adsabs/FOCAL huggingface dataset:
In order to investigate the signal-to-noise ratio (SNR), ρ of NS–WD binaries for LISA-type space GW detectors, we calculate the averaged square SNR $\overline{\rho ^{2}}$ over the sky location, inclination, and polarization as 
(30)$$\begin{eqnarray*}
\overline{\rho ^{2}} = \int _{f_{1}}^{f_{2}}\frac{4\cdot \frac{4}{5}fA^{2}(f)}{(P_{\rm n}(f)/R(f))} \rm d (\ln \it f),
\end{eqnarray*}$$(Moore, Cole & Berry 2015; Robson, Cornish & Liu 2019), where f1 and f2 are the lower and upper limits of the integral, respectively. The factor 4 in the numerator of the integrand comes from the addition of strain noise in the detector arms and the two-way noise in each arm (Larson, Hiscock & Hellings 2000). We calculate the GW amplitudes A(f) of NS–WD binaries using the phenomenological (PhenomA) waveform model in the Fourier domain (Ajith et al. 2007; Robson et al. 2019). A(f) is expressed as 
(31)$$\begin{eqnarray*}
A(f) = \sqrt{\frac{5}{24}}\frac{G^{5/6}\mathcal {M}^{5/6}}{\pi ^{2/3}c^{3/2}R_{\rm b}}f^{-7/6}\, {\rm Hz}^{-1},\,\,\,\it f\lt f_{\rm m},
\end{eqnarray*}$$
 (32)$$\begin{eqnarray*}
f_{\rm m} = \frac{0.2974\zeta ^{2}+0.04481\zeta +0.09556}{\pi (GM/c^{3})}\, {\rm Hz},
\end{eqnarray*}$$
 (33)$$\begin{eqnarray*}
\zeta = m_{1}m_{2}/M^{2},
\end{eqnarray*}$$where $\mathcal {M} \equiv m_1^{3/5} m_2^{3/5}/(m_1+m_2)^{1/5}$, and fm is the GW frequency at the point of merging. If f > fm, the index of the power-law relation between A(f) and f changes (Ajith et al. 2007) and is beyond the scope of this study. The power spectral density of total detector noise $P_{\rm n}=\frac{1}{L^{2}}\left[P_{\rm o}+2(1+\cos ^{2}(f/f_{\ast }))\frac{P_{\rm a}}{(2\pi f)^{4}}\right]$, where f* = c/(2πL), L = 2.5 × 109 m is the armlength of the detector, $P_{\rm o}=2.25\times 10^{-22} \,\rm m^{2}\left(1+(\frac{2\,mHz}{\it f})^{4}\right) \,\, \rm Hz^{-1}$ is the single-link optical metrology noise, and $P_{\rm a}=9.0\times 10^{-30} \,\rm (m\,s^{-2})^{2}\left(1+(\frac{0.4\,mHz}{\it f})^{2}\right)\left(1+(\frac{\it f}{8\,\rm mHz})^{4}\right) \,\,Hz^{-1}$ is the single test mass acceleration noise (LISA Science Study Team 2018; Robson et al. 2019). R(f) is the transfer function numerically calculated from Larson et al. (2000). The effective noise power spectral density can be defined as Sn(f) = Pn(f)/R(f). For Taiji and Tianqin, we use the sensitivity curve data in Ruan et al. (2020) and Wang et al. (2019), respectively.
Citation: Ajith et al. 2007
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Citation: Ajith et al. 2007
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In this model, the pulsar associated with the PWN loses its rotational energy via a pulsar wind composed of magnetic and high-energy particles to power the high-energy physical process inside the nebula (Atoyan & Aharonian 1996; Fang & Zhang 2010). The relativistic wind of particles driven by the pulsar is blown into the ambient medium and generates a termination shock wave, which accelerates the electrons to relativistic energy. These relativistic electrons interact with the magnetic field and low-energy background photons (the synchrotron, thermal, FIR, and microwave background radiation), and generate the multiband nonthermal photons with energies ranging from radio to high-energy gamma-ray bands (Zhang et al. 2008; Fang & Zhang 2010; Lu et al. 2017). According to the review of the leptonic model (see, e.g., Zhang et al. 2008; Venter & de Jager 2007; Torres et al. 2013), the electrons injected into PWNe are accelerated by the pulsar magnetosphere and the termination shock. Therefore, the relativistic particles injected into the PWNe are also assumed as two different power-law components from the pulsar magnetosphere and shock acceleration, respectively. The injected spectrum of relativistic electrons inside PWNe is described as
1



Q(Ee,t)=Q0(t)Ee/Ecut−α1ifEeEcutQ0(t)Ee/Ecut−α2ifEe≥Ecut,

where the Q
0 can be determined by the ∫Q(E

e
, t)E

e

dE

e
 =η
L(t); η is the conversion efficiency from spin-down power into electron luminosity. The maximum energy of the electrons was express as 



Emax(t)≈ε0L(t)L0

, and L
0 is initial spin-down power. The electron energy distribution was given by
2



dN(Ee,Tage)dt=∫0TageQ(Ee,t)exp−Tage−tτeffdt,

where the 



τeff−1=τesc(t)−1+τsyn(t)−1

, τ

esc
(t) is the escape timescale, and τ
syn(t) is the lifetime of the relativistic electron of the synchrotron emission loss. The details of temporal evolution about the electron in the PWNe are discussed by the Zhang et al. (2008; also see the version of Fang & Zhang 2010; Lu et al. 2017).
Citation: Torres et al. 2013
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Douchin & Haensel (2001; DH) formulated a unified EoS for NS on the basis of the SLy4 Skyrme nuclear effective force (Chabanat et al. 1998), where some parameters of the Skyrme interaction were adjusted to reproduce the Wiringa et al. calculation of neutron matter (Wiringa et al. 1988) above saturation density. Hence, the DH EoS contains certain microscopic input. In the DH model the inner crust was treated in the CLDM approach. More recently, unified EoSs for NS have been derived by the Brussels-Montreal group (Chamel et al. 2011; Pearson et al. 2012; Fantina et al. 2013; Potekhin et al. 2013). They are based on the BSk family of Skyrme nuclear effective forces (Goriely et al. 2010). Each force is fitted to the known masses of nuclei and adjusted among other constraints to reproduce a different microscopic EoS of neutron matter with different stiffness at high density. The inner crust is treated in the extended Thomas-Fermi approach with trial nucleon density profiles including perturbatively shell corrections for protons via the Strutinsky integral method. Analytical fits of these neutron-star EoSs have been constructed in order to facilitate their inclusion in astrophysical simulations (Potekhin et al. 2013). Quantal Hartree calculations for the NS crust have been systematically performed by (Shen et al. 2011b,a). This approach uses a virial expansion at low density and a RMF effective interaction at intermediate and high densities, and the EoS of the whole NS has been tabulated for different RMF parameter sets. Also recently, a complete EoS for supernova matter has been developed within the statistical model (Hempel & Schaffner-Bielich 2010). We shall adopt here the EoS of the BSk21 model (Chamel et al. 2011; Pearson et al. 2012; Fantina et al. 2013; Potekhin et al. 2013; Goriely et al. 2010) as a representative example of contemporary EoS for the complete NS structure, and a comparison with the other EoSs of the BSk family (Chamel et al. 2011; Pearson et al. 2012; Fantina et al. 2013; Potekhin et al. 2013) and the RMF family (Shen et al. 2011b,a) shall be left for future study.
Citation: Potekhin et al. 2013
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Citation: Potekhin et al. 2013
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Citation: Potekhin et al. 2013
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Citation: Potekhin et al. 2013
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Citation: Chamel et al. 2011
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Diffuse synchrotron emission associated with ultrarelativistic particles and magnetic fields in the intracluster medium (ICM) primarily consists of radio haloes and radio relics (see Ferrari et al. 2008; Brüggen et al. 2012; Feretti et al. 2012; Brunetti & Jones 2014 for recent reviews). It is thought that radio haloes are caused by cluster-wide post-merger turbulence (see e.g. Brunetti et al. 2001; Petrosian 2001), secondary electrons from proton–proton interactions (see e.g. Dennison 1980; Blasi & Colafrancesco 1999) or a combination of the two mechanisms (see Brunetti & Blasi 2005; Brunetti & Lazarian 2011; Pinzke, Oh & Pfrommer 2015), whereas radio relics are apparently associated with localized, post-merger shock-fronts (Ensslin et al. 1998). However, the non-detection of gamma-ray emission by the Fermi satellite (see e.g. Brunetti et al. 2012; Zandanel & Ando 2014; Ackermann et al. 2015) disfavours a purely hadronic model for the origin of radio haloes and challenges standard diffuse shock acceleration to explain radio relics (see e.g. Brunetti & Jones 2014; Vazza & Brüggen 2014). Additionally, the variety of the observed properties of cluster-scale radio emission is becoming increasingly difficult to describe within the current theoretical picture. For example: whilst in the ‘Sausage’ cluster (CIZA J2242.8+5301) van Weeren et al. (2010) observe a textbook example of an arc-like radio relic related to a shock; in ZwCl 2341.1+000 Ogrean et al. (2014) observe no X-ray shock at the position of a relic, and in the Bullet cluster (Shimwell et al. 2015), PLCKG287.0+32.9 (Bonafede et al. 2014b) and the Coma cluster (Ensslin et al. 1998) an apparent link is seen between radio galaxies and radio relics. Furthermore, whilst radio haloes are statistically detected in merging clusters (e.g. Cassano et al. 2013), the role of the cluster mass and its dynamical state is difficult to disentangle with current observations (see Cuciti et al. 2015). For example, in CL1821+643 Bonafede et al. (2014a) detect a giant radio halo in a cool core cluster with no obvious merging activity and Russell et al. (2011) observe no diffuse radio emission in Abell 2146, which is a less massive cluster, but a clear merging system. Recently upgraded and new facilities have significantly improved sensitivity to diffuse radio emission from the ICM and are already beginning to reveal increasingly complex phenomena (e.g. Owen et al. 2014) which may shed light on the connection between haloes and relics and further challenge a univocal interpretation of these sources. One such instrument is the Low-Frequency Array (LOFAR; van Haarlem et al. 2013) which can produce deep, high-resolution, high fidelity, low-frequency radio images.
Citation: Ensslin et al. 1998; Ensslin et al. 1998
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Consider a space–time scale invariance of the equations of motion under the consideration of the transformation in Minkowsky space (Milgrom 2009a; see also Milgrom 2014a,b):
(3)

\begin{equation}
(t,{\boldsymbol r}) \rightarrow (\lambda t,\lambda {\boldsymbol r}),
\end{equation}

where t and ${\boldsymbol r}=(x,y,z)$ are time and Cartesian coordinates, respectively, and λ is a positive number. The Newtonian gravitational acceleration for a spherically symmetric system,

(4)

\begin{equation}
g_{\rm N} = \frac{GM_{\rm b}}{r^2},
\end{equation}

then transforms as gN → λ−2gN, whereas the kinematical acceleration, $g\equiv {\rm d} \dot{x} / {\rm d} t$, scales as g → λ−1g. Here Mb(  r) is the enclosed baryonic mass within r. As a result, the Newtonian gravitational acceleration and the kinematical acceleration scale differently under equation (3). Linking purely gravitational interactions to symmetries such as defined in equation (3) suggests deeper physics and constitutes a motivation for viewing MOND as much more than a mere phenomenological description of galactic dynamics (Milgrom 2009c). In order to assure that both the gravitational and the kinematical accelerations scale symmetrically under equation (3), i.e. in order to maintain the invariant symmetry, the gravitational acceleration, g, has to scale proportionally to $g_{\rm N}^{1/2}$. In order to obtain the correct dimension, a constant with the unit of acceleration, needs to be introduced. This constant is referred to as a0, such that

(5)

\begin{equation}
g=(a_0g_{\rm N})^{1/2},
\end{equation}

i.e. g2 = a0gN. Thus g = (GMba0)1/2/r, and the circular velocity, which follows from the centrifugal acceleration g = v2/r, is

(6)

\begin{equation}
v = (GM_{\rm b}a_0)^{1/4}={\rm constant},
\end{equation}

which is exactly the BTFR (Milgrom 1983a, 2009a, 2014b; McGaugh et al. 2000; Famaey & McGaugh 2012). We refer to gravitational dynamics which thus conforms to low-acceleration scale invariance (equation 3) as low-acceleration SID. SID beautifully reproduces the deep MOND equations of motion. It is rather remarkable that such a simple principle as SID and discovered by Milgrom leads to one of the most important scaling relations which real galaxies are observed to obey. Note that equation (6) implies that each baryonic galaxy is surrounded by a logarithmic non-particle (and thus phantom) DM halo potential, which is however not a real halo as it is only evident if Newtonian dynamics is applied to the galaxy. If SID is true, then a Newtonian observer would thus deduce that each baryonic galaxy is surrounded by a PDMH the mass of which is proportional to radial distance (equation 27 below).
Citation: Milgrom 2009c
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For variable star classification, both convolutional neural networks (CNNs; LeCun, Bengio & Hinton 2015) and recurrent neural networks (RNNs; Hochreiter & Schmidhuber 1997; Cho et al. 2014) have been shown to be competitive to the traditional RF-based methods. Naul et al. (2018) used an RNN autoencoder network to learn low-dimensional representations of period-folded light curves in an unsupervised fashion. This representation was then, in a supervised context, used as feature inputs to an RF classifier. They showed that the learned features are at least as good as, and often better than, two sets of state-of-the-art hand-crafted features (Richards et al. 2011; Kim & Bailer-Jones 2016), in terms of downstream classification accuracy. Becker et al. (2020) used an RNN for which instead of period-folding, each input light curve is grouped with a moving time-sample window of size 50 and stride 25. Although period-folding improves performance (Naul et al. 2018), Becker et al. (2020)’s time-space RNN does not require the period to be calculated, and is thus less computationally expensive in terms of preprocessing. Again, they found similar performance to an RF classifier with the Nun et al. (2015) features over three data sets, although lower accuracy was seen for many sub-classes with the OGLE data set (Table 2; see Section 3.3 for data description). More recently, Jamal & Bloom (2020) systematically benchmarked the performance of different configurations of RNN and CNN network architectures on variable star classification. Aside from other work (e.g. Aguirre, Pichara & Becker 2018; Tsang & Schultz 2019) evaluating neural network (NN) performance retrospectively on previously labelled data sets, Dékány & Grebel (2020) used an RNN classifier to identify a new sample of fundamental-mode RR Lyrae (RRab) stars. Similarly, Dékány et al. (2019) found Classical and Type II Cepheids with a CNN classifier, also using the VISTA Variables in the Via Lactea (VVV) survey (Minniti et al. 2010) and using period-folded light curves.
Citation: Naul et al. 2018
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Many efforts have thus been devoted to the correction of surface effects, either from theoretical modelling (e.g., Gabriel et al. 1975; Balmforth 1992b; Houdek 1996; Rosenthal et al. 1999; Grigahcène et al. 2005) or through empirical formulae (e.g., Kjeldsen et al. 2008; Christensen-Dalsgaard 2012; Ball & Gizon 2014; Sonoi et al. 2015). Some aspects, however, are very complicated to model, and existing models make use of assumptions that can barely be justified, if at all. For instance, turbulent pressure modulations are usually described in the Gas-Γ1 (GGM) or reduced-Γ1 (RGM) approximations (Rosenthal et al. 1999), which amounts to neglecting the effects of turbulent dissipation and buoyancy on the mode (Belkacem et al. 2021). Another problem is the use of time-dependent mixing-length formalisms (Unno 1967; Gough 1977) to account for modal surface effects (e.g., Gabriel et al. 1975; Houdek 1996; Grigahcène et al. 2005; Sonoi et al. 2017; Houdek et al. 2017, 2019). While useful for the bulk of the convective region, the mixing-length hypothesis is no longer valid in the superadiabatic region just beneath the surface of the star, as shown by 3D hydrodynamic simulations of stellar atmospheres (see Nordlund et al. 2009, for a review). Finally, such formalisms require that the oscillations be separated from the convective motions, thus yielding separate equations. This is done either by assuming a cut-off in wavelength space, with oscillations having much shorter wavelengths than turbulent convection (Grigahcène et al. 2005), or by using 3D hydrodynamic simulations and separating the oscillations from convection though horizontal averaging (Nordlund & Stein 2001). The necessity to separate the equations for oscillations and convection is fundamentally problematic as there is no rigorous way to disentangle the two components, mainly because, in solar-type stars, they have the same characteristic lengths and timescales (Samadi et al. 2015). This is even truer if one wishes to model their mutual coupling.
Citation: Houdek et al. 2017
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Strong gravitational lensing systems are a powerful tool for cosmology. They have been used to study how dark matter is distributed in galaxies and clusters (e.g., Kochanek 1991; Hogg & Blandford 1994; Broadhurst et al. 2000; Koopmans & Treu 2002; Bolton et al. 2006; Koopmans et al. 2006; Bradač et al. 2008; Huang et al. 2009; Vegetti & Koopmans 2009; Jullo et al. 2010; Grillo et al. 2015; Shu et al. 2015, 2016, 2017; Meneghetti et al. 2020) and are uniquely suited to probe the low end of the dark matter mass function and test the prediction of the cold dark matter (CDM) model beyond the local universe (e.g., Vegetti et al. 2010, 2012; Hezaveh et al. 2016; Ritondale et al. 2019; Diaz Rivero & Dvorkin 2020; Caǧan Sengül et al. 2020, 2021; Gilman et al. 2021). Multiply lensed supernovae (SNe) are ideal for measuring time delays and H
0 because of their well-characterized light curves, and in the case of Type Ia, with the added benefit of standardizable luminosity (Refsdal 1964; Treu 2010; Oguri & Marshall 2010), provided microlensing can be accurately characterized (Yahalomi et al. 2017; Foxley-Marrable et al. 2018). Furthermore, SNe have the benefit of fading, so for these systems lens models can be validated using images that are uncontaminated by bright point sources (Ding et al. 2021). In recent years, strongly lensed SNe, both core-collapse (Kelly et al. 2015; Rodney et al. 2016) and Type Ia (Quimby et al. 2014; Goobar et al. 2017; Rodney et al. 2021), have been discovered. Time-delay H
0 measurements from multiply imaged SNe (e.g., Goldstein & Nugent 2017; Shu et al. 2018; Goldstein et al. 2018, 2019; Pierel & Rodney 2019; Suyu et al. 2020; Huber et al. 2022), combined with measurements from distance ladders (e.g., Freedman et al. 2019, 2020; Riess et al. 2019, 2022) and lensed quasars (e.g., Suyu et al. 2010, 2013; Treu & Marshall 2016; Bonvin et al. 2017; Birrer et al. 2020; Millon et al. 2020; Wong et al. 2020), can be an important test of the tension between H
0 measured locally and the value inferred from the cosmic microwave background (CMB; Planck Collaboration et al. 2020).
Citation: Hezaveh et al. 2016
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The 17 GHz polarization reversal during this CRF can be a yet unknown feature inherent to the fan–spine structure, where magnetic polarity around null point (NP) varies so rapidly as to affect the propagation of microwave polarization. A way to possibly explain this polarization change is to view it as a mode-coupling phenomenon, the process by which the rays reverse their original sense of polarization while passing through a quasi-transverse field region along the line of sight from the radiation source to the observer, depending on the degree of mode coupling there (Cohen 1960; Zheleznyakov 1970; Melrose 1975; White et al. 1992). This is an attractive scenario for a fan–spine structure, because the fan surface may well act as a quasi-transverse layer for the rays emitted underneath. To think about an ideal fan–spine structure with a flux rope inside, in this configuration, the magnetic fields above the fan surface are all in the negative magnetic polarity, and the rays emitted from either magnetic polarity underneath will be observed as LHCP everywhere. Therefore, the LHCP observed everywhere before the flare can simply be due to the fan–spine structure, without any strong mode-coupling phenomenon. On the other hand, if a magnetic flux rope rises to reconnect with the overlying fan field, the fan surface may partially open up to let the flux rope erupt out. Such a change of magnetic field structure can explain the instant reversal of the 17 GHz polarization at t3 more naturally. The reconnection between the magnetic fields inside and outside of the fan will occur across a current sheet, the so-called breakout current sheet (BCS), and the newly open field lines amount to the lower part of the rising and expanding BCS (see, e.g., Lynch et al. 2016; Karpen et al. 2017). A sustained BCS over the active region might affect the microwave polarization, as mode coupling across a current sheet is still a debatable issue (Zheleznyakov et al. 1996; Lee et al. 1998; Lee 2007). We here offer only the simplest interpretation, according to which the change from LHCP to RHCP of the 17 GHz emission over the inner ribbon is not just a signature for any magnetic field perturbation, but may indicate a specific form of a breakout eruption out of the closed fan structure. The implied magnetic field reconfiguration is in line with the recently reported decay of the coronal magnetic field at the flare site by Fleishman et al. (2020).
Citation: White et al. 1992
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To emphasize it again, one may suggest accordingly that several low-m modes of moderately growing collective oscillation with different amplitudes, number of spirals and pitch angles (radial wavelengths), including the most interesting m = 1 mode, may co-exist in the solar neighbourhood. The so-called lopsidedness, or the m = 1 azimuthal asymmetry, is often seen in the distribution of stars and gas in the outer discs of many disc galaxies (Zaritsky & Rix 1997; van Eymeren et al. 2011). Generally, there is no azimuthal symmetry, at least far from their centres, in multi-arm galaxies (Efremov 2011). As for us the spiral pattern of the Galaxy is not a single m model but a superposition of modes as suggested theoretically in the late 1970s (Bertin et al. 1977; Lin & Lau 1979; Bertin 1980; see also Griv & Wang 2014). The overall pattern is thus basically multiple armed. In addition, we argue that the Galaxy is the azimuthally asymmetric spiral system (cf. Levine et al. 2006). The system therefore may exhibit a complicated asymmetric, multi-arm, not well-defined spiral structure as seen, for instance, in the face-on spiral galaxy M101 (Fig. 13). Interestingly, many spiral structures in galaxies do not appear to be well-organized grand designs. Galaxies dominated by a single and symmetric pattern are exceedingly rare.

The pitch angle of the spiral pattern seems to be relatively small for all models considered, |tan p| ≪ 1. Thus, the original Lin–Shu approximation of tightly wound gravity perturbations used throughout the theory does not fail.
The relative amplitude of the surface density $\widetilde{\Sigma }_0/\Sigma _{\mathrm{basic}} \gtrsim 1$ for all models considered. The latter means that the non-axisymmetric variation found in the relative amplitude of the surface density does not represent a small perturbation in the basic equilibrium state of the Galaxy that is axisymmetric in the mean.
The above mentioned results are in agreement with our previous determinations (Griv et al. 2013, 2014, 2015a,b,c).
Citation: Levine et al. 2006
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