adsabs/FOCAL huggingface dataset:
The induction equation of the magnetic field is
(10)
\begin{equation}
\frac{\partial \boldsymbol {B}}{\partial t}={\nabla }\times \left(\boldsymbol {v}\times \boldsymbol {B}-\frac{4\pi }{c}\eta \boldsymbol {J}\right),
\end{equation}
where $\boldsymbol {J}=\frac{c}{4\pi }{\nabla }\times \boldsymbol {B}$ is the current density. The induction equation is the field escaping/creating rate due to magnetic instability or the dynamo effect. For the steady-state accretion flow, we neglect the dynamo effect. In the energy equation, we assumed a balance between the heating due to viscosity and cooling due to advection, convection and radiation as
(11)
\begin{equation}
Q^{-}_{{\rm adv}}+Q^{-}_{{\rm rad}}+Q^{-}_{{\rm con}}=Q^{+}_{{\rm diss}},
\end{equation}
where $Q^{-}_{{\rm adv}}=\scriptstyle\rho (\frac{{\rm d} e}{{\rm d}t}-\frac{p}{\rho ^{2}}\frac{{\rm d}\rho }{{\rm d}t})$ is advection cooling in ADAFs. e is the gas internal energy $(e=\frac{c^{2}_{{\rm s}}}{\gamma -1})$ and γ is the specific heat ratio. Also, we consider $Q^{+}_{{\rm diss}}-Q^{-}_{{\rm rad}}=fQ^{+}_{{\rm diss}}$ in ADAFs (where f, the advection parameter, is defined by Narayan & Yi 1994). Also, the viscous heating is defined as $Q_{{\rm diss}}= f(\nu +\frac{1}{3}\nu _{{\rm con}})\Sigma r^{2} (\frac{{\rm d} \Omega }{{\rm d}r})^{2}$. The outward energy flow by convection is $Q^{-}_{{\rm con}}=- {\nabla }\cdot \boldsymbol {F}_{c}$, where $F_{{\rm con}}=-\nu _{{\rm con}} \frac{1}{\gamma -1}\frac{{\rm d} c^{2}_{{\rm s}}}{{\rm d}r}-\frac{c^{2}_{{\rm s}}}{\rho }\frac{{\rm d} \rho }{{\rm d}r}$. So, the energy equation is written by considering the above definitions and the specific internal energy of inflow ε and outflow εw on the surface of the disc as follows:
(12)
\begin{eqnarray}
&amp;&amp;{\frac{\Sigma v_{r}}{\gamma -1}\frac{{\rm d} c^{2}_{{\rm s}}}{{\rm d}r}-2Hc^{2}_{{\rm s}}v_{r}\frac{{\rm d}\rho }{{\rm d}r}+\frac{1}{2\pi r}\frac{{\rm d}\dot{M}(r)}{{\rm d}r}(\epsilon _{w}-\epsilon )}\nonumber \\
&amp;&amp;-\frac{1}{r}\frac{{\rm d}}{{\rm d}r}\left(r\nu _{{\rm con}}\frac{\Sigma }{\gamma -1}\frac{{\rm d} c^{2}_{{\rm s}}}{{\rm d}r}-2Hr\nu _{m}c^{2}_{{\rm s}}\frac{{\rm d}\rho }{{\rm d}r}\right)\nonumber \\
&amp;&amp; -\frac{\nu \rho }{\gamma -1}\frac{{\rm d} c^{2}_{{\rm s}}}{{\rm d}r}+\nu _{{\rm con}}c^{2}_{{\rm s}}\frac{{\rm d}\rho }{{\rm d}r} = f\Sigma \left(\alpha -\frac{1}{3}\alpha _{\rm c}\right) c_{{\rm s}}H r^{2}\left(\frac{{\rm d} \Omega }{{\rm d}r}\right)^{2}. \nonumber\\
\end{eqnarray}
Citation: Narayan & Yi 1994
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The linear relationship that we observe between breakpoint energy and core temperature is in line with previous measurements (e.g. McComas et al. 1992; Štverák et al. 2009), for both the halo and strahl. According to Scudder & Olbert (1979), a linear trend in the halo relation also follows under the assumption that binary Coulomb collisions dominate electron dynamics in the solar wind. However, in order to align with available experimental data, Scudder & Olbert (1979) set a scaling factor of Ebp/kBTc = 7, which differs from our scaling factor of Ebp/kBTc = 5.5 ± 0.1. With a scaling factor of Ebp/kBTc = 7, Scudder & Olbert (1979) predict that a transformation of thermal electrons into the suprathermal population occurs as the solar wind flows out from the Sun. Findings by Štverák et al. (2009), on the other hand, show that the (nh + ns)/nc ratio remains roughly constant with heliocentric distance in the slow wind, suggesting a lack of interchange between the thermal and suprathermal populations. However Štverák et al. (2009) observes some variability in the (nh + ns)/nc ratio in the fast wind, which they attribute to either statistical effects due to a lack of samples or a possible “interplay” between thermal and suprathermal electrons. Scudder & Olbert (1979) also predict that the halo Ebp/kBTc ratio remains constant with heliocentric distance, whereas Štverák et al. (2009) find that the halo Ebp/kBTc ratio decreases with heliocentric distance. These findings by Štverák et al. (2009), along with the discrepancy between our calculated ratio of Ebp/kBTc = 5.5 ± 0.1 and the prediction of Ebp/kBTc = 7, suggest that the model of Scudder & Olbert (1979) requires a minor update to either the theory or to the input parameters. The discrepancy, however, may also be indicative of other processes, such as wave-particle scattering (e.g. Gary et al. 1994), that possibly modifies the ratio between breakpoint energy and core temperature while preserving its linear relationship.
Citation: Štverák et al. (2009)
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Citation: Štverák et al. (2009)
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Citation: Štverák et al. (2009)
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Citation: Štverák et al. 2009
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The direct detection of the first gravitational waves from the merger of two heavy black holes (BHs) in GW 150914 confirmed one of the toughest predictions of Einstein’s theory of general relativity. But while satisfying the world of physics in general, for astrophysics this was only the beginning: many were surprised by the large BH masses of, respectively, 36 and 29  M⊙ (Abbott et al. 2016), showcasing how the new field of multimessenger astrophysics had just re-opened the field of stellar evolution in a spectacular fashion. Stellar mass BHs had previously been revealed by their interaction in binary systems (Orosz et al. 2011), but the maximum stellar BH mass in our Milky Way is not higher than roughly 15–20  M⊙ (Belczynski et al. 2010). While we know that very massive stars (VMS) above 100  M⊙ exist (Crowther et al. 2010; Vink et al. 2015), this mass is significantly diminished via stellar winds already during core hydrogen (H) burning (Vink & Gräfener 2012). The heavy nature of the BH, as measured by LIGO/VIRGO therefore supported the assumption that the gravitational wave event occurred in a part of the Universe still pristine in its enrichment with heavy elements (‘metallicity (Z)’), lowering stellar wind mass-loss (Vink, de Koter & Lamers 2001; Vink & de Koter 2005). A low-Z solution was widely accepted until the announcement of a 70  M⊙ BH in LB-1 (Liu et al. 2019), spurring stellar evolution theorists to avoid heavy mass-loss in the Milky Way (Belczynski et al. 2020; Groh et al. 2020), either by arbitrarily lowering the mass-loss rates of VMS – seemingly contradicting VMS mass-loss calibrations (Vink & Gräfener 2012) – or by invoking the presence of a strong dipolar surface magnetic field that could quench the wind (Petit et al. 2017). While such magnetic fields in some 5–10 per cent of massive OB stars do indeed exist, no B-fields have yet been detected in VMS (Bagnulo et al. 2020). The problem of the formation of a $70\, \mathrm{ M}_\odot$ BH in a solar metallicity environment apparently resolved itself when the spectral signatures of LB-1 were re-interpreted (Abdul-Masih et al. 2020; El-Badry & Quataert 2020).
Citation: Vink & Gräfener 2012
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Citation: Vink & Gräfener 2012
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Previous works (e.g. Holt et al. 2011; Arribas et al. 2014; Villar Martín et al. 2014, 2015) have found very high reddening and densities associated with ionised outflows in local objects (e.g. Hα/Hβ ∼ 4.91 and ne ≳ 1000 cm−3, Villar Martín et al. 2014). Concerning the reddening, although we find that the outflowing gas is generally less affected by dust extinction than the disc, the median value of the total distribution is significantly affected by dust (Hα/Hβ ∼ 4.16), with tails up to Hα/Hβ ≳ 6. Similarly, the outflow density of MAGNUM galaxies is higher than the values in the disc gas, but appears to be far lower than the values found by these authors. This could stem from the fact that the galaxies studied by Holt et al. (2011), Arribas et al. (2014) are local luminous or ultra-luminous infrared galaxies (U/LIRGs), and those of Villar Martín et al. (2014, 2015) are highly obscured Seyfert 2, thus sampling sources that are more gas and dust rich compared to our sample. However, our values are also lower than the outflow densities found in Perna et al. (2017) (ne ∼ 1200 cm−3), who targeted optically selected AGNs from the SDSS, and Förster Schreiber et al. (2018b), who presented a census of ionised gas outflows in high-z AGN with the KMOS3D survey (ne ∼ 1000 cm−3). A possible explanation could be related to the high quality of our MUSE data, which also allows us to detect the faint [S II] emission associated with lower density regions. If we calculate the median densities of the disc and outflow components, weighting for the [S II] line flux, we obtain higher values (ne ∼ 170 cm−3 and ne ∼ 815 cm−3, for disc and outflow, respectively). This shows that previous outflow density values from the literature could be biased towards higher ne because they are based only on the most luminous outflowing regions, characterised by a higher S/N. This could also mean that outflows at high-z could be far more extended than the values we observe.
Citation: Arribas et al. (2014)
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Citation: Arribas et al. 2014
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As a final note, we point out that correcting for the effect of neutrinos did not change the finding that KIC 08626021 has a very thin helium-pure layer on top of its envelope. Such a thin layer might be explained by the presence of any mechanism competing against the separation of He, C, and O in the envelopes of DO and hot DB white dwarfs. For instance, Fontaine & Brassard (2005; see also Brassard et al. 2007) postulated the existence of a weak stellar wind of the order of ∼2 × 10−13M⊙ yr−1 in order to account for the presence of traces of C in Teff ∼ 20 000–30 000 K DB white dwarfs. Such a wind, similar to the solar wind, would be driven by deposition of acoustic energy generated by strong convective motions which characterize the outer layers of these stars. Perhaps a more likely mechanism is convective overshooting, which was first studied by Freytag et al. (1996) in a white dwarf context and more recently by Tremblay et al. (2015) and Cukanovaite et al. (2018) through detailed 3D simulations. Brassard & Fontaine (2015) explicitly used the overshooting prescription of Freytag et al. to demonstrate that element separation is indeed considerably slowed down in cooling hot white dwarfs. They found that only a “thin” layer of pure He (logq1 ∼ −8) has accumulated at the surface of their evolving model by the time the latter has cooled down to Teff ∼ 31 000 K. This is in line with our seismic inference for KIC 08626021. In addition, the new solution for KIC 08626021 does not change the fact that no C/O/He triple transition at the core boundary is found in the model that best reproduces the pulsation frequencies of this star. If puzzling from an evolutionary perspective, our seismic probing seemingly requires that mode trapping generated by two chemical transitions around logq ∼ −2.4 and logq ∼ −3.5 must be present. This can be obtained with our current models only if a carbon buffer exists between the envelope and the core. Alternately, enforcing a triple transition and searching for a new optimal solution within this additional constraint strongly degrades the quality of the achieved best frequency match. Improving the capacity of such a configuration to reproduce the observed pulsation modes would likely require the presence of an additional structure (of unclear origin) in the envelope to provide the needed mode trapping. We therefore leave that issue open at this stage.
Citation: Cukanovaite et al. (2018)
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The faster evolutionary timescales and higher luminosities of our H-burning sequences should have an important impact on the study of the formation of PNe (Schönberner et al. 2014; Toalá & Arthur 2014). The low-mass models of Schönberner (1983), which are still in use to complement the sequences of Blöcker (1995a), show crossing timescales of ~340 kyr (0.546 M⊙) and ~20 kyr (0.565 M⊙). Our H-burning sequences of similar mass and metallicity (Z0 = 0.02) show crossing timescales about ~3.5 to ≳15 times faster and even faster in the case of M15 models. The discrepancy is even larger in the case of the low-mass models of Vassiliadis & Wood (1994). In order to be able to produce PNe, the central stars need to evolve in less than a few tens of thousand years. If that is not the case, the circumstellar material dissipates before the star becomes hot enough to ionize it. This fact, together with the very long timescales of τcross ≳ 100 kyr of the low-mass models of older grids, leads to the conventional wisdom that low-mass post-AGB stars (≲0.55 M⊙) cannot form PNe; see, e.g., Jacoby et al. (2013), Bond (2015). In this context, the new models might help to explain the existence of single CSPNe with masses lower than ~0.55 M⊙ (Althaus et al. 2010; Werner & Rauch, in prep.). The new models should also have an impact on the question of whether single stellar evolution can form PNe in globular clusters (Jacoby et al. 2013; Bond 2015). Our H-burning post-AGB sequences with ages similar to that of globular clusters (9 to 12 Gyr) have values of τcross ~ 25–70 kyr. Timescales drop to τcross ~ 5–10 kyr for post-AGB sequences with slightly younger progenitors (5 to 7 Gyr); see Tables 2 and 3. Timescales are even shorter in the case of the models of Weiss & Ferguson (2009) and M15 (see Appendix B). The much shorter timescales of the new H-burning post-AGB sequences call into question the idea that single stellar evolution cannot produce PNe in globular clusters.
Citation: Vassiliadis & Wood (1994)
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We also introduce here NB2071 data, taken as part of the MDCS with the Multi-Object Infrared Camera and Spectrograph (MOIRCS; Ichikawa et al. 2006; Suzuki et al. 2008) on the Subaru Telescope (the same instrument that was used in the past MAHALO-Subaru survey; Koyama et al. 2013a). The observations were executed between April 30 and May 6, 2015, under photometric conditions with seeing FWHM ∼0.6 arcsec. The integration time is 125 min which was split into 180 s individual exposures. After combining with the existing NB2071 data (186 min integration), we reconstructed all the data using the reduction pipeline mcsred2 (Tanaka et al. 2011), which is written as iraf3 scripts (Tody 1993). As described in Shimakawa et al. (2018), we executed flat-fielding, masking objects from the combined data in the first run (thus the whole reduction process was conducted twice to remake secure object masks), sky subtraction (by median sky and then the polynomially fitted plane for residual sky subtraction), distortion correction, cross-matching, and image mosaicing with this pipeline. The reconstructed NB2071 image reaches 23.95 mag in 3σ limiting magnitude using a 1.4 arcsec diameter aperture, and its seeing FWHM is 0.63 arcsec. The image depth becomes deeper by 0.5 mag than the previous data (Koyama et al. 2013a). The world coordinate system (WCS, Calabretta & Greisen 2002; Greisen & Calabretta 2002) of the narrow-band image is carefully matched by the iraf scripts (ccmap and ccsetwcs) to that of the F814W image, based on 67 point sources. F814W has one of the best spatial resolutions amongst our data set. The standard deviation of point source separations between the NB2071 and F814 images suggests that the relative WCS uncertainty would be around 0.04 arcsec in the survey area. One should note, however, that the absolute astrometry would have 0.3 arcsec errors in right ascension and declination based on comparison with the Guide Star Catalogue 2 (Lasker et al. 2008).
Citation: Tody 1993
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The uncertainty for most frequency determinations in the spectrum of NEFA is of a few kHz in view of the high S/N of the data (see Fig. 20). However, we have assigned an uncertainty of 10 kHz for all lines showing a single component and intensity larger than 20 mK (S/N ≥ 20). Unlike linear molecules with a nitrogen atom, for which hyperfine splittings rapidly collapse, symmetric or asymmetric tops can show significant hyperfine splitting even for high-J and high-Ka transitions. As an example, the bottom panel of Fig. 10 shows the hyperfine structure of K = 3 component of the J = 6 → 5 rotational transition of CH3CN. The K = 0 and 1 components of the same transition do not show any measurable splitting, while the K = 2 exhibits an emerging shoulder (clearly seen in that figure) due to its hyperfine structure. Using the diagonal elements of the 14N quadrupole coupling tensor in NEFA (Ohba et al. 2005), we have computed the expected hyperfine splitting of all lines in the W band. Most of the lines we have identified have the hyperfine splitting concentrated around ±10 kHz of the central frequency. However, several lines present three hyperfine components with similar intensities. Two of these components are at practically the same frequency, while the third component is always on the opposite side producing a global splitting of 60–100 kHz. Hence, some of the observed lines could have a two-component structure, with intensity ratio 1:2, with a strong feature accompanied by less intense shoulder (a factor of two lower), either left or right of the central frequency. Many other lines also show a complex profile due to blending with lines coming from the vibrationally excited states and the other conformers of NEFA (see, for example, the bottom right panel of Fig. 20). We have fitted in most cases one single Gaussian profile to the observed lines. However, when the line profile exhibits two components we fitted two Gaussians. Depending on the degree of overlap between these components, the assigned uncertainty varies between 20 and 80 kHz. When two components were obvious in the line profile, the feature assigned to NEFA was based on the expected intensity of the transition (determined with the MADEX code; Cernicharo 2012), and by comparison with the intensity of other nearby lines of NEFA.
Citation: Ohba et al. 2005
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To check for any spectral variation in the optical/IR bands, we looked for variation in the V − J band colour against the V-band brightness. This colour variation was analysed for the epochs A, B, D, and E. During epochs A and B, the source showed a ‘redder when brighter’ (RWB) behaviour. During epoch E, a bluer when brighter behaviour was observed. During epoch D, we observed a complex behaviour. Upto a V-band brightness of around 15 mag, the source showed a ‘bluer when brighter’ behaviour, but for optical brightness fainter than 15.0 mag, a ‘redder when brighter’ behaviour was observed. The colour–magnitude diagrams for all the four epochs are shown in Fig. 10. The spectral variations shown by the source are thus complex. From studies on the optical–IR colour–magnitude diagram, it is known that FSRQs in general show an RWB trend, which is attributed to them having a luminous accretion disc (Gu et al. 2006; Bonning et al. 2012). The observed optical emission is a combination of thermal blue emission from the accretion disc and non-thermal red emission from the jet. As the source gets brighter, the non-thermal emission has a more dominant contribution to the total flux, giving rise to the RWB behaviour (Bonning et al. 2012). During epochs A and B, there is a trend of the object to become RWB, irrespective of its optical brightness. The optical flares dominated by synchrotron emission processes during A and B have corresponding γ-ray flares that are produced by EC processes. However, during epochs D and E, the colour variations were found to depend on the optical brightness. During the epochs when this complex spectral behaviour was noticed, the source showed an optical/IR flare with no or a weak corresponding flare in the γ-ray band. The source showed a much larger amplitude of variability in the optical/IR bands, while in the γ-ray band it was either faint or below the detection limit of Fermi. This definitely points to some complex physical changes and could be due to a combination of changes in the bulk Lorentz factor, electron energy density, and magnetic field as seen from our SED modelling of the multiband data.
Citation: Bonning et al. 2012
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Citation: Gu et al. 2006
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Although this penalty is small, we can still provide a quantitative estimate based on a few assumptions. The observations of M15 that measured the parallax to VLA J2130+12 (K14) employed an interferometric technique where the position of a weaker potential in-beam calibrator source (M15 S1 and VLA J2130+12) can be measured against a brighter primary calibration source, with the potential for using the in-beam calibrator to transfer more accurate calibration solutions to other in-beam targets. Based on a literature review for papers where VLBI parallax measurements were determined using an in-beam calibrator, we find 24 similar measurements, the majority of which have been used to measure parallaxes to pulsars (Fomalont et al. 1999; Brisken et al. 2003; Chatterjee et al. 2005, 2009; Ng et al. 2007; Middelberg et al. 2011; Deller et al. 2012, 2013; Ransom et al. 2014; Liu et al. 2016). As these measurements represent additional opportunities to detect the parallax of a VLA J2130+12-like object, they could be considered as potential trials. However, all of the reported in-beam calibrators were significantly brighter (4–86 mJy) than VLA J2130+12 (∼0.1–0.5 mJy). Given our conservative assumption of a uniform volume density of VLA J2130+12-like objects in the Galaxy, we should down-weight the number of trials from brighter sources by (fν,in-beam/fν,VLA J2130+12)−1.5. In that case, the number of trials penalty is only an additional ∼0.2 trials. In addition, we note that the PSRπ parallax project (a large VLBA program) has reported15

15

https://safe.nrao.edu/vlba/psrpi/

 111 additional in-beam calibrator sources that they used to measure parallaxes. Although they do not provide the flux densities of individual sources, they note that their median in-beam calibrator source is 9.2 mJy. We have measured the flux density function of secure 1–20 mJy FIRST sources (Helfand et al. 2015; 





) to estimate the expected distribution of the flux densities of in-beam calibrators. We found that the minimum flux density is likely ∼3.2 mJy, and using the same down-weighting we estimate an additional penalty of ∼0.9 trials.
Citation: Brisken et al. 2003
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Citation: Chatterjee et al.; 2009
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