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

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


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

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


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

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O B-Wavelength O B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model B-Model O B-Model O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O B-Model O O O O O O O B-Model O O O O O O O O O O O O O O O O O O B-Model O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model B-Model B-Model B-Model O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O B-Model O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O B-Model O O O O O O B-Model O O O O O O O B-Wavelength O O O O O O O O O O O O B-Wavelength O O


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

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


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

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


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. (

O O O O O O O O O O O O O O O O O O B-Model I-Model B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O B-Model I-Model O O B-Model I-Model O O O B-Formula I-Formula I-Formula I-Formula B-Formula I-Formula I-Formula B-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula O O O O O O B-Survey I-Survey I-Survey B-Citation I-Citation I-Citation I-Citation O O O B-Telescope B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation O B-Citation O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O B-Dataset I-Dataset B-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Model I-Model O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-Model I-Model O O O O O O B-Citation I-Citation I-Citation I-Citation


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

O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength B-TextGarbage O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength B-TextGarbage O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O B-Wavelength O B-Wavelength O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O B-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O


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)

O O O O O O O O O O O O O O O O O B-Model B-Model O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O B-ObservationalTechniques O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model B-Model O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Dataset O O O B-Dataset O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O B-ObservationalTechniques O O O O B-Dataset B-ObservationalTechniques O O O O O O O O O O O O O B-Dataset I-Dataset O O O O O B-Dataset O O O O O O B-ObservationalTechniques O O O O O O O O O O O O O O O O O O O O O O B-Dataset O O O O O O O O B-ObservationalTechniques O O B-Dataset I-Dataset O O O O


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

O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation O O O O O O O B-Citation I-Citation O B-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O B-Wavelength O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O B-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O B-Citation O O O O O O O O O O O O O O


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

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O B-Dataset I-Dataset I-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O B-Model I-Model O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey I-Survey B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Survey I-Survey O B-Citation I-Citation I-Citation I-Citation O O O O B-Survey I-Survey O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O B-Instrument O B-Instrument O B-Instrument O B-Instrument O B-Telescope O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


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

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


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

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O B-Model I-Model I-Model I-Model O O O O O O O O O O O O B-CelestialObjectRegion O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-Model I-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


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

O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O B-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O B-CelestialObject O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O B-CelestialObject I-CelestialObject B-CelestialObject O O O O O O O B-Wavelength I-Wavelength O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O B-Tag O O O O O O B-Tag O O O O O O O O B-Telescope O O O B-Archive I-Archive I-Archive I-Archive I-Archive B-Archive O O B-URL O O B-Archive I-Archive I-Archive O O B-URL O O O O B-Wavelength O B-Wavelength B-Instrument O O O O O O O B-Person I-Person O B-Wavelength O O O O O B-CelestialObject I-CelestialObject O O O B-Telescope O O O O O O B-Instrument O O B-Person I-Person O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O B-CelestialObject I-CelestialObject O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O B-Software O B-Software O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O B-Software O B-Software B-Software O B-Software O B-Software O O O O O O O O O O O O B-Wavelength O B-Wavelength O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O B-Telescope B-Wavelength O O B-Wavelength O O O O O B-Telescope B-Wavelength


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.

O O O O O O O O B-Wavelength B-Wavelength B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O B-CelestialObject I-CelestialObject O O O B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O B-Citation I-Citation O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O B-Observatory O O O O O O O O O O O O O O O O O O O O O O B-Model O B-CelestialObject I-CelestialObject O O O O O B-Software O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O O O O


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

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-TextGarbage I-TextGarbage O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


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

B-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Dataset B-Wavelength O O O O O O B-Formula I-Formula O B-Wavelength B-Dataset I-Dataset I-Dataset I-Dataset B-Dataset B-Citation I-Citation O B-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Telescope O O O B-Dataset O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O B-Wavelength O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O B-Wavelength O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O B-Wavelength O O O B-Wavelength I-Wavelength O O B-Wavelength O O O O O O O O B-Wavelength O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O B-Telescope B-Instrument B-Instrument O B-Proposal I-Proposal O B-Person I-Person O O B-Dataset O O O O O O O O O O O O O O O


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

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O B-Telescope B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O B-Wavelength I-Wavelength O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Dataset I-Dataset O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


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

O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength O O O O O B-Software O B-Citation I-Citation O O O O O O O B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument I-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument I-Instrument O O O O O O O O O O O O O O O O O O O O O O O


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

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Software B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-ObservationalTechniques O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O B-Citation I-Citation I-Citation O O O O O O O O B-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


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

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


for excision of data affected by radio frequency interference. After the initial data editing, and gain and bandpass calibration using observations of the compact source 0204+152, a standard self-calibration procedure was carried out for each target source, using line-free channels. The imaging was done with the task tclean , with the w-projection algorithm (Cornwell et al. 2008 ). In the case of J0229+0053, where the observing bandwidth was large, we additionally used the MT-MFS algorithm (second-order expansion; Rau Cornwell 2011 ) to image the target field. The synthesized beams of the final continuum images have full widths at half maximum (FWHMs) of (J0229+0044) and (J0229 + 0053). Both sources were found to be unresolved in our continuum images, with flux densities of mJy (J0229+0044, at ≈640 MHz) and mJy (J0229+0053, at ≈657 MHz). The quoted errors include the error measured from a two-dimensional Gaussian fit to a small region around each source and the typical error in the GMRT flux density scale, ≈10% at these frequencies. The task uvsub was then used to subtract out all detected continuum emission from the self-calibrated visibilities of each field. For each source, a spectral cube was made from these continuum-subtracted visibilities in the barycentric frame, using natural weighting. The H i 21 cm spectrum was extracted by taking a cut through the cube at the AGN location. The final spectrum for each source was then obtained by fitting a second-order polynomial to the line-free regions of each spectrum, and subtracting this out. We further smoothed the spectra by seven channels (J0229+0044) and two channels (J0229+0053), to velocity resolutions of ≈26.6 km s −1 and ≈11.2 km s −1 , respectively. The final optical depth rms noise values are ≈0.12 per 26.6 km s −1 (J0229+0044) and 0.0068 per 11.2 km s −1 (J0229+0053). Our final H i 21 cm spectra toward J0229+0044 and J0229+0053 are shown in Figures 1 (left) and (right), respectively. The velocity-integrated H i 21 cm optical depths are km s −1 (J0229+0044) and km s −1 (J0229+0053). Assuming K and a covering factor, f = 1, these integrated H i 21 cm optical depths imply H i column densities of N hi = (1.35 ± 0.14) × ( T s /100) × 10 22 cm −2 (J0229+0044) and N hi = (1.429 ± 0.015) × ( T s /100) ×10 22 cm −2 (J0229+0053). Note that these are conservative assumptions: a lower covering factor or a higher spin temperature would imply even higher H i column densities. The observational results are summarized in Table 1 . Figure 1. The H i 21 cm spectra toward (left) J0229+0044 and (right) J0229+0053, at velocity resolutions of ≈26.6 km s −1 and ≈11.2 km s −1 , respectively. The solid horizontal line in each panel indicates the AGN continuum flux density at the redshifted H i 21 cm line frequency. The 1 σ rms noise values on the spectra (the horizontal dashed lines) are 0.41 mJy per ≈26.6 km s −1 (J0229+0044) and 0.29 mJy per ≈11.2 km s −1 (J0229+0053). The velocity axes in both panels are

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