35 K), and the albedos of sea ice and snow depend on the stellar spectrum. For the visible band (0.7 μ m), the snow albedo is 0.80 and the ice albedo is 0.67. For the near-infrared band (>0.7 μ m), it is 0.68 for snow and 0.30 for sea ice. Neither oceanic dynamics nor sea ice dynamics are included in the simulations. By default, the time step of the experiments is 30 minutes, except for the f05_L26, f19_L51, and f19_L74 experiments, within which the time step is 15 minutes to avoid numerical instability. Each experiment was run for tens of Earth years until the sea ice and surface temperature reach equilibrium and the global-mean net energy imbalance at the top of the atmosphere (TOA) is within 1.0 W m −2 . Averages of the last 5 or 10 Earth years were used here. 3. Results 3.1. Effect of Varying the Horizontal Resolution Table 1 summarizes the global-mean characteristics of the slow rotation experiments. Overall, varying the horizontal resolution has a small effect on the surface temperature (Figures 1 (a)–(c)). In global mean, the surface temperature in the experiment of f45_L26 is 3.7 K higher than that of f19_L26 and 3.2 K higher than that of f05_L26. In the rapid rotation experiments, the difference is also small (Figure 2 ): the surface temperature difference between f45_L26 and f05_L26 is 1.0 K in global mean. In the following analyses, we focus on the results of slow rotation experiments, because the underlying mechanisms are the same. Figure 1. Surface temperature (K) in five experiments with resolutions of f45_L26, f19_L26, f05_L26, f19_L51, and f19_L74 (see Section 2 for detailed descriptions). In all these experiments, the stellar flux is 1800 W m −2 , star temperature is 3700 K, and rotation period (=orbital period) is 38.66 Earth days. Figure 2. Surface temperature in the rapid rotation experiments with two resolutions of f45_L26 (a) and f05_L26 (b). In these two experiments, the stellar flux is 1300 W m −2 , the star temperature is 2600 K, and the rotation period (=orbital period) is 4.25 Earth days. The global-mean surface temperature is 294.7 K in (a) and 293.7 K in (b). Table 1 Global-mean Characteristics of the Simulated Climate of a Slow Rotation Aquaplanet Under Five Different Resolutions in the Model ExoCAM Note. For the definition of total relative humidity, please see the text. The clear-sky greenhouse effect is defined as the difference in upward thermal infrared flux between the surface and the top of the model. For planetary albedo, the difference is also small (Figures 3 (a1)–(c1)). The f45_L26 experiment has a planetary albedo of 0.440, being 0.005 higher than that of f19_L26 and 0.006 higher than that of f05_L26, which corresponds to a difference in global-mean shortwave reflection of 2.25 and 2.70 W m −2 , respectively. The cloud longwave radiation effects


have been used for the calculations of lifetimes of excited levels. These lifetimes have been included in Table 1 . There are a number of even-parity metastable levels that can decay to lower levels only via forbidden electric quadrupole (E2) and magnetic dipole (M1) transitions. The most extensive calculation of radiative transition probabilities and lifetimes for the metastable levels of Ti II has been presented by Deb et al. ( 2009 ). Comparison of their lifetimes with the present results is given in Table 3 . We note a very reasonable agreement between the two calculations with standard deviation of about 20%. However, there are a few levels with considerable disagreement. For example, the lifetimes of the levels of Deb et al. ( 2009 ) exceed our values by five times. For the state we found extremely strong, almost half and half, mixing with the 3 d 2 4 s 2 P state. It makes even the configuration assignment for these levels somewhat ambiguous. The matrix elements for the levels with such strong mixing are very sensitive to the details of calculation and it may be the reason for a large disagreement with the CIV3 calculation in this case. Another example of large discrepancies is the levels which also show strong mixing with the 3 d 3 configuration levels. In this case, the lifetimes from the CIV3 calculation are two times smaller than our values. Table 2 Present Calculated Line Strengths ( S ), Oscillator Strengths ( f ik ), and Transition Probabilities ( A ki (s −1 )) for E1, E2, and M1 Transitions in Ti II Together with Their Wavelengths λ ( Å ) (This table is available in its entirety in machine-readable form.) Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available. Table 3 Comparison of the Calculated and Experimental Lifetimes (ns) for the Metastable States in Ti II The comparison of the present calculated lifetimes with the measurements of Hartman et al. ( 2003 , 2005 ) and Palmeri et al. ( 2008 ) has been presented in Table 3 for seven levels belonging to the 3 d 3 , 3 d 2 4 s , and 3 d 4 s 2 configurations. We have also included available theoretical results of Bautista et al. ( 2006 ) and Deb et al. ( 2009 ) in Table 3 . Our calculated lifetimes closely agree with the measurement of Palmeri et al. within the experimental uncertainties. However, the differences with the measurements of Hartman et al. ( 2003 ) are up to a factor of 2. It indicates the importance of correction due to the repopulation effects that was incorporated in the measurement of Palmeri et al. ( 2008 ). It may also be the reason of discrepancies between the previous theoretical results of Deb et al. ( 2009 ) and Bautista et al. ( 2006 ) and experimental results of Hartman et al. ( 2003 , 2005 ). Good agreement of the present results with measured lifetimes of Palmeri et al. ( 2008 ) confirms that our target wave function expansions adequately include main correlation


that the crucial difference between both models is the much higher proton fraction in the BHF approach. In this case, the DU threshold is already reached at ρ = 0.44 fm −3 ( x p = 0.136), whereas with the APR it is delayed to ρ = 0.82 fm −3 ( x p = 0.140). Figure 1. Pressure and energy density (a), and proton and muon fractions (b) as functions of baryon number density ρ in beta-stable matter for the APR and BHF EOS. The lower panels show NS mass (d) and radius (c) as functions of the central density ρ c . The DU onset is indicated by vertical dotted lines. On the contrary, the APR EOS is somewhat stiffer, i.e. features a larger pressure and energy density. We also mention that the APR EOS becomes superluminal at ρ = 0.85 fm −3 , whereas BHF remains always below the critical threshold (Burgio Schulze 2010 ; Taranto et al. 2013 ). By solving the standard Tolman–Oppenheimer–Volkov equations for the NS structure, this input yields the NS (mass,radius) – central density relations shown in panels (c) and (d) of Fig. 1 . We remark that both models reach maximum masses (slightly) above two solar masses and predict very similar radii in spite of their different matter composition. With BHF the DU process is active in nearly all stars, M /M ⊙ > 1.10, while with APR only in the most heavy ones, M /M ⊙ > 2.03. This has profound consequences for the cooling behaviour. 3 PAIRING GAPS AND CRITICAL TEMPERATURES Of vital importance for any cooling simulation is the knowledge of the 1S0 and 3PF2 pairing gaps for neutrons and protons in beta-stable matter, which on one hand block the DU and MU reactions, and on the other hand open new cooling channels by the PBF mechanism for stellar matter in the vicinity of the critical temperature (Yakovlev et al. 2001 ). As usual, we focus in this work on the most important proton 1S0 (p1S0) and neutron 3PF2 (n3P2) pairing channels and neglect the less important remaining combinations. As stressed before, the gaps should be computed in a framework that is consistent with the determination of the EOS, i.e. be based on the same NN interaction and using the same medium effects (TBF and effective masses), and indeed we follow this procedure here, by using the results of Zhou et al. ( 2004 ), which employed the same V18+UIX nuclear interaction and BHF SP spectra for the calculation of the gaps. To be more precise, and focusing on the more general case of pairing in the coupled 3PF2 channel, the pairing gaps were computed on the BCS level by solving the (angle-averaged) gap equation (Amundsen Østgaard 1985 ; Baldo et al. 1992 , 1998 ; Takatsuka Tamagaki 1993 ; Elgarøy et al. 1996 ; Khodel, Khodel Clark 1998 ) for the two-component L = 1, 3 gap function, with while fixing the (neutron or proton) density, Here e ( k ) are the BHF SP energies, equation ( 2 ), containing contributions due to two-body and three-body forces, μ ≈ e ( k F ) is the (neutron) chemical potential determined self-consistently from equations ( 6 )–( 8 ), and


CGs spanning all redshifts, the only available path forward is to utilize cosmic simulations of galaxy evolution. The Millennium Simulation (Springel et al. 2005 ; Lemson Virgo Consortium 2006 ) provides a tool to study the history of CGs in the universe. It used 2160 3 particles with mass M = 8.6 × 10 8 h −1 M ⊙ to trace the evolution of a comoving cube with side length 500 h −1 Mpc, where h is the Hubble constant parameterization such that H 0 = 100 h km s −1 Mpc −1 . The Millennium Simulation used a ΛCDM model with cosmological parameters Ω M = 0.25, Ω b =0.045, Ω Λ = 0.75, and h = 0.73, consistent with observational results from the Carnegie Hubble Program (Freedman et al. 2012 ) and the WMAP (Hinshaw et al. 2013 ) mission. 10 10 In this paper all distances and masses are scaled to h = 1. The Millennium Simulation used only dark matter particles to which associated properties were later assigned. Dark matter halos were identified using a friends-of-friends algorithm as described in Springel et al. ( 2005 ). Galaxies were added to the simulation post facto using semianalytic techniques (e.g., De Lucia Blaizot 2007 ; Guo et al. 2010 , 2011 , 2013 ). Galaxies are initially associated with individual dark matter halos, which may become subhalos of larger structures over time. The techniques of De Lucia Blaizot ( 2007 ), for example, expanded on the methods of Croton et al. ( 2006 ) and incorporated the effects of rapid star formation and gas loss in galaxy mergers, changes in galaxy properties with varying stellar mass functions and stellar populations, and attenuation due to dust. The simulation results were saved in a collection of 64 redshift “snapshots.” The identified dark matter halos were then assigned galaxy properties using the semianalytic techniques discussed in the references above. The snapshots, combined with the high resolution of the simulation and the sophisticated semianalytic galaxy formation and evolution models, provide an excellent tool for studying the history of CGs over cosmic time. Throughout this paper, we adopt the De Lucia Blaizot ( 2007 ) catalog of galaxies created through this semianalytic approach. 1.2. Previous Work A number of previous studies have utilized the Millennium Simulation galaxy catalogs to investigate CGs. These studies have been limited to relatively low redshifts to facilitate comparison to observations, such as the well-known Hickson catalog (Hickson 1982 ; Hickson et al. 1992 ). By using a light cone in the Millennium Simulation galaxy catalogs (Henriques et al. 2012 ), it has also been possible to create “mock” catalogs of CGs, which can be compared to observations and are subject to analogous limitations (e.g., interloping foreground or background galaxies; McConnachie et al. 2008 ; Díaz-Giménez Mamon 2010 ; Díaz-Giménez Zandivarez 2015 ; Farhang et al. 2017 ). By comparing mock CGs in projection in the Millennium Simulation to observed Hickson compact groups (HCGs), McConnachie et al. (


field strength can be narrowed by 10 ν Lar max{ ν Rad , ν Em }. Utilizing the fact that Fe ii λ 5362.970 Å () absorption line is fully radiative aligned for all of the orbital phases, we deduce that the upper limit field strength is ∼108 mG. Additionally, we find that the Fe i λ 5586 Å () absorption line presents a more than 3 σ detectability polarization signal at the orbital phases 0.544, 0.564, and 0.988 and that the polarization direction for all those phases aligns with the radiative pumping direction rather than the magnetic field direction. This gives us an upper limit for the field strength of ∼80 mG. The accuracy of the field strength is increased by at least two decades compared to the previous 10 G upper limit, constrained from the non-detection of the Zeeman effect. 5. Discussion GSA is the most probable and natural explanation for the discovered polarization signals of the ground-state absorption lines that are realigned to one direction as opposed to the orbital synchronization. We provide here the mean magnetic field of the photosphere surface medium that corresponds to the central part of the absorption line. Figure 2 (d) illustrates that such magnetic field is reasonable on the stellar surface. A full magnetic field tomography requires further study, which is beyond the scope of current observation precision. Higher-resolution spectral observation will enable us to study the wings in the absorption line profiles, separating the emission components from outflows. Through our analyses, we assume that the anisotropic pumping comes from the secondary (following Leone et al. 2018 ). However, when constraining the magnetic field strength, a narrower range might be achieved if accounting for the photons from the primary. We calculate the extended radiation field of the primary following Zhang et al. ( 2015 ) with the Lambert cosine law and limb-darkening (Claret Bloemen 2011 ) considered, and find that the lower limit for magnetic field strength can be ∼2 mG (see Figure 4 (a)). Additionally, we could interpret the orbital synchronization as a result of local polarized flux illuminating the medium rather than pumping from the secondary. Nonetheless, even under such an assumption, the realigned polarization direction of the two ground-state lines that we report here can still be explained by the magnetic realignment of the angular momentum on the ground state. Moreover, beyond the optical band, GSA can be implemented with multi-frequency data ranging from ultraviolet to submillimeter to trace not only the spatial but also the temporal variations of magnetic field (Yan Lazarian 2007 , 2012 ; Shangguan Yan 2013 ; Zhang Yan 2018 ). 6. Summary Polarizations of absorption lines from the ground state with a high polarization degree are discovered in the binary system of 89 Her. We conclude the following. 1. The polarization directions of the two Fe i lines show little variation across the orbital period as opposed to the polarization of


are not very important for this discussion. The effect of number counts magnification is small compared to WL, RSD, or BAO. For F x B :All magnification only increase FoM γ with , while the effect is a 15 per cent increase for F x B :Counts. This discussion therefore focuses on the number counts results (Counts). In F x B -〈 FB 〉 the surveys overlap, which gives sample variance cancellations, but it does not include the Bright–Faint cross-correlations. This reduces the bias constraints and therefore the magnification constraints. The non-overlapping surveys (F+B) does not have sample variance cancellations from overlapping volumes and there the ratio drops further. Finally, could the low magnification effect be caused by a strong covariance between the counts–shear and magnification signals? The F x B -〈δ γ〉 line is F x B :All, but without all counts-shear cross-correlations or equivalently F x B :Counts adding shear–shear. The effect of magnification is also low when only including the shear-shear lensing observables. A lower Faint bias amplitude improves the forecast. One can understand this from a signal-to-noise argument. The variance (Δ 2 ) of the magnification signal when assuming Gaussian fluctuations (equation 3 ) is where i and j are the two redshift bins. The auto-correlation terms dominate for well separated bins in photo-z space, which leads to the approximation in the second line. If ignoring RSD, the magnification–magnification correlations and the shot-noise, the magnification signal-to-noise is where α j and b j are, respectively, the magnification slope and the galaxy bias in redshift bin j . The and terms are the matter auto-correlations in bin i and j , respectively. This approximation is invalid for low Faint bias amplitudes. Equation ( A4 ) shows two important criteria for magnification. A higher magnification slope increase the signal, while a lower bias of the background population decrease the errors. This criteria can be useful if focusing solely on magnification. However, one should focus on RSD, BAO, and WL for the combined constraints, since these effects give stronger cosmology constraints. APPENDIX B: PHOTOMETRIC REDSHIFTS AND GALAXY DENSITIES B1 Photometric redshifts The bias measurements are also affected by redshift uncertainties. Our two fiducial galaxy samples are: a photometric (Faint) and a spectroscopic (Bright) with respectively 0.05(1 + ) and 0.001(1 + ) Gaussian redshift uncertainties. The Faint sample is analysed in broad redshift bins since the Faint photo-z is broad. Improving the Faint photo-z would only substantially change the forecast if also using narrow bins for the Faint sample. We focus instead on the Bright redshift uncertainty and fix the Faint photo-z to the fiducial value. Fig. B1 shows the F x B :All Bright bias error ratios between the case of using spectroscopic (Bright) sample and the case of including redshift uncertainties (photo-z) in the Bright sample. A vertical line (0.0035)


When some of these minor planets are perturbed to orbits with proximity to the WD, they are thought to be tidally disrupted and form a circumstellar disk (Veras et al. 2014 , 2015 ), which eventually accretes onto the WD (Jura 2008 ; Rafikov 2011 ; Metzger et al. 2012 ). The spectroscopic analysis of WD atmospheres (Wolff et al. 2002 ; Dufour et al. 2007 ; Desharnais et al. 2008 ; Klein et al. 2010 ; Gänsicke et al. 2012 ), as well as infrared spectroscopy of the debris disks themselves (Reach et al. 2005 , 2009 ; Jura et al. 2007 , 2009 ; Bergfors et al. 2014 ), are typically consistent with “dry” compositions, characteristic of inner solar system objects. Studies that analyzed the atmospheric composition of large samples of nearby He-dominated WDs, inferred their collective water mass fraction to be of the order of ∼1%, and no more than a few percent even for particular subsets (Jura Xu 2012 ; Jura Young 2014 ; Pietro Gentile Fusillo et al. 2017 ). On the other hand, an increasing number of individual WDs (Farihi et al. 2013 ; Raddi et al. 2015 ; Xu et al. 2017 ) have now been inferred to contain a large water mass fraction in their atmospheres, ranging between 26% and 38%. Polluted WDs are therefore the only current means to understand exoplanetary composition. However, linking the inferred quantity of water in WD atmospheres to the origin of polluting planetary material is not trivial, and requires additional assumptions and calculations. Several studies have previously focused on water retention inside minor planets, as they evolve through and off the main-sequence of their host stars. Understanding how water survives inside minor planets as a function of their intrinsic characteristics, is a necessary first step in beginning to understand the origin and nature of polluting planetary material. The seminal work of Stern et al. ( 1990 ) introduced a simple sublimation model that considered the initial orbital distance and size of minor planets as they evolve around a post-main-sequence 1 star. Jura Xu ( 2010 ) considered a more advanced model, taking into account conductive heat transport to the interior, and also the minor planets’ orbital expansion during the post-main-sequence stellar evolution of a 1 and 3 host stars. Malamud Perets ( 2016 ; hereafter MP16 ) utilized a modern and more sophisticated code that consistently accounts for the thermal, as well as physical (rock/water differentiation), chemical (rock hydration and dehydration), and orbital evolution of icy minor planets. Contrary to previous models, it starts at the beginning of the main sequence (of a 1 host star), and considers new parameters: the formation time of the minor planet (which affects its early evolution through radiogenic heating and thus its internal differentiated state) and also the variation in the initial minor planet composition. Malamud Perets ( 2017 ; hereafter MP17 ) finally investigated multiple host star masses, ranging from 1 to 6.4 (corresponding to


0.2 and 10.0 . Although one of the main problems of this survey was the poor and sparse sampling and the small number of observations per star, which complicates the statistical analysis and increases the uncertainty on the frequency of Jupiters in our survey, we find a total occurrence rate of Jupiter-mass planets in the M 67 sample of 18.0% (precisely 15.8% for the MS stars and 23.0% for the evolved stars). It is worth noting that on average we need a minimum number of 20 observations per star to exclude Jupiter-mass planets at high confidence when a periodogram analysis is applied. The Jupiter-mass planets in our sample imply that our results are consistent with the planet frequency of much larger surveys carried out for field star samples. For example, from the ELODIE survey, Naef et al. (2005) estimated that a fraction of 7.5 1.5% stars host giant planets with periods shorter than 10 yr, while Cumming et al. (2008) derived a frequency of 12 1.6% from the Keck survey and Mayor et al. (2011) 13.9 1.7% from the HARPS/CORALIE survey. As a general conclusion, our simulation study seems to confirm the recent finding ( Meibom et al. 2013 ) that the frequency of massive planets around stars of open clusters agrees with the frequency of these planets around field stars. However, we note that when we only investigate the frequency of hot Jupiters around MS stars of our survey, we find a hot Jupiter occurrence rate (5.7%) that is substantially higher than what is observed in field stars (see also Brucalassi et al. 2016 ). We have shown that the search for planets in open clusters is a powerful test benchmark for the theory of planet formation and stellar evolution. The new generation of spectrographs such as ESPRESSO ( Pasquini et al. 2009 ) will extend this search more effectively. It is clear, however, that to efficiently perform a planet search survey in star clusters, a multi-object capability, even with relatively low multiplex (10–50), is desirable. Unfortunately, no such facility is currently planned. Appendix A: Accompanying plots and table Table A.1 Observed targets in M 67. Notes. Object name, basic stellar parameters, number of observations for each instrument (H: HARPS, S: SOPHIE, C: CORALE, HET: HRS at Het, H-N: HARPS-N), total number of observations, mean stellar RV, average measurements error, average corrected measurements error, observed RV dispersion. Binary candidates are indicated in bold face. Fig. A.1 Contours of the planet detection efficiency for the MS stars in the domains of 1–1000 days for planet period and 0.2–10 for planet mass. A 0.01 FAP level has been used as detection planet threshold in the periodogram analysis. A filled circle indicates the planet position. Fig. A.2 Contours of the planet detection efficiency for the evolved stars in the domains of 1–1000 days for planet period and 0.2–10 for planet mass. A 0.01 FAP level has been used as detection planet threshold in the periodogram analysis. A filled circle


test the stability of our reconstruction and the sensitivity of the model to various free parameters, we have considered different combinations of parameters. In particular, we either fixed , B sat, n , and c e as listed in Table 1 , or let them be free parameters within ranges 0.2–0.8, 50–850, and 0.2–0.5, respectively. These tests showed that the resulting reconstructions of TSI differed by up to 0.1 W m −2 on decadal timescales. The overall secular change always lies in the range 0.90–1.0 W m −2 . Consequently, we conclude that the reconstruction is independent of the exact choice of the free parameters (see also Krivova et al. 2007 ; Dasi-Espuig et al. 2016 ). 3.3. SATIRE-M reconstruction on millennial timescales Keeping all the parameters fixed, we now employ the SATIRE-M model to reconstruct solar total and spectral irradiance back to 6755 BC from the cosmogenic isotope data. Figure 7 a shows the TSI reconstructions over approximately the last 9000 years based on the three isotope series, as introduced in Sect. 2.3 (U16-14C in blue, U16-10Be in green, Wu18 in black). Figures 7 b and c are enlargements over the periods 1000 BC–2000 AD and 1400 AD–2000 AD, respectively. The decadally averaged TSI reconstruction based on the SN v2 series is also shown (solid red) for comparison. The reconstruction based on the sunspot record by Chatzistergos et al. (2017) is shown by the dashed red curve. Yellow shading highlights the difference between these two reconstructions. Fig. 7. Three TSI reconstructions based on different isotope records: U16-14C (blue), U16-10Be (green) and the composite Wu18 (black) plotted over the periods: panel a) 6755 BC–2000 AD, panel b) 1000 BC–2000 AD, and panel c) 1400 AD–2000 AD. The uncertainty range of the reconstruction based on the Wu18 composite is indicated by the grey shaded area. Decadal averages of the reconstruction based on the directly observed SN are shown in red after 1639. The solid line is the reconstruction based on the WDC-SILSO series while the dashed line is based on the record by Chatzistergos et al. (2017) . The yellow shaded area highlights the difference between them. It is worth noticing that the reconstructions based solely on either 14 C (U16-14C) or 10 Be (U16-10Be) show temporal discrepancies due to differences in the relevant geochemical production processes and local climatic influences (Sect. 2.3.1 and Wu et al. 2018 ). The reconstruction based on the composite (Wu18) of one global 14 C and six regional 10 Be series has remedied this (see Fig. 12 in Wu et al. 2018 ), and shows the common solar signal extracted from seven individual isotope series. We therefore consider this latter reconstruction to be more robust than reconstructions based on individual isotope data. On the millennial timescale, the variability of TSI () obtained from all three isotope records is very similar (≈0.11%). Since in the second half of the twentieth century, the activity of the Sun was comparatively high (see


but decrease in an old stellar population (hence, the increase in the abundances of α elements). In Fig. 15 , α-rich stars are highlighted with triangles. However, the AMR for these stars seems to have an unexpected positive trend. To investigate this, we slice [α/M] into six portions and fit a straight line to illustrate the evolution of [M/H] with age in every [α/M] slice, which is shown in Fig. 16 . As the derived age may suffer from a marginal effect, we exclude the oldest stars in the fitting process. They are marked with crosses in Fig. 16 . Figure 16. AMRs for different [α/M] slices. Straight lines are fitted to illustrate the relation between [M/H] and age. Crosses denote the oldest stars, which are not used in the fitting. All six [α/M] slices have a positive slope in the AMR. All the slices have an unexpectedly positive gradient in the AMR with the exception of the highest-α slice, which has a negative gradient of −0.004 dex Gyr −1 . The average of all the gradients is about 0.01 dex Gyr −1 . Notice that there are few stars in the 0.15 > [α/ M ] > 0.10 slice, which is just the watershed between the high-α population and the low-α population. We combine this slice with the highest-α slice, which finally gives a negative gradient of ∼−0.01 dex Gyr −1 . We examined whether the positive gradient does exist in the APOGEE-DR12 data set. In this data set, the three low [α/M] slices ranging from 0.05 to 0.15 also have a positive relation, but the other three [α/M] slices have a negative relation. If these positive correlations in some of the [α/M] slices are real, this may indicate that there is fresh metal-poor gas inflowing during the evolution of the thin Galactic disc. The infall of pristine gas dilutes the gas reservoir, lowering the subsequently formed stars’ metallicities but retaining the [α/M] ratio. These stars contribute a positive trend in the AMR in a given [α/M] slice. Thus, the AMR in different [α/M] slices may give us an opportunity to measure the gas infall rate. Actually, Chiappini, Matteucci Gratton ( 1997 ) and Chiappini, Matteucci Romano ( 2001 ) proved the power of the inflow chemical evolution model. In these references, two main inflow episodes are assumed to form the thin and thick discs. The time-scale for the formation of the thick disc is much shorter than that of the thin disc. The model-predicted metallicity distribution function generally agrees with the observations in the solar neighbourhood [fig. 7 in Chiappini et al. ( 1997 ) and Hayden et al. ( 2015 )]. However, without the aid of a dynamic process to build the Galactic chemical evolution model, it is hard to measure the detailed gas infall rate in this way because it is impossible to confirm which stars are born in situ. Even worse, the potential biases involved in our adopted sample are difficult to measure and they probably play a crucial role when determining the AMR in different [α/M] slices. High-quality spectroscopic data with wide coverage


we find τ m ≈ 12 days, and we obtain a similar value for SN 2017ein. Therefore, the different M ej values inferred for SN 2007gr and SN 2017ein are mainly a result of different opacity values adopted in the analysis. Moreover, the discrepancy in the ejected mass could also be related to the fitting methods and wave bands of the light curve used in the analysis. SN 2017ein is one of the two SNe Ic showing possible evidence for early shock breakout cooling. Another candidate is LSQ14efd, with its V -band light curve showing a bump feature at early times, which was also interpreted as cooling of the shocked stellar envelope (Barbarino et al. 2017 ). In comparison with SN 2017ein, LSQ14efd is more luminous and energetic, with an R -band peak absolute magnitude of −18.14 mag, kinematic energy E kin = 5.3 B, and ejecta mass M ej = 6.3 M ⊙ , making it stand between normal SNe Ic and SNe Ic-BL. 7. <italic>HST</italic> Progenitor Observation 7.1. Pre- and Post-explosion <italic>HST</italic> Images and Data Reduction We searched the pre-explosion HST images from the Mikulski Archive for Space Telescopes (MAST) 29 29 http://archive.stsci.edu/ and the Hubble Legacy Archive 30 30 http://hla.stsci.edu/ and found publicly available F555W and F814W WFPC2 images taken on 2007 December 11 (PI: W. Li). An F438W-band image at the location of SN 2017ein was taken by HST on 2017 June 12 with the WFC3/UVIS configuration (PI: van Dyk). This image was released and publicly available immediately after the observation. We use this image as a post-explosion image to identify the position of the SN progenitor. Table 8 lists the information of these images. Table 8 Pre- and Post-explosion HST Images on the Site of SN 2017ein The pre- and post-discovery HST images around the SN position are shown in Figure 16 , where the zoomed-in regions centered at the SN site are also shown. There is clearly a point-like source near the SN position in both the F555W and F814W images. The position of this point-like source is obtained by averaging the measured values with four different methods (centroid, Gauss, o -filter center algorithm of IRAF task phot, and IRAF task Daophot). On all pre-explosion images, the separation between the position transformed from the post-explosion SN site and the center of the nearby point-like source is within the uncertainty of the transformed position, suggesting that this nearby point source is the progenitor of SN 2017ein. The coordinates of the SN on the post-explosion F438 image are found to be (539.302 ± 0.002, 564.516 ± 0.003) with different methods (centroid, Gauss and o -filter center algorithm of IRAF task phot, IRAF task imexamine, and SExtractor) and are converted to (798.70, 1766.77) and (798.38, 1766.67) on the pre-explosion F555W and F814W images, respectively, as the coordinates of the progenitor. Figure 16. Top: regions around SN 2017ein showing the prediscovery HST F555W (left) and F814W (middle) images and the post-explosion HST F438W


what is the driving mechanism of photoevaporation between FUV, EUV, X-ray, and what are the exact values of mass-loss rate is still open. In order for the photoevaporation to start the accretion rate have to drop below the photoevaporation rate. As soon as it starts, a cavity free from gas and dust is generated, with the very large grains rapidly migrating inward (Alexander Armitage 2007 ). CQ Tau was considered by Donehew Brittain ( 2011 ) and Mendigutía et al. ( 2012 ) to have a high accretion rate ( yr −1 ), which can be considered high for disc dispersal to be the main mechanism acting in the formation of the CQ Tau cavity (Owen 2016 ). A combination between the clearing mechanism and photoevaporation can, instead, be considered as a possible option (e.g. Williams Cieza 2011 ; Rosotti et al. 2013 ; Rosotti, Ercolano Owen 2015 ) to be further investigated. Dead zones . The suppression of magnetorotational instability inside the disc can create regions of low disc ionization, the so-called ‘dead zones’ (e.g. Flock, Henning Klahr 2012 ). In these regions the rate of gas flow decreases with an accumulation of gas in the outer edge. At the same time the pressure maxima is able to trap large particles with a consequent ring-like feature in both gas and dust components (Flock et al. 2015 ). The ring is in general located at about the same radius (Pinilla et al. 2016 ) in both the components. However, when dead zones and MHD wind are present at the same time, a difference in the inner radii position can be observed. The presence of dead zones can increase the turbulence present in the disc and generate asymmetric vortices in the disc (Ruge et al. 2016 ) at (sub)mm wavelengths. Such structures can be also created by disc–planet interaction if the α viscosity is low. We cannot exclude this mechanism by our observations. Higher resolution data are need to better constrain the profile of the ring-like disc, mainly its symmetry and variability (Pinilla et al. 2016 ). However, dead zones can explain ring-like structures, but not cavities such as the one clearly present in the CQ Tau system. A combination between the mechanism described above can be also a possible solution, which, however, we will not address in this paper. 7 CONCLUSIONS Discs where it is possible to clearly distinguish a cavity are of particular interest in the study of protoplanetary disc evolution and of the planet formation process. In particular, we have studied the disc around the CQ Tau pre-main-sequence star. We have made use of spatially resolved ALMA observations of the dust continuum and of three CO isotopologues, 12 CO, 13 CO, and C 18 O, together with the observed SED of CQ Tau. We employed the chemical–physical code DALI to model the CQ Tau disc and to derive the surface density profile of the dust (small and large grains separately) and of the gas. Finally, we ran 3D SPH simulations to test whether an embedded planet could be able to create the observed disc structure.


follows: the second Fisher matrix is computed from all ’s except for the two entries at the extrema of the anti-diagonal, which are set to zero; and so on until we compute the 10th Fisher matrix, where is non-zero only for i = j . The inset in Fig. 4 illustrates this procedure, with shading going from black (only diagonal elements considered) to the lightest of grey (all the cross-correlations between thin bins considered). The larger figure shows the structure of the full tomographic matrix of our hybrid method for this test of the importance of off-diagonal correlations. In this case, white means no correlation included. Figure 4. General structure of the full angular power spectrum tomographic matrix, , in our hybrid approach. Block diagonal matrices represent the thick bins, which we consider as independent. The inset illustrates the structure of one of those thick bins, with the thin bins shown. Shades of grey refer to the tests described in Section 4.5 . Now, we consider two extrema: the first and the last of the thick bins. Referring to the inset of Fig. 4 , for both of these thick bins, we start from the full angular power spectrum tomographic matrix and at each step we remove one off-diagonal, from the lightest grey until we remain only with the black, main diagonal. In Fig. 5 , we illustrate the result of this test, by plotting the absolute bias on cosmological parameters induced by neglecting lensing magnification (normalized to the reference values of Table 2 ), as a function of how many cross-correlations between thin bins we include. Apart from the first point(s), for which the bias may be lower, but just because the Fisher matrices are very noisy, it appears clear that the behaviour is very flat. As expected, the trend is flatter at low redshift in the first thick bin. Figure 5. Absolute bias on cosmological parameters induced by neglecting lensing magnification, as function a of off-diagonal elements included, for an analysis carried out either in the first or in the last of the thick redshift bins only, normalized to what is obtained by including all cross-correlations between thin bins in the given thick bin. Fig. 6 shows the bias on cosmological parameters due to neglecting lensing, as a function of how many off-diagonal spectra are considered in the full angular power spectrum, i.e. the larger matrix in Fig. 4 . On the horizontal axis, 1 means black elements in the larger matrix, all the way to 10, representing the inclusion of all elements up to the lightest grey shade. Each point is normalized to its previous value, e.g. the seventh blue bullet point tells us that the bias on Ω b will increase by if we include up to the seventh off-diagonal, with respect to what we would guess by considering only up to the sixth. We notice a net trend: the bias on cosmological parameter best-fit values induced by neglecting lensing may be significant if we considered only the main diagonal or the first few off-diagonals, but then it does


al. 2012 ; E. Torresi et al. 2018, in preparation) to estimate a number of physical parameters, such as the number of ionizing photons, covering factors, and mass of ionized gas, with the aim of better understanding the nature of the ionizing source and the properties of the ionized gas itself. We organize this paper as follows. Section 2 presents a description of the sample and the corresponding observations, while the reduction process and calibration of the data are presented in Section 3 . Section 4 shows the catalog of H α +[N ii ] and [O iii ] images and the corresponding flux measurements. In addition, we show [O iii ]/H α +[N ii ] emission-line ratio images. Section 4 presents the results of measuring the physical parameters mentioned before. In Section 5 , we discuss all of the previous results in light of the two AGN classes (LEGs and HEGs). A summary and potential future observations are presented in Section 6 . Throughout this paper, we use H 0 = 71 km s −1 , Ω M = 0.27, and Ω Λ = 0.73. 2. Sample Selection and Observations The sample selection and observations are described in detail in Tremblay et al. ( 2009 ). To summarize, we present a sample of 19 3CR radio sources from the low- z ( z 0.3) extragalactic radio-source Revised Third Cambridge Catalogue (3CR; Bennett 1962a , 1962b ; Spinrad et al. 1985 ). The sample comes from the original HST proposal for 98 3CR sources that was awarded for observations prior to the ACS side 2 electronics failure in 2007 January. Although only 19 sources were observed (Table 1 ), these objects represent an unbiased sample in selection due to the nature of the HST snapshot mode (to fill gaps in the HST schedule, sources are randomly picked from the target list). Moreover, the observed 19 objects span almost the whole redshift range (0.0075 z 0.224) of the original sample and show a wide variety of emission-line ratios, radio power, or spectroscopic properties. With regard to their radio morphologies, the sample consists of four FR Is and 14 FR IIs, taking the double-lobed 3C 314.1 apart (Table 2 ). In terms of their optical spectroscopic classification, eight of the objects in our sample are classified as LEGs and 10 are HEGs, of which four have broad lines, named broad-line objects (BLOs). Of particular interest is 3C 314.1, an RG whose spectral classification is extremely LEG (Capetti et al. 2011 ) interpreted as relic RG (Capetti et al. 2013 ). Table 2 summarizes the radio and spectroscopic classification of the sample. This table also collects the total radio luminosities at 178 MHz, the radio core powers (at 5 GHz), and the X-ray luminosities for the sample. The uncertainties on the radio luminosities are negligible with respect to those of the X-ray luminosities, which amount to ∼0.2 dex. Table 1 Observing Log Note. Log of the HST /ACS WFC observations (Program 10882, PI: W.B. Sparks). Col. (1): 3C source name. Col (2): redshift. Cols. (3)–(4): R.A. and decl. Cols. (5)–(6): ramp filters used


because of missing short spacings. There can be small-scale structure in Stokes Q and U that the interferometer detects, and that can in principle become visible as a component in the Faraday depth spectrum. These are sometimes called Faraday ghosts and are independent of position on the sky (e.g. Shukurov Berkhuijsen 2003 ). Oppermann et al. ( 2012 , 2015 ) have created a map of the smoothly varying Galactic Faraday component, φ gal , by utilizing all-sky Faraday RMs of compact background sources from the literature. We list φ gal at the locations of each of our targets in Table 5 . The effect of the Galactic ISM on an extragalactic source is mainly as a foreground Faraday-rotating screen. The correction for this effect is to subtract φ gal from detected components. In this work, we note that this effect does exist and has possibly affected our measurements but we do not correct for it as it is not adequately constrained. In an effort to analyse Faraday complexity introduced by the ionosphere at the different observation epochs, we look for rotation in the polarization angle (χ) as a function of time. This we do by producing full Stokes images for each scan of the phase calibrator for each epoch. We then restrict our analysis to those scans that have Stokes V flux and p 0 that are below the leakage, and also Stokes I that is above 3σ. We then analyse the resulting q, u , and χ as functions of scan, i.e time. However, the resulting images prove to be too noisy to lead to a conclusion on ionospheric effects. Typical Faraday RM variations from the ionosphere are up to ∼1 rad m −2 . Typical variations are of order 1 rad at 1 m wavelength as χ(λ 2 ) ∼ λ 2 . Variations of this order are seen at 327 MHz at the VLA (Erickson et al. 2001 ). At our lowest frequency even a 90° change at 327 MHz scales to only about 6° at 1300 MHz, and at 1900 MHz. This is small enough to ignore. Note also that it is only the time variation during an epoch that will affect the observations. A constant offset from the ionosphere will be accounted for by the calibration. In the absence of an absolute polarization calibrator, the solution is referenced to the mean feed position angle that is not expected to change as it is hardwired into the instrument. We therefore conclude that the expected ionospheric rotation is negligible and thus not corrected. 4 DISCUSSION Our RM Synthesis analysis shows Faraday complexity, of varying degrees, in four of the six sources in our KAT-7 sample. The most polarized source, J0240−231, displays the most complex Faraday spectrum with several emission components (see Fig. 3a and Table 5 ). The presence of Faraday thick components can be seen in the Faraday spectrum as well. Our analysis clearly resolves this complex spectrum both near the main peak and the smaller peaks. This source also shows the most rapidly changing polarized intensity that depolarizes toward larger wavelengths (see the bottom panel of Fig. 2a ). The behaviour of q


intensities of the rotational lines at their ground states. For example, for CHOH, the expected peak intensity of its line at 44 069 MHz transition, nm MHz) calculated by MADEX ( Cernicharo 2012 ) is only 0.3 K. For the 46 980 MHz ethanol line (7 transition of the trans conformer, nm MHz), the expected peak intensity is 0.2 K for the conditions of the experiment. The first experimental run was held in October 2015 using the quartz windows. To obtain the spectra we performed ON/OFF scans, according to Eqs. ( 4 ) and ( 7 ), with ON: chamber filled with the gas, and OFF: empty chamber. However, no lines were observed. Fig. 8 Observed lines of methanol and ethanol at 44 069 and 46 980 MHz, respectively. The problem arose from the quartz windows which reduce the sensitivity (see Fig. 6 ) and, in addition, introduce baseline artefacts due to internal reflections. We have also noticed that thermal emission from people around the chamber leads to significant degradation of the baseline. In the following experiments we installed the Upilex windows which have a much better transmission (see Sect. 2.4 ). Figure 8 shows the lines of CHOH and CHCHOH after 10 min of ON-OFF observing time at a total static pressure of 0.3 mbar when the chamber was filled with each of these gases. From just a single measurement of the ethanol line we could estimate a broadening coefficient of 20 MHz/mbar. Figure 9 shows the methanol line observed at different pressures (baseline ripples can be seen in the 0.1 mbar spectrum). As pointed out in the previous section, in the pressure broadened regime, the peak height remains constant while the linewidth changes with pressure. For pressures below 0.02 mbar the line reaches its Doppler width (see Fig. 10 ). Typical integration times were 10 min during these measurements except for the lowest pressure for which we integrated during 40 min. All spectra were fitted to Voigt profiles, with the Doppler width fixed to the expected value at 300 K (97 kHz), and peak intensities, collisional linewidths (FWHM) and integrated intensities where derived from the fit. Figure 10 shows these experimental values versus pressure, and the linear fits that show the linear dependence of collisional width and integrated intensity with pressure. The self-broadening coefficient thus derived is MHz/mbar (HWHM). The upper panel of Fig. 10 also shows the expected evolution of the peak intensity using the derived broadening parameter. Fig. 9 Observed line of methanol at 44 069 MHz (7 transition) for different values of the total gas pressure. The integration time was 40 min for the narrower feature. The spectral resolution is 180 kHz obtained by a five channel smoothing of the original data. A shift by K is introduced in the vertical scale of each spectrum with respect to the previous one, as pressure decreases. The Upilex windows were adopted for all the other observing periods. In the second observing run in April 2016 we used HCOOH and OCS as probe


in Fig. 2 correspond to ≈48 per cent of the total number of initial simulated objects, which survived during the integration time. In panels (c) and (d) of Fig. 2 , the distribution of the final osculant orbital elements, a s , e s , and i s of the ploonets with respect to the star, are shown. We observe in a peaked distribution of low-eccentric orbits with similar size than that of the planet (nearby ploonets). As expected, non-nearby ploonets are distributed in the osculating a s − e s plane following the characteristic pattern of constant Tisserand parameter. The periapsis argument is almost uniformly distributed (not shown in Fig. 2 ) and thereby no preferred orbital orientation is found. Finally, the distribution of the mean orbital motion of the surviving exomoons is plotted in panel (d) of Fig. 2 . There are three recognizable peaks close or at resonances (planet:moon) 1:2 (inner ploonets), 3:2, and 5:2 (outer ploonets). It is worthy to mention that the resonances found are transient states of the system. Moreover, almost all the orbits resulted chaotic/unstable according to the assessing of the Mean Exponential Growth factor of Nearby Orbits (MEGNO) parameter (Cincotta, Giordano Simó 2003 ), according to the implementation provided by REBOUND (Rein Tamayo 2015 ). This calculation is not shown in the plot. 3 PLOONET DETECTABILITY If according to the previous analytical and numerical models, a population of small ploonets could arise in young planetary systems hosting close-in giant planets, and we additionally assume that some of them survive to the long-term orbital evolution of the system, the next question we should address is what are the observable signatures that evidence the presence of these objects?. Besides the direct photometric or indirect stellar radial-velocity detection (that could be hard to distinguish from the observational signature of an actual small planet), we consider and evaluate here, two additional and distinctive observational signatures of ploonets: (1) the transit of rapidly evaporating planetary embryo-sized objects with an orbit closely related to an already detected close-in giant planet and (2) characteristic TTVs of the parent planet transit signal. The very existence of ploonets depends on two basic conditions: (1) planetary moons around giant close-in planets are formed before or during the migration process when abundant circumstellar gas and dust is accreted by the planet (Namouni 2010 ; Heller Pudritz 2015 ); and (2) the moons survive planetary migration (Namouni 2010 ; Spalding et al. 2016 ). Although it is hard to ensure that both conditions will be fulfilled under general circumstances, the characteristic time-scales of moon formation (10 3 –10 5 yr, Canup Ward 2006 ) and planetary migration (10 3 –10 7 yr, Armitage 2010 ) seem to favour the idea that some migrating giant planets could arrive to their final orbit, carrying along several volatile rich moons. So far, we have studied the


will be composed. 3 NUMERICAL ANALYSIS In this analysis all notable features of the apertures such as spiders and gaps are accounted for in order to achieve more comprehensive results. The quality of the main mirrors is assumed to be perfect, without any optical or mechanically induced aberrations such as inter-segment piston or tip-tilt errors. The diffraction-limited PSFs are computed using the fast Fourier transform (FFT) method with a data matrix of size 4096 × 4096 elements in the aperture plane, which is chosen as a compromise in consideration of the required computational power and desirable linear resolution. Actually, a two-fold oversampling is sufficient to comply with the Nyquist criterion. Application of the FFT in this condition would result in nearly three data points per λ/ D of the PSF, which is rather crude for S/N calculations at the diffraction limit. In order to obtain more convenient PSF data sampling, here the central 1024 × 1024 part of the overall matrix is attributed to the pure aperture with the final linear scales of ≈ 11.0, 26.2, 32.2 and 39.4 mm px −1 for the Keck, GMT (also HDRT), TMT and ELT apertures, respectively. This leads to nearly six data points per λ/ D , which is sufficient to adequately represent the PSF for further processing. At the same time, these linear scales are still too low to sense for all notable features of the apertures as we intended to do initially. For example, the inter-mirror non-reflective gaps in the hexagonal segmentation are set to 4 mm, which is of the order of 2.5 times less than the scale for the Keck aperture. In order to resolve this problem the grey pixel approximation method (Troy Chanan 2003 ) is applied. The simple idea is to rescale the numerical intensity of a pixel in accordance with the portion of area that it covers on the corresponding feature. The OTFs are then calculated through FFT of the corresponding PSFs. The main parameters of the apertures adopted in these calculations are given in Table 1 . Table 1. Main parameters of the apertures. Notes . a The central obscuration is determined as a ratio , where S obs and S eff are the areas of central obstruction and clear aperture, respectively. b The original size of the sub-pupils in HDRT was proposed to be 6.5 m, presumably as an optimal maximum in consideration of technological issues. But here we consider 8.4 m mirrors, as practically proven and also in order to make a direct comparison with the GMT. c The value is calculated assuming an obstructing circle of size 8.4 m. The long-exposure atmospheric OTFs are determined following the corresponding expressions (equations 4 and 5 ). Relative ICs are then constructed directly by using equation ( 3 ). In these calculations, for each case, the values of spatial parameters (i.e. r, r 0 , L 0 ) were normalized to the aperture size D , and the spatial frequencies ( u , v ) to the cut-off limit D /λ. This allows us to conveniently present the final graphs purely as a