adsabs/FOCAL huggingface dataset:
To model the inner coma plasma, we use the simplified model by Eriksson et al. (2017). Neutral gas flows outward from the comet with a velocity of about 0.7 km s−1 (Gulkis et al. 2015), with the density decreasing as r−2(1)
\begin{equation}
n_{{\rm n}} (r) \approx n_{0} \left( \frac{R}{r} \right)^{2},
\end{equation}
where n0 is the neutral gas density at the surface of a comet with radius R, and nn is the density at the cometocentric distance r. Assuming that steady ionization by solar EUV radiation dominates, this gives a peak in plasma density at some cometocentric distance, and a decrease of this density as r−1 at large distances (since the density of neutrals is typically much higher than the plasma density):
(2)
\begin{equation}
n_{{\rm e}} (r) \approx n_{0} \frac{\nu R}{u} \frac{R}{r} \left(1-\frac{R}{r} \right),
\end{equation}
where ne is the electron density at some distance r, ν is an ionization frequency depending on the distance to the sun and u is the outflow velocity of the plasma (Haser 1957; Mandt et al. 2016; Eriksson et al. 2017; Vigren & Eriksson 2017; Vigren 2017). Assuming that the plasma is dominated by water ions from the comet, ion–electron pairs are created with particle energies of less than 0.1 and about 12 eV, respectively (due to conservation of momentum). When the density is high enough close to the nucleus, neutral-electron collisions will cool the electrons to temperatures of 0.1 eV or less. Beyond some distance rce the electrons are not efficiently cooled, and a mixture of cool (0.1 eV) and warm (5–10 eV) electrons are observed (Edberg et al. 2015; Mandt et al. 2016; Eriksson et al. 2017). Collisions between neutrals and ions are important out to larger distances. We investigate the region where electron-neutral collisions can be neglected, and warm electrons are present and magnetized, while the ions are unmagnetized due to collisions and their large gyroradius. This is a region favourable for lower hybrid waves and is where Rosetta spend much of its time during the 2 yr investigation of 67P (Mandt et al. 2016). We use three populations to model the plasma, cold and warm electrons, and H2O + ions
(3)
\begin{equation}
n_{{\rm ew}} (r) \approx n_{0} \frac{\nu R}{u} \frac{R}{r} \left(1-\frac{r_{{\rm ce}}}{r}\right) \quad \quad r \ge r_{{\rm ce}},
\end{equation}
(4)
\begin{equation}
n_{{\rm ec}} (r) \approx n_{{\rm e}} (r_{{\rm ce}}) \frac{r^2_{{\rm ce}}}{r^2} = n_0 \frac{\nu R}{u} \frac{Rr_{{\rm ce}}}{r^2} \quad \quad r \ge r_{{\rm ce}},
\end{equation}
(5)
\begin{equation}
n_{{\rm i}} (r) \approx n_{0} \frac{\nu R}{u} \frac{R}{r} \left(1-\frac{R}{r} \right),
\end{equation}
where new, nec and ni are the densities of warm and cold electrons, and ions, respectively (Eriksson et al. 2017). For distances smaller than rce, the electron motion is disrupted by collisions and lower hybrid waves are likely to be heavily damped.
Citation: Eriksson et al. (2017)
Citation function: Uses
Citation: Eriksson et al. 2017
Citation function: Uses
Citation: Eriksson et al. 2017
Citation function: Uses
Citation: Eriksson et al. 2017
Citation function: Uses
Multiwavelength searches for the donor stars have been pursued for more than a decade. Some have observed ULXs in the optical range (e.g. Gutiérrez & López-Corredoira 2006; Ptak et al. 2006; Roberts et al. 2011; Gladstone et al. 2013; Fabrika et al. 2015). As several of the ULXs are located in or near young star clusters (e.g. Fabbiano, Zezas & Murray 2001; Roberts et al. 2002; Poutanen et al. 2013), some donor stars of ULXs might as well be RSGs (Copperwheat et al. 2005, 2007; Patruno & Zampieri 2008), which are bright in the near-infrared (NIR) band. In light of this, we started an observing campaign of ULXs in the NIR (Heida et al. 2014; López et al. 2017), tailored to detect RSG donor stars (−8  H, Ks  −11; Elias, Frogel & Humphreys 1985; Drilling & Landolt 2000). We targeted sources at distances of up to 10 Mpc, within uncertainties. Of the 97 ULXs observed by Heida et al. (2014) and López et al. (2017), we detected a NIR candidate counterpart for 33 ULXs. Of these 33 NIR sources, 19 had the absolute magnitude consistent with an RSG. So far, we performed spectroscopic follow-up observations for 7 out of these 19 candidate RSGs and confirmed the RSG nature for 3 counterparts: ULX RX J004722.4−252051 (in NGC 253; Heida et al. 2015a), ULX J022721+333500 (in NGC 925), and ULX J120922+295559 (in NGC 4136; Heida et al. 2016). Additionally, we discovered that four counterparts, initially classified as RSG based on photometry, are actually nebulae partially powered by the X-ray emission of the ULX: ULX J022727+333443 (in NGC 925), ULX J120922+295551 (in NGC 4136), ULX Ho II X-1 (in Holmberg II; Heida et al. 2016), and [SST2011] J110545.62+000016.2 (in NGC 3521; López et al. 2019). This means that, at the time of writing this manuscript, the photometric and spectroscopic observations provided 3 confirmed RSGs, 12 candidate RSGs, 4 confirmed nebulae, and 14 candidate stellar clusters/active galactic nuclei (AGNs). Recently, Lau et al. (2019) observed 96 ULXs within 10 Mpc in the mid-IR with the Spitzer Space Telescope. They detected and identified 12 ULXs with candidate counterparts whose absolute mid-IR magnitude is consistent with being RSGs.
Citation: Elias, Frogel & Humphreys 1985
Citation function: Motivation; Motivation
We first focus on the properties of the PDLA obtained through the VPFit code. Together with the fitted absorption profile, both the column density and the redshift of the PDLA are derived: (8)\begin{equation} \log(N) = 20.9290 \pm 0.0024;~~~ z_{\rm abs} = 3.082097 \pm 0.000053. \label{eq:col_dens_zabs} \end{equation}log(N)=20.9290±0.0024;zabs=3.082097±0.000053.The redshift value obtained here differs by no more than 0.000163 from the value obtained based on metallic lines and is thus entirely consistent with it (see Sect. 3.2 above). We took the refractive index n of air into account that causes a shift in the observed wavelengths: λair = λvac/n. We used the Ciddor equation (Ciddor 1996), taking the atmospheric conditions at the time of the measurement into account (air temperature 12°C, pressure 744.9 hPa, and relative humidity 3%, as reported in the header of the original FITS file). The errors are the formal errors provided by VPFit and are certainly underestimated, as they do not include uncertainties linked to the continuum determination. In their pioneer study, Leibundgut & Robertson (1999) obtained a column density and redshift \begin{eqnarray*} \log(N) = 20.85 \pm 0.03;~~~ z_{\rm abs} = 3.0825. \end{eqnarray*}log(N)=20.85±0.03;zabs=3.0825.Our estimate of the column density is higher than theirs by 2.6σ (referring to their error estimate), and we find a slightly lower redshift (the difference amounts to 7.6σ according to our own error estimate). The latter discrepancy might be due to our lower spectral resolution (R ~ 1840 instead of 3300), which might cause the metallic absorption lines in the blue wing of the Lyα absorption trough to be less easily recognized and be partly included in the Voigt profile fit. This would result in a slightly overestimated column densitiy and in a slight blue shift. However, our VPFit estimate of the redshift, based on the Lyα line alone, agrees within only 0.5σ with the PDLA redshift estimate based on metallic lines.
Citation: Ciddor 1996
Citation function: Uses; Uses
Citation: Leibundgut & Robertson (1999)
Citation function: Background; Background; Differences
We quantitatively assess the possibility of bulge formation in our sample of the 12 massive galaxies with reliable size measurements of dust continuum emission. Quiescent galaxies generally have a dense core with high stellar mass surface densities within 1 kpc of galaxy centers of 





, while star-forming galaxies mostly do not (van Dokkum et al. 2014; Barro et al. 2015). For our sample, we create stellar mass maps by spatially resolved SED modeling with multiband HST data (Wuyts et al. 2012; Lang et al. 2014) to calculate stellar mass surface densities within 1 kpc from the 870  μm center. None of the members of our sample satisfy the criterion of a dense core at the current moment (Table 2). The spatial distribution of star formation within galaxies allows us to understand when the dense core is formed by subsequent star formation. Exploiting the geometric information of the best-fit exponential models at 870  μm, we derive the SFR surface densities within the central 1 kpc (ΣSFR1 kpc) from the Spitzer/Herschel-based total SFRs over galaxies. For nine galaxies with compact dust emission of 





, they are intensely forming stars in the central region with ΣSFR1 kpc = 40 (19–65) M⊙ yr−1 kpc−2 (Table 2). Then, bulge formation timescales to reach 





 kpc−2) = 10 are estimated by
3





taking into account mass loss due to stellar winds (w = 0.6 in Chabrier IMF; see also van Dokkum et al. 2014). The estimated bulge formation timescales are 





 (8.16–8.79) for the nine galaxies with R1/2,870 μm  1. 5 kpc. They can complete the dense core formation by z = 2 when the current level of star formation is maintained for several hundred megayears. Galaxies forming stars in disks as extended as the rest-optical light would have to keep the current star formation for a longer time (∼2 Gyr). This is not consistent with stellar populations obtained in high-redshift quiescent galaxies, where timescales for star formation are τ  1 Gyr (e.g., Belli et al. 2015; Onodera et al. 2015).
Citation: Lang et al. 2014
Citation function: Uses; Uses
For Region 1, we adopt a thick, uniform disk approximation and assume that we view this disk edge-on. In this case, the density can be obtained by dividing the central/maximum column density toward the axis by the diameter/width of the disk, i.e., the depth. The average of color excess E(H â Ks) is â¼1.5 Â± 0.7 mag for 20 sources detected toward the central part of Region 1 (within 60â³ of the symmetric axis), and  cmâ2 is roughly obtained, using the reddening law, E(H â Ks) = 0.065 Ã AV (Chini & Wargau 1998), and the standard gas-to-extinction ratio,  cmâ2 magâ1 (Dickman 1978). This estimated column density seems to be consistent with that estimated from the CO data, â¼1.3â4.1 Ã 1022 cmâ2. Adopting a width of â¼30 (â¼1.4Â pc) as the depth of Region 1, we can derive a number density of  cmâ3. Since Region 2 is located around the symmetric axis of the cloud, the column density in Region 2 is expected to be close to the central/maximum column density if the local density is uniform. The average of color excess E(H â Ks) is â¼1.1 Â± 0.4 mag for 41 sources toward Region 2, and  cmâ2 is roughly obtained. This column density also seems to be consistent with that estimated from the CO data, â² 2.1 Ã 1022 cmâ2. Adopting the width of â¼80 (â¼3.5Â pc) as the depth of Region 2,  cmâ3 can be obtained in Region 2. The estimated number density in Region 1 is â¼3â4Â times higher than that in Region 2, supporting the idea that Region 1 was strongly compressed by UV and then became higher in density. This result does not seem to match the simulation results for the nonmagnetized clouds that the number density in the tip is expected to be higher by more than one order of magnitude than that of the area away from the tip (e.g., Figures 3, 7, and 10 of Miao etÂ al. 2009). However, the simulation taking into account the magnetic pressure predicts a smaller difference of a factor of 10 (e.g., Figure 8 of Miao etÂ al. 2006), which is more consistent with our observations. Motoyama etÂ al. (2013) also suggests flatter column density profiles in the magnetized cases than in the nonmagnetized ones.
Citation: Dickman 1978
Citation function: Uses; Uses
In the interpretation of clumpy star formation in a disk-like galaxy, as usually observed in high-z galaxies (e.g., Elmegreen et al. 2009; Förster Schreiber et al. 2011; Murata et al. 2014; Tadaki et al. 2014), the ellipticity of a source may be an intrinsic property related to the viewing angle of the disk. That is, large ellipticity implies that its viewing angle is close to edge-on and that the stellar disk lies in the elongated direction. If we consider that Lyα is emitted in directions perpendicular to the disk, as predicted by the recent theoretical studies for Lyα line transfer (e.g., Verhamme et al. 2012; Yajima et al. 2012b), the pitch angle of Lyα emission will be at right angles to that of UV continuum. Moreover, in such a case, it is also expected that the size in Lyα emission aHL(NB711) shows a positive correlation with ellipticity measured in rest-frame UV continuum because the Lyα-emitting region in bipolar directions perpendicular to the disk can be viewed from longer distances if the viewing angle of the disk is closer to edge-on, that is, larger ellipticity. However, as presented in the top panel of Figure 17, we do not find such positive correlation between aHL(NB711) and ellipticity for the 54 ACS-detected LAEs. Furthermore, as shown in the bottom panel of Figure 17,14 the observed distribution of the LAEs in the EW0– plane seems not to be quantitatively consistent with the interpretation of clumpy star formation in a disk-like galaxy, where EW0 is expected to decrease significantly toward the edge-on direction (i.e., larger ellipticity) via radiative transfer effects for Lyα resonance photons (e.g., Verhamme et al. 2012; Yajima et al. 2012b); this result is consistent with Shibuya et al. (2014). Therefore, the interpretation of clumpy star formation in a disk-like galaxy seems not to be preferred for our LAE sample. This conclusion can be reinforced with the absence of an ACS source with a large size and round shape; if there are multiple clumpy star-forming regions in a disk-like galaxy, some such galaxies will be viewed face-on, resulting in alarge size and round shape. We emphasize again that this result is not affected by a selection bias against them if they are bright enough (i.e., I814 ≲ 26 mag), as shown in Figures 7 and 18.
14
Note that, considering the strong positive correlation between aHL and  shown in Figure 8, this plot is qualitatively identical to the distribution in the EW0–aHL plane shown in the top panel of Figure 16.
Citation: Verhamme et al. 2012; Verhamme et al. 2012
Citation function: Uses; Uses; Differences
Citation: Elmegreen et al. 2009
Citation function: Background; Background
On the basis of the absolute PM estimate derived in the previous section, we performed a numerical integration of the orbit of Terzan 5 in the Galactic potential. We used the three-component (bulge, disk, and halo) axisymmetric model from Allen & Santillan (1991), which has been extensively used and discussed in the literature to study orbits and dynamical environmental effects on Galactic stellar systems (e.g., Allen et al. 2006; Montuori et al. 2007; Ortolani et al. 2011; Moreno et al. 2014; Zonoozi et al. 2014), thanks to its relative simplicity and fully analytic nature. We adjusted the various model parameters to make the rotation velocity curve match the value of 243 km s−1 measured at the Solar Galactocentric distance of 8.4 kpc (see above). The cluster PMs were reported in the Cartesian Galactocentric reference frame, resulting in a velocity vector (vx, vy, vz) = (−60.4 ± 1.3, 85.7 ± 11.1, 35.0 ± 6.0) km s−1 at the position (x, y, z) = (−2.51 ± 0.30, 0.39 ± 0.02, 0.17 ± 0.01) kpc. We adopted the convention in which the X axis points opposite to the Sun (i.e., the Sun position is (−8.4,0,0)). The orbit was then time-integrated backwards for 12 Gyr, starting from the given initial (current) conditions and using a second-order leapfrog integrator (e.g., Hockney & Eastwood 1988) with a rather small and constant time step (∼100 kyr, corresponding to 





 of the dynamical time at the Sun distance, computed as 





, where 





 is a characteristic Galactic mass parameter). During the >105 time steps used to describe the entire orbit evolution, the errors on the conservation of both the energy and the Z component of angular momentum were kept under control and never exceeded one part over 105 and 1013, respectively. To take into account the uncertainties on the kinematic data, we generated a set of 1,000 orbits starting from the phase-space initial conditions normally distributed within a 3σ range around the cluster velocity vector components and the current position, with σ being equal to the quoted uncertainties on these parameters. For all of these orbits we repeated the backward time integration. The probability densities of the resulting orbits projected on the equatorial and meridional Galactic planes are shown in Figures 13 and 14, respectively. Darker colors correspond to more probable regions of the space, that is, to Galactic coordinates crossed more frequently by the simulated orbits. As is apparent, the larger distances reached by the system during its evolution are R = 3.5 kpc and 





 kpc at a 3σ level of significance, which roughly correspond to a region having the current size of the bulge.
Citation: Hockney & Eastwood 1988
Citation function: Uses; Uses
A scenario that could potentially support superdiffusive parallel transport for energetic ions interacting with SMFRs in the large-scale solar wind is when (1) these structures can be viewed as coherent, quasi-helical magnetic field structures with a typical width L

I
 of intermediate size and sharp boundaries (Greco et al. 2009), and (2) energetic particles have gyroradii r

g
 that are small compared to the typical SMFR width L

I
. There is observational support at 1 au for all these assumptions (e.g., Greco et al. 2009; Cartwright & Moldwin 2010; le Roux et al. 2015). Thus, it is reasonable to envisage that the particle guiding centers follow the helical magnetic field lines (negligible cross-field drifts) to propagate through SMFR structures in a coherent fashion for a considerable distance before scattering during exit of the structure through the narrow magnetic boundaries. To be more specific, SMFRs identified at 1 au typically have widths L

I
 ≈ 0.01 − 0.001 au (Cartwright & Moldwin 2010; Khabarova et al. 2015), while data analysis of low-frequency 2D turbulence suggests elongated SMFR structures with an average length L

I∣∣ so that L

I∣∣/L

I
 ≈ 2 − 3 (Weygand et al. 2011). Based on the expression for the path length s

I
 of a SMFR helical field line (Equation (9)), we estimate that the distance a particle guiding center travel through a SMFR structure by following magnetic field lines can be considerable because s

I
 ≈ 0.004 − 0.04 au. Furthermore, the protons accelerated by SMFRs reach kinetic energies of ≲5 MeV (Khabarova & Zank 2017) in the solar wind at 1 au, thus easily fulfilling the requirement r

g
 ≪ L

I
. Consequently, the transport through SMFRs can be characterized as involving an enhanced probability of relatively long transport distances or step sizes along the background/guide field perpendicular to the shock surface (in the z-direction) between scattering events indicating Lévy walks as discussed by Zimbardo & Perri (2020) and Zimbardo et al. (2021).
Citation: Cartwright & Moldwin 2010
Citation function: Uses
Citation: Cartwright & Moldwin 2010
Citation function: Uses
In recent years, there has been an increasing interest in identifying embedded filaments at an early stage of fragmentation, where star formation activities have not yet started. Kainulainen et al. (2016) studied the Musca molecular cloud using the NIR, 870 μm dust continuum and molecular line data, and suggested that the Musca cloud is a very promising candidate for a filament at an early stage of fragmentation and shows very few signs of ongoing star formation. However, the identification of such filaments is still limited in the literature (e.g., Kainulainen et al. 2016). In the I05463+2652 site, we have selected two elongated filamentary features (“s-fl” and “nw-fl”). The Herschel temperature map reveals these filaments with a temperature of ∼11 K. It has been suggested that the thermally supercritical filaments (i.e., 






M


line


>


M


line
,
crit




) can be unstable to radial collapse and fragmentation (André et al. 2010). However, thermally subcritical filaments (i.e., 






M


line





M


line
,
crit




) may lack prestellar clumps/cores and embedded protostars (André et al. 2010). In the I05463+2652 site, the observed masses per unit length of the filaments are computed to be 




∼
60



M


⊙




 pc−1 (for filament “s-fl”) and 




∼
200



M


⊙




 pc−1 (for filament “nw-fl”), which are much higher than the critical mass per unit length at T = 10 K (i.e., 






M


line
,
crit


=
16



M


⊙




 pc−1; see Section 3.2). For the purpose of comparison, we also provide the observed masses per unit length of some well known filaments (such as DR21 (






M


line


∼
4500



M


⊙




 pc−1), Serpens South (






M


line


∼
290



M


⊙




 pc−1), Taurus B211/B213 (






M


line


∼
50



M


⊙




 pc−1), and Musca (






M


line


∼
20



M


⊙




 pc−1)) (see Table 1 in André et al. 2016). Based on the analysis of masses per unit length, the elongated filaments (“s-fl” and “nw-fl”) are thermally supercritical (see Section 3.2). Furthermore, these two filaments contain clumps (or fragments), indicating the signature of gravitational fragmentation. Arzoumanian et al. (2013) pointed out that supercritical filaments may undergo gravitational contraction and increase in mass per unit length through the accretion of background material.
Citation: André et al. 2010
Citation function: Background
Citation: André et al. 2010
Citation function: Background
One of the theoretical models to account for different depletion times is the turbulence model of Krumholz & McKee (2005). According to this model, turbulence will determine the density PDF of the clouds. The most important parameter is the SFE per free-fall time, which is the ratio between the free-fall time and the depletion time. The general equation for free-fall time is
(15)$$\begin{eqnarray*}
t_{\text{ff}}=\sqrt{\frac{3\pi }{32G\rho _{\mathrm{mol, mid}}}},
\end{eqnarray*}$$where ρmol, mid is the volume density of the molecular gas in the middle of the disc. If we assume the galaxy is filled with gas, then the volume density can be calculated as
(16)$$\begin{eqnarray*}
\rho _{\mathrm{mol, mid}}=\frac{\Sigma _{\text{mol}}}{2 H_{\mathrm{mol}}} ,
\end{eqnarray*}$$where Hmol is the scale height of the disc and Σmol is the surface density of the molecular gas measured from the 12CO J = 2–1 cube (see Section 3.2). Assuming the gas disc is in equilibrium and that vertical gravity is dominated by gas self-gravity, then we can calculate the scale height as (Wilson et al. 2019)
(17)$$\begin{eqnarray*}
H_{\mathrm{mol}}= 0.5\frac{\sigma _v^2}{\pi G \Sigma _{\text{mol}}} ,
\end{eqnarray*}$$where σv is the velocity dispersion of the molecular gas. Combining all the equations above, we can write the free-fall time as
(18)$$\begin{eqnarray*}
t_{\text{ff}}=\frac{\sqrt{3}}{4G} \frac{\sigma _v}{\Sigma _{\text{mol}}} .
\end{eqnarray*}$$Therefore, the SFE per free-fall time can be calculated as (Wilson et al. 2019)
(19)$$\begin{eqnarray*}
\epsilon _{\text{ff}}=\frac{t_{\text{ff}}}{t_{\text{dep}}}=\frac{\sqrt{3}}{4G}\frac{\sigma _v \Sigma _{\text{SFR}}}{\Sigma ^2_{\mathrm{mol}}} .
\end{eqnarray*}$$Assuming a constant SFE per free-fall time, the depletion time will decrease as the surface density of the gas increases. To calculate ϵff, we need maps of Σmol, ΣSFR, and σv. We plot ϵff versus Σmol in Fig. 11 (left plot). As we can see, there is a clear decreasing trend for ϵff versus Σmol for Arp 240, while ϵff stays relatively constant for the other U/LIRGs. Furthermore, in the low surface density regions, ϵff can be above 1.0. For normal clouds, ϵff can be as high as several 10 per cent (Lee et al. 2016). Therefore, our method probably overestimates the true efficiency in these galaxies.
Citation: Wilson et al. 2019
Citation function: Uses; Uses
Citation: Wilson et al. 2019
Citation function: Uses; Uses