adsabs/FOCAL huggingface dataset:
Flows with 



Rem≪1

 and 



N∼(1)

 have the distinct property that the induced magnetic field is quickly diffused away, yet the Lorentz force is not negligible. This limit is referred to as the quasi-static approximation to MHD (which we call “QMHD” henceforth; Moffatt 1967; Sommeria & Moreau 1982; Davidson 1995; Knaepen & Moreau 2008; Davidson 2013), and has been studied mainly in metallurgy and in MHD experiments due to the typically low conductivity of liquid metals (Alemany et al. 1979; Sommeria 1988; Gallet et al. 2009; Klein & Pothérat 2010; Pothérat & Klein 2014; Baker et al. 2018), although recent numerical studies on its turbulent properties and anisotropy have been done as well (Zikanov & Thess 1998; Burattini et al. 2008; Favier et al. 2010, 2011; Reddy & Verma 2014; Verma 2017). After nondimensionalizing the equations of MHD using the uniform density ρ, ℓ, and u, and taking the limits above, one is left with a single dynamical equation for the velocity
2



∂v∂t+v·∇v=−∇p*−Ro−1xˆ∥Ω×v−N∇−2(xˆ∥B0·∇)2v+F,

where p
* is the total pressure modified by rotation and magnetic pressure, Ro
−1 ≡ 2Ωℓ/u is the inverse Rossby number (quantifying the relative strength of the Coriolis force), 



xˆ∥Ω

 and 



xˆ∥B0

 are unit vectors in the direction of rotation and the background magnetic field, respectively, and 
F
 is a generic forcing term that can include dissipation such as viscosity and a body force (to be specified in Section 3). The background magnetic field is fixed in time and is uniform in space, such that 



∇×B0=B0∇×xˆ∥B0=0

. Care must be taken if considering a spatially dependent background magnetic field 
B


0
(
x
), as the resulting equation will not be the same. See the discussion in Section 5. This equation is accompanied with the incompressibility condition ∇ · 
v
 = 0. The induced magnetic field can be found using a diagnostic relation
3



b=−∇−2xˆ∥B0·∇v,

which would be 



b=−∇−2B0·∇v/η

 in dimensional variables.
Citation: Favier et al. 2010
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Citation: Zikanov & Thess 1998
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This work, which focuses on mass reconstruction from gravitational lensing, is only the first in a series, which will exploit our mesh-free numerical techniques. Two regimes are typically distinguished in lensing mass reconstruction. Strong lensing is usually confined to the inner-most core of the gravitational lens and produces spectacular observational constraints such as multiple images of the same source, gravitational arcs or even rings. The domain of weak lensing is further away from the centre of the lens but spans large areas and manifests itself by the weak distortion in the shape of background galaxies behind the lens. Reconstruction techniques are divided into two classes, although this distinction is by no means unique or even consistent in some cases. Parametric techniques (e.g. Kneib et al. 1996; Broadhurst et al. 2005; Smith et al. 2005; Halkola, Seitz & Pannella 2006; Jullo et al. 2007; Zitrin et al. 2009; Oguri 2010; Newman et al. 2013; Jullo et al. 2014; Monna et al. 2014; Johnson et al. 2014, for some recent examples) assume a parametric form of the underlying mass density distribution for the lens and typically make the assumption that light traces mass in the positioning of these parametric forms. On the other hand, free-form1 methods (see e.g. Broadhurst, Taylor & Peacock 1995; Bartelmann et al. 1996; Abdelsalam, Saha & Williams 1998; Bridle et al. 1998; Seitz, Schneider & Bartelmann 1998; Bradač et al. 2005a; Cacciato et al. 2006; Liesenborgs, De Rijcke & Dejonghe 2006; Diego et al. 2007; Jee et al. 2007; Coe et al. 2008; Bradač et al. 2009; Merten et al. 2009; Williams & Saha 2011; Merten et al. 2011, 2015; Diego et al. 2015, for some recent examples) usually do not make this assumption and purely rely on the input data either based on weak lensing, strong lensing or a combination of the two. This is possible while using a reconstruction mesh and directly inverting the underlying equations describing lensing on this mesh. In the following, we introduce a free-form method combining weak and strong lensing, which uses our new mesh-free numerical framework. This method translates original ideas by Bartelmann et al. (1996), Seitz et al. (1998), Bradač et al. (2005a), Cacciato et al. (2006) and Merten et al. (2009) into the flexible and efficient mesh-free numerical domain. Alternative implementations of such ideas can e.g. be found in Bradač et al. (2009).
Citation: Smith et al. 2005
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Magnetic reconnection (MR) may occur in various space and astrophysical plasma environments, among which the planetary magnetopause boundaries separating the solar wind and magnetospheric origins of plasmas and magnetic field are some of the most likely sites for the occurrence of MR. Due to the easy access to the in situ spacecraft observations the Earth’s magnetopause is the most widely studied space plasma environment for MR (Paschmann et al. 1979; Vaivads et al. 2004; Graham et al. 2014). In particular, the Magnetospheric Multiscale (MMS) mission has contributed greatly to the kinetic physics of magnetopause reconnection (Burch et al. 2016; Hasegawa et al. 2017; Zhong et al. 2020). Many studies have shown that an initial Harris type equilibrium profile with constant total pressures 





 and antiparallel magnetic field with or without a guide field (Harris 1962) may tend to develop MR geometry. In particular, two major categories of MR have been proposed: the steady state model with a single X line and the outflow approaching the Alfvén speed (Petschek 1964), and the tearing mode instability with a series of X and O lines and mild plasma velocity (Furth et al. 1963). Numerous fluid and kinetic simulations have been carried out to examine the various aspects of MR processes for the past 50 yr (Hau & Chiou 2001; Guo et al. 2015; Landi et al. 2015). In particular, the effects of pressure or temperature anisotropy on MR have been examined by a number of authors (Chen & Palmadesso 1984; Shi et al. 1987; Birn & Hesse 2001; Chiou & Hau 2002, 2003; Hung et al. 2011). In the MHD models the double-polytropic (DP) laws are widely adopted as the energy closures to study the effects of temperature anisotropy and energy closures on MR and tearing mode instability (Chiou & Hau 2002, 2003; Hung et al. 2011). It is shown that the mirror type temperature anisotropy of 





 may greatly enhance the growth rate of tearing mode instability and the merging rate of single X-line reconnection. In particular, the coupling of tearing and mirror instabilities may lead to relatively larger magnetic islands as compared to the cases with isotropic pressure and the mirror waves with anticorrelated density and magnetic field may be present in the vicinity of X lines.
Citation: Petschek 1964
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Citation: Zhong et al. 2020
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Energy flows induced into magnetically dominated relativistic magnetospheres of compact objects are commonly modelled by numerical simulations in the force-free electrodynamics (FFE) limit. Fueled by the track record of observations in the era of multimessenger astrophysics, current targets for such simulations include the magnetospheres of rapidly spinning black holes, spiraling neutron stars, magnetars, and pulsars. The tenuous, magnetically dominated atmosphere (magnetosphere) of pulsars is an active field of scientific interest. They fascinate both observers (e.g. Lorimer et al. 1995; Ransom et al. 2005; Abdo et al. 2013; Jankowski et al. 2018) and theorists (e.g. Kennel & Coroniti 1984; Lyubarskii 1996; Contopoulos, Kazanas & Fendt 1999; Goodwin et al. 2004; Timokhin 2006; Timokhin & Arons 2013; Contopoulos 2019; Pétri 2020). With the remarkable progress in scientific computing, their rotating magnetosphere has captured designers of numerical methods that integrate FFE and magnetohydrodynamics (MHD) with ever-improving accuracy (e.g. Komissarov 2006; Spitkovsky 2006; Tchekhovskoy, Spitkovsky & Li 2013; Parfrey, Spitkovsky & Beloborodov 2017; Carrasco & Shibata 2020). Recently, particle-in-cell (PIC) simulations were able to resolve a broad range of scale separations and allow for unprecedented insight into the microphysics of pulsar magnetospheres across the global scale (Cerutti et al. 2015; Philippov, Spitkovsky & Cerutti 2015a; Kalapotharakos et al. 2018; Philippov & Spitkovsky 2018; Guépin, Cerutti & Kotera 2020). In this fascinating flurry of outcomes, only few references scrutinized whether the results from ideal plasma simulations are the best possible model for the pulsar magnetosphere that contains an inherently non-ideal region, namely the equatorial current sheet (ECS) beyond the closed zone (Contopoulos 2016; Contopoulos 2019; Contopoulos, Pétri & Stefanou 2020). Here, we study with rigorous technical depth how this non-ideal region can affect the global dynamics of the force-free aligned rotator magnetosphere – effectively serving as a blueprint for force-free magnetospheres of other compact objects.
Citation: Komissarov 2006
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Work in recent years has shown that rotation is a key ingredient in shaping the evolution of massive stars with very low metallicities (Z  SMC metallicity down to Population III stars; see Meynet & Maeder 2017, and references therein). Fast rotators (with initial vrot ≳300 km s−1) are expected to lead to chemically homogeneous evolution (CHE) in which the star becomes brighter and hotter, and thus more ionizing photons, specially in the extreme UV, are emitted than in the corresponding non-rotating case (e.g. Brott et al. 2011; Levesque et al. 2012; Yoon, Dierks & Langer 2012). Presently, although we still know little about rotation velocities of massive stars and their variation with environment, observations seem to favor fast rotators at low Z (e.g. Martayan et al. 2007; Hunter et al. 2008). Model predictions suggest that the effects of rotation, like CHE, should be enhanced at lower metallicities. There is an increase of theoretical and observational evidence which supports the significant role of rotation among the generations of first stars, with Z=0 or extremely low metallicities, and fast rotating massive stars were likely common phenomena in the early Universe (e.g. Leitherer 2008; Chiappini et al. 2008; Maeder & Meynet 2012; Yoon et al. 2012). Modern models for low-metallicity massive fast-rotating single stars which undergo CHE have been published by Szécsi et al. (2015); the authors called them transparent wind UV intense stars (or TWUIN stars). Considering all this and the extremely low-Z of SBS 0335 − 052E, we compare our observations with the TWUINs predictions,6 following the same approach that we used previously for non-rotating WCE and massive O stellar models. Taking the computed Q(He ii)=7.37 × 1048 photon s−1 for the most massive 294 M⊙ TWUIN, we require that ∼430 (∼300) such stars are necessary to explain the Q(He ii)Int (Q(He ii)$_{\rm He\, \small {II}-MB}$). Again, hundreds of these super-massive TWUINs do not match the M⋆, SSCs of SBS 0335 − 052E. If we instead, apply the same approach using lower mass TWUIN models, it makes even harder to account for the observations. Besides the Q(He ii) budget, we have measured values of He ii λ4686/Hβ as high as 0.06 within the He ii λ4686 main body region. Under ionization-bounded conditions, even the most massive TWUIN models cannot reproduce these values of He ii λ4686/Hβ (see table B.1 from Szécsi et al. 2015).
Citation: Hunter et al. 2008
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A pulsar rotates at an angular velocity Ω with inertial moment I and magnetic moment $\boldsymbol {\mathcal {M}}$. It is described by the canonical rotation-down equation in the magnetic dipole model:
(4)
\begin{eqnarray*}
\dot{\Omega } = - K \Omega ^3,
\end{eqnarray*}
where $K = \frac{\mu _0 | \boldsymbol{\mathcal {M}} |^2 \sin ^2 \theta }{6 \pi c^3 I}$, μ0 is vacuum permeability, and c is speed of light. θ is inclination angle, namely, the angle between $\boldsymbol {\mathcal {M}}$ and $\boldsymbol {\Omega }$. The possible change of macroscopic magnetic moment of pulsars at the moment of a glitch occurring was discussed by Link and Epstein (Link et al. 1992; Link & Epstein 1997). Namely, K and Ω changed while the rotation-down equation remains the same at glitches, 
(5)
\begin{eqnarray*}
\frac{\Delta \dot{\Omega }}{\dot{\Omega }} \approx \frac{\Delta K}{K} = 2 \frac{\Delta (| \boldsymbol{\mathcal {M}} | \sin \theta)}{| \boldsymbol{\mathcal {M}} | \sin \theta } - \frac{\Delta I}{I} .
\end{eqnarray*}
From observations, we know $\frac{\Delta \dot{\Omega }}{\dot{\Omega }} \sim 10^{-3}$. Merely variation of orbit angular momentum cannot describe the magnetic moment changing, as $- \frac{\Delta I}{I} = \frac{\Delta \Omega }{\Omega } \lesssim 10^{-6} \ll \frac{\Delta \dot{\Omega }}{\dot{\Omega }}$. It motivates us to consider the origin of the equation (5) related with conservation of total angular momentum. As Einstein-de Haas effect suggests that $\boldsymbol {S}$ and $\boldsymbol {\Omega }$ can transfer into each other caused by the total angular momentum conservation, 
(6)
\begin{eqnarray*}
\Delta \boldsymbol {J} = \Delta (\boldsymbol {S} + I \boldsymbol {\Omega }) = \boldsymbol {T} \Delta t \approx 0,
\end{eqnarray*}
where $\boldsymbol {S}=(1/\gamma)\boldsymbol {\mathcal {M}}$, Δt is the duration of a glitch, and $\boldsymbol {T}$ is the torque. The total angular momentum conservation would turn to be reasonable, when glitches regarding as instantaneous processes, namely Δt → 0, as the traditional glitch model (Baym et al. 1969) does. In principal, $\boldsymbol {T} \Delta t \ne 0$ is permitted in our model. For the first step, we wish to obtain approximated results with the simplest case of equation (6).
Citation: Link et al. 1992
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We begin with our results from global DNS MHD simulations of the MRI in cylindrical (r, ϕ, z) geometry using the DEBS (Schnack et al. 1987; Ebrahimi et al. 2009) initial-value code to solve the non-linear, viscous and resistive MHD equations

(1)

\begin{eqnarray}
\frac{\mathrm{\partial} \boldsymbol A }{ \mathrm{\partial} t } &amp;=&amp; -{\boldsymbol E} = S\boldsymbol V\times \boldsymbol B - \eta \boldsymbol J
\end{eqnarray}


(2)

\begin{eqnarray}
\rho \frac{\mathrm{\partial} \boldsymbol V }{ \mathrm{\partial} t } &amp;=&amp; -S \rho \boldsymbol V\cdot \ \nabla \boldsymbol V + S\boldsymbol J \times \boldsymbol B +P_{\rm m} \nabla ^2 \boldsymbol V -S \frac{\beta _0}{2}\nabla P
\end{eqnarray}


(3)

\begin{eqnarray}
\frac{\mathrm{\partial} P }{ \mathrm{\partial} t } &amp;=&amp; -S\nabla \cdot (P \boldsymbol V) - S (\Gamma -1) P \nabla \cdot \boldsymbol V
\end{eqnarray}


(4)

\begin{eqnarray}
\frac{\mathrm{\partial} \rho }{ \mathrm{\partial} t } &amp;=&amp; -S\nabla \cdot (\rho \boldsymbol V)
\end{eqnarray}


(5)

\begin{eqnarray}
\boldsymbol B &amp;=&amp; \nabla \times \boldsymbol A
\end{eqnarray}


(6)

\begin{eqnarray}
\boldsymbol J &amp;=&amp; \nabla \times \boldsymbol B,
\end{eqnarray}

where the variables, ρ, P, V, B, J, and Γ are the density, pressure, velocity, magnetic field, current, and ratio of the specific heats, respectively. We use the same normalization (Schnack et al. 1987; Ebrahimi et al. 2009; Ebrahimi & Bhattacharjee 2014), where time, radius and velocity are normalized to the outer radius a, the resistive diffusion time τR = a2/μ0η, and the Alfvén velocity $V_{\rm A} = B_0/\sqrt{\mu _0 \rho _0}$, respectively. The dimensionless parameters, S = τRVA/a and Pm, are the Lundquist number and the magnetic Prandtl number (the ratio of viscosity to resistivity), respectively. the initial state satisfies the equilibrium force balance condition $\frac{\beta _0}{2}\nabla p = \rho V_{\phi }^2/r$, where $\beta _0 \equiv 2 \mu _0 P_0/B_0^2$ is normalized to the axis value, and the initial pressure and density profiles are assumed to be radially uniform and unstratified. Pressure and density are evolved, however, they remain fairly uniform during the computations. A no-slip boundary condition is used for the poloidal flow and flow fluctuations. The inner and outer radial boundaries are perfectly conducting so that the tangential electric field, the normal component of the magnetic field, and the normal component of the velocity vanish. The tangential component of the velocity is the rotational velocity of the wall. The azimuthal (ϕ) and axial (z) boundaries are periodic. We assume a radial pressure gradient balances the centrifugal force in equilibrium, but radial gravity and a radial pressure force are interchangeable for our incompressible, unstratified circumstance. The pressure gradient, rather than gravity, is what balances the centrifugal force in cylindrical laboratory experiments designed to test the MRI (Goodman & Ji (2002)).
Citation: Ebrahimi & Bhattacharjee 2014
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Figure 1 shows that in the regions where activity was detected visually, i.e., Hapi, Seth, and Ma’at pits have lower (8–13%/100 nm) spectral slopes than the rest of the comet surface (13–22%/100 nm). In addition to those places, Seth alcoves, the wall of the large Anuket alcove, around the circular features, both clustered and isolated bright features (see Thomas et al. 2015b; Auger et al. 2015; Pommerol et al. 2015b, for definitions) show similar lower spectral slopes than the rest of the surface, even though there was no visual detection of activity features rising from them at the time of the observations used in this study4. This may be because the observing geometry was not suited for their detections during the observations. In the regions we investigated, the Hapi region displays the lowest spectral slopes 8–11%/100 nm (see also Fornasier et al. 2015) together with the isolated bright features (IBFs) and the clustered bright features in the Imhotep region. The locations of the bright features on the Imhotep image (image #4) are shown in Fig. B.4. According to the spectral slope values, the IBFs of Imhotep seem to be more similar to the Hapi region than the active pits of Seth and Ma’at regions. Active pits, alcoves, and the large alcove of Anuket have slope values of typically 10–13%/100 nm. The Ma’at region, which is located on the smaller lobe (head) of the comet, displays higher spectral slope values than the Seth region, which is located on the larger (body) lobe of the comet. In the investigated regions, the highest slope values are detected in the Imhotep region (see Fig. 1d). Here it should be mentioned that the comparison of spectral slopes is performed under the assumption of no spectral reddening between the phase angles of the images we investigated, although the spectral slopes show reddening by phase as presented in Fornasier et al. (2015). Unfortunately, the previous work does not cover all the phase angles of the images we investigated, but the spectral slope variation between 35–54° (Fig. 3 of  Fornasier et al. 2015) is small so that we can make this comparison. However, if we follow the linear trend of the phase reddening, for the image taken in 70.45° phase angle (image #4), the spectral slopes would vary from 15%/100 nm to 18%/100 nm in the observations we used.
Citation: Fornasier et al. 2015
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Citation: Fornasier et al. 2015
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Progress in this field will require large statistical samples of metal-poor stars in a variety of environments within the Local Group. Unfortunately, metal-poor stars are exceedingly rare and difficult to find, being overwhelmed by the more numerous metal-rich populations in the Galaxy. Examination of the Besançon model of the Galaxy (Robin et al. 2003), which is guided by a theoretical framework for the formation and evolution of the main stellar populations, suggests that a typical halo field has only one in ∼2000 stars with [Fe/H]  −3 between 14  V  18 (Youakim et al. 2017). Enormous effort has gone into the discovery and study of extremely, ultra, and hyper metal-poor stars with [Fe/H]  −3.0, −4.0, and −5.0, respectively. Most of the known metal-poor stars have been found in dedicated surveys, such as objective prism surveys (the HK survey and Hamburg-ESO survey, Beers, Preston & Shectman 1992; Christlieb et al. 2002, 2008; Beers & Christlieb 2005; Frebel et al. 2006; Schörck et al. 2009), wide-band photometric surveys (Schlaufman & Casey 2014), and blind spectroscopic surveys, such as the Sloan Digital Sky Survey (SDSS) SEGUE and BOSS surveys (Yanny et al. 2009; Eisenstein et al. 2011; Dawson et al. 2013), and from the Large Sky Area Multi-Object Fibre Spectroscopic Telescope (LAMOST; Cui et al. 2012). According to the SAGA data base (see Suda et al. 2017, and references therein), there are ∼500 stars with [Fe/H]  −3.0, though fewer than half have detailed chemical abundances. Recently, narrow-band photometric surveys have shown higher success rates for finding metal-poor stars, particularly SkyMapper (Keller et al. 2007; DaCosta et al. 2019) and the Pristine survey (Starkenburg et al. 2017b; Youakim et al. 2017; Aguado et al. 2019a). Pristine photometry with follow-up Keck II/DEIMOS spectroscopy has also been used to increase sample sizes and improve the chemodynamical studies of faint satellites (Draco II and Sgr II, Longeard et al. 2018, 2019). At the same time, Simon (2018) has shown that Gaia DR2 proper motion cleaning may also be a promising way to find new metal-poor members of ultra-faint dwarf galaxies.
Citation: Frebel et al. 2006
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Thermonuclear (type-I) X-ray bursts are intermittently observed from many neutron star low-mass X-ray binaries (LMXBs; Strohmayer & Bildsten (2006) and references therein). Such a burst originates from an unstable thermonuclear burning of the accreted matter accumulated on the neutron star surface (Joss 1977; Lamb & Lamb 1978; Strohmayer & Bildsten 2006). For most bursts, the observed X-ray intensity rises in ≈0.5–5 s, decays in ∼10–100 s as the neutron star surface cools down after the nuclear burning, and the typical recurrence time is a few hours to days (Galloway et al. 2008). The burst spectrum is traditionally described with a blackbody model, and the best-fit burst blackbody normalization, which can be identified as the burst emission area, usually matches well with the expected surface area of a neutron star (Hoffman et al. 1977; Swank et al. 1977). These motivated an effort to measure the neutron star radius using the burst continuum spectrum, where the normalization of the burst blackbody is expected to be proportional to the square of the stellar radius (e.g., van Paradijs 1978; Goldman 1979; van Paradijs 1979; van Paradijs & Lewin 1986). Note that such a radius measurement is extremely important to probe the superdense and degenerate core matter of neutron stars, which is a fundamental problem of physics (e.g., Lattimer & Prakash 2007; Bhattacharyya et al. 2017). However, a reliable radius measurement using this method has so far not been possible due to a number of systematic uncertainties, which include (1) burst emission from and the visibility of an unknown fraction of the neutron star surface and (2) plausible deviation of the burst spectrum from a blackbody, etc. (Bhattacharyya 2010; Bhattacharyya et al. 2010; Kajava et al. 2017a). Nevertheless, the use of continuum burst spectrum remains a promising method to measure the neutron star radius for the following reasons: (1) neutron star LMXBs provide many complementary methods to measure neutron star parameters, the joint application of which has a potential to significantly reduce the systematics (Bhattacharyya 2010) and (2) it was generally believed that the much more intense burst emission could be reliably distinguished from the persistent (i.e., non-burst) emission during the burst.
Citation: van Paradijs 1978
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