adsabs/FOCAL huggingface dataset:
These trends make physical sense and agree with the limited previous measurements. Physically, elevated SFR/M
⋆ may trace more intense radiation fields and stronger heating of the gas, suggesting higher temperatures. The anticorrelation with M
⋆ may reflect the impact of dust shielding. Based on the existence of the mass–metallicity relation (e.g., Tremonti et al. 2004; Kewley & Ellison 2008), we expect the low-mass members of our sample to also have lower dust-to-gas ratios (e.g., Leroy et al. 2011; Rémy-Ruyer et al. 2014; Casasola et al. 2020) and more intense radiation fields. In literature studies, CO line ratios do appear enhanced in low-metallicity regions or galaxies (e.g., Lequeux et al. 1994; Bolatto et al. 2003; Druard et al. 2014; Kepley et al. 2016; Cicone et al. 2017, among many others). Higher SFR/L
CO may indicate poorly shielded, low-metallicity gas in which the CO persists only in the core of a molecular cloud (e.g., see discussion in Glover & Clark 2012; Schruba et al. 2012; Bolatto et al. 2013b; Rubio et al. 2015). Alternatively, higher SFR/L
CO can indicate more efficiently star-forming gas, which will often be denser gas with more nearby heating sources. These are both factors that can lead to higher line ratios, especially R
32 and R
31 (see Section 2). Given that our sample skews toward relatively massive and thus nearly solar metallicity targets, we expect that these density and heating effects likely represent the main drivers of the observed correlations. The correlations that we see agree with the results of Lamperti et al. (2020), who showed a correlation between SFR/L
CO,low and R
31, and Yajima et al. (2021), who used a subset of the data we consider here and showed a correlation between R
21 and SFR/L
CO,low. Qualitatively, Figure 5 echoes other results at low and high redshift that show a correlation between normalized star formation activity and excitation (e.g., Weiß et al. 2005; Bolatto et al. 2013b; Liu et al. 2021).
Citation: Cicone et al. 2017
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The last decade and a half has seen a revolution in the study of overdensities in the early Universe. While the study and careful characterization of large associations of galaxies in the local Universe has been possible for nearly a century, and in the intermediate redshift Universe for a significant fraction of that time (e.g., Shapley & Ames 1926; Shapley 1930; Zwicky 1937; Abell 1958; Zwicky et al. 1961), the study of their progenitors presented several practical problems which have prevented their study until relatively recently. The primary problem, inherent to the study of nearly all galaxy populations in the early Universe, is the extreme apparent faintness of galaxy populations at these distances. While some phenomena exist in the early Universe, such as quasars or radio galaxies, which are so powerful and intrinsically bright that they have been able to serve as beacons to early searches near the epoch of H I reionization (z ~ 5.5–10, Becker et al. 2001, 2015; Planck Collaboration XIII 2016), the bulk of the galaxy population residing in the early Universe does not contain such phenomena (Miley & De Breuck 2008; Ouchi et al. 2008; Lemaux et al. 2014b; Ueda et al. 2014; Talia et al. 2017). As such, the first searches for these more typical primeval galaxies were largely doomed to failure (Davis & Wilkinson 1974; Partridge 1974; Pritchet & Hartwick 1987; Parkes et al. 1994). It was not until the advent of the 10m-class ground-based telescopes largely used in conjunction with the Hubble Space Telescope (HST) that the prospect of detecting and characterizing moderate samples of such galaxies became even remotely feasible (e.g., Steidel et al. 1999; Shapley et al. 2003; Giavalisco et al. 2004; Stanway et al. 2004; Malhotra & Rhoads 2004; Malhotra et al. 2005; Vanzella et al. 2005, Le Fèvre et al. 2005). With this, the prospect of finding and characterizing analogs of the progenitors of the massive clusters and superclusters of galaxies scattered throughout the local Universe began to come within the realm of possibility.
Citation: Planck Collaboration XIII 2016
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The size of ENLRs have been defined in different ways in the literature. Bennert et al. (2002) and Schmitt et al. (2003b) used the Hubble Space Telescope (HST) to obtain narrow band images of $\rm [O\, III]$, and adopted the maximum 3σ detected radius as the radius of the ENLR. This method is subject to the instrumental sensitivity limit that could be very different in different observations. Studies with long-slit spectroscopic observations define the radius based on isophote (Greene et al. 2011; Hainline et al. 2013, 2014), or the distance at which the ionization state changes from AGN to star-forming activities (Bennert et al. 2006a,b). The long-slit based observations also have drawbacks: the morphology of ENLR is sometimes irregular so that the derived size depends on the orientation of slits (Greene et al. 2011; Husemann et al. 2013). We have compared the measured size based on the IFU and the mock long-slit observation in Fig. 4 following the method discussed below. In most cases, long-slit observations tend to underestimate the true size of ENLR. IFU spectroscopic data allow us to use 2D maps to define the sizes of ENLRs. Common definitions include the radius of a specified $\rm [O\, III]$ surface brightness isophote (Liu et al. 2013, 2014), or the $\rm [O\, III]$ flux weighted radius (Husemann et al. 2013, 2014; Bae et al. 2017). We followed the same method as Liu et al. (2013) but chose a different threshold. The isophote threshold of 10−15$\rm erg\, s^{-1}cm^{-2}arcsec^{-2}$ was used for quasars related studies. This is suitable for such bright objects but are not as useful for fainter Syferts in our sample as it will leave a large number of AGN undetected. The typical 3σ depth of the MaNGA observation in $\rm [O\, III]$ surface brightness can reach 10−17$\rm erg\, s^{-1}cm^{-2}arcsec^{-2}$. For our AGN sample, the majority of AGN spaxels have surface brightnesses above 10−16$\rm erg\, s^{-1}cm^{-2}arcsec^{-2}$ which is thus adopted in this work as the threshold to define the sizes of the ENLRs (hereafter R16). If all spaxels are above this threshold, we extrapolated the fitted $\rm [O\, III]$ surface brightness profile to determine R16 (see Section 3.4 for more detail). It should be noted that the surface brightness can be affected by cosmological dimming, which has a scale factor of (1 + z)4 (Liu et al. 2013; Hainline et al. 2014). That is important for works trying to compare sample with different redshift, especially for high redshift quasars.
Citation: Husemann et al. 2013
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Citation: Husemann et al. 2013
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The giant planet metallicity correlation supports the core-accretion scenario for the formation of planets (Pollack et al. 1996; Ida & Lin 2004; Mordasini et al. 2009), in which it is assumed that planetesimals are formed by the condensation of heavy elements. The discovery of this correlation has led to an increased interest on the abundances of other elements in planet hosts(e.g. Sadakane et al. 2002; Bodaghee et al. 2003; Beirão et al. 2005; Gilli et al. 2006; Ecuvillon et al. 2006; Bond et al. 2006, 2008; Robinson et al. 2006; Gonzalez & Laws 2007; Takeda et al. 2007; Delgado Mena et al. 2010; González Hernández et al. 2010, 2013; Kang et al. 2011; Brugamyer et al. 2011; Adibekyan et al. 2015; da Silva et al. 2015; Mishenina et al. 2016; Suárez-Andrés et al. 2018). Using the same sample of this study, Adibekyan et al. (2012b) found that the [X/Fe] ratios of Mg, Al, Si, Sc, and Ti both for giant and low-mass planet hosts are systematically higher than those of stars without detected planets at low metallicities ([Fe/H] ≲ from –0.2 to 0.1 dex depending on the element). Furthermore, this work confirmed the previous suggestion by Haywood (2009) that planets form preferentially in the thick disk rather than in the thin disk at lower metallicities. A plausible explanation for this behaviour is that if the amount of iron is low, it needs to be compensated with other elements that are important for planet formation, such as Mg and Si, and these elements are more abundant in the thick disk Adibekyan et al. (2012b,a). In a subsequent work, Delgado Mena et al. (2018) focused on heavier elements among the same sample of stars with and without planets, we found that planet hosts present higher abundances of Zn for [Fe/H]  –0.1 dex, as a consequence of thick-disk stars having enhanced [Zn/Fe] ratios (Delgado Mena et al. 2017). Moreover, Delgado Mena et al. (2018) also found a statistically significant underabundance of Ba for low-mass planet hosts that had been previously suggested by Mishenina et al. (2016).
Citation: González Hernández et al. 2010
Citation function: Motivation
However, the transition between the two extremes of modern (metal-rich) and primordial (metal-poor) star formation, and in particular the role of dust coupling and stellar radiation feedback at low metallicity, has thus far received limited exploration. Krumholz (2011) present analytical models for radiation feedback and predict a weak scaling of IMF peak mass with metallicity, while Myers et al. (2011) and Bate (2014, 2019) carry out radiation-hydrodynamic simulations of star formation over a metallicity range from $0.01{-}3\, Z_{\rm {\odot }}$ and find negligible effects on gas fragmentation. However, these studies do not explore lower metallicities, despite available evidence for the existence of a low-metallicity ISM in the past through the discovery of stars with metallicities as low as $10^{-4}\, \rm {Z_{\odot }}$ (Caffau et al. 2011; Starkenburg et al. 2018), as well as several others with $\rm {[Fe/H]} \lt -5$ (Christlieb et al. 2004; Keller et al. 2014; Frebel et al. 2015; Aguado et al. 2017, 2018; Ezzeddine et al. 2019; Nordlander et al. 2019). Coming from the opposite direction, Bromm et al. (2001), Omukai et al. (2005), and Omukai, Hosokawa & Yoshida (2010) consider the thermodynamics of gas of increasing metallicity, and find that dust and metal line cooling permits fragmentation to reach masses ≲1 M⊙ only once the metallicity exceeds ∼10−3.5 Z⊙. Dust is a more efficient coolant than metal lines, and permits fragmentation to lower masses at lower metallicity (e.g. Meece, Smith & O’Shea 2014; Chiaki & Yoshida 2020; Shima & Hosokawa 2021), but exactly by how much depends on the poorly known distribution of dust grain sizes in the early Universe (Schneider et al. 2006, 2012; Omukai et al. 2010; Schneider & Omukai 2010; Chiaki et al. 2015). However, the early Universe star formation models are fundamentally misanalogous to the modern ones that consider decreasing metallicity, in that the early Universe models consider dust solely as a coolant that enables fragmentation, whereas the modern ones assign it a more nuanced role, as both a source of cooling and later, once stellar feedback begins, a source of heating – a changeover that seems crucial to explaining why the IMF in the present-day Universe peaks at ${\sim}0.2\, \rm {M_{\odot }}$ rather than ${\sim}10^{-2}\, \rm {M_{\odot }}$ (Kroupa 2001; Chabrier 2003, 2005).
Citation: Ezzeddine et al. 2019
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Citation: Nordlander et al. 2019
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Without knowledge of nucleus shape and spin parameters (pole orientation and shape), a thermophysical model is pointless, and we instead adopted a NEATM (Near Earth Asteroid Thermal Model) model, used extensively for asteroids (Harris 1998) and TNOs (Müller et al. 2020, and references therein). NEATM is based on the asteroid standard thermal model (STM; Lebofsky et al. 1989) but accounts for phase angle effects; additionally, the temperature distribution is modified by an adjustable η−1/4 factor, which represents the combined and opposed effects of roughness (η  1) and thermal inertia (η > 1). For fixed surface (thermal inertia, roughness) and spin properties, η is also a function of the subsolar temperature, and, therefore, of the heliocentric distance (e.g., Spencer et al. 1989; Lellouch et al. 2013). Given the rh = 20 au distance of our measurements (and the expected large size of 2014 UN271), we adopted a beaming factor η = 1.175 ± 0.42, based on measurements of 85 Centaurs and TNOs (Lellouch et al. 2013, 2017). We also specified a bolometric emissivity ϵb = 0.90 ± 0.06 and a relative radio emissivity ϵr = ϵmm/ϵb = 0.70 ± 0.13, as inferred from combined Spitzer/Herschel/ALMA measurements of nine objects (Brown & Butler 2017; Lellouch et al. 2017). The lower-than-unity relative radio emissivity is interpreted as resulting from (i) the sounding of a colder dayside subsurface and (ii) the loss of outgoing thermal radiation due to volume scattering in the subsurface and/or Fresnel reflection at the surface. The few available radio observations of cometary nuclei also generally indicate radio emissivities lower than 1, for example ∼0.5 for Hale-Bopp (Fernández 2002) and  0.8 for 8P/Tuttle (Boissier et al. 2011). Comets are also found to have low thermal inertias (e.g.,  10,  30, and  45 MKS for 8P/Tuttle, 22P/Kopff, and 9P/Tempel 1, respectively; Boissier et al. 2011; Groussin et al. 2009, 2013), consistent with a beaming factor, η, of order unity. Based on NEATM analysis of a large sample of comet nuclei observed with Spitzer at rh = 3.5–6 au, Fernández et al. (2013) find a mean η of 1.03 ± 0.11. The large 29P/Schwassmann-Wachmann nucleus (D = 65 km) has η = 1.1 ± 0.2 (Schambeau et al. 2021). These numbers are fully consistent with our choice of η. Given the values of rh, η, and ϵb, NEATM calculations indicate that the object’s spectral index over 224–242 GHz is 1.93, slightly lower than the Rayleigh-Jeans limit of 2.
Citation: Lellouch et al. 2013
Citation function: Uses
A strong property of the isothermal gas that defines the interstellar medium (ISM) is the absence of a characteristic mass scale owing to the scale-free nature of gravity. From the collapse condition of an isothermal sphere, one can derive the Jeans mass as
(2)$$\begin{eqnarray*}
M_{\mathrm{J}} = \frac{4 \pi}{3} \rho \left(c_{\mathrm{s}} t_{\rm ff}\right)^3
\end{eqnarray*}$$with cs being the sound speed, given by
(3)$$\begin{eqnarray*}
c_{\mathrm{s}} = \sqrt{\frac{k_{\mathrm{B}} T}{\mu \, m_{\mathrm{H}}}}
\end{eqnarray*}$$and the free-fall time tff is defined here as
(4)$$\begin{eqnarray*}
t_{\mathrm{ff}} = \sqrt{\frac{3\pi }{32G \rho }}.
\end{eqnarray*}$$One sees immediately that for an isothermally collapsing gas, we cannot choose a unique characteristic density that would result in a unique characteristic mass. The larger the density of the gas during collapse and fragmentation, the smaller the Jeans mass. At very large densities, though, owing to the increased dust absorption coefficient, the gas becomes opaque to its own radiation. This is sometimes referred to as the opacity limit (Low & Lynden-Bell 1976; Rees 1976). At this point, the fragmentation is halted, setting a scale below which no fragments form. It is possible to estimate the characteristic density at which this process occurs by requiring the optical depth of one Jeans radius to be unity
(5)$$\begin{eqnarray*}
\tau = \kappa _{\rm dust} \rho R_{\rm J} = 1\,\,\,{\rm with}\,\,\,R_{\rm J} = c_{\mathrm{s}} t_{\rm ff}.
\end{eqnarray*}$$For typical molecular clouds conditions in the Milky Way with T = 10 K, μ = 2.2, and κdust = 0.1 cm2 g−1, we find the critical density that defines the opacity limit
(6)$$\begin{eqnarray*}
\rho _{\rm crit} = \frac{32 G}{3 \pi \kappa _{\rm dust}^2 c_\mathrm{ s}^2 } \simeq 5 \times 10^{-14} \,{\rm g}\,{\rm cm}^{-3} .
\end{eqnarray*}$$At this critical density, we obtain a unique Jeans mass of the order of
(7)$$\begin{eqnarray*}
M_{\mathrm{J}} = 0.670 \frac{c_{\mathrm{s}}^3}{\sqrt{G^3 \rho _{\mathrm{crit}}}} \approx 6 \times 10^{-4} \, \mathrm{M_\odot }.
\end{eqnarray*}$$Note that the critical density can also be derived using slightly more complicated arguments, leading to a very similar value for typical Milky Way conditions (Krumholz 2017). This mass corresponds to the smallest gas clumps that can overcome the pressure gradients and collapse. At this characteristic density, the gas evolution transitions from isothermal to adiabatic, which prevents the collapse of smaller fragments, even at higher densities. The Jeans mass at the opacity limit is obviously much smaller than the observed characteristic mass of the IMF. It does not even correspond to the minimal mass of a star, as the smallest of these fragments will not be able to collapse enough to reach stellar densities in their centres.
Citation: Rees 1976
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Magnetic field fluctuations in the solar wind are highly turbulent. The measured power spectral density (PSD) of the fluctuating magnetic field always exhibits power laws k−α, where k is the wavenumber, and α is the spectral index. A single spacecraft measures the PSD as a function of f−α in the frequency domain, which can be converted to the spatial domain under the Taylor hypothesis. According to the physical processes at different scales, the PSD in the solar wind can be divided into several segments, which can be fitted with different α. The inertial range, which is dominated by magnetohydrodynamic (MHD) turbulence, follows the cascade models with spectral indices αi from around 3/2 to 5/3 (Bruno & Carbone 2013; Chen et al. 2020). The PSDs become steepened below the ion scales (ion thermal gyroradius ρi or ion inertial length di), where kinetic mechanisms should be taken into account. Sometimes a sharp transition range is observed with αt ∼ 4 (Sahraoui et al. 2010; Bowen et al. 2020a). This transition range may be caused by imbalanced turbulence (Voitenko & Keyser 2016; Meyrand et al. 2021), energy dissipation of kinetic waves (Howes et al. 2008), ion-scale coherent structures (Lion et al. 2016), or a reconnection dominated range (Mallet et al. 2017). At smaller scales, a flatter sub-ion kinetic range forms with the spectral index αk ∼ 7/3, which can be explained as the MHD Alfvénic turbulence developing into a type of kinetic wave turbulence, e.g., kinetic Alfvén waves (KAWs; Schekochihin et al. 2009) or whistler waves (Cho & Lazarian 2004). Intermittency in the kinetic range could lead to an −8/3 spectrum (Boldyrev & Perez 2012; Zhao et al. 2016). Ion-cyclotron-wave (ICW) turbulence could lead to a steeper −11/3 spectrum (Krishan & Mahajan 2004; Galtier & Buchlin 2007; Meyrand & Galtier 2012; Schekochihin et al. 2019).The kinetic range always behaves as the KAW turbulence with the slope of −2.8 in the near-Earth space (Bale et al. 2005; Chen et al. 2013; Chen 2016). The spectral indices increase again beyond the electron kinetic scales in observations, indicating the conversion of turbulence energy to electrons (Sahraoui et al. 2009; Alexandrova et al. 2012; Chen et al. 2019) or transitions to a further cascade (Schekochihin et al. 2009; Chen & Boldyrev 2017). In simulations, Meyrand & Galtier (2013) obtained a −8/3 spectrum at electron scales under the 3D electron–MHD model.
Citation: Chen et al. 2020
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We can use the equivalent width of Hα (EWHα, see Table 4) to put additional constraints on the recent star formation history of the AGNs. To do so, we first need to estimate the largest fraction of the Hα luminosity that could arise from star formation, and for this we use the group of AGNs with the highest EWHα. There are a number of reasons why AGNs could have lower EWHα, but the maximum values will only be found when both AGN and star formation contribution are maximal. The group of six AGNs with the highest EWHα consists of ESO 137-G034, NGC 3081, NGC 2110, NGC 7582, NGC 2992, and NGC 5728, and their median EWHα is 70 Å. These also tend to have the highest log [OIII]/Hβ, with a median ratio of 1.07. Similarly, their median log [NII]/Hα is 0.01. To assess the star formation contribution to the Hα flux, we consider lines from the most extreme AGN photoionisation models of Groves et al. (2004), to the location of solar metallicity star-forming galaxies (see also Davies et al. 2014b). Since the AGNs are very close to the highest [OIII]/Hβ ratios that the models can produce, we find that at most 10% of their Hα flux could be due to star formation. Applying this correction reduces the EWHα that is associated with star formation to  7 Å. We also need to make a correction for the old stellar population, since EWHα in models compares the line flux to the continuum due to stars associated with the line emission. We find that 5% of the continuum is associated with young stars. We therefore estimate that the maximum EWHα associated with the most recent star-forming episode is  7 Å/5%, which is  140 Å. Comparing this to Starburst99 models (specifically Figs. 83 and 84 in Leitherer et al. 1999) rules out continuous star formation since it would imply a timescale exceeding several Gyr, inconsistent with the stellar population synthesis results. Instead, it means that the recent star formation must have ceased. Based on the rate at which the EWHα falls after star formation stops, we estimate that the end of star formation must have typically happened at least 6 Myr prior.
Citation: Davies et al. 2014b
Citation function: Uses
Even before studying the relationship between the IMF and the CMF, it is important to realize that how the IMF originates from the observed CMF depends directly on the definition of the cores, assumed to be the gas mass reservoir used for the formation of each star or binary system. As shown by Louvet et al. (2021), defining this mass reservoir may seem obvious in the observed map of a cloud, but core characteristics (size, mass) depend heavily on the spatial scales probed by the observations. In addition, the theoretical definition of cores also depends on whether the star-formation scenario is quasi-static or dynamic. In the former scenario, cores are gas condensations sufficiently dense to be on the verge of gravitational collapse, and they convert the core gas into stars (Shu et al. 1987; Chabrier 2003; McKee & Ostriker 2007; André et al. 2014). After a quasi-static phase of concentration of the cloud gas into cores, cores become distinct from their surrounding cloud and start to collapse, and their future stellar content becomes independent of the properties of the parental cloud. In the latter scenario, dynamics play a major role during all phases of the star-formation process (e.g., Ballesteros-Paredes et al. 2007; Hennebelle & Falgarone 2012; Padoan et al. 2014). In particular, global infall of filament networks and gas inflow toward cores are expected to be important drivers of star formation (e.g., Smith et al. 2009; Vázquez-Semadeni et al. 2019; Padoan et al. 2020). In this framework, filaments, cores, and stellar embryos simultaneously accrete gas, and the gas reservoir associated with star formation largely exceeds the extent of the observed cores. This so-called clump-fed scenario was proposed in various recent papers and described in detail in the review by Motte et al. (2018a, see references therein). One of the main objectives of the ALMA-IMF Large Program is to discriminate between the quasi-static and dynamic scenarios by quantifying the role of cloud kinematics in defining core mass and in possibly changing it over time.
Citation: Shu et al. 1987
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