adsabs/FOCAL huggingface dataset:
In this section, we consider the plasma properties under the propagation of strong waves. In strong waves, the motion of electrons in the plasma becomes relativistic. However, different from free electrons that have a relativistic drift velocity in the direction of the incident electromagnetic wave (see Section 3.1), in plasma the space-charge potential is important in preventing the drift of electrons (Waltz & Manley 1978). For nonrelativistic electrons in plasma, if the wave duration τ is much larger than c/ωp, where 





 is the plasma frequency, the drift velocity would be close to zero (Waltz & Manley 1978; Sprangle et al. 1990b). In this case, electrons in plasma under a strong wave would have a typical Lorentz factor (





) similar to that (γ) in the laboratory frame, so that 





 is satisfied. Due to the relativistic and magnetic force effects, the propagation and dispersion properties of an electromagnetic wave depend on its amplitude. For a circular polarized wave, the dispersion relation in the laboratory frame is given by (e.g., Gibbon 2005; Macchi 2013; Macchi et al. 2013; see the Appendix)
11





The dispersion relation of strong electromagnetic waves is altered due to the effective electron mass increased by the relativistic effect (e.g., Sarachik & Schappert 1970; Gibbon 2005; Macchi 2013). One can define the effective plasma frequency as
12





so that the wave can propagate in the region where 





. With respect to the nonrelativistic linear case, this is known as relativistically self-induced transparency. We note that since the dispersion depends on the electromagnetic field amplitude in the nonlinear case, the dispersion relation must be taken with care. The propagation of a pulse will be affected by the complicated effects of nonlinear propagation and dispersion, and finally the spatial and temporal shape of the pulse itself would also be modified. In particular, for linear polarization, the relativistic factor γ is not a constant (see Section 3.1). The propagation of the linearly polarized wave with a relativistic amplitude would lead to generation of the higher-order harmonics. Sprangle et al. (1990b) proved that the propagation of the first harmonic component, i.e., of the “main” wave, is still reasonably described by Equation (11) with 





. Thus, we will directly adopt Equation (11) in the following discussion.
Citation: Macchi 2013
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Citation: Macchi 2013
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Each pulsar system in this analysis was observed with XMM-Newton (Jansen et al. 2001), using the European Photon Imaging Camera (EPIC) with the pn detector in full frame mode with thin filters (the data from the MOS and RGS detectors had insufficient counts for analysis). PSR J0337 was observed on 2013 August 1 (observation number 0722920101) for 16.2 ks. An X-ray source was detected 16 away from the radio position of Ransom et al. (2014), consistent with the 2″ astrometric precision of XMM;12

12
See xmm.vilspa.esa.es/docs/documents/CAL-TN-0018.pdf.
 we show an image of the detection in Figure 1. We measured 164 ± 13 background-subtracted counts between 0.2 and 2.0 keV, as determined using calc_data_sum in Sherpa (Freeman et al. 2001; Doe et al. 2007) and uncertainty given by a Poisson distribution.13

13
Note that our count-rate for PSR J0337 is below the 2σ upper limit from Prinz & Becker (2015), who analyzed the same data set. Nonetheless, we are confident in our detection (Figure 1) and do not know the reason for the discrepancy.
 The chance coincidence probability, given the number of sources in the field with similar or higher count rates, is approximately 8 × 10−5. PSR J0636 was observed on 2013 October 13 (observation number 0722920201) for 15.0 ks, and we found an X-ray source within 03 of the radio position of Stovall et al. (2014); see Figure 1. The chance coincidence probability for PSR J0636 is also approximately 8 × 10−5. We measured 170 ± 13 counts between 0.2 and 2.0 keV. Finally, PSR J0645 was observed on 2014 March 29 (observation number 0722920301) for 34.9 ks, but removing a flare from the data reduced the effective observation length to 23 ks. No source was found by the XMM pipeline near the radio position of Stovall et al. (2014, see Figure 1), and we measured only 18 ± 9 source counts between 0.2 and 2.0 keV. The time resolution of 73.4 ms was too coarse to detect pulsations at the rotational periods of the pulsars (2.73, 2.87, and 8.85 ms; Ransom et al. 2014; Stovall et al. 2014), but the observed flux can guide future searches for pulsed X-rays. We reprocessed the data using SAS v13.0.1, specifically epchain. Using HEAsoft v6.14 and CIAO v4.6, and some custom scripts, we extracted the source counts from within a radius of 25″, and background counts from an annular region with radii of 50″ and 125″, restricted to the same CCD chip with other sources removed. We limited the data to events with PATTERN ≤ 4 (singles and doubles), but also experimented with using PATTERN ≤ 12 (singles, doubles, and triples). We found that the change in the results when including triple events was negligible. Because of the high background rate at low energies and the expected softness of the source spectra, we limited our analysis to energies between 0.2 and 2.0 keV. We grouped the counts such that each energy bin had at least 15 events in it and subtracted the background from the source.
Citation: Freeman et al. 2001
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Finally, it is worth noting that two-body relaxation and tidal interactions affect the IMF in different ways. The former causes mass segregation with higher-mass stars moving inward and lower-mass stars outward, which enables the lower-mass stars to evaporate from the cluster (see also, e.g., Chandrasekhar 1942; Spitzer 1969; Binney & Tremaine 2008). The cluster then forms a dense core of high-mass stars and once it starts to collapse, binaries form in the centre. These perturb their neighbours, and we begin to observe massive stars escaping from the mass segregated core (see also Hills 1975; Hut 1985). On the other hand, if the relaxation timescales are long, the cluster does not segregate as quickly and the tidal harassment is the dominant reason for mass-loss. Stars are peeled-off from the outer regions independent of their masses. Consequently, the relative contributions of these two processes determine the mass distribution of the escapers. This is shown in Fig. 5, where the mass distribution of escaping stars divided by the original IMF in models R07_Sal13 and R07_Sal13_Nb. When the environment is present, the tidal shocks enhance fraction of escaping stars at intermediate masses. Instead, the loss of massive stars, similar in the two models, can be linked to the relaxation process ongoing in the core that is composed almost exclusively of massive stars and binaries at later times. In our model, the percentage of mass loss is small so this does not significantly affect the mass function of the remaining members. However, the same process happens in protoclusters still embedded in the parent cloud. Their gas density is orders of magnitude higher than our n = 10 cm−3, and structures are closer to the cluster (Kruijssen et al. 2012; Kruijssen 2012). At the same time, the IMF of massive protoclusters is much wider, since massive stars are still on the main sequence, so that the evolutionary timescale is also reduced (Allison et al. 2009; Yu et al. 2011). In the end, the effects we described could indeed play a crucial role when inferring the IMF of young clusters.
Citation: Hut 1985
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Deriving the completeness limits of the WISE photometry is mandatory to assess the reliability of our catalogue of starless cores. We examined the histograms of the number of mid-infrared (MIR) sources versus magnitude; taking into account the effects of the cuts required to fulfil the criteria of Koenig et al. (2012), rough completeness limits are [3.6] ~ 14, [4.6] ~ 12, [12] ~ 9 and [22] ~ 7. These values are 1–3 mag brighter than the sensitivity limits quoted in the WISE Explanatory Supplement3 for the relevant sky region. Once converted into flux units and, for example, compared with the models of Class I and Class 0 sources of 0.5 M⊙ by Whitney et al. (2004), it can be seen that the completeness limits at 3.6 and 4.6μm are faint enough to detect such objects taking into account a distance of 700 pc and a further foreground reddening up to AV = 20. Even in the worst case of edge-on discs, these objects would be detectable at 3.6 and 22μm. Furthermore, the completeness limit at 22 μm is faint enough to allow detection of Class I and Class 0 sources of even-lower-mass central objects. Alternatively, one can compute the bolometric luminosity following Kryukova et al. (2012). Starting from our completeness limit at 22 μm, after conservatively dereddening it by AV = 20, we assumed a spectral index γ = −2 (see Table 3 for definition) to compute the MIR luminosity from Eq. (6) of Kryukova et al. (2012). Equation (7) of Kryukova et al. (2012) then yields Lbol ~ 1.7–2.8 L⊙, depending on whether the NIR flux is neglected (which may be the case) or extrapolated from γ = −2. A comparison with the birthline of Palla & Stahler (1993) indicates a mass of ~ 0.4–0.5 M⊙ for the central protostar. For the sake of comparison, we can roughly estimate the completeness limit in central masses of the Herschel protostellar cores in Giannini et al. (2012) using their quoted completeness limit at 70 μm of 0.21 Jy and following Dunham et al. (2008). By using Eq. (2) of Dunham et al. (2008), scaled to a distance of 700 pc, we found that the flux density at 70 μm translates into a bolometric luminosity of the central (proto)star Lbol ~ 0.28 L⊙ (we note that Dunham et al. 2008 indicate this luminosity as Lint). We highlight the fact that the 70 μm emission is in principle a more sensitive protostellar tracer than WISE. However, this contrasts with the much lower number of protostellar cores found by Giannini et al. (2012), which may be due to a poorer effective sensitivity because of their selection criteria.
Citation: Kryukova et al. (2012)
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Citation: Kryukova et al. (2012)
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Citation: Kryukova et al. (2012)
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3D General Circulation Models (GCMs) with simplified thermal forcing are one possible intermediate step between 3D GCMs with full coupling between radiation and dynamics like those used by Showman et al. (2009) and Amundsen et al. (2016), and shallow water models, i.e. atmosphere models with one atmosphere layer comprising vertically averaged flow (Showman, Cho & Menou 2010). Fully coupled GCMs have the highest accuracy in stellar radiation and flow coupling and thus the highest predictive power. They are, however, computationally much more expensive and their complexity makes it more difficult to test underlying modelling assumptions compared to GCMs with simplified thermal forcing. The latter are thus better suited to run simulations for various scenarios, to understand large-scale flow and circulation properties in 3D climate models under different conditions (Liu & Showman 2013; Mayne et al. 2014; Tsai et al. 2014; Carone et al. 2015, 2016; Komacek & Showman 2016; Hammond & Pierrehumbert 2017; Mayne et al. 2017). Such models have been proven to be very useful: superrotation in hot Jupiters was first inferred by Showman & Guillot (2002) in a 3D GCM with Newtonian cooling. Recently, Showman, Tan & Zhang (2019) used Newtonian cooling to establish a clean, simple environment to diagnose flow dynamics in brown dwarfs, Jupiter, and Saturn-like planets. Shallow water models present an even simpler model framework and represent 3D flow patterns in an atmosphere depth-dependent (2D) formalism (Showman & Polvani 2010, 2011; Penn & Vallis 2017). There are other useful radiative forcing parametrizations such as those using the dual-band radiative scheme, which can also explore a large parameter space and basic assumptions (see e.g. the model used by Komacek et al. 2017). Generally, a hierarchy of models with various levels of complexity has proven to be extremely beneficial to understand complex flow patterns in full 3D climate simulations. Here, we establish a clean, simple environment to understand possible dynamical feedback between the lower boundary and observational flow via Newtonian cooling.
Citation: Komacek & Showman 2016
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The short-plateau SNe 2006Y, 2006ai, and 2016egz most likely come from partially stripped massive progenitors,36

36
The lack of nebular spectra for SNe 2006Y and 2006ai remains a caveat.
 but a remaining question is their exact formation channel. If it is single-star evolution as assumed in this work, the main theoretical uncertainties are RSG wind mass-loss rates and stellar rotation (e.g., Hirschi et al. 2004; Georgy 2012; Chieffi & Limongi 2013; Meynet et al. 2015; Renzo et al. 2017). We assume no rotation and tweak the wind efficiency by hand, but it is debatable whether such high mass-loss rates are physically plausible. Observationally, there is indeed a wide range of measured RSG wind mass-loss rates (e.g., de Jager et al. 1988; van Loon et al. 2005; Mauron & Josselin 2011; Goldman et al. 2017; Beasor et al. 2020). In addition, recent observational and theoretical studies on RSGs and SNe II indicate that RSG wind mass-loss rates may be independent from metallicity (Goldman et al. 2017; Chun et al. 2018; Gutiérrez et al. 2018). Thus, it could be possible that the short-plateau SNe 2006Y, 2006ai, and 2016egz originate from single-star evolution. However, it is unlikely the case if RSG mass-loss rates are metallicity dependent (as in the main-sequence O/B stars; e.g., Vink et al. 2000, 2001; Mokiem et al. 2007), given the estimated subsolar host metallicities (Table 2). In such a case, interacting binary evolution is more plausible, as Eldridge et al. (2017, 2018) indeed show some interacting binary products also result in short-plateau SNe. It is also important to note that any mass-loss models need to reproduce the observed populations of not only SNe II but also RSGs. For example, Neugent et al. (2020) recently show that the luminosity function of RSGs can be used to constrain their mass-loss rates. Future statistical studies with both RSG and SN II populations at various metallicities are required to distinguish the formation channels of short-plateau SNe.
Citation: Goldman et al. 2017
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As mentioned above, the magnetic reconnection is introduced as breaking and reconfiguration of the oppositely directed magnetic field lines in highly conducting plasma. The magnetic field lines collapse near the X-point and form an extended magnetic singularities known as a current sheet. There are two mechanism of the current-sheet formation. The first kind of current-sheet formation is associated with the MHD instabilities (e.g., resistive tearing mode and ideal kink mode) known as spontaneous magnetic reconnection (e.g., White 1984; Baty 2000; Vekstein 2017). The second kind of current sheet can be formed in the MHD stable configuration, where some external perturbations trigger the forced magnetic reconnection (Hahm & Kulsrud 1985). The forced magnetic reconnection may be activated by nonlinear MHD waves, which may be caused by explosive solar activities (e.g., Sakai et al. 1984; Dewar et al. 2013; Beidler et al. 2017). The forced magnetic reconnection may be developed due to boundary perturbations, which induce a surface current in such a way that it opposes the progress of the reconnection (Ishizawa & Tokuda 2000, 2001; Fitzpatrick 2003). The multimode simulation approach has been adopted to investigate the thinning of the current sheet induced by forced magnetic reconnection (Birn et al. 2005). The motion of the photospheric footpoints of the coronal magnetic field may also trigger the forced magnetic reconnection, which may be caused by the explosive solar coronal events (e.g., Vekstein & Jain 1998; Jain et al. 2005; Vekstein 2017). Although there is a remarkable development in the theory of the forced magnetic reconnection, Jess et al. (2010) have suggested that there is no observational evidence of explosive flare or coronal activities triggered by forced magnetic reconnection. They have observed a microflare activity driven by forced magnetic reconnection. The lower solar atmosphere (photosphere & chromosphere) is dominated by cool, partially ionized and collision dominated plasma. Most of the energy releases during the forced magnetic reconnection may be consumed by such plasma systems (e.g., Litvinenko 1999; Chen et al. 2001; Chen & Ding 2006; Litvinenko et al. 2007).
Citation: Vekstein 2017
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Citation: Vekstein 2017
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The SFR reported in Table C.1 refers to a stellar mass range from Mlow = 0.1M⊙ to Mup = 100M⊙, is averaged over the past Δt = 100 Myr, and was calculated using the standard SFR(LIR) relationship from Kennicutt (1998; here scaled to a Chabrier 2003, IMF) (1)\begin{equation} \label{eq:sfr} \textit{SFR}=10^{-10}\times L_{\rm IR}[{L}_{\sun}]\, {M}_{\sun}~{\rm yr}^{-1}. \end{equation}SFR=10-10×LIR[L⊙] M⊙yr-1.This calibration relies on the starburst synthesis models of Leitherer & Heckman (1995), and it is based on the assumption of solar metallicity, and an optically thick (τdust ≫ 1) starburst region, in which case LIR is a good proxy of the system’s bolometric luminosity (LIR ≃ Lbol), and hence a sound, calorimetric probe of the obscured, current stellar birth rate. A possible caveat is that the contribution to the dust heating by more evolved stellar populations (the cirrus component; e.g. Helou 1986; Lonsdale Persson & Helou 1987; Walterbos & Greenawalt 1996) is not taken into account. If the cirrus ISM component heated by the more general galactic UV radiation field contributes to LIR, then the Kennicutt (1998) relationship overestimates the SFR. Another issue is the fact that some percentage of the UV photons can escape the starburst region without being absorbed, and hence are not reprocessed into IR photons (indeed, some of our SMGs are visible in the rest-frame UV images; Miettinen et al. 2017b). The MAGPHYS code also gives the SFR as an output, and contrary to the aforementioned LIR diagnostic, the model permits for the heating of the dust by older and longer-lasting stellar populations. We found that the SFR(LIR) is somewhat higher on average than SFRMAGPHYS: the SFR(LIR) /SFRMAGPHYS ratio was found to range from 0.47 to 6.92 with a median of \hbox{$1.31^{+0.83}_{-0.17}$}1.31-0.17+0.83, where the ± errors represent the 16th–84th percentile range (see the corresponding panel in Fig. 2). If, instead of Δt = 100 Myr, the aforementioned comparison is done by using the SFRMAGPHYS values averaged over the past Δt = 10 Myr, the median SFR(LIR) /SFRMAGPHYS ratio is found to be \hbox{$1.15^{+0.38}_{-0.27}$}1.15-0.27+0.38, which is consistent with the results obtained by da Cunha et al. (2015). Unless otherwise stated, in our subsequent analysis we use the SFR averaged over the past 100 Myr as calculated using Eq. (1).
Citation: Kennicutt (1998)
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Citation: Kennicutt (1998
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On the other hand, a clear physical interpretation of the observed pulse broadening phenomenon requires a good understanding of the interstellar electron density structure. A power-law model of electron density fluctuations is commonly adopted in theoretical constructions on radio wave propagation (Lee & Jokipii 1976; Rickett 1977, 1990) and is compatible with observational indications (e.g., Armstrong et al. 1995). Recent advances in understanding the properties of magnetohydrodynamic (MHD) turbulence (Goldreich & Sridhar 1995; Lithwick & Goldreich 2001; Cho & Lazarian 2002, 2003) stimulate a renewed investigation on density statistics (Beresnyak et al. 2005; Kowal et al. 2007; Lazarian et al. 2008; Burkhart et al. 2009, 2010, 2015; Collins et al. 2012; Federrath & Klessen 2012), which provide important insight into key physical processes such as star formation in the turbulent and magnetized ISM (see reviews by, e.g., McKee & Ostriker 2007; Lazarian et al. 2015). The density spectrum in compressible astrophysical fluids was systematically studied in Kowal et al. (2007) by carrying out an extensive set of MHD numerical simulations with varying compressibility and magnetization. Instead of a single Kolmogorov slope with a power-law index of 





, significant variations in the spectral slope of density fluctuations are present. For supersonic turbulence, their results are consistent with earlier findings in both magnetized (Beresnyak et al. 2005) and nonmagnetized (Kim & Ryu 2005) fluids. It shows that the density power spectrum becomes shallower as the sonic Mach number (





) increases, where VL is the turbulent velocity at the outer scale of turbulence and cs is the sound speed in the medium, and there is a significant excess of density structures at small scales in highly supersonic turbulence. This behavior is naturally expected as the gas is compressed in shocks by supersonic flows and the interacting shocks produce local density enhancements (Mac Low & Klessen 2004; Padoan et al. 2004b).
Citation: Collins et al. 2012
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Citation: Cho & Lazarian; 2003
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In the supersonic part of WR outflows, the presence of instabilities and inhomogeneities should be taken into account. Invoking density inhomogeneities, or “clumping”, in stellar models has an influence on the mean opacity, due to the enhanced density in clumps (Moffat et al. 1988; Hamann & Koesterke 1998). However, a porous structure could also imply lowered mean opacity, counteracting the effect of small-scale clumping (Shaviv 1998; Oskinova et al. 2007). Assuming that the material near the Fe-opacity peak is clumped, Gräfener et al. (2012) were able to extend the surface radii of their hydrostatic helium star models, in practical terms, by significantly enhancing the iron bump opacity (see also Appendix A). The surface temperatures of such hydrostatic, strongly inflated models computed with plane parallel grey atmospheres are then compared with the fictitious effective temperatures at τ = 20 of the atmosphere calculations performed by Hamann et al. (2006). This effective temperature at τ = 20 should not be confused with the actual blanketed temperature at the base of WNE wind models, which is about a factor of 2 larger (see e.g. Appendix D). As we show in Sect. 4, strongly inflated hydrodynamic solutions imply supersonic flows already at the base of the inflated envelopes for the typical mass-loss rates of WNE stars (cf. the plane parallel atmosphere model in Fig. 4). Moreover, it would be inconsistent to think that the iron opacity bump is simultaneously responsible for both the inflation of the envelope and the acceleration of the flow. While the detailed effects of clumping and porosity remain a subject for future research, we concentrated in this work on the homogeneous case as those instabilities are expected to initiate above the sonic point (Sundqvist et al. 2013; Owocki 2015). If this is not the case and clumping is already present at the relatively high densities and optical depth of the sonic point of massive helium star models, it might affect to some extent the local opacity.
Citation: Hamann et al. (2006)
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