adsabs/FOCAL huggingface dataset:
For our dataset of absolute magnitudes, we used data collected at the Institute of Astronomy of V. N. Karazin Kharkiv National University within the long-term observational programme to study asteroid magnitude-phase curves (Shevchenko et al. 2010, 2012, 2014a, 2016; Slyusarev et al. 2012). We also used some observational data obtained within several other programmes (Belskaya et al. 2010; Chiorny et al. 2007, 2011; Dotto et al. 2009; Hahn et al. 1989; Kaasalainen et al. 2004; Lagerkvist et al. 1998; Michalowski et al. 1995; Mohamed et al. 1994, 1995; Oszkiewicz et al. 2021; Shevchenko et al. 1992, 2003, 2009, 2014b, 2021; Velichko et al. 1995; Wilawer et al. 2022). All magnitudes were measured in the Johnson V band and extrapolated to zero phase angle using the HG1G2 system proposed by Muinonen et al. (2010), with some modifications presented by Penttilä et al. (2016). For computations, the online calculator1 for the HG1G2 photometric system was used. Since we derived absolute magnitudes in our data from the light curve maxima, and the definition of H is based on the rotationally averaged brightness, we added a half of the light curve amplitude corrected to zero phase angle to our results. We used the average correction coefficients from Zappala et al. (1990) for low- and moderate-albedo asteroids. This correction is typically very small because our light curve observations covered small phase angles. Absolute magnitudes obtained at different aspects were averaged. In such a manner, we obtained a homogeneous dataset of absolute magnitudes of about 400 asteroids up to H = 16.5 mag. Our database includes the absolute magnitude data, the G1 and G2 parameters, and the albedo and diameter values from different databases (such as Tedesco et al. 2002; Masiero et al. 2011, 2012; Nugent et al. 2015; Usui et al. 2011). The database is available at the CDS. Figure 1 shows the correlations of the absolute magnitudes from the largest datasets (MPC (HMPC), Pan-STARRS (HPS), and ATLAS (HATLAS)) with those of the Kharkiv dataset (HKH). For the ATLAS dataset, we used the absolute magnitudes in a cyan filter, since this filter overlaps the Johnson V band (Mahlke et al. 2021).
Citation: Velichko et al. 1995
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Citation: Shevchenko et al.; 2014b
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In this section, we describe a few numerical experiments carried out to analyse the importance of various hypotheses used to compute structural kernels. All models were computed using the Clés stellar evolution code (Scuflaire et al. 2008b) with the following ingredients: the CEFF equation of state (Christensen-Dalsgaard & Daeppen 1992), the OPAL opacities from Iglesias & Rogers (1996), supplemented at low temperature by the opacities of Ferguson et al. (2005) and the effects of conductivity from Potekhin et al. (1999) and Cassisi et al. (2007). The nuclear reaction rates are those from the NACRE project (Angulo et al. 1999), supplemented by the updated reaction rate from Formicola et al. (2004) and convection was implemented using the classical, local mixing-length theory (Böhm-Vitense 1958). We also used the implementation of microscopic diffusion from Thoul et al. (1994), for which three groups of elements are considered and treated separately: hydrogen, helium and the metals (all considered to have diffusion speeds of 56Fe). The oscillation frequencies and eigenfunctions were computed using the Liège adiabatic oscillation code (Scuflaire et al. 2008a). We took much care to analyse the numerical quality of the eigenfunctions and the models before computing structural kernels. Irregularities and poor quality of the computed eigenfunctions can bias the results and lead to wrong structural kernels and thus wrong inferences from inverted results. From our experience in hare-and-hounds exercises and inversions, we have determined that adding seismic constraints to the model is very efficient at bringing the reference model into the linear regime thus validating the inversion process. In other words, fitting the average large and small frequency separations is already a big improvement in terms of linearity, although individual seismic constraints, such as individual frequency ratios and individual small frequency separations are the best way to maximise the chances of being in the linear regime. Individual large frequency separations can also be used, but due to their sensitivity to surface effects, they should not be used in observed cases. As such, since in this study we did not use very elaborate seismic fitting techniques, our tests serve the only purpose of isolating various contributions to the errors and to test various hypotheses usually done when carrying out structural inversions in the context of helio- and asteroseismology.
Citation: Formicola et al. (2004)
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We compare our results with a new reduction of observations from the Lowell Observatory SSS, which is running a long-term stellar activity survey complementary to the MWO HK Project. The SSS observes solar and stellar light with the same spectrograph, with the solar telescope consisting of an exposed optical fiber that observes the Sun as an unresolved source (Hall & Lockwood 1995; Hall et al. 2007). The basic measurement of SSS is the integrated flux in 1 Å bandpasses centered on the Ca ii H & K cores from continuum-normalized spectra, ϕHK, which can then be transformed to the S-index using a combination of empirical relationships derived from stellar observations:
7





where 





 is the continuum flux scale for the Ca ii H & K wavelength region, which converts ϕHK to physical flux (erg cm−2 s−1). 





 is a function of Strömgren 





 and is taken from Hall (1996). 





 (simply K in other works) is the conversion factor from the MWO HKP-2 H & K flux (numerator of Equation (1)) to physical flux (Rutten 1984). Ccf is a factor that removes the color term from S and is a function of Johnson 





 (Rutten 1984). Finally, Teff is the effective temperature. See Hall et al. (2007) and Hall & Lockwood (1995) for details on the extensive work leading to this formulation. What is important to realize about this method of obtaining S is that it requires three measurements of solar properties, 





, 





, and 





, along with the determination of one constant, 





. The solar properties are taken from best estimates in the literature, which vary widely depending on the source used, and can dramatically affect the resulting SSSS for the Sun. Hall et al. (2007) used 





, 





, and 





. The constant 





 was empirically determined to be 0.97 ± 0.11 erg cm−2 s−1 in Hall et al. (2007) as the value that provides the best agreement between SSSS and 





 from Baliunas et al. (1995) for an ensemble of stars and the Sun. This combination of parameters resulted in a mean SSSS of 0.170 for the Sun using observations covering cycle 23. A slightly different calibration of SSS data in Hall & Lockwood (2004) used a flux scale 





 based on Johnson 





, set to 0.65 for the Sun, and 





 K. In Table 1 we estimated that this calibration resulted in a mean S = 0.168 for cycle 23. Hall et al. (2009), which included a revised reduction procedure and one year of data with the upgraded camera (see below), found 





.
Citation: Rutten 1984
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Citation: Rutten 1984
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Notes. Intrinsic Lν(1400)/Lν(900) ratios obtained from different stellar population models: the BC03, assuming different initial mass functions (Salpeter, Salp, and Chabrier, Chab), star-formation histories (constant, cSFR, exponentially declining with τ = 0.1Gyr, exponentially rising with τ = −0.1Gyr), metallicties (Z⊙ and 0.02 × Z⊙), and stellar-population ages; the BPASS (Binary Population and Spectral Synthesis code Stanway et al. 2016); the Starburst99 models. We consider a range of wavelengths around 900 Å and 1400 Å, comparable to that covered by the narrow-band and the HST/ACS F606W filters in the rest frame, to estimate the average Lν. As described in Bruzual & Charlot (2003), BC03 provides the spectral energy distribution of stars obtained from a comprehensive library of theoretical model atmospheres (KBFA in the table). The library consists of Kurucz (1996) spectra for O-K stars, Bessell et al. (1991) and Fluks et al. (1994) spectra for M giants, and Allard & Hauschildt (1995) spectra for M dwarfs. In BPASS the stellar evolutionary tracks contain a contribution from isolated stars and binary systems. Also, the stellar atmosphere models are selected from the BaSeL v3.1 library (Westera et al. 2002), supplemented by Wolf-Rayet stellar atmosphere models from the Potsdam PoWR group (Hamann & Gräfener 2003). With Starburst99, it is possible to generate SEDs assuming a bunch of stellar evolutionary tracks, including stars with and without rotation (GenevaV40 and GenevaV00 respectively, Leitherer et al. 2014), and stellar atmospheres (the combination of model atmosphere from Pauldrach et al. 1998; Hillier & Miller 1998, is the recommended option). The 70%ROT+30%noROT entry indicates a model that is a combination of GenevaV40 for the 70% and GenevaV00 for the 30% (Levesque et al. 2012). The GenevaV40 and GenevaV00 tracks were released for metallicity equal to Z = 0.014 (~Z⊙, Eldridge 2012). The change in the intrinsic ratio due to the different evolutionary tracks and stellar atmospheres is shown for a Salpeter IMF, Z⊙, cSFR, and 100 Myr old stellar population. In the bottom part of the table, we report the ratios calculated from the best fit templates of AGN (Bongiorno et al. 2012), in which the SEDs are dominated by the radiation coming from an (un-)obscured AGN. (1) The intrinsic Lν(1400)/Lν(900) ratio for an unobscured TypeII AGN can be as low as 2.35 (Richards et al. 2006). In the estimation of the ratios we take into account the HI absorption occurred in star atmospheres, but we neglect that within the interstellar and circum-galactic medium.
Citation: Bruzual & Charlot (2003)
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Finally, we confirm our hypothesis on the origin of the bi-modal A(Li) distribution, and of the isthmus, by comparing results from our GCE model with data. In Fig. 8 we show the normalised A(Li) distribution of all the stars in our sample (blue histogram) compared with the result from three models of GCE: (i) imposing a gently declining SFH (SFR_0b model, dashed red lines); (ii) a gently declining SFH plus a single star formation burst at a ∼6 Gyr look-back time (SFR_1b model, dashed blue lines); and (iii) our best model (SFR_2b, black-solid lines), which contains a gently declining SFR plus two star formation bursts at ∼6 Gyr and ∼1.5 Gyr look-back times, the latter being the most impulsive. In our best model the first star formation peak is only 68% as intense as the latter and lasts 25% longer. The SFR_2b model is the one that best reproduces the observed A(Li) distribution while recovering the presently observed SFR and the thin-disk stellar and HI mass (Mor et al. 2019; Isern 2019; Ruiz-Lara et al. 2020). This result is robust as it only depends on the observed A(Li) distribution. Possible biases from the determination of the stellar ages do not have an impact on our conclusions. Figure 8 clearly shows that only a two-peaked SFH can explain the observed bi-modal A(Li) distribution when accounting for most known 7Li production and depletion mechanisms (solid black line). It is important to remark that we cannot quantify the exact intensity and length of the star formation bursts from our data and models, but we can only give a qualitative analysis. This is a consequence of: (i) the large age determination uncertainties still present in current data; (ii) the fact that the data we use is restricted to the solar neigbourhood and thus do not represent the entire Galaxy; and finally (iii) the fact that our model still misses some 7Li production and destruction processes that are currently under study (e.g. the effect of planet engulfment). In the future, new data from large surveys such as Galah (Buder et al. 2021) combined with better determinations of A(Li) in 7Li-poor low-luminosity cold dwarf stars will result in large, unbiased samples of MS stars. These new catalogues will allow us to better understand the many channels of 7Li production and destruction that occur inside dwarf stars. Also, future catalogues that include precise age determinations will allow us to better constrain the SFH of the MW, also by analysing its A(Li) distribution.
Citation: Ruiz-Lara et al. 2020
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Strong outflows are commonly associated with the early stages of stellar evolution. They are likely responsible for transporting excess angular momentum away from the star–disc system and regulating the mass-accretion process and spin evolution of newly born stars (e.g. Hartmann & Stauffer 1989; Matt & Pudritz 2005; Bouvier et al. 2014). There are at least three possible types of outflows around young stellar objects: (1) a disc wind launched from the accretion disc (e.g. Blandford & Payne 1982; Ustyugova et al. 1995, 1999; Romanova et al. 1997; Ouyed & Pudritz 1997; Königl & Pudritz 2000; Pudritz et al. 2007), (2) an X-wind or a conical wind launched near the disc–magnetosphere interaction region (e.g. Shu et al. 1994, 1995; Romanova et al. 2009) and (3) a stellar wind launched from open magnetic field lines anchored to the stellar surface (e.g. Decampli 1981; Hartmann & MacGregor 1982; Kwan & Tademaru 1988; Hirose et al. 1997; Strafella et al. 1998; Matt & Pudritz 2005; Romanova et al. 2005; Cranmer 2009). However, despite recent efforts, the exact launching mechanisms of the winds and outflows as well as the mechanism behind the collimation of the ejected gas into jets are still not well understood (e.g. Edwards et al. 2006; Ferreira, Dougados & Cabrit 2006; Kwan, Edwards & Fischer 2007; Tatulli et al. 2007b; Kraus et al. 2008; Eisner, Hillenbrand & Stone 2014). Hence, high-resolution interferometric observations which can resolve the wind-launching regions are crucial for addressing this issue. If a high spectral resolution is combined with a high spatial resolution, the emission-line regions near the base of the wind (e.g. Brγ emission regions in Herbig Ae/Be stars) can be resolved in many spectral channels across the line (e.g. Weigelt et al. 2011; Kraus et al. 2012b,c; Garcia Lopez et al. 2015). This allows us to study the wavelength-dependent extent and the kinematics of the winds, which can be derived from the line visibilities and wavelength-dependent differential and closure phases. Such observations would help us to distinguish the different types of outflow scenarios.
Citation: Ouyed & Pudritz 1997
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An estimate of a sputtering cross-section can be inferred from our measurements with σs ≈ V∕d, where V is the volume occupied by 

${Y}_{\textrm{s}}^{\infty}$Ys∞
 molecules and d the depth of sputtering. 

$\sigma_{\textrm{s}}\approx {Y}_{\textrm{s}}^{\infty}/l_{\textrm{d}}/\textrm{ml}$σs≈Ys∞/ld/ml
, where ml is the number of CO or CO2 molecules cm−2 in a monolayer (about 6.7 × 1014 cm−2 and 5.7 × 1014 cm−2, respectively,with the adopted ice densities). As is shown in Table 1, the sputtering radius rs would therefore be about 1.26 to 2.12 times larger than the radiolysis destruction radius rd in the case of the CO2 ice, and 2.03 to 2.36 for CO in the considered energy range (~0.5-1 MeV/u). The net radiolysis is the combined effect of the direct primary excitations and ionisations, the core of the energy deposition by the ion, and the so-called delta rays (energetic secondary electrons) travelling at much larger distances from the core; that is, several hundreds of nanometres at the considered energies in this work (e.g. Mozunder et al. 1968; Magee & Chatterjee 1980; Katz et al. 1990; Moribayashi 2014; Awad & Abu-Shady 2020). The effective radiolysis track radius that we calculate is lower than the sputtering one, which points towards a large fraction of the energy deposited in the core of the track. The scatter on the ratio of these radii is due to the lack of more precise data. It nevertheless allows to put a rough constraint on the estimate of Nd in the absence of additional depth measurements, with 

${N}_{\textrm{d}} \lesssim {Y}_{\textrm{s}}^{\infty}/\sigma_{\textrm{d}}$Nd≲Ys∞/σd
. If the rs∕rd ratio is high, a large amount of species come from the thermal sublimation of an ice spot less affected by radiolysis, and the fraction of ejected intact molecules is higher. The aspect ratio corresponding to these experiments evolves between about ten and twenty for CO2 and CO, whereas for water ice at a stopping power of Se ≈ 3.6 × 103eV∕1015 H2 O molecules cm−2, we show that it is closer to one (Dartois et al. 2018). The depth of sputtering is much larger for CO and CO2 than for H2O at the same energy deposition, not only because their sublimation rate is higher, but also because they do not form OH bonds. For complex organic molecules embedded in ice mantles dominated by a CO or CO2 ice matrix, with the lack of OH bonding and the sputtering for trace species being driven by that of the matrix (in the astrophysical context), the co-desorption of complex organic molecules present in low proportions with respect to CO/CO2 cannot only be more efficient, but will thus arise from deeper layers.
Citation: Awad & Abu-Shady 2020
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These properties can also be related to the fractal nature of radiative mixing layers. Recently, Fielding et al. (2020) showed that the area of the cooling surface in radiative mixing layer simulations obeys a fractal scaling, with
(31)$$\begin{eqnarray*}
\frac{A_{\rm T}}{A_{\rm L}} = \left(\frac{\lambda }{L} \right)^{2-D},
\end{eqnarray*}$$where λ is the smoothing scale and D = 2.5 was the fractal dimension argued to hold by analogy with well-known fractals, and verified in their simulations. Turbulence combustion fronts are indeed well known to be fractals, due to the dynamical self-similarity of turbulence in the inertial range. Experimental measurements by e.g. instantaneous laser tomography have given values ranging from D = 2.1−2.4 in a variety of flow geometries, with a preferred value of D = 2.35 (Hentschel & Procaccia 1984; Sreenivasan, Ramshankar & Meneveau 1989); it has been argued that this fractal dimension is universal (Catrakis, Aguirre & Ruiz-Plancarte 2002; Aguirre & Catrakis 2005). From equation (19), the fractal dimension can be used to calculate the turbulent flame speed (Gouldin et al. 1986; Peters 1988). The fractal scaling and consequent increase in area AT should extend all the way down to the Gibson scale λG, which is defined to be the scale where the turbulent velocity equals the laminar flame speed, v(λG) = SL. This is often unresolved in simulations. If we use the Kolmogorov scaling v∝λ1/3, then we obtain:
(32)$$\begin{eqnarray*}
\frac{S_{\rm T}}{S_{\rm L}} = \frac{A_{\rm T}}{A_{\rm L}} = \left(\frac{\lambda _{\rm G}}{L} \right)^{2-D} = \left(\frac{u^{\prime } }{S_{\rm L}} \right)^{3(D-2)} ,
\end{eqnarray*}$$where we have used equation (31) and v(λG) = SL. Thus, in equation (20), we have n = 3(D − 2). The experimental value of D = 2.35 gives n = 1.05, in good agreement with Damköhler’s scaling, and fair agreement with the scaling in equation (23). The Fielding et al. (2020) value of D = 2.5 gives n = 1.5, or ST = u′(u′/SL)1/2. If one uses the laminar $S_L \propto t_{\rm cool}^{-1/2}$ from our static simulations, this would imply $S_T \propto t_{\rm cool}^{1/4}$. However, in the Fielding et al. (2020) model, the speed at which a cooling layer advances is $S_L \propto t_{\rm cool}^{1/2}$, so they end up with $S_T \propto t_{\rm cool}^{-1/4}$ as well. The scalings are sensitive to the fractal dimension D and the measurement error on D obtained from the simulations is unclear at this point. In addition, the cutoff scale of turbulence may not be the Gibson scale. We caution that fractal arguments have not proven to be fully robust in the turbulent combustion context. For instance, the measured fractal parameters fluctuate depending on the extraction algorithm, and have not been able to correctly predict the turbulent burning velocity (Cintosun, Smallwood & Gülder 2007).
Citation: Sreenivasan, Ramshankar & Meneveau 1989
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Type 1 AGN (NLSy1, quasars) and aligned CB-SMBH models expected signatures. Two SMBH and their BLRs induce more rich and complex differential phase patterns. There are many configurations for which the aligned CB-SMBH differs between them and single SMBH. The features of synthetic spectra given in Figs. C.2b and C.2c show a similarity with those found in 3C 390.3 (Landt et al. 2014, see their Fig. A1). This object is well-known as a double-peaked line emitter in the optical band. The double-peaked profiles can be also associated with accretion disc emission (Eracleous & Halpern 1994, 2003; Gezari et al. 2007). However, if the binary model is appropriate for this object, then associated differential phases will have a complex double S-shaped structure. This model reflect the possibility of a non-coplanar CB-SMBH, with highly inclined orbits of clouds in both BLRs. If a single SMBH model with a BLR d of 95 light days is true (see Shapovalova et al. 2010b) a differential signal would be 0.9°. Even that spectral lines of objects can share some characteristics, our model predicts that corresponding differential phases are distinct because of different SMBH and the clouds’ orbital parameters. The optically bright quasar PG 1211+143 (Landt et al. 2014) has a convex Paα shape slightly depressed of the centre, as in our synthetic case present in Fig. C.2a. The predicted differential phase would resemble an asymmetric double S shape, caused by non-coplanarity of the CB-SMBH system and high values for the clouds’ orbital elements Ωc and ωc. Moreover, the high rise spectral line in Fig. 5a is also observed in the spectrum of SDSSJ032213.90+005513.4 (Kim et al. 2010, see their Fig. 1). If the CB-SMBH model is appropriate for this object, then the expected differential phase would be similar in morphology with the previous case but distinct in their details because of different values of Ω2. In addition, asymmetric two horn feature (blue line) found in Fig. C.3b, is also highly consistent with observed line in Mrk 79 (Landt et al. 2008, see their Fig. 13). Anticipated differential phases differ from those seen in previous cases because of large values, 230°  Ω1, Ω2   330° , and decreasing ωk, k = 1, 2.
Citation: Shapovalova et al. 2010b
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