adsabs/FOCAL huggingface dataset:
The Virgo, however, remains the only cluster in which intracluster X-ray sources have been probed and detected. The Chandra observations utilized by Hou et al. (2017) covered only a small portion (∼3 deg2) of Virgo, but its large angular size (∼100 deg2) renders a full mapping a challenging, if not infeasible, task with contemporary X-ray telescopes, thus limiting our ability to extend the search for intracluster X-ray sources in Virgo. Located at a distance of ∼20.0 Mpc (Blakeslee et al. 2009), the Fornax cluster is a dynamically more evolved, more compact and less massive system compared to Virgo. Like Virgo, Fornax has been an important laboratory to explore the physics of hierarchical structure growth. Recent optical surveys including the Hubble Space Telescope ACS Fornax Cluster Survey (ACSFCS; Jordán et al. 2007) and the Fornax Deep Survey with VST (FDS; Iodice et al. 2016) have significantly advanced our knowledge about the ETGs (Côté et al. 2007; Turner et al. 2012), dwarf galaxies (Venhola et al. 2017), GC populations (Jordán et al. 2015), as well as the ICL (Iodice et al. 2017) of this cluster. In the X-ray band, a survey of the inner ∼30′ region of Fornax has been conducted with Chandra observations (Scharf et al. 2005), which resulted in the detection of more than 700 point-like sources (including CXB sources) against an extended, asymmetric diffuse X-ray emission from the intracluster medium (Ikebe et al. 1996; Jones et al. 1997). The X-ray sources in the BCG, NGC 1399, have been extensively studied with a focus on their connection with GCs (Angelini et al. 2001; Paolillo et al. 2011; D’Ago et al. 2014). The X-ray sources located outside the main stellar content of NGC 1399, however, have received little attention so far, except for the work of Phillipps et al. (2013), which studied the incidence rate of X-ray sources in compact stellar systems, including GCs and the so-called ultra-compact dwarfs (UCDs; Phillipps et al. 2001).
Citation: Côté et al. 2007
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In order to determine the dust emission from the remnant, several physical properties are required: the densities and temperatures of the electrons and nuclei, the dominant type of nucleus, and the radiation field strength and spectrum. Observations of Cas A reveal a complex structure, with material covering a wide range of densities and temperatures emitting at different wavelengths. The supernova explosion has driven a forward shock into the circumstellar material, thought to be from the stellar wind of the progenitor (Hwang & Laming 2009), while the ejecta from the supernova itself crosses the reverse shock as it expands (DeLaney et al. 2004). Both shocks are visible as X-ray emitting regions, with typical densities of $n \sim 1{\text{-}}10 \, {\rm cm}^{-3}$ and temperatures $T \gtrsim 10^7 \, {\rm K}$ (Willingale et al. 2003; Lazendic et al. 2006; Patnaude & Fesen 2014; Wang & Li 2016). The ejecta is mostly comprised of heavy elements, principally oxygen (Chevalier & Kirshner 1979; Willingale et al. 2003). As well as the X-ray emitting gas, the shocked ejecta also consists of denser clumps or knots, emitting in the optical and IR (Hurford & Fesen 1996; DeLaney et al. 2010; Patnaude & Fesen 2014) and associated with the dust emission (Arendt et al. 1999). Electron densities in the shocked clumps are $n_{\rm e}\sim 10^3{\text{-}}10^5\, {\rm cm}^{-3}$ (Smith et al. 2009; DeLaney et al. 2010; Lee et al. 2017), while the gas temperatures are of order $10^4 \, {\rm K}$ (Arendt et al. 1999; Docenko & Sunyaev 2010). The SNR also contains ejecta that has not yet encountered the reverse shock and is consequently much cooler. Smith et al. (2009) estimated a maximum electron density of $n_{\rm e}\lesssim 100 \, {\rm cm}^{-3}$ for the unshocked ejecta based on forbidden line ratios, while observations of radio absorption by DeLaney et al. (2014) and Arias et al. (2018) give $n_{\rm e}\sim 10 \, {\rm cm}^{-3}$ and $T \sim 100 \, {\rm K}$. Raymond et al. (2018) inferred a pre-shock temperature of ${\sim } 100 \, {\rm K}$ from [Si i] IR emission lines.
Citation: Lazendic et al. 2006
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Citation: Smith et al. (2009)
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The spherical evolution model was originally introduced to model the evolution of overdensities (Gunn & Gott 1972). This model assumes a spherical underdensity ρi embedded in an expanding, homogeneous background with density $\bar{\rho }$. The evolution of each radius is determined by the total mass M contained within the proper radius R via the acceleration equation in the Newtonian regime.1 The model makes no assumption about the background cosmology with the evolution given as

(1)

\begin{equation}
\frac{\ddot{R}}{R} = \frac{-4\pi G}{3} \sum _{n}(\rho _n + 3p_n),
\end{equation}

where R is the proper radius, the double dot indicates the second derivative with respect to proper time t, G is the gravitational constant, and ρn and pn are the density and pressure components, respectively, of any contributing component i.e., radiation, matter, dark energy (Padmanabhan 1996). The same equation, known as the Friedmann equation, applies to an unperturbed region, which yields the expansion history of the universe. The spherical model has been applied to solve the evolution of overdensities and underdensities (e.g. Gunn & Gott 1972; Peebles 1980; Lilje & Lahav 1991; Sheth & van de Weygaert 2004). Using the spherical model, the evolution equation in a Λ = 0 universe becomes

(2)

\begin{equation}
\ddot{R} = -\frac{GM}{R^2}.
\end{equation}

To solve the above equation, the initial density and velocity profiles are needed. For the case of an overdensity, which eventually collapses and virializes as a halo, the initial density profile is usually taken to be a spherical top-hat and the initial velocity is assumed to be the Hubble flow at the initial time ti. We will use the subscript i to indicate quantities at the initial time throughout the paper. With these assumptions, the equation can be solved analytically and the solution for the size of the radius as a function of time takes the following parametric form (Gunn & Gott 1972; Lilje & Lahav 1991):

(3)

\begin{eqnarray}
R &amp;=&amp; A(1-\cos \theta ), \nonumber \\
t+T &amp;=&amp; B(\theta - \sin \theta ), \nonumber \\
A^3 &amp;=&amp; GMB^2,
\end{eqnarray}

where A, B, and T are constants that can be fixed once the initial conditions are fixed and θ is an indicator of time. For voids with the same initial settings, the analytical solutions can also be found by taking an inverse top-hat model for the density profile (Gunn & Gott 1972; Peebles 1980; Lilje & Lahav 1991; Sheth & van de Weygaert 2004):

(4)

\begin{eqnarray}
R &amp;=&amp; A(\cosh \theta -1), \nonumber \\
t+T &amp;=&amp; B(\sinh \theta -\theta ), \nonumber \\
A^3 &amp;=&amp; GMB^2.
\end{eqnarray}

Note that the parametric solutions above apply to any Λ = 0 universe. For this study we use the flat EdS cosmology.
Citation: Lilje & Lahav 1991
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Citation: Lilje & Lahav 1991
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Figure 4 shows the cooling rate of the plasma due to emission (



λem=ρκemaradTe4

) and inverse-Compton scattering (λ
sc = ρ
κ
es
E
rad 4k

b

T

e
/m

e

c
2), in addition to the heating rate through absorption (λ
abs = ρ
κ
abs
E
rad). As can be seen, the cooling is predominantly concentrated near the equatorial plane which has an optical depth of order unity (τ
es ∼ 1). Because the Compton scattering rate exceeds the emission rate, it is conceivable that most radiation actually gets Compton upscattered before leaving the corona. We estimate that the Compton-y parameter (y = τ
es 4k

b

T

e
/m

e

c
2), which measures the average fractional energy gain of photons due to Comptonization (e.g., Rybicki & Lightman 1986), can easily exceed y ≳ 1 in the T

e
 ≳ 5 × 108 K plasma near the midplane of the corona. Pinpointing the exact value of the Compton y parameter is nontrivial because absorption will play an important role in some optically thick patches near the midplane. A more detailed calculation that takes into account emission, absorption, and scattering in the plasma along photon geodesics will be required to further constrain the Compton-y parameter. Nevertheless, this work suggests that the corona will upscatter and significantly harden thermal radiation from the disk and cyclosynchrotron emission from the corona (see also Dexter et al. 2021; Scepi et al. 2021). In contrast, the bottom row in Figure 3 shows that in RADTOR, the ions and electrons are strongly coupled in the cold disk, which remains optically thick to both scattering and absorption. Because this disk extends all the way to the event horizon, we expect a strong thermal emission component in the emergent spectrum. Compton upscattering of disk photons by the winds sandwiching the inner disk to temperatures necessary to significantly harden the spectrum is not expected because these winds are predominantly cold (T

e
 ≲ 5 × 107 K). The hot pockets of gas with temperatures T

e
 ≳ 108 K within r ≲ 5r

g
 in Figure 3 are relatively rare and seem to be more prominent at later times when the disk becomes numerically underresolved due to thermal collapse (Appendix A.2).
Citation: Rybicki & Lightman 1986
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In this paper, we consider resonance scattering on a two-level atom with an infinitely sharp and unpolarized lower level. As for the frequency redistribution, we consider both CRD and angle-averaged PRD. In an unmagnetized one-dimensional spherically symmetric atmosphere, the polarized radiation field is axially symmetric and is described by 





. We also take into account the effects of radial velocity fields. We solve the concerned transfer equation in the CMF and in the nonrelativistic regime of velocity fields. To efficiently handle the sphericity effects, we solve the spherical transfer equation in the (p, z) coordinate system (Hummer & Rybicki 1971), which is also called the tangent-ray method. Here z is the distance along the tangent rays and p is impact parameter (see Figure 1 in Megha et al. 2019). Following Frisch (2007), we express the Stokes vector components in terms of their irreducible components. From here on we present all the basic equations in the irreducible basis (see Sampoorna & Trujillo Bueno 2010 for details). The CMF polarized PRD transfer equation for a spherically symmetric medium in (p, z) representation under the nonrelativistic limit is given by (see also Equation (17) of Megha et al. 2019)
1





where x denotes the nondimensional frequency and 





 denotes the irreducible Stokes vector with “+” and “−” referring to the outgoing and incoming rays, respectively. The radial optical depth is defined as dτr = −χl(r)dr, where r is the radial distance and χl(r) is the line averaged absorption coefficient. In the CMF the monochromatic optical depth along the tangent ray is given by dτ = [φ(x) + βc]dτr/μ, where φ(x) is the line absorption profile function and βc = χc(r)/χl(r) with χc(r) denoting the continuum absorption coefficient. The direction cosine of the tangent ray about the radius vector of the intercepting radial shell is given by 





. In Equation (1), 





 denotes the CMF term, which has the form
2





where χ(r, x) = χl(r)φ(x) + χc(r), and
3





The symbol V denotes the ratio of radial (vr) to the thermal (





) velocities. In Equation (1), 





 represents the irreducible CMF total source vector and is given by
4





where the line source vector is of the form
5





Here ϵ gives the probability of destruction of photons by inelastic collisions, Bν0 is the Planck function at the line center frequency ν0, and 





. The continuum is assumed to be unpolarized. Therefore, the continuum source vector is given by 





. The frequency-averaged PRD mean intensity vector is given by
6





where 





 is the 2 × 2 nonmagnetic angle-averaged PRD matrix (Domke & Hubeny 1988; Bommier 1997), and
7





The Rayleigh phase matrix 





 in the irreducible basis is given in Appendix A of Frisch (2007). It is useful to rewrite Equation (7) as
8





where
9
Citation: Megha et al. 2019
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The number density of SMGs in either BOSS1244 or BOSS1542 is significantly higher than that of the blank fields. It is reasonable to attribute the excess of SMGs to the overdensity at z = 2.24. This has been successfully verified with H α emitters (Shi et al. 2021; Zheng et al. 2021). We link the excess of SMGs in our two MAMMOTH fields to the presence of 850 $\rm{\mu m}$-detected SMG overdensity at z = 2.24. There are 43 (54) SMGs detected over an effective area of 264 arcmin2 in the deep 850 $\rm{\mu m}$ map of BOSS1244 (BOSS1542). Considering the redshift distribution, we calculate the fraction of SMGs located in 2.2  z  2.3 to be 5.7 per cent comparing to the whole redshift range in the AS2UDS survey (Dudzevičiūtė et al. 2020), which has a survey area of ∼1 deg2 and make the cosmic variance negligible (Simpson et al. 2019). Then we obtain that the volume density of SMGs in this redshift slice is 2.6 × 10−5 cMpc−3 at S850 ≥ 4.0 mJy in the blank fields. If we simply assume the two overdensities span a narrow redshift range (δz  0.042 given by the band width of H2S(1) filter), the volume of the redshift slice of z = 2.246 ± 0.021 over 264 arcmin2 corresponds to a co-moving box of 54.3 × 665.6 (=36142) h−3 cMpc3. If the excess of SMGs (i.e. (1.8–1)/1.8 × 54 for BOSS1542) are associated with the z = 2.24 overdensities, we obtain that SMGs in the two overdensities may reach a volume density of ∼(40–70) × 10−5 cMpc−3, 15–30 times that of the blank fields. After enlarging the redshift slice of the two protoclusters to that of blank field (δz = 0.1), we still obtain the volume density of SMG to be 6–11 times that of the blank fields. The overdensity factor of SMGs, although with large uncertainties, is even higher than that of H α emission-line galaxies (HAEs) in these two protoclusters (Shi et al. 2021), indicating that there are more extreme starbursts with enhanced star formation in respect to normal SFGs (i.e. HAEs) in the two z = 2.24 protoclusters.
Citation: Simpson et al. 2019
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In SID/Milgromian dynamics there appears an interesting effect that leads to an observable prediction which does not exist in the Newtonian plus DM model. It is relevant for a satellite object falling within the gravitational field of a host such that the host field does not vary significantly across the satellite. This external gravitational field effectively truncates the isothermal PDMH, as deduced by an observer who interprets the observations within Newtonian dynamics. The Milgromian dynamics/MOND equation for a spherical, axisymmetric or cylindrical system embedded in an external field is (Milgrom 1983a; Sanders & McGaugh 2002)

(24)

\begin{equation}
{\boldsymbol g}_{{\rm N,i}}+{\boldsymbol g}_{{\rm N,e}}=\mu (| ({\boldsymbol g}_{\rm i} + {\boldsymbol g}_{\rm e})|/a_0) ({\boldsymbol g}_{\rm i}+{\boldsymbol g}_{\rm e}),
\end{equation}

where ${\boldsymbol g}_{{\rm N,i}}$ is the Newtonian acceleration from the baryonic matter of the internal system, ${\boldsymbol g}_{{\rm N,e}}$ is the Newtonian acceleration from the baryonic matter of the external gravitational source generating the background uniform field and ${\boldsymbol g}_{\rm i}$ and ${\boldsymbol g}_{\rm e}$ are the internal and external gravitational accelerations. For an external field dominated system, $g_{\rm e}=|{\boldsymbol g}_{\rm e}| \gg g_{\rm i}=|{\boldsymbol g}_{\rm i}|$, equation (24) is expanded around ge to lowest order as

(25)

\begin{eqnarray}
g_{{\rm N,e}}&amp;=&amp;\mu (|{\boldsymbol g}_{\rm e}|/a_0) {\boldsymbol g}_{\rm e},\nonumber \\
g_{{\rm N,i}}&amp;=&amp;\mu (|{\boldsymbol g}_{\rm e}|/a_0) {\boldsymbol g}_{\rm i},
\end{eqnarray}

with a dilation factor of $\Delta _1=(1+{\rm d}\ln \mu /{\rm d} \ln x)_{x=g_{\rm e}/a_0}$. Δ1 approaches 1 in the Newtonian limit and approaches 2 in the deep-MOND limit. The value of Δ1 also depends on the direction relative to the external field (for more details see Milgrom 1983a; Bekenstein & Milgrom 1984; Zhao & Tian 2006). μ(x) = x in the low-acceleration regime where SID is valid (i.e. in deep-MOND limit).6
Citation: Sanders & McGaugh 2002
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The extended star-forming region S235 is known to be a part of the giant molecular cloud G174+2.5 in the Perseus Spiral Arm (e.g., Heyer et al. 1996) and contains two known sites: the S235 complex and the S235AB region (see Figure 1 in Dewangan & Anandarao 2011 and also Figure 1 in Kirsanova et al. 2014). The present work is focused on the S235 complex and does not include the S235AB region. Different values of the distance (1.36, 1.59, 1.8, 2.1, and 2.5 kpc) to the extended star-forming region S235 have been reported in the literature (e.g., Georgelin et al. 1973; Israel & Felli 1978; Evans & Blair 1981; Brand & Blitz 1993; Burns et al. 2015; Foster & Brunt 2015). In the present work, we have chosen a distance of 1.8 kpc following Evans & Blair (1981), which is an intermediate value of the published distance range. The H ii region associated with the S235 complex is predominantly ionized by a single massive star, BD+35o1201, of O9.5V type (Georgelin et al. 1973). The S235 complex has been studied using multiple data sets spanning near-infrared (NIR) to radio wavelengths. The S235 complex is known as an active site of star formation, harboring young stellar clusters (e.g., Kirsanova et al. 2008; Camargo et al. 2011; Dewangan & Anandarao 2011; Chavarría et al. 2014) associated with known star-forming subregions, namely East 1, East 2, and the Central region (e.g., Kirsanova et al. 2008). In our previous work on the S235 complex using Spitzer-IRAC data (Dewangan & Anandarao 2011, hereafter Paper I) we detected several young stellar objects (YSOs) including a high mass protostellar object (HMPO) candidate as well as signatures of outflow activities. Using 13CO (1−0) line data, Kirsanova et al. (2008) found three molecular gas components (i.e., −18 km s−1





 km s−1 (red), −21 km s−1 





 km s−1 (central), and −25 km s−1 





 km s−1 (blue)) in the direction of the S235 complex. However, the complex is well traced in mainly two molecular gas components (central and blue). More recently, Kirsanova et al. (2014) derived physical parameters of dense gas (i.e., gas density and temperature) in subregions of the complex using ammonia (NH3) line observations. However, the properties of dense gas have not been explored with respect to the ionizing star location. Previous studies indicated that the S235 H ii region is interacting with its surrounding molecular cloud and the S235 complex has been cited as a possible site of triggered star formation (Kirsanova et al. 2008, 2014; Camargo et al. 2011).
Citation: Kirsanova et al. 2008
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The first interstellar discovery of MF took place in 1975 from the microwave emission spectrum of Sgr B2, which agrees with the rotational constants of the syn isomer (Curl 1959; Brown et al. 1975; Nummelin et al. 2000). Subsequently, it was detected in several other sources such as comet Hale–Bopp, and protostars and hot corinos (e.g., in Orion A and the protoplanetary nebula CRL 618) (Ellder et al. 1980; Ikeda et al. 2001; Cazaux et al. 2003; Bottinelli et al. 2004a, 2004b; Remijan et al. 2005, 2006; Remijan & Hollis 2006). Later, the less stable trans rotamer was detected in both the laboratory and the interstellar medium (ISM; Ruschin & Bauer 1980; Blom & Günthard 1981; Müller et al. 1983; Neill et al. 2011, 2012). The detailed mechanistic route for the interstellar synthesis of MF is a subject of considerable debate (Horn et al. 2004; Herbst 2005; Garrod & Herbst 2006; Snyder 2006; Bennett & Kaiser 2007; Occhiogrosso et al. 2011; Lawson et al. 2012). The initially assumed gas-phase model involving an ion–molecule reaction of protonated methanol (





) with formaldehyde (H2CO) fails to reproduce the large MF column density, because this pathway demands a significant activation barrier (∼128 kJ mol−1) for one of the intermediate steps (Horn et al. 2004). Instead, gas-phase radiative association between the methyl cation (





) and formic acid (HCOOH) seems energetically promising to produce H+MF and thereafter neutral MF via dissociative recombination with electrons:
1







2





However, this reaction scheme fails to reproduce the huge MF concentration observed in hot cores (Horn et al. 2004). Alternative routes suggested more recently involve ion–molecule reactions with a low barrier or no barrier between protonated methanol and formic acid (acid-catalyzed Fischer esterification) or between protonated formic acid and methanol (





 transfer):
3







4





followed by reaction (2) or exothermic proton transfer of 





 (H+MF) to a base with a higher proton affinity than MF (Ehrenfreund & Charnley 2000; Neill et al. 2011, 2012).
Citation: Horn et al. 2004
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