adsabs/FOCAL huggingface dataset:
The recent detection of gravitational-wave (GW) emission from a merging neutron star binary (Abbott et al. 2017d) and merging black hole binaries (BHBs; Abbott et al. 2016a, 2016b, 2017a, 2017b, 2017c; The LIGO Scientific Collaboration & The Virgo Collaboration 2018) by the Laser Interferometer Gravitational-Wave Observatory (LIGO)/Virgo have ushered in an exciting new era of GW astrophysics. The astrophysical origin of the detected mergers is currently under debate, with numerous explanations proposed. These explanations can be very roughly divided into two main categories: mergers due to isolated binary evolution (e.g., Belczynski et al. 2016; de Mink & Mandel 2016; Mandel & de Mink 2016; Marchant et al. 2016), and mergers due to dynamical interactions (e.g., Portegies Zwart & McMillan 2000; Wen 2003; O’Leary et al. 2006, 2009, 2016; Antonini & Perets 2012; Kocsis & Levin 2012; Antonini et al. 2014; Antonini & Rasio 2016; Rodriguez et al. 2016; VanLandingham et al. 2016; Askar et al. 2017; Arca-Sedda & Gualandris 2018; Fragione & Kocsis 2018; Hoang et al. 2018; Randall & Xianyu 2018; Arca-Sedda & Capuzzo-Dolcetta 2019). Orbital eccentricity has been explored as a way to distinguish between these merger channels in both the LIGO/Virgo and Laser Interferometer Space Antenna (LISA) frequency bands. In contrast to mergers from isolated binary evolution, merging binaries from dynamical channels have been shown to have measurable eccentricities when they enter the LISA and/or LIGO/Virgo band, and can potentially be used as a way to distinguish between channels (e.g., O’Leary et al. 2009; Cholis et al. 2016; Gondán et al. 2018; Lower et al. 2018; Randall & Xianyu 2018; Rodriguez et al. 2018; Samsing 2018; Zevin et al. 2019). Unlike LIGO/Virgo, which can only detect merging BHBs in the final inspiral phase before merger, LISA will be able to detect eccentric stellar-mass BHBs for long timescales before they merge in the LIGO/Virgo band (e.g., O’Leary et al. 2006; Breivik et al. 2016; Nishizawa et al. 2016; Chen & Amaro-Seoane 2017; Nishizawa et al. 2017; D’Orazio & Samsing 2018; Kremer et al. 2019; Samsing & D’Orazio 2018). This provides us with invaluable insight into the dynamical evolution of eccentric binaries leading up to the merger, which has important implications about the astrophysical context in which merging binaries evolve.
Citation: O’Leary et al. 2006
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Citation: O’Leary et al. 2006
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After each step of calculations, the network should optimize the model based on its current and previous states to improve the subsequent mapping. Our model utilizes a computationally memory efficient optimization due to its dependence to only the first-order gradients, namely the ‘adaptive moment estimation’ (or Adam). For more details, we refer the readers to Kingma & Ba (2014). Adam optimization, compared to other gradient-based optimization, is very suitable for noisy and sparse gradients, and for simulated data that show very large scatter with respect to a given quantity of parameter (Kingma & Ba 2014). With this optimizer, we have to decide few parameters in advance. The learning step α and the parameters controlling the moving averages of the first- and second-order moments, namely β1 and β2 (both ∈[0,1)), respectively. For this purpose, we chose to minimize the MSE between the target and the prediction from the model: in what follows, we will alternatively call the MSE the ‘objective function’ f($\bf x$): with ${\bf x}$ the parameters of the model to be updated, such as weights and biases. At a given time t ≤ T, where T is the maximal learning time-step, we can update the parameters of the model as shown in the following:
(11)
\begin{eqnarray*}
g_t &amp;=\nabla _\mathrm{ \text{$x$}} f(\mathrm{\text{$x$}}_{t-1}),
\end{eqnarray*}
(12)
\begin{eqnarray*}
\mu _{1,t} &amp;=\beta _1 \times \mu _{1,t-1} + (1-\beta _1)\times g_t,
\end{eqnarray*}
(13)
\begin{eqnarray*}
\bar{\mu }_{1,t} &amp;=\mu _{1,t}/(1-\beta _1^t),
\end{eqnarray*}
(14)
\begin{eqnarray*}
\mu _{2,t} &amp;=\beta _2 \times \mu _{2,t-1} + (1-\beta _2)\times g_t^2,
\end{eqnarray*}
(15)
\begin{eqnarray*}
\bar{\mu }_{2,t} &amp;=\mu _{2,t}/(1-\beta _2^t),
\end{eqnarray*}
(16)
\begin{eqnarray*}
\mathrm{\text{$x$}}_t &amp;=\mathrm{\text{$x$}}_{t-1} - \alpha _t \times \bar{\mu }_{1,t}/ (\sqrt{\bar{\mu }_{2,t}} + \epsilon),
\end{eqnarray*}
where $\alpha _t=\alpha \sqrt{1-\beta _2^t}/(1-\beta _1^t)$ is the time-step at t. Equation (11) shows the gradients of the objective function at t with respect to the model parameters. Equations (12) and (14) update the estimations of the first and second moments. Our moments are biased towards the initial values; thus, we require equations (13) and (15) to account for the corrections. Finally, we update the model parameters with equation (16).
Citation: Kingma & Ba (2014)
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Citation: Kingma & Ba 2014
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In order to provide constraints on the gas masses in these galaxies independently from the CO measurements, we can use the Rayleigh–Jeans dust continuum emission. This will provide the first constraints to the αCO conversion factor in “normal” galaxies at z > 3 in the following. The Rayleigh–Jeans dust continuum emission has been used to estimate dust and gas masses, assuming an average emissivity and dust temperature for the dominant cold dust component and a constant dust-to-gas ratio (Hildebrand 1983; Eales et al. 2012; Bourne et al. 2013; Scoville 2013; Scoville et al. 2013, 2016, 2017; Groves et al. 2015). The dependence on cold dust temperature and dust-to-gas ratio may make the Rayleigh–Jeans method less reliable than at lower redshifts (e.g., Pavesi et al. 2018a). On the other hand, the opposing effects of increasing dust temperatures and decreasing dust-to-gas ratios that may occur in “normal” galaxies at high redshift may partially compensate for each other, as also found in recent simulations that are consistent with this approach to gas mass measurement (e.g., Liang et al. 2018; Privon et al. 2018). We here adopt Equations (10) and (13) of Scoville et al. (2016) to derive gas mass estimates based on our continuum flux measurements through the same assumptions that were used in those lower-redshift samples (Scoville et al. 2016, 2017). The 34 GHz upper limits imply 3σ gas mass limits of 2.8 × 1011 M⊙ for HZ10 and 1.6 × 1011 M⊙ for LBG-1, adopting the relation derived by Scoville et al. (2016, 2017). We also use the ∼230 GHz continuum fluxes to derive approximate estimates, although these measurements may not lie on the Rayleigh–Jeans tail and therefore may not accurately trace the cold dust component. These continuum measurements would imply gas masses of ∼1.3 × 1010 M⊙ for HZ4, ∼2.5 × 1010 M⊙ for LBG-1, ∼4.4 × 1010 M⊙ for HZ9, and ∼1.1 × 1011 M⊙ for HZ10, with dominant systematic uncertainties due to the extrapolation of the method to very high redshift.
Citation: Hildebrand 1983
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GIADA characterizes individual dust particles by means of two independent sensors. At the instrument entrance the particle crosses a laser curtain, and is detected by photoelectric sensors (GDS, grain detection system) registering a signal (proportional to the particle cross section times the albedo) and the time at which the laser curtain is crossed. Then the particle hits the impact sensor (IS, with the same GDS cross section, A = 10−2 m2), which registers the individual particle impact momentum and its travel time from GDS to IS. The combination of GDS and IS measurements (GDS+IS particles) provides the particle mass and velocity, and constrains the particle bulk density by means of calibration curves (Della Corte et al. 2016) derived on the ground using cometary analogues (Ferrari et al. 2014). If the particle is too small to be detected by the GDS system, it may be detected by the IS sensor only (IS particles): in this case the particle momentum is converted to the mass assuming the mean value of the velocities of the GDS+IS particles in the same momentum bin, or assuming the velocities predicted by tail models (Fulle et al. 2010) if Ngds+is = 0 in that mass bin. The spacecraft velocities listed in Table 1 are always much lower than the dust velocities measured by GIADA. In this condition, in the Sun-facing coma (assumed to have uniform and R-dependent space density ρ), the dust flux from the nucleus surface corresponds to the dust flux at nadir-pointing GIADA scaled by the factor 2πR2/A. The dust number loss rate at the nucleus surface per GIADA detection is Qn = 2πR2(AΔt)−1, where Δt is the total dust collection time (Tables 5–8). In the same Tables, we show the mass loss rates Qm and the mean dust velocities already integrated in each mass bin, corresponding to the four GIADA collection periods considered in this paper: from 2015 February 19 to 28 (Table 5), from 2015 March 13 to 17 (Table 6), on 2015 March 28 (Table 7), and from 2015 August 23 to September 3 (Table 8). In Table 9 we show the data obtained during the first post-perihelion excursion at low phase angles (60  α  64°, 125  R  290 km). The R-values are too small to use the NAC DUST-MON sequences. The uncertainty affecting Afρ and the loss rates measured by GIADA and OSIRIS depends on the number of detections in each mass bin: an estimate of the relative error is given by 






N


p


−
1

/

2




 and by 






(


N


gds
+
is


+


N


is


)


−
1

/

2




. The dispersion of the dust velocities in Tables 2–4 provides the error affecting the dust velocities measured by OSIRIS, close to 30%. The relative error of the dust velocities provided by each GDS+IS detection is below 10%.
Citation: Fulle et al. 2010
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From the theoretical point of view, we normalize the disk size to a fixed black hole mass and luminosity (thus to a fixed accretion rate; see Equations (14) and 17); therefore, we expect that the disk size τ
0 is independent of AGN properties. However, there are two possibilities that may cause the observed dependence in Figure 12. First, we adopt a constant virial factor f
BLR when estimating the black hole mass using Equation (1). Dynamical modeling of broad-line regions (BLRs) generally showed that f
BLR might depend on AGN properties and change from object to object (e.g., Pancoast et al. 2011; Li et al. 2013; Pancoast et al. 2014; Grier et al. 2017; Li et al. 2018; Williams et al. 2018). Observational calibrations of the virial factor also tend to support this conclusion (e.g., Ho & Kim 2014; Mejía-Restrepo et al. 2018; Yu et al. 2019). If there are systematic correlations between f
BLR and luminosity L
5100, black hole mass M
•, or accretion rate 



Ṁ

, using a constant f
BLR will lead to the apparent dependence of τ
0 on AGN properties. Such a bias can be eliminated once we have a solid understanding of the virial factor in the future. Second, it is possible that the disk’s temperature profile does change with the accretion rate. For example, the standard and slim-disk models predict different temperature profiles
12


12
However, we note that the temperature profiles of slim disks (T ∝ R
−1/2) become different from those of standard disks (T ∝ R
−3/4) only within the photon-trapping radius (e.g., Wang & Zhou 1999).  (Shakura & Sunyaev 1973; Abramowicz et al. 1988). There are also other physical processes that may contribute to the correlation between β and 



Ṁ

 (see, e.g., Li et al. 2021; Kammoun et al. 2021). Figure 7 implies that τ
0 and β are highly anticorrelated. As a result, a shallower temperature profile (larger β) will lead to a smaller disk size τ
0 and vice versa. In our sample, we find that high-luminosity and high-mass black holes generally have low accretion rates, giving rise to the dependence of τ
0 on luminosity and black hole mass.
Citation: Yu et al. 2019
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It is well known that star formation is inefficient on galactic scales. The observed linear correlation between molecular gas surface density and star formation rate (SFR) surface density in normal star-forming galaxies suggests a nearly constant gas depletion time-scale around ∼2 Gyr, much longer than the dynamical time-scale of galactic discs (Kennicutt 1989; Bigiel et al. 2008; Saintonge et al. 2011; Leroy et al. 2013; Genzel et al. 2015; Tacconi et al. 2018). In contrast, the SFE on GMC scales shows a large variation ranging from less than a few per cent to nearly unity (Zuckerman & Evans 1974; Krumholz & Tan 2007; Wu et al. 2010; Evans, Heiderman & Vutisalchavakul 2014; Heyer et al. 2016; Lee, Miville-Deschênes & Murray 2016; Vutisalchavakul, Evans & Heyer 2016). The origin of this large scatter is usually explained as a combination of the time variability of the SFR during the course of cloud evolution and intrinsic scatter of SFEs due to the diversity of GMC properties (Feldmann & Gnedin 2011; Kruijssen & Longmore 2014; Lee et al. 2016; Grudić et al. 2018a; Kruijssen et al. 2018). For example, recent theoretical models and high-resolution magneto-hydrodynamics simulations suggest that the SFE depends on the local virial parameters of the cloud controlled by large-scale turbulence (e.g. Krumholz & McKee 2005; Padoan, Haugbølle & Nordlund 2012). However, it has recently been recognized that large-scale turbulence can only account for an ∼0.3 dex scatter, which is not sufficient to explain the observed SFE variations (Lee et al. 2016). Another source of variation comes from different stellar feedback channels that alter the dynamical states of the GMCs (Fall, Krumholz & Matzner 2010; Murray, Quataert & Thompson 2010; Dale et al. 2014; Myers et al. 2014; Raskutti, Ostriker & Skinner 2016; Kim et al. 2017; Grudić et al. 2018b). Previous studies found that GMC simulations adopting different stellar feedback mechanisms (stellar winds, ionizing radiation, or supernovae) lead to dramatically different final SFEs. The problem has recently been recognized to be more subtle than previously thought, since even small differences in numerical treatments, such as different radiative transfer schemes, massive star sampling, and momentum and energy deposition algorithms, can lead to drastic changes for the final SFE (Dale et al. 2005; Roškar et al. 2014; Raskutti et al. 2016; Grudić et al. 2018b; Kim, Kim & Ostriker 2018). Therefore, how the SFE depends on GMC properties and the strength of stellar feedback remains an open question.
Citation: Kruijssen et al. 2018
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Snow lines of abundant volatile species are one of the possible origins of the observed substructures in dust continuum emission (Zhang et al. 2015; Okuzumi et al. 2016; Pinilla et al. 2017). Recent disk surveys have shown that the locations of the observed gap/ring structures do not seem to be related to the radial locations of the snow lines (Huang et al. 2018; Long et al. 2018; van der Marel et al. 2019). To estimate the positions of the snow lines in observed disks, the temperature profile is often assumed to be a simple power law (Huang et al. 2018; Long et al. 2018), which is broken if the disk has shadows on the disk surface (Dullemond et al. 2001; Baillié & Charnoz 2014; Ueda et al. 2019). Figure 5 shows the radial positions of snow lines of H2O, NH3, CO2, H2S, C2H6, CH4, and CO at 






t





=
0


 and 11. For simplicity, we define the snow lines as the radial location where the midplane temperature reaches 150, 70, 55, 50, 40, 25, and 20 K for H2O, NH3, CO2, H2S, C2H6, CH4, and CO, respectively. We clearly see that the radial positions of snow lines move with time and multiple snow lines emerge even for a single species. This means that it is necessary to determine the disk temperature precisely when we evaluate the snow line locations. These snow lines would induce additional ring and gap structures and some of them would overlap with the TWI-induced substructures. It should be noted that the oscillation timescale of the TWI is much shorter than the dust radial drift timescale. Therefore, sintering-induced substructures would not coincide with the locations of the snow lines if the TWI is present. However, the dust-size variation can be induced by sublimation and recondensation, which potentially produces millimeter substructures. Since the radial locations of the snow lines are important not only for the substructure formation but also for the chemical composition of forming planets (e.g., Sato et al. 2016; Öberg & Wordsworth 2019), we should investigate how the TWI evolves in planet forming disks.
Citation: Dullemond et al. 2001
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To further reduce the number of fitting parameters, we assume that no source is unique in terms of the acceleration spectral shape, i.e. all the source components have the same H spectral index α, He spectral index, maximum rigidity Rm, and He-to-H Galactic injection flux ratio χ. The spectrum of He seems harder than that of H as indicated by many spectral studies, implying, e.g. time-dependent particle acceleration (Zhang et al. 2017), or more efficient He injection in the shock acceleration process (Malkov, Diamond & Sagdeev 2012). It is thus assumed the He spectral index to be α − 0.077 according to the sub-TeV data fit (Aguilar et al. 2015b). To be consistent with the conventional scenario, we also consider that the nearby SNR can inject a total CR energy of 1050 erg into the ISM, i.e.
(15)$$\begin{eqnarray}
\int _{\text{GeV}}^{\infty }{\left[ \frac{{\rm d}R_{\text{H}}}{{\rm d}E}+\chi \left(E \right) \frac{{\rm d}R_{\text{He}}}{{\rm d}E} \right] N\left(E \right) E{\rm d}E}=10^{50}\text{ erg},
\end{eqnarray}$$where E is the particle kinetic energy, N refers to the injection spectrum of H with $N\left( \text{GV}\right) \approx 4.7\times 10^{52}\text{ GV}^{-1}$ (for the fitted parameters in Table 1). For brevity, we hereafter treat all of N and Q as quantities for H components. With these respects, in the naive approach, the spectral fitting parameters are $\chi \left( \text{GV}\right)$, α, Rm, ϕ, θ, MA, $\left| z/h \right|$, $\mu Q_{\text{d}}\left( \text{GV}\right)$, $Q_{\text{c}}\left( \text{GV}\right)$, tc, where $\theta =\arcsin \left(\rho /r_{\text{n}} \right)$ is the angle between the regular magnetic field line and the line-of-sight vector towards the nearby source. In the quasi-local approach equation (11), the alignment of the field line must uniquely be determined, leading to an additional angular parameter, which can be chosen as the angle φ around the line-of-sight vector (towards the nearby source with φ = 0° shown in Fig. 2d). The fitting results of the CR spectrum for models with the naive and quasi-local approach are shown with Figs 1(a) and 2(a), respectively.
Citation: Malkov, Diamond & Sagdeev 2012
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In order to make a linear analysis, first we have to prepare the PNS models as a background. The PNS properties depend on not only the density and pressure profiles but also the distributions of temperature (or entropy per baryon) and electron fraction inside the PNS, while such profiles can be determined only via the numerical simulation of the core-collapse supernova explosion. In this study, as in Sotani & Sumiyoshi (2019), we particularly adopt the profiles obtained via the numerical simulations performed by solving the general relativistic neutrino-radiation hydrodynamics under the spherical symmetry. In the simulations, hydrodynamics and neutrino transfer in general relativity are solved simultaneously (Yamada 1997; Yamada, Janka & Suzuki 1999; Sumiyoshi et al. 2005). To describe the neutrino transfer, the Boltzmann equation is directly solved with the multi-angle and multi-energy neutrino distributions for four species, νe, $\bar{\nu }_\mathrm{ e}$, νμ/τ, and $\bar{\nu }_{\mu /\tau }$, i.e. we implement six species of neutrinos by assuming μ-type and τ-type (anti-)neutrinos have identical distributions. For the collision term associated with neutrino emission, absorption, and scattering with leptons, nucleons, and nuclei handles, the basic neutrino reactions are adopted (Bruenn 1985; Sumiyoshi et al. 2005). The metric adopted in the numerical code is given by
(1)$$\begin{eqnarray*}
\mathrm{ d}s^2 = -\mathrm{ e}^{2\Phi (t,m_\mathrm{ b})}\mathrm{ d}t^2 + \mathrm{ e}^{2\Lambda (t,m_\mathrm{ b})}\mathrm{ d}m_\mathrm{ b}^2 + r^2(t,m_\mathrm{ b})(\mathrm{ d}\theta ^2 + \sin ^2\theta \mathrm{ d}\mathrm{ }\phi ^2), \nonumber\\
\end{eqnarray*}$$where t and mb denote the coordinate time and the baryon mass coordinate, respectively (Misner & Sharp 1964). In addition, mb is related to the circumference radius (r) via the baryon mass conservation, while the metric functions, Φ(t, mb) and Λ(t, mb), are evolved together with hydrodynamical variables in the numerical simulations (Yamada 1997). The numerical simulations for core-collapse supernovae have been done with 255 grid points in the radial mass coordinate, 6 grid points in the neutrino angle, and 14 grid points in the neutrino energy. The rezoning of radial mesh is made during the simulations to resolve the accreting matter. We remark that the radial grids of mass coordinate are non-uniformly arranged to cover not only the dense region inside the central object but also the region for accreting matter.
Citation: Sumiyoshi et al. 2005
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Citation: Sumiyoshi et al. 2005
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We note in passing that recent studies address improved satellite modellimg that ameliorates many of these issues, including the core–cusp issue via non-sphericity of the stellar velocity distribution (Hayashi, Chiba & Ishiyama 2020) and the detectability of MWG satellites (Nadler et al. 2020). Other proposed solutions include those invoking baryonic physics, ranging from inclusion of baryon-contraction-induced diversity (Lazar et al. 2020), through dynamical friction-mediated coupling with baryonic clumps (El-Zant, Shlosman & Hoffman 2001; El-Zant et al. 2004; Tonini, Lapi & Salucci 2006; Romano-Díaz et al. 2008; Goerdt et al. 2010; Cole, Dehnen & Wilkinson 2011; Del Popolo et al. 2014; Nipoti & Binney 2015), or through dynamical feedback driven by starbursts or active galactic nuclei (AGNs; Read & Gilmore 2005; Mashchenko, Couchman & Wadsley 2006; Mashchenko, Wadsley & Couchman 2008; Peirani, Kay & Silk 2008; Governato et al. 2012; Pontzen & Governato 2012; Zolotov et al. 2012; Martizzi, Teyssier & Moore 2013; Teyssier et al. 2013; Madau, Shen & Governato 2014; Ogiya & Mori 2014; Pontzen & Governato 2014; El-Zant, Freundlich & Combes 2016; Silk 2017; Freundlich et al. 2020). Alternatively, modifications to the particle physics model of the dark matter have been proposed. Such proposals include ‘pre-heated’ warm dark matter (e.g. Colín, Avila-Reese & Valenzuela 2000; Bode, Ostriker & Turok 2001; Macciò et al. 2012; Schneider et al. 2012; Shao et al. 2013; Lovell et al. 2014; El-Zant, Khalil & Sil 2015) and self-interacting dark matter, whereby energy flows into the central cores of haloes through conduction (e.g. Burkert 2000; Kochanek & White 2000; Spergel & Steinhardt 2000; Miralda-Escudé 2002; Peter et al. 2013; Zavala, Vogelsberger & Walker 2013; Elbert et al. 2015). Ultralight axions, with boson mass ∼10−22 eV, have also been considered as dark matter candidates in connection with these same small (sub)galactic scale problems (e.g. Peebles 2000; Hu, Barkana & Gruzinov 2000; Peebles 2000; Marsh & Silk 2014; Schive et al. 2014b; Hui et al. 2017; Mocz et al. 2019; Nori et al. 2019; see Niemeyer 2019 for recent review). Here the zero-point momentum associated with a long de Broglie wavelength corresponding to the small mass comes along with ‘fuzziness’ in particle positions. This in turn leads to a hotter halo core with non-diverging central density and a cut-off in halo mass. Such axion fields can also be relevant for inflationary scenarios or late dark energy models. The non-thermal production implies that the axions are present with the required abundance for dark matter; they behave as cold dark matter on larger scales despite the tiny masses (Marsh 2016, 2017).
Citation: Madau, Shen & Governato 2014
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Citation: Pontzen & Governato 2014
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