adsabs/FOCAL huggingface dataset:
For the stars below 





, our Ca abundances are determined from the only Cai line detected, the 4226.73 Å resonance line. This line is known to produce lower Ca abundances than other Ca i lines for EMP stars, at least in part because of NLTE effects (e.g., Spite et al. 2012), leading T10 to dismiss the significance of the even lower [Ca/Fe] ratio they derived for Scl 07-50. However, NLTE models do not agree well on the correction for the 4226.73 Å line for stars with similar atmospheric parameters to Scl 07-50 and Scl 11_1_4296, with recent predictions ranging from −0.02 dex (Starkenburg et al. 2010) to +0.21 dex (Mashonkina et al. 2007; L. Mashonkina 2014, private communication). We therefore attempted several additional tests to verify the low Ca abundances. First, we compared the Ca lines of both stars with those of the ultra metal-poor giant CD 





 245 (Bessell  Norris 1984), which is comparable in temperature to Scl 11_1_4296 and ∼200 K warmer than Scl 07-50 (see Figure 2). Scl 11_1_4296 has weaker Ca i λ4226.73 Å and near-infrared Ca ii triplet lines than CD 





 245, confirming its low Ca abundance. Scl 07-50 has similar Ca K and Cai λ4226.73 Å EWs to CD 





 245, consistent with a lower Ca abundance given the temperature difference.5

5
The Ca triplet lines of Scl 07-50 are stronger than those of CD 





 245, but NLTE and 3D corrections for those lines are much larger and even less well understood.
 Second, we compared to stars with similar parameters (after adjusting their spectroscopic temperatures according to the Frebel et al. 2013 formula) from Roederer et al. (2014). These stars were selected to have 4400 K 





 4900 K, 





, 





, and a detection of the Ca i resonance line, resulting in a sample of 13 stars. For this sample, Ca abundances from Ca i 4226.73 Å are 0.09 dex lower than the mean abundance from all other Ca i lines.6

6
The only outlier where Ca i 4226.73 Å and the other lines have a significantly larger abundance difference is the coolest star, CS 22950–046, which is similar in temperature to Scl 07-50, raising the possibility of a sharp temperature dependence in the abundance derived from the resonance line. However, because the theoretical studies of Mashonkina et al. (2007) Merle et al. (2011), and Spite et al. (2012) do not indicate strong changes in NLTE corrections at 





 K, we regard CS 22950–046 as a random outlier rather than a systematic one.
 This offset is in excellent agreement with the most recent NLTE corrections for Ca determined by Spite et al. (2012), which give 0.08 dex for 





 K, 





, 





. Finally, we stacked the four strongest Ca i non-resonance lines and determined upper limits of 





 dex and 





 dex for Scl 07-50 and Scl 11_1_4296, respectively, by comparing to synthesized spectra. We therefore conclude that even after factoring in the uncertain NLTE effects, Scl 07-50 and Scl 11_1_4296 indeed have low Ca abundances.
Citation: Bessell  Norris 1984
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Therefore, we now fit the two pn spectra between 3 and 10 keV using a power-law model with Galactic absorption, a narrow neutral Fe Kα core (En = 6.4 keV and σn = 0 eV), and a disc line model (RELLINE; Dauser et al. 2010, 2013) to account for the mildly broad line. For the third component, the energy was fixed at 6.4 keV and the spin at zero (since it is not constrained). All parameters of the Fe Kα narrow component and the emissivity index for the mild relativistic Fe K line component were tied between the two epochs. From this modelling (χ2/d.o.f. = 585.4/668), we infer an accretion disc emissivity index lower than 2.1 and a disc inclination lower than 24.6°, which is consistent with the inclination angle inferred from the variable O VII soft X-ray emission line (



θ
=
9
.

9

−
1.4


+
1.0




$ \theta=9.9^{+1.0}_{-1.4} $


) arising from the accretion disc too (Reeves et al. 2021a). For the narrow core of the Fe Kα line, we measure a EWn ≲ 20 eV, which is in the lower range of the values found for type-1 AGN (∼30−200 eV; Liu & Wang 2010; Shu et al. 2010; Fukazawa et al. 2011; Ricci et al. 2014). This is consistent with the very weak covering factor of 0.06 for the putative torus, which is inferred from the ratio of the infrared to the bolometric luminosity of the source (Ezhikode et al. 2017). Moreover, the torus covering factor measured for Mrk 110 is one of the lowest reported in the Ezhikode et al. (2017) sample; this is also in agreement with the lack of Compton hump. The equivalent widths of the moderately broad Fe Kα line are EWb = 61





−
27


+
23



$ ^{+23}_{-27} $


 eV and EWb = 43





−
27


+
22



$ ^{+22}_{-27} $


 eV for 2019 and 2020, respectively. Likewise, if we allow the inner disc radius to be free to vary and assume a standard value of three for the disc emissivity index, as well as fixing the inclination angle at 9.9° (χ2/d.o.f. = 585.1/668), we infer Rin = 120





−
67


+
263



$ ^{+263}_{-67} $


Rg. This strengthens that the moderately broad Fe line could originate from the accretion disc but not too close to the inner stable circular orbit (ISCO), as was found for the O VII soft X-ray emission line (Reeves et al. 2021a). Its origin from the outer accretion disc is also consistent with the timing analysis reported in Lobban et al. (in prep.) where a hint of an extra variability is found at the Fe Kα complex energy range in the fractional variability spectra.
Citation: Reeves et al. 2021a
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Citation: Reeves et al. 2021a
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When B
X is positive (see the center gray area in Figure 2(a), and corresponding area in Figures 2(e)–(f)), electrons at two energy ranges both present isotropic PAD. As early as 1972, Eastwood et al. (1972) have pointed out that a strong field line curvature would scatter particles. Such a nonadiabatic mechanism has been studied successfully. Büchner and Zelenyi 1989 were the first to use the curvature parameter κ
2 = R
min/ρ
max, the ratio between the minimum curvature radius R
min and the maximum particle Larmor radius ρ
max, to carry out the trapped particle motion in magnetic field reversals with arbitrary curvature radii in 1989. The parameter depends on the total kinetic energy of the particles and the field geometry, followed by the particle adiabatic invariants. κ ≫ 1 corresponds to the usual adiabatic case. As κ decreases toward unity, the particle motion becomes stochastic due to deterministic chaos. Such behavior, which for κ ≈ 1 becomes strongly chaotic, applies, e.g., to thermal electrons in Earth's magnetotail and makes its collisionless tearing mode instability possible. While for κ  1, it corresponds to the quasi-adiabatic regime, where new current sheet equilibriums can be built (e.g., Zelenyi et al. 2004). We use the curvature radius of magnetic field line R
C (Figure 2(a)), electron cyclotron radius R
e (Figure 2(a)) at energy range 6.52–8600 eV separated into two small channels, which is marked by color lines, and the improved adiabatic parameter 1/κ
2 = R
e/R
C, the ratio between R
e and R
C (Figure 2(c)), to investigate and approve the nonadiabatic motion of electrons (Büchner & Zelenyi 1989; Delcourt et al. 2017). Understandably, R
C of the magnetic field line in the current sheet is much smaller, showing a strongly curved shape, seen in Figure 2(b). R
e of electrons is much larger than outside, and the higher-energy range electrons have the larger R
e, seen in Figure 2(c). Typically, R
e of electrons and R
C of the magnetotail field line differ by 3 orders of magnitude (see the red lines in Figures 2(d), 4(d), (i), (m), and (r)). Electrons would be scattered inside the current sheet when the R
e and R
C can be compared. Lavraud et al. (2016) have observed a similar pitch-angle scattering process at the magnetopause during a reconnection event, and pointed out that the small curvature radius is the reason by using the κ parameter to analyze first electron MMS data. Thus, when the spacecraft start entering the current sheet, electrons would be scattered along the strongly curved magnetic lines (see the area marked by the first and fourth dotted lines in Figure 2(f)). Meanwhile, high-energy electrons are more easily scattered than low-energy electrons, as electrons at 6.52–35 eV are only scattered at the center of the current sheet (see the area marked by the second and third dotted lines in Figure 2(e)).
Citation: Zelenyi et al. 2004
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The electron-positron creation process may induce dynamical instability during the most advanced phases of massive star evolution. Pair creation absorbs part of the thermal energy of the plasma, consequently lowering the thermal pressure. The plasma is not a perfect gas anymore, and temperature variations do not lead to changes in pressure (Kippenhahn, Weigert & Weiss 2012). Regions in which this process happens become locally dynamically unstable. To check if a star is globally stable or not, a perturbation method should be adopted (Ledoux & Walraven 1958). However, Stothers (1999) showed that an evaluation of the first adiabatic exponent properly weighted and integrated over the whole star, 〈Γ1〉, is a very good approximation to determine the dynamical stability of a star. As done by other authors (e.g. Marchant et al. 2019; Farmer et al. 2019, 2020), we adopted the Stothers (1999) stability criterion, which states that a star is stable if
(4)$$\begin{eqnarray*}
\mbox{$\langle \Gamma _{1} \rangle _{\rm }$} = \frac{\int ^{M}_0 \frac{\Gamma _1 P}{\rho } dm}{\int ^{M}_0 \frac{P}{\rho } dm} \gt \frac{4}{3},
\end{eqnarray*}$$where Γ1 is the first adiabatic exponent, P is the pressure, ρ is the density and dm is the element of mass. We decided to compute the above integrals in two ways. In the first case, the integral is calculated from the centre of the star (M = 0) up to the mass of helium core (M = MHe), defining 〈Γ1〉Core; in the second case, we compute the integral from the centre to the surface of the star (M = MTOT), to include the contribution of the envelope, thus 〈Γ1〉TOT. These two values are computed at each time-step for all tracks. In the case of pure-He stars, 〈Γ1〉Core = 〈Γ1〉TOT. Since parsec is a hydro-static code, we cannot follow the evolution through the dynamical collapse; we stop the computation if the 〈Γ1〉 4/3 + 0.01, to be conservative, and label the star as a PI. Since we cannot follow the hydrodynamical evolution, we cannot distinguish between PPI and PISN: we classify both of them as PI and we assume that both of them leave no compact object. This makes our results for the BH mass even more conservative, because stars that undergo a PPI might still retain most of their mass after weak pulses and form a massive BH by core collapse ( Farmer et al. 2019; Marchant et al. 2019).
Citation: Farmer et al.; 2020
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In regions of high C/O, planets form primarily from carbonates, and in regions of low C/O, the Mg/Si determines the types of silicates that dominate the compositions (e.g., Brewer et al. 2016, and references therein). This means that the C/O ratio controls the distribution of Si among carbide and oxide species. If C/O is greater than 0.8, Si exists in solid form primarily as SiC, and also graphite and TiC will be formed; for C/O ratios below 0.8, Si is present in rock-forming minerals as ${\rm{SiO}}_4^{4 - }$SiO44− or SiO2, serving as seeds for Mg silicates for which the exact composition will be controlled by the Mg/Si value (Bond et al. 2010; Thiabaud et al. 2015b). Moreover, Thiabaud et al. (2015a) have shown that the condensation of volatile species as a function of radial distance allows for C/O enrichment in specific parts of the protoplanetary disk of up to four times the solar values, leading to the formation of planets that can be enriched in C/O in their envelope up to three times the solar value. This is the case of HD209458b observed by Giacobbe et al. (2021) for which a scenario of planet formation beyond the water snowline and migration toward its host star through disk or disk-free migration was hypothesized (see also Brewer et al. 2017). At the same time, Mg/Si governs the distribution of silicates: for Mg/Si  1, Mg forms orthopyroxene (MgSiO3) and the excess Si is present as other silicate species such as feldspars (CaAl2Si2O8, NaAlSiO8) or olivine (Mg2SiO4); for Mg/Si values ranging from 1 to 2, Mg is distributed between olivine and pyroxene; for Mg/Si > 2, all available Si is consumed to form olivine with excess Mg available to bond with other minerals, mostly oxides such as MgO or MgS (Bond et al. 2010; Thiabaud et al. 2015b). The peak of the Mg/Si-C/O distribution for our targets is therefore consistent with Si which will take solid form as ${\rm{SiO}}_4^{4 - }$SiO44− and SiO2 and Mg equally distributed between pyroxene and olivine.
Citation: Thiabaud et al. 2015b
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Citation: Thiabaud et al. 2015b
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Adaptive optics (AO; Beckers 1993) has become a key technology for all the main existing telescopes and is considered an enabling technology for future Extremely Large Telescopes (ELTs; Ramsay et al. 2016; Boyer 2018; Bouchez et al. 2018). AO requires sufficiently bright reference sources for the measurement of the wavefront (WF) distortions introduced by the atmospheric turbulence: Sodium laser guide stars (LGS; Foy & Labeyrie 1985; Tallon & Foy 1990) are currently the only valid option to increase the low sky coverage allowed by the use of natural stars (Ellerbroek & Andersen 2008). A Sodium LGS is generated by a laser beam at 589 nm wavelength that excites the Sodium atoms concentrated in a ∼13 km thick layer at about 90 km above the ground (Pfrommer & Hickson 2014), returning a photon flux at the same wavelength (Happer et al. 1994; Thomas et al. 2008). The Sodium layer vertical extension and its variable density profile (Pfrommer, Hickson & She 2009; Holzlöhner et al. 2016) lead to some peculiar complications of the WF sensing process (Lombini 2011). The Shack–Hartmann WF Sensor (SHWS) is the current baseline for the LGS WF sensors (WSs) for the future ELT AO instruments  (Boyer & Ellerbroek 2016; Stuik et al. 2016; Males et al. 2018; Sauvage et al. 2018). The LGS spots appear elongated in the sub-apertures located off-axis with respect to the upward laser beam, due to the parallactic effect; the elongation points at the laser launch location and its amplitude increases with the distance from the launcher itself (Fig. 1). The LGS angular elongation ϵ can be approximated by
(1)$$\begin{eqnarray}
\epsilon \approx r \frac{\Delta H}{H^2} \text{cos}(\xi) ,
\end{eqnarray}$$where r is the sub-aperture distance from the launcher, H is the Sodium layer mean altitude, ΔH is the layer vertical extension, and ξ is the Zenith angle. The spot position angle ω is
(2)$$\begin{eqnarray}
\omega = \text{atan}\left(\frac{y_l-y_{s}}{x_l - x_{s}}\right) ,
\end{eqnarray}$$
Citation: Ellerbroek & Andersen 2008
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Citation: Bouchez et al. 2018
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Citation: Pfrommer & Hickson 2014
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Citation: Stuik et al. 2016
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Under the symmetry assumption of Friedmann–Lemaître cosmologies, all fluids are characterized by their density and their equation of state. In spatially flat cosmologies with the matter density parameter Ωm and the corresponding dark energy density 1 − Ωm one obtains for the Hubble function $H(a)=\dot{a}/a$ the expression,
(1)$$\begin{eqnarray*}
\frac{H^2(a)}{H_0^2} = \frac{\Omega _\mathrm{m}}{a^{3}} + \frac{1-\Omega _\mathrm{m}}{a^{3(1+w)}},
\end{eqnarray*}$$The comoving distance χ is related to the scale factor a through
(2)$$\begin{eqnarray*}
\chi = -c\int _1^a\:\frac{\mathrm{d}a}{a^2 H(a)},
\end{eqnarray*}$$where the Hubble distance χH = c/H0 sets the distance scale for cosmological distance measures. Small fluctuations δ in the distribution of dark matter grow, as long as they are in the linear regime |δ| ≪ 1, according to the growth function D+(a) (Linder & Jenkins 2003),
(3)$$\begin{eqnarray*}
\frac{\mathrm{d}^2}{\mathrm{d}a^2}D_+(a) + \frac{2-q}{a}\frac{\mathrm{d}}{\mathrm{d}a}D_+(a) - \frac{3}{2a^2}\Omega _\mathrm{m}(a) D_+(a) = 0,
\end{eqnarray*}$$and their statistics is characterized by the spectrum $\langle \delta (\boldsymbol {k})\delta ^*(\boldsymbol {k}^\prime)\rangle = (2\pi)^3\delta _D(\boldsymbol {k}-\boldsymbol {k}^\prime)P_\delta (k)$. Inflation generates a spectrum of the form $P_\delta (k)\propto k^{n_s}T^2(k)$ with the transfer function T(k) (Bardeen et al. 1986) which is normalized to the variance σ8 smoothed to the scale of 8 Mpc h−1,
(4)$$\begin{eqnarray*}
\sigma _8^2 = \int _0^\infty \frac{k^2\mathrm{d}k}{2\pi ^2}\: W^2(8 \mathrm{Mpc}/h\times k)\:P_\delta (k),
\end{eqnarray*}$$with a Fourier-transformed spherical top-hat W(x) = 3j1(x)/x as the filter function. From the CDM spectrum of the density perturbation, the spectrum of the dimensionless Newtonian gravitational potential Φ can be obtained,
(5)$$\begin{eqnarray*}
P_\Phi (k) \propto \left(\frac{3\Omega _\mathrm{m}}{2 (k\chi _H)^2}\right)^2\:P_\delta (k),
\end{eqnarray*}$$by applying the comoving Poisson equation $\Delta \Phi = 3\Omega _\mathrm{m}/(2\chi _H^2)\delta$ for deriving the gravitational potential Φ (in units of c2) from the density δ. Because our analysis relies on the assumption of Gaussianity, we need to avoid non-linearly evolving scales and will restrict our analysis to large angular and spatial scales, where the cosmic density field can be approximated to follow a linear evolution, conserving the near-Gaussianity of the initial conditions. We increase the variance of the weak lensing signal and of the intrinsic alignment signal of elliptical galaxies on small scales because of non-linear structure formation using the description of Smith et al. (2003) and Casarini et al. (2011, 2012). Consequently, the cross-correlation between weak lensing and elliptical galaxy shapes will likewise have increased variances on small scales. Shapes of spiral galaxies are set by the initial conditions of structure formation; therefore, we did not apply changes to the linear CDM-spectrum P(k).
Citation: Bardeen et al. 1986
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(3) Extended cold-accretion model. The actual behavior of cold accretion will be more complicated than suggested by the analytical work of Dekel & Birnboim (2006), which investigated the behavior of mean halos under many simplifications. One possibility is that cold-accretion behavior depends upon the environment. Galaxies with the same halo mass may experience different accretion histories depending on whether they reside in highly crowded regions such as proto-galaxy clusters or in sparse regions that will eventually develop into fields or voids. Keres et al. (2005) used detailed numerical simulation to show that the intensity and time variation of cold-mode accretion indeed depends on the galactic environment. According to their results, there is a tendency for cold-mode accretion to persist into lower redshifts in the region of lower galaxy number densities. Keres et al. (2005) stated that this environmental dependence is driven largely by the galaxy mass dependence of the cold–hot accretion fraction, but they also recognized a truly environmental effect that massive galaxies in low-density environments tend to have higher cold-accretion fractions than those in denser regions. Because disk galaxies, especially those with larger stellar masses (





), tend to reside in low-density regions such as fields and poor groups (Blanton & Moustakas 2009), this effect may be important in modeling the evolution of such galaxies. We therefore implement the third type of cold accretion. Because the evaluation of cold accretion by Dekel & Birnboim (2006) is based on many simplified assumptions that make the problem analytically amenable, it is considered that there remains a considerable quantitative ambiguity. In view of this, we take a simple approach in specifying the cosmological history of cold accretion. Specifically, we parameterize the third type of cold accretion using four parameters: the characteristic time, 





, when cold accretion gives way to hot accretion; the characteristic mass, 





, which divides hot and cold accretion at 





; and two parameters, 





 and 





, that describe the change in the characteristic mass before and after 





, respectively. In this parameterization, the critical mass is specified as
18







19





If 





, the halo gas is assumed to collapse to the disk plane with the freefall time (





). Otherwise, the gas is assumed to accrete over the larger of the cooling and freefall times (





). This specification, depending on the adopted parameters, accommodates a wide variety of accretion histories. We set 





, 





, and 





 throughout this paper. This specification of parameters moves the end of cold accretion to more recent epochs than the prediction of Dekel & Birnboim (2006) for halos with 





 and realizes the prolonged cold accretion suggested in Keres et al. (2005). Under this parameterization, the model gives the best match to the observed disk sizes (Figure 7) and galaxy colors (Figure 9) without changing other observational predictions to a significant degree.
Citation: Blanton & Moustakas 2009
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Figure 3 shows the column densities of H2, c-C3H2 and CH3OH extracted along the dotted line present in Fig. 1, as well as the N(H2) calculated with the model of L1544 described in Keto & Caselli (2010) assuming a beam size of 40′′. The column densities of c-C3H2 and CH3OH were calculated assuming that the lines are optically thin, using the formula given in Eq. (1) of Spezzano et al. (2016). We assumed a Tex of 6 K for c-C3H2 and 6.5 K for CH3OH, as done in Spezzano et al. (2013) and Bizzocchi et al. (2014), respectively. The same works reported that both lines present moderate optical depths (τ  0.4). This plot shows that the decrease of N(H2) towards the south-west, where cyclopropenylidene is more abundant, is much steeper than towards the north-east, where methanol is more abundant. A full map of the N(c-C3H2)/N(CH3OH) column density ratio can be seen in Fig. A.1, showing a clear peak towards the south-east side of L1544. Figure 3 also shows that c-C3H2 and CH3OH both belong to the same dense core (identified by the brightest peak in N(H2)), but trace different parts of it. We obtain the same result by comparing the line-width and velocity maps of the two molecules, see Fig. B.1. Despite the different spatial distributions, the two molecules trace the same kinematic patterns (velocity gradient and amount of non-thermal motions). This indicates that the velocity fields are dominated by the bulk motions (gravitational contraction and rotation) of the prestellar core, which similarly affect the two sides of the core and do not depend on the chemical composition of the gas. In summary, c-C3H2 and CH3OH trace different parts of the same dense core and no velocity shift is present (unlike for the L1551 case; Swift et al. 2006). We note that the observed transitions of c-C3H2 and CH3OH have relatively high critical densities (between a few ×104 and 106 cm-3), so that these lines are not expected to trace the more diffuse filamentary material surrounding the prestellar core.
Citation: Bizzocchi et al. (2014)
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