adsabs/FOCAL huggingface dataset:
As mentioned in Sections 2, six sources (G035.19–00.74, G049.48–00.36, G133.94+01.06, G031.28+00.06, G043.89–00.78 and G059.78+00.06) were observed by both the ARO 12 m and IRAM 30 m telescopes, which can be used to check beam size effects potentially influencing our abundance ratios. A comparison between the spectra from the ARO 12 m and the IRAM 30 m is shown in Figure 3. Measured line parameters are given in Tables 1 and 2. If the scale of our targets is smaller than the beam size, filling factors are less than unity. So, measured line intensities are diluted. In this case, the intensity of detected lines has to be adjusted for the beam dilution effect 





/(





 + 





) (ηBD), where θs and θbeam are source size and beam size, respectively (Zhang et al. 2017). Thus, the brightness temperatures (TB) of the sources can be derived from the main beam brightness temperature (Tmb) dilution:
5





There are two Tmb values, measured by the IRAM 30 m and the ARO 12 m with beam sizes of ∼25″ and ∼63″. Therefore, the source size can be estimated using Equation (5). We employed CS, C34S, 13CS, and C33S line data to estimate the size of those six sources, and the results are listed in Table 4. Source sizes turn out to be in the range 24″–126″ and are quite different between estimations from different isotopes. To the contrary, the sulfur isotope abundance ratios do not show significant differences between the ARO 12 m and the IRAM 30 m measurements. Within the error ranges, the average abundance ratios determined from the ARO 12 m (17.6 ± 2.7 and 4.9 ± 0.7 for 32S/34S and 34S/33S, respectively) are consistent with those from the IRAM 30 m observations (18.1 ± 4.1 and 5.5 ± 0.8; the errors given in this subsection represent standard deviations for individual sources). In addition, two sources (Sgr B2, G111.54+00.77 (NGC 7538)) among our sample were also observed by the 7 m antenna of the Crawford Hill Observatory (Frerking et al. 1980). The I(13CS)/I(C34S) line intensity ratios measured by Frerking et al. (1980) yield 0.62 ± 0.04 and 0.43 ± 0.3 with a beam size of ∼22, which is also consistent with our results from the ARO 12 m (0.60 ± 0.03 and 0.38 ± 0.04). Thus, our measurements of sulfur isotope ratios are not seriously affected by beam size effects.
Citation: Zhang et al. 2017
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For all galaxies the extended profiles of $\Sigma _\mathrm{H\,\small {I}}$ obtained from observations at the WSRT telescope were found in Yim & van der Hulst (2016) and Noordermeer et al. (2005). The surface density of $\Sigma _\mathrm{H_2}$ is usually calculated from observations of CO molecule lines, but the exact value of the conversion factor XCO remains debatable. If CO intensity profile is available, we follow the procedure described in Yim & van der Hulst (2016) to obtain $\Sigma _\mathrm{H_2}$. For NGC 4258, NGC 4725 (Yim & van der Hulst 2016), and NGC 2985 (Young et al. 1995), the CO(J = 1 → 0) line was used to calculate $\Sigma _\mathrm{H_2}$:

\begin{equation*}
\Sigma _\mathrm{H_2} (\text{M}_{\odot }\,\mathrm{pc}^{-2}) = 3.2\times I_\mathrm{CO}(\mathrm{K\,km\,s^{-1}})\,.
\end{equation*}
However, for three of four remaining galaxies only the total mass of molecular hydrogen $M_\mathrm{H_2}$ was found. Regan et al. (2001) make a conclusion based on the BIMA survey data that $\Sigma _\mathrm{H_2}(R)$ profile decreases exponentially with a scale equal to the scale length of the disc h on the average. Therefore for these remaining galaxies we found central surface densities from the formula of the total mass of the molecular disc $\displaystyle \Sigma _\mathrm{H_2}(0) = \frac{M_\mathrm{H_2}}{2 {\pi} \, h^2}$ and then extended them exponentially with the appropriate h scale length. If more than one photometry is used for an examined galaxy this approach gives several possible profiles of $\Sigma _\mathrm{H_2}(R)$ and several estimates of Q, respectively both for one-fluid and two-component cases. We approximate the $\Sigma _\mathrm{H_2}(R)$ and $\Sigma _\mathrm{H\, \small {I}}(R)$ profiles using linear interpolation between points. The total gas surface density was corrected for the presence of helium and other heavy elements using $\Sigma _\mathrm{g} = 1.36\,(\Sigma _\mathrm{H\,\small {I}} + \Sigma _\mathrm{H_2})$ formula (see for example Leroy et al. 2008).
Citation: Yim & van der Hulst (2016)
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Citation: Yim & van der Hulst (2016)
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Citation: Yim & van der Hulst 2016
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We have also plotted the scaling relation of S and 





 as suggested by the Schmidt SF relation 





 (green dashed line). The relation is normalized such that the line passes through the MW average 





 For data points that lie around this relation, 





 is smaller for higher densities. For 





 the ISM around the Schmidt relation has a fV,hot of only a few percent. Surprisingly, for ISM in star-burst regimes, little hot gas exists and the medium is thermally stable. Observationally, however, powerful winds are ubiquitously associated with such high SF rates, and the mass loading (





) is on the order of unity or even higher (e.g., Heckman et al. 2000; Steidel et al. 2004). Note that we have found the PEH rate to be a very important factor in determining the thermal state of the ISM. If the PEH rates we have adopted are reasonable, then the data seem to suggest that one needs other mechanism(s) to drive a wind for the high density regions. For example, “clustering” of SNe may work, although a factor of 10 or more increase in S is needed for 





 above the average value to have a thermally driven wind. Another factor is the pre-SN feedback, such as photo-ionization, radiation pressure and winds from massive stars, which can create low density tunnels, facilitating SN energy to leak out (e.g., Rogers & Pittard 2013). Alternatively, runaway OB stars, which can easily migrate more than a hundred parsecs, may lead to a significant fraction of core collapse SNe exploding outside the immediate high density SF clouds. For a low density medium 





 the critical SN rate for the ISM to have a thermal runaway is much less stringent. Another possible mechanism for wind launching is by the cosmic rays. As the cosmic rays diffuse out, the pressure gradient exerts accelerating force on the baryonic gas. Recent simulations have shown that this mechanism is promising to drive winds with a reasonable mass loading (Uhlig et al. 2012; Hanasz et al. 2013; Salem & Bryan 2014).
Citation: Heckman et al. 2000
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The momentum equations for the neutron and proton–electron fluids in the MHD approximation are (Mendell 1991a, 1991b; Glampedakis et al. 2011)
5







6





where 





 is the smooth-averaged velocity of the proton–electron fluid, ρn,p are the mass densities of the fluids, pn,p are scalar potentials related to thermodynamic variables in Equation (146), and 





 is the external driving force associated with the magnetic dipole torque on the star. The neutron fluid is inviscid, while the proton–electron fluid has kinematic viscosity νee arising from electron–electron scattering. The two fluids are coupled by the mutual friction force 





, which arises from electron scattering from magnetized neutron vortices and pinning interactions. The force acts equally and oppositely on the two fluids and is given by (see, e.g., Hall 1960; Khalatnikov 1965; Hills & Roberts 1977; Barenghi et al. 1983; Chandler & Baym 1986; Mendell 1991b; Peralta 2007; Glampedakis et al. 2011)
7





where 





 and 





 are the mutual friction coefficients; the first term is dissipative and the second term is nondissipative. The mutual friction coefficients are related to scattering and pinning parameters in Section 3. Electron scattering from flux tubes is connected with the evolution of the magnetic field and describes processes analogous to ohmic and Hall diffusion; see, for example, Graber et al. (2015). These effects are small compared with the inertial modes studied in this paper; see Appendix B for further discussion. The restoring force due to tension of the vortex lines is (see, e.g., Hall 1960; Khalatnikov 1965; Hills & Roberts 1977; Baym & Chandler 1983; Mendell 1991a; Peralta 2007; Glampedakis et al. 2011)
8





where νn is the vortex line tension parameter, defined in (124). The vortex line tension is negligible compared with other terms in (5) and (6); see Equation (168). We set the vortex tension to zero everywhere in this paper except in the analysis of the Donnelly–Glaberson instability in Section 4.2.1, where it determines the instability condition. In a type II superconductor, the magnetic stresses arise from the tension of the array of the quantized flux tubes and is given by (Easson & Pethick 1977)
9





where 





 is the lower critical field for type II superconductivity. The evolution of the magnetic field is determined by the induction equation
10
Citation: Chandler & Baym 1986
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Citation: Glampedakis et al. 2011
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Citation: Baym & Chandler 1983
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Citation: Easson & Pethick 1977
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As seen in the previous section, the mass of the PNS increases with the accretion, which eventually approaches the maximum mass allowed with the adopted EOSs. Then, the PNS would gravitationally collapse to a black hole. The moment when the PNS approaches its maximum mass corresponds to the onset of the instability. In order to determine the onset of instability in the evolution of the PNSs, we make a linear analysis with the radial perturbation on the PNS models at each time-step after corebounce. For this purpose, one can derive the perturbation equations as
(3)$$\begin{eqnarray*}
\frac{\mathrm{ d}\xi }{\mathrm{ d}r} &amp;=&amp; -\left[\frac{3}{r} + \frac{p^{\prime }}{p+\varepsilon }\right]\xi - \frac{\eta }{r\Gamma },
\end{eqnarray*}$$(4)$$\begin{eqnarray*}
\frac{\mathrm{ d}\eta }{\mathrm{ d}r} &amp;=&amp; \left[r(p+\varepsilon) e^{2\Lambda }\left(\frac{\omega ^2}{p} e^{-2\Phi } - 8\pi \right) - \frac{4p^{\prime }}{p} + \frac{r(p^{\prime })^2}{p(p+\varepsilon)}\right]\xi \nonumber\\
&amp;&amp;-\, \left[\frac{\varepsilon p^{\prime }}{p(p+\varepsilon)} + 4\pi r(p+\varepsilon)e^{2\Lambda }\right]\eta ,
\end{eqnarray*}$$where p, ε, and Γ denote the pressure, energy density, and adiabatic index for the background PNS models, while ξ and η are perturbative variables given by ξ ≡ Δr/r and η ≡ Δp/p with the radial displacement, Δr, and the Lagrangian perturbation of pressure, Δp (Chandrasekhar 1964; Chanmugan 1977; Gondek, Haensel & Zdunik 1997).3 The prime in the equations denotes the radial derivative and the adiabatic index is given by
(5)$$\begin{eqnarray*}
\Gamma \equiv \left(\frac{\partial \ln p}{\partial \ln n_{\rm b}}\right)_s = \frac{p+\varepsilon }{p}c_\mathrm{ s}^2,
\end{eqnarray*}$$where nb, s, and cs denote the baryon number density, entropy per baryon, and sound velocity, respectively. We remark that one can derive the Sturm–Liouville type second-order differential equation with respect to ξ from equations (3) and (4). To solve the eigenvalue problem with respect to the eigenvalue ω2, one should impose the appropriate boundary conditions. The boundary condition at the stellar surface comes from the condition to remove the singularity in equation (4) (Chanmugan 1977), i.e.
(6)$$\begin{eqnarray*}
\eta = -\left[\left(\frac{\omega ^2R_{\rm PNS}^3}{M_{\rm PNS}} + \frac{M_{\rm PNS}}{R_{\rm PNS}}\right) \left(1-\frac{2M_{\rm PNS}}{R_{\rm PNS}}\right)^{-1}+ 4\right]\xi ,
\end{eqnarray*}$$while the boundary condition at the centre is the regularity condition, i.e.
(7)$$\begin{eqnarray*}
3\Gamma \xi + \eta = 0.
\end{eqnarray*}$$In addition, as normalization of the eigenfunction, we set ξ = 1 at the stellar centre. Then, with the resultant eigenvalue ω2, the frequency of radial oscillations are given by
(8)$$\begin{eqnarray*}
f_{\xi } = {\rm sgn}(\omega ^2)\sqrt{|\omega ^2|}/2\pi ,
\end{eqnarray*}$$where the system is unstable when ω2 becomes negative.
Citation: Chanmugan 1977
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Citation: Chanmugan 1977
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To calculate the synchrotron emission from the previous RMHD jet models, we need to establish some assumptions. While the radio continuum emission we are interested in is being produced by a population of non-thermal electrons (and maybe positrons), the RMHD simulations discussed previously account only for the evolution of the thermal electrons present in the jet. Establishing a relationship between the thermal and non-thermal populations requires a detailed prescription for the particle acceleration processes that connect both populations, presumably taking place in strong shocks or in magnetic reconnection events (see e.g., Sironi et al. 2015). A proper treatment of particle acceleration/injection in shocks (e.g., Kirk et al. 2000) or magnetic reconnection (e.g., Lyubarsky 2005) requires a microscopic description of the fluid, such as in particle-in-cell (PIC) simulations (e.g., Nishikawa et al. 2016), and its implementation in macroscopic RMHD models, such as the one used here, still falls outside current computing capabilities, given the vastly different scales involved. Nevertheless, as a first-order approximation, we consider that the internal energy of the non-thermal population is a constant fraction of the thermal electrons considered in the RMHD simulations (e.g., Gómez et al. 1995, 1997; Komissarov & Falle 1997; Broderick & McKinney 2010; Porth et al. 2011). Alternatively, the non-thermal population can also be considered to be proportional to the magnetic energy density (e.g., Porth et al. 2011), which determines the particle acceleration efficiency in shocks and magnetic reconnection events. No significant differences are found in our emission calculations when considering the latter approach for particle acceleration, given the similarities between the gas pressure and magnetic energy density distributions in our RMHD simulations, except for the particular case of jet spine brightening discussed in more detail in Section 3.3. On the other hand, we note that particle acceleration at shock fronts is probably the most important ingredient for computing the expected non-thermal emission from our RMHD simulations. Our results should therefore be considered in these cases as a first-order approximation, which could be used as a base model to test different prescriptions for in situ particle acceleration in future modeling.
Citation: Nishikawa et al. 2016
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Citation: Sironi et al. 2015
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Citation: Broderick & McKinney 2010
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The relative escape fraction of galaxies brighter than M1500 ~ −20.2 (L = 0.5L∗) should be ~16% to provide a photoionization rate Γ-12 ~ 0.95, in agreement with the observed value at z ~ 3, shown in Fig. 7. Alternatively, the escape fraction can remain at approximately a few percent, but the LF must be integrated down to very faint magnitudes, at M1500 = −14.2 (Fontanot et al. 2014; Alavi et al. 2014) to yield Γ-12 ~ 0.9. The calculations above are quite conservative, since we are assuming a rather steep LF (α = −1.73). At z ~ 3 the estimated slopes of the galaxy LF are generally flatter, with α ~  [−1.4,−1.5] (Sawiki & Thompson 2006; Finkelstein et al. 2015; Parsa et al. 2015), with the exception of the LF of LAEs by Cassata et al. (2011), which has α ~ −1.8 at z ≥ 3. Adopting the parametrization of Sawiki & Thompson (2006), with α = −1.43, and integrating down to M1500 = −14.2, the ionizing emissivity is Γ-12 ≤ 0.31, which is insufficient to keep the Universe reionized. Similarly, if we adopt the LF by Cucciati et al. (2012) with a slightly steeper slope (α = −1.50), but brighter M∗, we find an emissivity of Γ-12 ≤ 0.26 at M1500 = −14.2, far from providing enough ionizing photons to maintain the reionization of the Universe. The latter LF is based on the VVDS (Le Fèvre et al. 2013) spectroscopic survey, so it should be robust against interlopers in the z ~ 3 LF. At z ≥ 3, Cassata et al. (2011) find that the LF of LAEs is relatively steep, with a slope of ~− 1.8. However, these galaxies are much fainter than the typical UV selected galaxies discovered at the same redshifts. They measured a star formation rate density, which is a factor of 5 lower than that by Reddy & Steidel (2009), with the implication of a lesser contribution of the LAEs to the HI ionizing background at z ~ 3. Table 3 summarizes the different HI photoionization rates derived for different parametrization of the z ~ 3 galaxy LF and at different luminosities.
Citation: Finkelstein et al. 2015
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There is not yet a clear consensus for observational efforts to detect primordial galaxy alignments in clusters or superclusters. Rood & Sastry (1972) were the first to claim that satellite galaxies in Abell 2199 tend to point in the direction of the major axis of the BCG. Subsequently, primordial galaxy alignment was found in more clusters, such as Abell 521 (Plionis et al. 2003), Abell 1689 (Hung et al. 2010), Coma (Djorgovski 1983; Kitzbichler & Saurer 2003), Virgo (West & Blakeslee 2000), Abell 999 and Abell 2197 (Adams, Storm & Strom 1980; Thompson 1976), and in some cluster samples [Yang et al. 2006 (0.01  z  0.2); Plionis 1994; Plionis et al. 2003 (z  0.15); West, Jones & Forman 1995 (z  0.2); Agustsson & Brainerd 2006 (median redshift z = 0.058); Faltenbacher et al. 2007 (0.01  z  0.2)]. However, some other measurements have been consistent with random orientations of satellite galaxies in clusters [e.g. Hawley & Peebles 1975; Dekel 1985; van Kampen & Rhee 1990; Godłowski & Ostrowski 1999; Strazzullo et al. 2005 (z  0.27); Torlina, De Propris & West 2007; Trevese, Cirimele & Flin 1992; Panko, Juszczyk & Flin 2009 (z  0.18); Sifón et al. 2015 (0.05  z  0.55)]. On one hand, the primordial alignment is primarily found in unrelaxed clusters, such as Coma (Sanders et al. 2013; Simionescu et al. 2013), Abell 1689 (Kawaharada et al. 2010), Virgo (Urban et al. 2011) and Abell 521 (Maurogordato et al. 2000; Ferrari et al. 2003, 2006), which agrees with stronger alignment in dynamically young clusters. On the other hand, at higher redshifts, the primordial alignment is denied in many clusters (Sifón et al. 2015) other than Abell 521 (z ∼ 0.25). This is unexpected because the fraction of the dynamically young clusters at high redshifts is larger (Hashimoto et al. 2007; Maughan, Forman & Van Speybroeck 2008; Mann & Ebeling 2012; Weißmann, Böhringer & Chon 2013), according to the hierarchical clustering models of structure formation.
Citation: West, Jones & Forman 1995
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We performed our spectral fit in the XSPEC v12.8.2 and 12.9.0 (Arnaud 1996) spectral analysis environments. We verified that the resulting fits are consistent across both versions of XSPEC. Twenty-three parameters describe the spectral continuum and emission lines that NuSTAR observes in the 4–79 keV range. Six parameters describe two iron emission lines (we use the Gaussian function for both lines), three describe the cyclotron resonant scattering absorption feature (CRSF), one parameter describes the interstellar absorption (





), and one parameter describes the cross-normalization of the FPMA and FPMB modules (





). The absorbing column is frozen at 





 cm−2, a value that approximates the galactic absorption to Her X-1  (Fürst et al. 2013). We utilized the tbabs absorption model with the “WILM” abundance table and the “BCMC” cross-sections (Wilms et al. 2000). This leaves 12 parameters to describe the RDRS model. One of these is an RDRS model normalization that we freeze at 1.0. One is a numerical switch that allows us to turn on or off any of the three principal seed-photon processes for the Comptonization (see Section 2). We freeze the distance to the Her X-1 system at D = 6.6 kpc (Reynolds et al. 1997), and the NS mass and radius are set to their standard values (





 and 10 km). The distance to Her X-1 obtained by Reynolds et al. of 





 kpc is sufficiently consistent, for our purposes, with a more recently determined distance of 





 kpc obtained by Leahy & Abdallah (2014). Thus, we adopt the Reynolds et al. distance for these calculations. The value of the input magnetic field strength to the RDRS model is tied to the centroid of the fitted cyclotron absorption line (





) via 





 where z* is the gravitational redshift to the NS surface. The six remaining parameters describing the RDRS model (BW) are: mass accretion rate (





), plasma Comptonizing temperature (Te), accretion cap radius (r0), scattering cross-section perpendicular to the magnetic field (





), scattering cross-section parallel to the magnetic field (





), and average scattering cross-section (





). The scattering cross-section perpendicular to the magnetic field (





) is frozen at the Thomson electron scattering cross-section (





). This leaves five free parameters, 





, Te, r0, 





, and 





, to describe the X-ray continuum.
Citation: Fürst et al. 2013
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The extent of the evolution of the faint red-sequence population, however, is still under debate. As opposed to local clusters that exhibit a flat faint end, or even an upturn at the faint end of their red-sequence LFs (e.g., Popesso et al. 2006; Agulli et al. 2014; Moretti et al. 2015; Lan et al. 2016), various studies have revealed that clusters at intermediate and high redshifts show a continual decrease in the fraction of the faint red-sequence population with redshift, which indicates a gradual buildup of the faint red-sequence population over time since z ∼ 1.5 (e.g., Dressler et al. 1997; Smail et al. 1998; De Lucia et al. 2004, 2007; Kodama et al. 2004; Tanaka et al. 2007; Gilbank et al. 2008; Rudnick et al. 2009, 2012; Stott et al. 2009; Martinet et al. 2015; Zenteno et al. 2016; Sarron et al. 2018; Zhang et al. 2019). This is also supported by findings that cluster galaxies on the high-mass end of the red sequence are on average older than those on the low-mass end (e.g., Nelan et al. 2005; Sánchez-Blázquez et al. 2009; Demarco et al. 2010a; Smith et al. 2012). Contrary to the above-mentioned studies, a number of studies have reported that there is little or no evolution of the faint end of the red-sequence cluster LF up to z ∼ 1.5 (e.g., Andreon 2006; Crawford et al. 2009; De Propris et al. 2013, 2015; Andreon et al. 2014; Cerulo et al. 2016), which in turn suggests the early formation of the faint end, similar to bright red-sequence galaxies. De Propris et al. (2013) proposed that the discrepancy is primarily caused by surface brightness selection effects, which lowers the detectability of faint galaxies at high redshift. Nevertheless, a recent study by Martinet et al. (2017) extensively investigated the effect of surface brightness dimming with 16 CLASH clusters in the redshift range of 0.2  z  0.6. They concluded that surface brightness dimming alone could not explain the observed redshift evolution of the faint end. Other possible explanations of the discrepancy invoke the radial and mass dependence of the faint red-sequence population, both of which are also debated in local cluster LF studies (see, e.g., Popesso et al. 2006; Barkhouse et al. 2007; Lan et al. 2016). While there may be a (weak) dependence of the red-sequence LF on cluster mass (or cluster properties that are mass proxies) at intermediate redshift (e.g., De Lucia et al. 2007; Muzzin et al. 2007; Rudnick et al. 2009; Martinet et al. 2015), it remains unclear whether this effect exists at higher redshift. It is also possible that the disagreements in the literature are driven by the large cluster-to-cluster variations, sample selections, or methods used to derive the LF, as observed in most of the above-mentioned works.
Citation: Smith et al. 2012
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Citation: De Propris et al. (2013)
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