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Galaxies like the Milky Way are surrounded by complex populations of satellites at all stages of tidal disruption. In this paper, we present a dynamical study of the disrupting satellite galaxies in the Auriga simulations that are orbiting 28 distinct Milky Way-mass hosts across three resolutions. We find that the satellite galaxy populations are highly disrupted. The majority of satellites that remain fully intact at present day were accreted recently without experiencing more than one pericentre ($n_{\rm peri} \lesssim 1$) and have large apocentres ($r_{\rm apo} \gtrsim 200$ kpc) and pericentres ($r_{\rm peri} \gtrsim 50$ kpc). The remaining satellites have experienced significant tidal disruption and, given full knowledge of the system, would be classified as stellar streams. We find stellar streams in Auriga across the range of pericentres and apocentres of the known Milky Way dwarf galaxy streams and, interestingly, overlapping significantly with the Milky Way intact satellite population. We find no significant change in satellite orbital distributions across resolution. However, we do see substantial halo-to-halo variance of $(r_\text{peri}, r_\text{apo})$ distributions across host galaxies, as well as a dependence of satellite orbits on host halo mass - systems disrupt at larger pericentres and apocentres in more massive hosts. Our results suggest that either cosmological simulations (including, but not limited to, Auriga) are disrupting satellites far too readily, or that the Milky Way's satellites are more disrupted than current imaging surveys have revealed. Future observing facilities and careful mock observations of these systems will be key to revealing the nature of this apparent discrepancy., Comment: 16 pages, 10 figures, 1 table, submitted to MNRAS

$\Lambda$CDM cosmology predicts the hierarchical formation of galaxies which build up mass by merger events and accreting smaller systems. The stellar halo of the Milky Way has proven to be useful a tool for tracing this accretion history. However, most of this work has focused on the outer halo where dynamical times are large and the dynamical properties of accreted systems are preserved. In this work, we investigate the inner galaxy regime, where dynamical times are relatively small and systems are generally completely phase-mixed. Using the FIRE-2 and Auriga cosmological zoom-in simulation suites of Milky Way-mass galaxies, we find the stellar density profiles along the minor axis (perpendicular to the galactic disk) within the NFW scale radii (R$\approx$15 kpc) are best described as an exponential disk with scale height <0.3 kpc and a power law component with slope $\alpha\approx$-4. The stellar density amplitude and slope for the power law component is not significantly correlated with metrics of the galaxy's accretion history. Instead, we find the stellar profiles strongly correlate with the dark matter profile. Across simulation suites, the galaxies studied in this work have a stellar to dark matter mass ratio that decreases as $1/r^2$ along the minor axis., Comment: 29 pages, 13 figures, 1 table, Submitted to ApJ, comments welcome!

We construct time-evolving gravitational potential models for a Milky Way-mass galaxy from the FIRE-2 suite of cosmological-baryonic simulations using basis function expansions. These models capture the angular variation with spherical harmonics for the halo and azimuthal harmonics for the disk, and the radial or meridional plane variation with splines. We fit low-order expansions (4 angular/harmonic terms) to the galaxy's potential for each snapshot, spaced roughly 25 Myr apart, over the last 4 Gyr of its evolution, then extract the forces at discrete times and interpolate them between adjacent snapshots for forward orbit integration. Our method reconstructs the forces felt by simulation particles with high fidelity, with 95% of both stars and dark matter, outside of self-gravitating subhalos, exhibiting errors $\leq4\%$ in both the disk and the halo. Imposing symmetry on the model systematically increases these errors, particularly for disk particles, which show greater sensitivity to imposed symmetries. The majority of orbits recovered using the models exhibit positional errors $\leq10\%$ for 2-3 orbital periods, with higher errors for orbits that spend more time near the galactic center. Approximate integrals of motion are retrieved with high accuracy even with a larger potential sampling interval of 200 Myr. After 4 Gyr of integration, 43% and 70% of orbits have total energy and angular momentum errors within 10%, respectively. Consequently, there is higher reliability in orbital shape parameters such as pericenters and apocenters, with errors $\sim10\%$ even after multiple orbital periods. These techniques have diverse applications, including studying satellite disruption in cosmological contexts., Comment: 28 pages, 13 figures, and 4 tables. Submitted to APJ

Measurements of the accelerations of stars enabled by time-series extreme-precision spectroscopic observations, from pulsar timing, and from eclipsing binary stars in the Solar Neighborhood offer insights into the mass distribution of the Milky Way that do not rely on traditional equilibrium modeling. Given the measured accelerations, we can determine a total mass density, and from this, by accounting for the mass in stars, gas, and dust, we can infer the amount of dark matter. Leveraging the FIRE-2 simulations of Milky Way-mass galaxies, we compare vertical acceleration profiles between cold dark matter (CDM) and self-interacting dark matter (SIDM) with constant cross-section of 1 cm$^2$ g$^{-1}$ across three halos with diverse assembly histories. Notably, significant asymmetries in vertical acceleration profiles near the midplane at fixed radii are observed in both CDM and SIDM, particularly in halos recently affected by mergers with satellites of Sagittarius/SMC-like masses or greater. These asymmetries offer a unique window into exploring the merger history of a galaxy. We show that SIDM halos consistently exhibit higher local stellar and dark matter densities and steeper vertical acceleration gradients, up to 30% steeper near the Solar Neighborhood. SIDM halos also manifest a more oblate halo shape in the Solar Neighborhood. Furthermore, enhanced precision in acceleration measurements and larger datasets promise to provide better constraints on the local dark matter density, complementing our understanding from kinematic analysis of their distribution within galaxies., Comment: 14 pages, 5 figures, and 2 tables. Submitted to APJ

Understanding the physical mechanism behind the formation of a co-rotating thin plane of satellite galaxies, like the one observed around the Milky Way (MW), has been challenging. The perturbations induced by a massive satellite galaxy, like the Large Magellanic Cloud (LMC) provide valuable insight into this problem. The LMC induces an apparent co-rotating motion in the outer halo by displacing the inner regions of the halo with respect to the outer halo. Using the Latte suite of FIRE-2 cosmological simulations of MW-mass galaxies, we confirm that the apparent motion of the outer halo induced by the infall of a massive satellite changes the observed distribution of orbital poles of outer-halo tracers, including satellites. We quantify the changes in the distribution of orbital poles using the two-point angular correlation function and find that all satellites induce changes. However, the most massive satellites with pericentric passages between 30-100kpc induce the largest changes. The best LMC-like satellite analog shows the largest change in orbital pole distribution. The dispersion of orbital poles decreases by 20{\deg} during the first two pericentric passages. Even when excluding the satellites brought in with the LMC-like satellite, there is clustering of orbital poles. These results suggest that in the MW, the recent pericentric passage of the LMC should have changed the observed distribution of orbital poles of all other satellites. Therefore, studies of kinematically-coherent planes of satellites that seek to place the MW in a cosmological context should account for the existence of a massive satellite like the LMC., Comment: 20 pages, 10 figures. ApJ submitted, Comments are welcome

The Milky Way's (MW) inner stellar halo contains an [Fe/H]-rich component with highly eccentric orbits, often referred to as the "last major merger." Hypotheses for the origin of this component include Gaia-Sausage/Enceladus (GSE), where the progenitor collided with the MW proto-disk 8-11 Gyr ago, and the Virgo Radial Merger (VRM), where the progenitor collided with the MW disk within the last 3 Gyr. These two scenarios make different predictions about observable structure in local phase space, because the morphology of debris depends on how long it has had to phase mix. The recently-identified phase-space folds in Gaia DR3 have positive caustic velocities, making them fundamentally different than the phase-mixed chevrons found in simulations at late times. Roughly 20\% of the stars in the prograde local stellar halo are associated with the observed caustics. Based on a simple phase-mixing model, the observed number of caustics are consistent with a merger that occurred 1--2 Gyr ago. We also compare the observed phase-space distribution to FIRE-2 Latte simulations of GSE-like mergers, using a quantitative measurement of phase mixing (2D causticality). The observed local phase-space distribution best matches the simulated data 1--2 Gyr after collision, and certainly not later than 3 Gyr. This is further evidence that the progenitor of the "last major merger" did not collide with the MW proto-disk at early times, as is thought for the GSE, but instead collided with the MW disk within the last few Gyr, consistent with the body of work surrounding the VRM.

The physical mechanisms responsible for bar formation and destruction in galaxies remain a subject of debate. While we have gained valuable insight into how bars form and evolve from isolated idealized simulations, in the cosmological domain, galactic bars evolve in complex environments with mergers, gas accretion events, in presence of turbulent Inter Stellar Medium (ISM) with multiple star formation episodes, in addition to coupling to their host galaxies' dark matter halos. We investigate bar formation in 13 Milky Way-mass galaxies from the FIRE-2 (Feedback in Realistic Environments) cosmological zoom-in simulations. 8 of the 13 simulated galaxies form bars at some point during their history: three from tidal interactions and five from internal evolution of the disk. The bars in FIRE-2 are generally shorter than the corotation radius (mean bar radius $\sim 1.53$ kpc), have a wide range of pattern speeds (36--97 km s$^{-1}$kpc$^{-1}$), and live for a wide range of dynamical times (2--160 bar rotations). We find that bar formation in FIRE-2 galaxies is influenced by satellite interactions and the stellar-to-dark matter mass ratio in the inner galaxy, but neither is a sufficient condition for bar formation. Bar formation is more likely to occur, and the bars formed are stronger and longer-lived, if the disks are kinematically cold; galaxies with high central gas fractions and/or vigorous star formation, on the other hand, tend to form weaker bars. In the case of the FIRE-2 galaxies these properties combine to produce ellipsoidal bars with strengths $A_2/A_0 \sim$ 0.1--0.2., Comment: 39 pages (including Appendix), 25 figures, accepted in The Astrophysical Journal

Dark Matter (DM) subhalos are predicted to perturb stellar streams; stream morphologies and dynamics can constrain the mass distribution of subhalos. Using FIRE-2 simulations of Milky Way-mass galaxies, we show that presence of a Large Magellanic Cloud (LMC)--analog significantly changes stream-subhalo encounter rates. Three key factors drive these changes. First, the LMC--analog brings in many subhalos, increasing encounter rates for streams near the massive satellite by up to 20--40%. Second, the LMC--analog displaces the host from its center-of-mass (inducing reflex motion), causing a north-south asymmetry in the density and radial velocity distribution of subhalos. This asymmetry results in encounter rates varying by 50--70% across the sky at the same distance. Finally, the LMC--mass satellite induces a density wake in the host's DM halo, further boosting the encounter rates near the LMC--analog. We also explore the influence of stream orbital properties, finding a 50% increase in encounters for streams moving retrograde to the LMC--analog's orbit in the opposite hemisphere. The dependence of encounter rates on stream location and orbit has important implications for where to search for new streams with spurs and gaps in the Milky Way., Comment: 28 pages, 17 figures, 3 tables, Accepted in APJ

Observational studies are finding stars believed to be relics of the earliest stages of hierarchical mass assembly of the Milky Way (i.e., proto-Galaxy). In this work, we contextualize these findings by studying the masses, ages, spatial distributions, morphology, kinematics, and chemical compositions of proto-galaxy populations from the 13 Milky Way (MW)-mass galaxies from the FIRE-2 cosmological zoom-in simulations. Our findings indicate that proto-Milky Way populations: i) can have a stellar mass range between $1\times10^{8}<\mathrm{M}_{\star}<2\times10^{10}[\mathrm{M}_{\odot}]$, a virial mass range between $3\times10^{10}<\mathrm{M}_{\star}<6\times10^{11}[\mathrm{M}_{\odot}]$, and be as young as $8 \lesssim \mathrm{Age} \lesssim 12.8$ [Gyr] ($1\lesssim z \lesssim 6$); ii) are predominantly centrally concentrated, with $\sim50\%$ of the stars contained within $5-10$ kpc; iii) on average show weak but systematic net rotation in the plane of the host's disc at $z=0$ (i.e., $0.25\lesssim\langle\kappa/\kappa_{\mathrm{disc}}\rangle\lesssim0.8$); iv) present [$\alpha$/Fe]-[Fe/H] compositions that overlap with the metal-poor tail of the host's old disc; v) tend to assemble slightly earlier in Local Group-like environments than in systems in isolation. Interestingly, we find that ~60% of the proto-Milky Way galaxies are comprised by 1 dominant system ($1/5\lesssim$M$_{\star}$/M$_{\star,\mathrm{proto-Milky Way}}$$\lesssim4/5$) and 4-5 lower mass systems (M$_{\star}$/M$_{\star,\mathrm{proto-Milky Way}}$$\lesssim1/10$); the other ~40% are comprised by 2 dominant systems and 3-4 lower mass systems. These massive/dominant proto-Milky Way fragments can be distinguished from the lower mass ones in chemical-kinematic samples, but appear (qualitatively) indistinguishable from one another. Our results could help observational studies disentangle if the Milky Way formed from one or two dominant systems., Comment: Accepted in MNRAS. 16 pages, 12 figures and 3 tables

A variety of observational campaigns seek to test dark-matter models by measuring dark-matter subhaloes at low masses. Despite their predicted lack of stars, these subhaloes may be detectable through gravitational lensing or via their gravitational perturbations on stellar streams. To set measurable expectations for subhalo populations within LambdaCDM, we examine 11 Milky Way (MW)-mass haloes from the FIRE-2 baryonic simulations, quantifying the counts and orbital fluxes for subhaloes with properties relevant to stellar stream interactions: masses down to 10^6 Msun, distances < 50 kpc of the galactic center, across z = 0 - 1 (lookback time 0 - 8 Gyr). We provide fits to our results and their dependence on subhalo mass, distance, and lookback time, for use in (semi)analytic models. A typical MW-mass halo contains ~16 subhaloes >10^7 Msun (~1 subhalo >10^8 Msun) within 50 kpc at z = 0. We compare our results with dark-matter-only versions of the same simulations: because they lack a central galaxy potential, they overpredict subhalo counts by 2-10x, more so at smaller distances. Subhalo counts around a given MW-mass galaxy declined over time, being ~10x higher at z = 1 than at z = 0. Subhaloes have nearly isotropic orbital velocity distributions at z = 0. Across our simulations, we also identified 4 analogs of Large Magellanic Cloud satellite passages; these analogs enhance subhalo counts by 1.4-2.7 times, significantly increasing the expected subhalo population around the MW today. Our results imply an interaction rate of ~5 per Gyr for a stream like GD-1, sufficient to make subhalo-stream interactions a promising method of measuring dark subhaloes., Comment: 14 pages, Published in MNRAS

We argue that the layer electric polarization of noncentrosymmetric layered heterostructures can be generically controlled by light yielding a layer photovoltaic effect (LPE). The LPE possesses a rich phenomenology and can arise from myriad distinct mechanisms displaying strong sensitivity to symmetry (e.g., point group and time-reversal) as well as the presence/absence of a Fermi surface. We systematically classify these and unveil how LPE manifests for a range of light polarizations and even for unpolarized light. These unusual layer photoresponses can be realized in a range of layered heterostructures such as bilayer graphene aligned on hexagonal Boron Nitride and manifest sizeable layer polarization susceptibilities in the terahertz frequency range that can be used as novel means of bulk photodetection., Comment: 8 pages, 2 figures

The shape and orientation of dark matter (DM) halos are sensitive to the micro-physics of the DM particle, yet in many mass models, the symmetry axes of the Milky Way's DM halo are often assumed to be aligned with the symmetry axes of the stellar disk. This is well-motivated for the inner DM halo but not for the outer halo. We use zoomed cosmological-baryonic simulations from the Latte suite of FIRE-2 Milky Way-mass galaxies to explore the evolution of the DM halo's orientation with radius and time, with or without a major merger with a Large Magellanic Cloud (LMC) analog, and when varying the DM model. In three of the four CDM halos we examine, the orientation of the halo minor axis diverges from the stellar disk vector by more than 20 degrees beyond about 30 galactocentric kpc, reaching a maximum of 30--90 degrees depending on the individual halo's formation history. In identical simulations using a model of self-interacting DM with $\sigma = 1 \, \mathrm{cm}^2 \, \mathrm{g}^{-1}$, the halo remains aligned with the stellar disk out to $\sim$200--400 kpc. Interactions with massive satellites ($M \gtrsim 4 \times 10^{10} \, \rm{M_\odot}$ at pericenter; $M \gtrsim 3.3 \times 10^{10} \, \rm{M_\odot}$ at infall) affect the orientation of the halo significantly, aligning the halo's major axis with the satellite galaxy from the disk to the virial radius. The relative orientation of the halo and disk beyond 30 kpc is a potential diagnostic of SIDM if the effects of massive satellites can be accounted for., Comment: Submitted to ApJ, 19 pages, 12 figures, 3 tables

In the $\Lambda$-Cold Dark Matter model of the Universe, galaxies form in part through accreting satellite systems. Previous work have built an understanding of the signatures of these processes contained within galactic stellar halos. This work revisits that picture using seven Milky Way-like galaxies in the \textit{Latte} suite of FIRE-2 cosmological simulations. The resolution of these simulations allows a comparison of contributions from satellites above M$_{*}$$\gtrsim$10$\times$$^{7}$M$_{\odot}$, enabling the analysis of observable properties for disrupted satellites in a fully self-consistent and cosmological context. Our results show that, the time of accretion and the stellar mass of an accreted satellite are fundamental parameters that in partnership dictate the resulting spatial distribution, orbital energy, and [$\alpha$/Fe]-[Fe/H] compositions of the stellar debris of such mergers $at$ $present$ $day$. These parameters also govern the resulting dynamical state of an accreted galaxy at $z=0$, leading to the expectation that the inner regions of the stellar halo (R$_{\mathrm{GC}}$ $\lesssim$30 kpc) should contain fully phase-mixed debris from both lower and higher mass satellites. In addition, we find that a significant fraction of the lower mass satellites accreted at early times deposit debris in the outer halo (R$_{\mathrm{GC}}$ $>$50 kpc) that are $not$ fully phased-mixed, indicating that they could be identified in kinematic surveys. Our results suggest that, as future surveys become increasingly able to map the outer halo of our Galaxy, they may reveal the remnants of long-dead dwarf galaxies whose counterparts are too faint to be seen $in$ $situ$ in higher redshift surveys., Comment: Submitted for publication in ApJ

Recent studies have suggested that the Milky Way (MW)'s Dark Matter (DM) halo may be significantly tilted with respect to its central stellar disk, a feature that might be linked to its formation history. In this work, we demonstrate a method of constraining the orientation of the minor axis of the DM halo using the angle and frequency variables. This method is complementary to other traditional techniques, such as orbit fitting. We first test the method using a simulated tidal stream evolving in a realistic environment inside an MW-mass host from the FIRE cosmological simulation, showing that the theoretical description of a stream in the action-angle-frequency formalism still holds for a realistic dwarf galaxy stream in a cosmological potential. Utilizing the slopes of the line in angle and frequency space, we show that the correct rotation frame yields a minimal slope difference, allowing us to put a constraint on the minor axis location. Finally, we apply this method to the Sagittarius stream's leading arm. We report that the MW's DM halo is oblate with the flattening parameter in the potential $q\sim0.7-0.9$ and the minor axis pointing toward $(\ell,b) = (42^{o},48^{o})$. Our constraint on the minor axis location is weak and disagrees with the estimates from other works; we argue that the inconsistency can be attributed in part to the observational uncertainties and in part to the influence of the Large Magellanic Cloud., Comment: 16 pages, 12 figures

Berry curvature and skew-scattering play central roles in determining both the linear and nonlinear anomalous Hall effects. Yet in {\it PT}-symmetric antiferromagnetic metals, Hall effects from either intrinsic Berry curvature mediated anomalous velocity or the conventional skew-scattering process individually vanish. Here we reveal an unexpected nonlinear Hall effect that relies on both Berry curvature and skew-scattering working in cooperation. This anomalous skew-scattering nonlinear Hall effect (ASN) is {\it PT}-even and dominates the low-frequency nonlinear Hall effect for {\it PT}-symmetric antiferromagnetic metals. Surprisingly, we find that in addition to its Hall response, ASN produces helicity dependent photocurrents, in contrast to other known {\it PT}-even nonlinearities in metals which are helicity blind. This characteristic enables to isolate ASN and establishes new photocurrent tools to interrogate the antiferromagnetic order of {\it PT}-symmetric metals.

In the Gaia era it is increasingly apparent that traditional static, parameterized models are insufficient to describe the mass distribution of our complex, dynamically evolving Milky Way (MW). In this work, we compare different time-evolving and time-independent representations of the gravitational potentials of simulated MW-mass galaxies from the FIRE-2 suite of cosmological baryonic simulations. Using these potentials, we calculate actions for star particles in tidal streams around three galaxies with varying merger histories at each snapshot from 7 Gyr ago to the present day. We determine the action-space coherence preserved by each model using the Kullback-Leibler Divergence to gauge the degree of clustering in actions and the relative stability of the clusters over time. We find that all models produce a clustered action space for simulations with no significant mergers. However, a massive (mass ratio prior to infall more similar than 1:8) interacting galaxy not present in the model will result in mischaracterized orbits for stars most affected by the interaction. The locations of the action space clusters (i.e. the orbits of the stream stars) are only preserved by the time-evolving model, while the time-independent models can lose significant amounts of information as soon as 0.5--1 Gyr ago, even if the system does not undergo a significant merger. Our results imply that reverse-integration of stream orbits in the MW using a fixed potential is likely to give incorrect results if integrated longer than 0.5 Gyr into the past.

The optical responses of metals are often dominated by plasmonic resonances - the collective oscillations of interacting electron liquids. Here we unveil a new class of plasmons - quantum metric plasmons (QMPs) - that arise in a wide range of parity violating magnetic metals. In these materials, a dipolar distribution of the quantum metric (a fundamental characteristic of Bloch wavefunctions) produces intrinsic non-reciprocal bulk plasmons. Strikingly, QMP non-reciprocity manifests even when the single-particle dispersion is symmetric: QMPs are sensitive to time-reversal and parity violations hidden in the Bloch wavefunction. In materials with asymmetric single-particle dispersions, quantum metric dipole induced non-reciprocity can continue to dominate at large frequencies. We anticipate that QMPs can be realized in a wide range of parity violating magnets, including twisted bilayer graphene heterostructures, where quantum geometric quantities can achieve large values.

We describe a public data release of the FIRE-2 cosmological zoom-in simulations of galaxy formation, available at http://flathub.flatironinstitute.org/fire, from the Feedback In Realistic Environments (FIRE) project. FIRE-2 simulations achieve parsec-scale resolution to explicitly model the multi-phase interstellar medium while implementing direct models for stellar evolution and feedback, including stellar winds, core-collapse and Ia supernovae, radiation pressure, photoionization, and photoelectric heating. We release complete snapshots from 3 suites of simulations. The first comprises 20 simulations that zoom in on 14 Milky Way-mass galaxies, 5 SMC/LMC-mass galaxies, and 4 lower-mass galaxies including 1 ultra-faint; we release 39 snapshots across z = 0 - 10. The second comprises 4 massive galaxies, with 19 snapshots across z = 1 - 10. Finally, a high-redshift suite comprises 22 simulations, with 11 snapshots across z = 5 - 10. Each simulation also includes dozens of resolved lower-mass (satellite) galaxies in its zoom-in region. Snapshots include all stored properties for all dark matter, gas, and star particles, including 11 elemental abundances for stars and gas, and formation times (ages) of star particles. We also release accompanying (sub)halo catalogs, which include galaxy properties and member star particles. For the simulations to z = 0, including all Milky Way-mass galaxies, we release the formation coordinates and an "ex-situ" flag for all star particles, pointers to track particles across snapshots, catalogs of stellar streams, and multipole basis expansions for the halo mass distributions. We describe publicly available python packages for reading and analyzing these simulations., Comment: 22 pages. Accepted for publication in ApJS, matches the published version, with updated references. Now includes up to 39 snapshots per simulation and formation coordinates for all star particles. Data available at http://flathub.flatironinstitute.org/fire

The electronic wavefunctions in moir\'e materials are highly sensitive to the details of the local atomic configuration enabling Bloch band geometry and topology to be controlled by stacking and strain. Here we predict that large injection currents (under circular polarized irradiation) can develop in strained twisted bilayer graphene (TBG) heterostructures with broken sublattice symmetry; such bulk photovoltaic currents flow even in the absence of a p-n junction and can be controlled by the helicity of incident light. As we argue, large injection current rates proceed from strong and highly peaked interband Berry curvature dipole distributions (arising from the texturing of Bloch wavefunctions in strained TBG heterostructures). Strikingly, we find that TBG injection current displays pronounced responses in the THz regime and can be tuned by chemical potential. These render injection currents a useful photocurrent probe of symmetry breaking in TBG heterostructures and make TBG a promising material for THz technology.

We argue that edge electrons in monolayer WTe$_2$ can possess a "cooperative" orbital moment (COM) that critically impacts its edge magnetoresistance behavior. Arising from the cooperative action of both Rashba and Ising spin orbit coupling, COM quickly achieves large magnitudes (of order few Bohr magnetons) even for relatively small spin-orbit coupling strengths. As we explain, such large COM magnitudes arise from an unconventional cooperative spin canting of edge spins when Rashba and Ising spin orbit coupling act together. Strikingly, COM can compete with spin moments to produce an unusual anisotropic edge magnetoresistance oriented at an oblique angle. In particular, this competition produces a direction along which $\mathbf{B}$ is ineffective at gapping out the edge spectrum leaving it nearly gapless. As a result, large contrasts in gap sizes manifest as $\mathbf{B}$ is rotated granting giant anisotropic magnetoresistance of 0.1-10 million % at 10 T and low temperature.

It has been known for nearly 20 years that the pseudo phase-space density profile of equilibrium simulated dark matter halos, $\rho(r)/\sigma^3(r)$, is well described by a power law over 3 decades in radius, even though both the density $\rho(r)$, and the velocity dispersion $\sigma(r)$ deviate significantly from power laws. The origin of this scale-free behavior is not understood. It could be an inherent property of self-gravitating collisionless systems, or it could be a mere coincidence. To address the question we work with equilibrium halos, and more specifically, the second derivative of the Jeans equation, which, under the assumptions of (i) Einasto density profile, (ii) linear velocity anisotropy - density slope relation, and (iii) $\rho/\sigma^3\propto r^{-\alpha}$, can be transformed from a differential equation to a cubic algebraic equation. Relations (i)-(iii) are all observed in numerical simulations, and are well parametrized by a total of 4 or 6 model parameters. We do not consider dynamical evolution of halos; instead, taking advantage of the fact that the algebraic Jeans equation for equilibrium halos puts relations (i)-(iii) on the same footing, we study the (approximate) solutions of this equation in the 4 and 6 dimensional spaces. We argue that the distribution of best solutions in these parameter spaces is inconsistent with $\rho/\sigma^3\propto r^{-\alpha}$ being an fundamental property of gravitational evolution, and conclude that the scale-free nature of this quantity is likely to be a fluke., Comment: ApJ, Accepted