adsabs/FOCAL huggingface dataset:
We first assess the mass–size relation regulated by collision-induced turbulence, i.e. the mass–size relation of clumps in the molecular ring. In our clump–clump collision scenario, the turbulent energy injected by the collisions cascades down to small scales and counterbalances self-gravity to produce a rough virial equilibrium (i.e. the clumps are able to maintain virialization; see Section 5.1). These virialized clumps should always have their energy dissipation rates (per unit mass) $\dot{\epsilon }_{\rm diss,clump}=\frac{1}{4}\frac{\sigma _{\rm obs,los}^3}{R_{\rm clump}}$ (equation 14) match their virial energy dissipation rates (per unit mass)
(33)$$\begin{eqnarray}
\dot{\epsilon }_{\rm diss,vir} =\frac{1}{4}\left(\alpha _{\rm vir,crit}\, GM_{\rm clump}/5\right)^{3/2}R_{\rm clump}^{-5/2}
\end{eqnarray}$$(Li 2017b), i.e. $\dot{\epsilon }_{\rm diss,clump}\approx \dot{\epsilon }_{\rm diss,vir}$, where as before αvir, crit ≈ 2 is the boundary between gravitationally bound and unbound objects (Kauffmann et al. 2013, 2017). The virial energy dissipation rate (per unit mass) $\dot{\epsilon }_{\rm diss,vir}$ is the energy dissipation rate (per unit mass) a molecular gas structure would have if it were virialized. We therefore expect
(34)$$\begin{eqnarray}
\dot{\epsilon }_{\rm diss,vir}\approx \dot{\epsilon }_{\rm diss,clump}\approx \dot{\epsilon }_{\rm inject,coll}
\end{eqnarray}$$for the clumps in the molecular ring of NGC 404, where we have used $\dot{\epsilon }_{\rm diss,clump}\approx \dot{\epsilon }_{\rm inject,coll}$, i.e. the energy dissipation rates (per unit mass) of clumps are approximately equal to the energy dissipation rates (per unit mass) from clump–clump collisions in the molecular ring (see Section 4.4). We indeed find very good agreements between the estimated $\dot{\epsilon }_{\rm diss,vir}$, the measured $\dot{\epsilon }_{\rm diss,clump}$, and our predicted $\dot{\epsilon }_{\rm inject,coll}$ in the molecular ring (see panel c of Fig. 9), providing more evidence that the turbulence induced by clump–clump collisions can support and maintain molecular ring clumps in virial equilibrium.
Citation: Li 2017b
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As we see, in the magnetospheres of Crab-like pulsars the Cherenkov drift resonance might lead to the hard X-rays. In the previous section, we have seen that this emission inevitably leads to the non-vanishing pitch angles (see equation 14), generating the synchrotron emission. In Fig. 2 we show the behaviour of energy of synchrotron photons, $\epsilon _{_{{\rm GeV}}}$ versus γb in the interval [0.5; 1] × 107 for different values of Lorentz factors of the plasma component: γp = 1 (solid line), γp = 10 (dashed line), γp = 50 (dash–dotted line). We have taken into account the dipolar character of the magnetic field, $B\approx 3.2\times 10^{19}\times \sqrt{P\dot{P}}\times R^3/R_{lc}^3$ G (Goldreich & Julian 1969), where R = 106 cm is the neutron star's radius. The rest of the parameters is: $P = P_{_{{\rm Cr}}}$, $\dot{P}=\dot{P}_{_{{\rm Cr}}}$, $n_b = n_{_{GJ}}$, where $n_{_{GJ}} = B/Pec$ is the Goldreich–Julian number density (Goldreich & Julian 1969). As it is evident from the plots by increasing γp, the resulting emission energy increases as well, which directly follows from the analytical behaviour, $\epsilon _{_{{\rm GeV}}}\propto \gamma _p^{1/8}$ (this can be seen by combining equations 8, 12–14). We see that the QLD by means of the feedback of ChDI guarantees the synchrotron emission over 100 GeV. We can roughly estimate the possible VHE luminosity by multiplying the number of particles involved in the process with the single emission power, $P_{{\rm syn}}\approx 2e^4\gamma _b^2B^2\langle \psi \rangle ^2/3m^2c^3$. It is worth noting that the thickness of the layer, d, where the electrons accelerate to the highest energies, is of the order of Rlc/2γb. Then, by taking into account the corresponding number of particles, $4\pi R_{lc}^2n_{_{GJ}}d$, one can show that in the emission energy band 150 GeV the highest energy electrons lead to the bulk luminosity of the order of 1033 erg s−1 which is in a good agreement with observations (Lessard et al. 2000; Albert et al. 2008).
Citation: Goldreich & Julian 1969
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Citation: Goldreich & Julian 1969
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Citation: Lessard et al. 2000
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The Barnard 5 (B5) dark cloud is located at the North-East of the Perseus complex (235 pc; Hirota et al. 2008). It contains four known protostars of which the most prominent is the Class I protostar IRS1. SCUBA continuum emission maps at 850 μm carried out with the JCMT only revealed dust emission towards known protostars and at about 2–4 arcmin north from IRS 1 (Hatchell et al. 2005) whilst molecular maps of CO, NH3, and other species show several chemically differentiated clumps (S. B. Charnley, in prep.). Methanol emission in B5 displays a particularly interesting distribution since it shows a bright so-called methanol hotspot at about 250 arcsec north-west from IRS 1, a region showing no infrared sources and no detected sub-mm continuum emission (see Fig. 1 in Hatchell et al. 2005; Wirstrom et al. 2014). The subsequent detection of abundant water, with absolute abundances of about 10-8, with the Herschel Space Observatory by Wirstrom et al. (2014) suggests that efficient non-thermal processes triggering the evaporation of icy methanol and water are at work. The methanol hotspot therefore represents an ideal target to detect cold COMs in dark clouds since they are supposed to be formed from methanol, either at the surface of interstellar grains, or directly in the gas phase after the evaporation of methanol. The Perseus molecular cloud was recently mapped with Herschel as part as the Gould Belt Survey key program (André et al. 2010) using the photometers PACS and SPIRE in five bands between 70 μm and 500 μm.Figure 1 presents the Barnard 5 molecular cloud as seen by Herschel/SPIRE at 250 μm. The Herschel data has been retrieved from the Herschel Science Archive. The data were calibrated and processed with the Herschel pipeline and are considered as a level-3 data product. Dust emission is compared with the integrated intensity map of the A+-CH3OH 30 − 20 transition as observed with the IRAM 30 m telescope (this work).The methanol hotspot is located between the two dense cores East 189 and East 286 (Sadavoy, priv. comm.) revealed by Herschel for the first time, and the methanol emission peaks at the edge of core East 189. East 189 and East 286 have the following properties derived through a fitting of their observed spectral energy distribution: M = 0.5M⊙, Td = 12 K, R = 3.6 × 10-2 pc, nH = 3 × 104 cm-3, and M = 0.7M⊙, Td = 9.9 K, R = 2.7 × 10-2 pc, nH = 1.2 × 105 cm-3 (Sadavoy  2013).
Citation: Wirstrom et al. 2014
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Citation: Wirstrom et al. (2014)
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Citation: Hirota et al. 2008
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Citation: Sadavoy  2013
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Next, we fit the emission lines using the code described in detail in Dong et al. (2005). The optical spectra show strong, narrow emission lines such as [O ii] λ3727, [O i]





, 





, [N ii]





, and [S ii]





 [O iii]





 is instead weak. As we verified above, broad 





 is evidently presented (see also Greene & Ho 2007; Dong et al. 2012). The SDSS data are used to fit the blue part such as in the 





+[O iii] region (as not covered by the MMT spectrum), and the MMT data for the red part such as [O i] lines, the 





+[N ii] region, and [S ii] lines. We fit the MMT spectrum first. Every narrow or broad component of the emission lines is modeled with Gaussians, starting with one Gaussian and adding in more if the fit can be improved significantly according to the F-test. The [S ii]





 doublet lines are assumed to have the same profile and fixed in separation by their laboratory wavelength; the same is applied to [N ii]





 doublet lines, and to [O i]





 and [O i]





 emission lines. The flux ratio of the [N ii] doublet 





 is fixed to the theoretical value of 2.96 (e.g., Acker et al. 1989; Storey & Zeippen 2000). In the best-fit model, it turns out that one Gaussian is used for the broad component of 





, while two Gaussians for the narrow component of 





, each line of the [N ii], and [S ii] doublet and the two [O i] lines, respectively. The reduced 





 is 1.21 for the 





+[N ii] region. Note that the [N ii]





 and [S ii] doublet lines show asymmetric line profiles clearly in the MMT spectrum, which are actually common in high-resolution spectra (Xiao et al. 2011); thus these narrow lines, and narrow 





 also, need two Gaussians to model. Then we fit the 





+[O iii] region based on the SDSS spectrum. As the spectral signal-to-noise (S/N) of this region is not high and the 





 emission line is much weaker than 





, we assume the broad and narrow components of 





 have the same profiles as the respective components of 





. The [O iii]





 doublet lines are assumed to have the same profile, and the flux ratio of 





 is fixed to the theoretical value of 2.98 (e.g., Storey & Zeippen 2000; Dimitrijević et al. 2007); the best-fit model turns out to adopt two Gaussians for each [O iii] doublet line. The reduced 





 is 0.95 for the 





+[O iii] region. [O ii] λ3727 is fit independently, and one Gaussian is sufficient to model. We also fit the 





 lines of the N and S branches of the extended emission. One Gaussian is statistically sufficient for either branch, with reduced 





 of 0.95 (N) and 0.97 (S), respectively. The best-fit line parameters, centroid, FWHM (corrected for instrumental broadening), and flux of every branch agree well with those directly integrated/measured from the spectra.
Citation: Storey & Zeippen 2000
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Citation: Storey & Zeippen 2000
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The de-projected distance that corresponds to the core-position changes of Markarian 421 is approximately 3.5 ∼ 8.7 pc (equivalent to (1.0 − 2.6) × 105 Schwarzschild radii (Rs)) for a jet-viewing angle of 2°–5° (Lico et al. 2012). One of the leading models for explaining the blazar phenomenon is the so-called internal-shock model, in which discrete ejecta with higher speeds catch up with the preceding slower ejecta, and the collision leads to a shock wave in the colliding ejecta (Spada et al. 2001; Guetta et al. 2004). Based on this model, core wandering can be naturally explained because the model predicts some scattering of the shock locations caused by the randomness of the ejecta speed. Therefore, we assume that the distances of the shock locations from the black hole immediately after the flare, 





, are proportional to the product of the square of the bulk Lorentz factor (





) of the ejecta and the separation length (Δ) of the colliding ejecta. Assuming that a typical separation length is a scale of about 10 times the innermost stable circular orbit for non-rotating black holes (





), in light of numerical simulations of relativistic outflows around black holes (McKinney et al. 2013), very fast ejecta with a Lorentz factor of approximately 





 are required to explain the observed magnitude of the core wandering. The 





 is comparable to previously reported maximum values (Γ of 40 ∼ 50; Lister et al. 2009, 2013) based on statistical studies by a long-term monitor using VLBI. Moreover, the radio core returned to the reference stationary position after 2012 March 12 (the 10th epoch). This can be explained if the emission from the reference position is identical to the radio core that is in a quiescent state. The radio-core emission in a quiescent state is expected to be persistent. As one of the possibilities for reproducing the observed core wandering, this persistent radio core was obscured by the flare-associated radio core, which therefore must be optically thick against SSA and short lived (a lifetime of approximately 2 weeks), for several epochs. Such a flare-associated radio core must be located at least 





 downstream from the persistent radio core. In addition, Koyama et al. (2015) recently conducted multi-epoch astrometric observations of Markarian 501, which is also one of the most nearby TeV blazars by using VERA. However, they detected no significant positional changes of the radio core during its quiescent state. This fact, therefore, seems to support the radio core wandering seen after the large X-ray flare.
Citation: Lister et al.; 2013
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Citation: Koyama et al. (2015)
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Citation: McKinney et al. 2013
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In addition to the processes that release SiO into the gas phase, it is also important to
        discuss the properties of the responsible shock. Shocks are divided into three types: jump
        shocks (J-type, Hollenbach & McKee 1979),
        continuous shocks (C-type, Draine 1980), and a
        mixture of both, which is a C-type shock with an introduced discontinuity (CJ-type, Chieze et al. 1998). The type of shock depends mainly on
        the presence of a magnetic field, since a magnetic field is necessary for the shock
        condition to become continuous, the ionization of the preshock gas, since only charged
        particles couple to the magnetic field, and on the velocity of the shock, since J-type
        shocks can have higher velocities than C-type shocks (Flower
          & Pineau des Forêts 2003; Tielens 2005;
          Anderl et al. 2013). A main difference between the
        types is that J shocks lead to partial or complete dissociation of molecules, such as
        molecular hydrogen. Because we observed a lot of H2 emission (see Fig. 3), pure J shocks are fairly improbable in this case, since they would dissociate
        the molecular hydrogen. Studies by Gusdorf et al.
          (2008b) have shown that even CJ-type shocks at a velocity of 25 km s-1 are energetic enough to
        dissociate the ambient hydrogen. However, in a more recent paper, Gusdorf et al. (2015) have found that CJ-type shocks reproduce
          H2 observations
        even better. They found that C-type shocks are not able to reproduce their H2 excitation temperatures. In
        conclusion, the strong observed H2 emission suggests that we are not observing J-type shocks;
        however, we cannot differentiate further between C-type or CJ-type shocks with the present
        data. Another important parameter of the shocks is the velocity. However, it is very
        difficult to estimate the shock velocity in the current case. The SiO signal in the line
        wings is present until 15 km s-1 apart from the rest velocity. This is most likely not the
        maximum shock velocity, as the strong SiO signal at ambient velocity indicates jets or
        outflows with a large velocity component in the plane of the sky. In conclusion, this means
        that SiO emission in this case can be the effect of shocks with comparably high velocities
          (vshock>
          25 km s-1), because the expected C-type or CJ-type shocks can reach
        very high velocities, depending on the preshock density (Le
          Bourlot et al. 2002). These shocks would most likely be a result of the ongoing
        star formation. However, low-velocity shocks are also able to release the SiO if it is
        present in the core mantles.
Citation: Tielens 2005
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X-ray radiation observed from clusters of galaxies is emitted by hot, low-density and metal-enriched plasmas filling the space between galaxies (for a review, see Sarazin 1986). We focus attention on relaxed galaxy clusters that are not disturbed by ongoing mergers with other groups (or clusters) of galaxies. The measured X-ray surface brightness and derived plasma density profiles of such clusters are sharply centrally peaked and decrease with radius, while the derived plasma temperature profiles have minima at the centres (for a review, see e.g. Peterson  Fabian 2006, and references therein). These central low-temperature dense regions are coined as cool-cores (Molendi  Pizzolato 2001, formerly known as cooling flows) and galaxy clusters having cool cores are called cool-core clusters. If no external energy sources are present in cool cores, the radiative losses in clusters centres would lead to gas cooling well below X-ray temperatures in a fraction of the Hubble time. The absence of the low temperature emission lines in the spectra of cool-core clusters (e.g. Tamura etal. 2001) and the lack of intense star formation suggest that external energy sources for plasma heating do exist in the cool cores. A likely explanation is that the energy produced by the central active galactic nuclei (AGNs) balances radiative losses of the X-ray emitting plasma (e.g. Churazov etal. 2000; McNamara etal. 2000). The activity of the central AGNs manifests itself via the presence of X-ray cavities (or bubbles) inflated by relativistic outflows from the AGNs that are present in majority of cool-core clusters (for a review, see Fabian 2012; Bykov etal. 2015). These bubbles are typically bright in the radio band (e.g. Boehringer etal. 1993), implying that relativistic electrons (and, perhaps, positrons) are present inside them. The bubbles rise buoyantly in cluster atmospheres and pure mechanical interaction can provide efficient energy transfer from the bubble enthalpy to the gas (e.g. Churazov etal. 2000, 2001, 2002). These buoyancy arguments suggest that the energy supplied by the AGNs matches approximately the gas cooling losses. This conclusion has been confirmed by the analysis of many systems that differ in X-ray luminosity by several orders of magnitude (e.g. Brzan etal. 2004; Hlavacek-Larrondo etal. 2012).
Citation: Peterson  Fabian 2006
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Similar to Balachandran & Flanagan (2007), who also studied the detectability of mode resonances (see also Flanagan & Racine 2007), we assume that the frequency-domain GW signal has the form
(30)
\begin{equation}
\tilde{h}(f) = \mathcal {A} f^{-7/6} \text{e}^{\text{i}\Psi (f)},
\end{equation}
where the amplitude (Maggiore 2007)
(31)
\begin{equation}
\mathcal {A}=\left(\frac{5}{24\pi ^{4/3}}\right)^{1/2}\left(\frac{G\mathcal {M}}{c^3}\right)^{-5/6}\frac{\mathcal {K}}{d}.
\end{equation}
Here $\mathcal {M}=[(M M^{\prime })^{3}/(M+M^{\prime })]^{1/5}$ is the chirp mass, d is the distance to the source and $\mathcal {K}$ is the antenna response (for an optimally oriented source $\mathcal {K}=1$). Our model of the phase evolution Ψ(f) accounts for the zeroth-order post-Newtonian point-particle contribution and for the resonant tidal excitation of individual g-modes. We ignore higher order post-Newtonian terms, spin, the equilibrium tide and non-linear tidal effects (such as those considered in Essick, Vitale & Weinberg 2016), and assume that the signal shuts off at the GW frequency corresponding to the innermost stable circular orbit f = 2fISCO ≃ 1.6 × 103 Hz [2.8 M⊙/(M + M΄)] (Cutler & Flanagan 1994; Poisson & Will 1995). In Appendix B, we show that under these assumptions,
(32)
\begin{equation}
\Psi (f) = \Psi _{\rm pp}(f) - \sum _a\left(1-\frac{f}{f_a}\right) \delta \phi _a \Theta \left(f-f_a\right),
\end{equation}
where, by the stationary-phase approximation, the point-particle phase is (Cutler & Flanagan 1994)
(33)
\begin{equation}
\Psi _{\rm pp}(f) = 2\pi f t_{\rm c} -\phi _{\rm c}-\frac{\pi }{4} +\frac{3}{4}\left(\frac{8\pi G\mathcal {M}f}{c^3}\right)^{-5/3},
\end{equation}
δϕa is the phase shift due to the tidal resonance with a mode a with eigenfrequency fa, and Θ(f − fa) is the Heaviside step function. Here tc and ϕc are constants of integration that set a reference time and phase. The duration of each resonance is, in general, much shorter than the orbital decay time-scale due to radiation reaction (their ratio is ${\simeq } 0.1\times [(\mathcal {M}/1.2\,\mathrm{M}_{\odot })(f/500 \text{ Hz})]^{5/6}$; see Lai 1994; Balachandran & Flanagan 2007; Flanagan & Racine 2007). We therefore model the resonance as an instantaneous process, which should be a good approximation since nearly all the g-modes we consider have $f_a^{\rm (GR)} < 500\,{\rm Hz}$ (the one exception is the na = 1 hyperonic g-mode of the 1.6 M⊙ HS model which has $f_a^{\rm (GR)}=740\,{\rm Hz}$).
Citation: Cutler & Flanagan 1994
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Citation: Cutler & Flanagan 1994
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Citation: Balachandran & Flanagan (2007)
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Citation: Balachandran & Flanagan 2007
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An LyC candidate at z = 3.212 in the GOODS-Southern field, named Ion2 (GDS-ID 033203.24-274518.8), was first identified by Vanzella et al. (2015). This candidate is a 





 galaxy with SFR 





 (sSFR





), EW(Lyα)





 Å, and EW(





)





 Å (de Barros et al. 2016). The compact star-forming region, showing strong [O iii]λλ4959,5007 emission lines (with a rest-frame equivalent width of 1500 Å) and a large Oxygen ratio 





/





 (





 at 1σ, de Barros et al. 2016) measured with Keck/MOSFIRE, makes Ion2 the highest redshift “Green Pea” galaxy the currently known and, accordingly to the photoionization models (Jaskot & Oey 2013; Nakajima & Ouchi 2014), an ideal candidate LyC emitter. A plausible spectroscopic LyC detection was subsequently discussed in de Barros et al. (2016). However, the presence of a close companion not resolved with ground-based spectroscopy and imaging (02, see Figure 1) cast some doubts on the association of the observed flux with Ion2,and thus on the reliability of the LyC leakage. Thanks to the Lyβ and Lyγ detection in the Very Large Telescope (VLT)/VIMOS Ion2 spectrum (see Figure 6 panel (A), or de Barros et al. 2016, Figure 2), the spectroscopic redshift of component A is unambiguously z = 3.2. The 4 hr exposure is not enough to detect such absorption features with a signal-to-noise ratio (S/N) of 





 (as observed here) for component B, which at these wavelengths is mag = 27.2 in the continuum.11

11
From ESO/Exposure Time Calculator, an S/N 





 is expected at this magnitude, wavelength, and integration time. This would imply an S/N 





 if Lyβ and Lyγ absorption lines arise from component B.
 Therefore these features arise from component A at z = 3.2. The [O iii] emission is also mainly associated with component A because the K-band magnitude is dominated by the strong [O iii] lines and the K-band spatial emission is more prominent from A. This is shown in Figure 2 where the VLT/HAWKI K-band image has been extracted from the HUGS survey (Fontana et al. 2014).
Citation: Nakajima & Ouchi 2014
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