Radial Anisotropy Research Articles

Magnetic skyrmions in cylindrical ferromagnetic nanostructures with chiral interactions

We study the geometrical conditions for stabilizing magnetic skyrmions in cylindrical nanostrips and nanotubes of ferromagnetic materials with chiral interactions. We obtain the low-temperature equilibrium state of the system implementing a simulation annealing technique for a classical spin Hamiltonian with competing isotropic exchange and chiral interactions, radial anisotropy and an external field. We address the impact of surface curvature on the formation, the shape and the size of magnetic skyrmions. We demonstrate that the evolution of the skyrmion phase with the curvature is controlled by the competition between two characteristic lengths, namely the curvature radius, $R$ (geometrical length) and the skyrmion radius, $R_{sk}$ (physical length). In narrow nanotubes ($R<R_{sk}$) the skyrmion phase evolves to a stripe phase, while in wide nanotubes ($R>R_{sk}$) a mixed skyrmion-stripe phase emerges. Most interestingly, the mixed phase is characterized by spatially separated skyrmions from stripes owing to the direction of the applied field relative to the surface normal. In the stability regime ($R \gtrsim R_{sk}$) skyrmions remain circular and preserve their size as a consequence of their topological protection. Zero-field skyrmions are shown to be stable on curved nanoelements with free boundaries within the same stability region ($R\gtrsim R_{sk}$). The experimental and technological perspectives from the stability of skyrmions on cylindrical surfaces are discussed.

Crustal shear wave velocity and radial anisotropy in the Xiaojiang fault zone system (SE Tibet) revealed by ambient noise interferometry

The Xiaojiang fault zone system (XJFS) is located in the southeastern Tibet with high seismicity. In this study, we invert Rayleigh and Love wave dispersion curves obtained from three dense seismic arrays jointly for high-resolution 3-D crustal average shear wave velocity and radial anisotropy models simultaneously in XJFS. Our model reveals that the upper crust and mid-lower crust generally exhibit negative and positive radial anisotropy, respectively, implying that the deformation pattern is depth-dependent. To the east of the Lvzhijiang Fault, most of the low velocity zones in the mid-crust correspond to the positive radial anisotropy (Vsh > Vsv); the channelized weak zone seems to be continuous across the Red River Fault at depth of 20 km, probably within a thin layer. West of the Lvzhijiang Fault, where it is inferred to be the inner zone of the Permian Emeishan Large Igneous Province, the high velocity zone and positive radial anisotropy in the mid-lower crust can be attributed to the underplating and intruded magmatic rocks. In the upper crust, the high and low velocity zones are mostly belt-shape and follow the north-south direction parallel to the regional major faults; the lateral variation of the radial anisotropy spatially corresponds to the activity of different segments of the Xiaojiang fault zone. Our models depict detailed geometry of the channelized weak zone in the mid-lower crust and provide new insight into the role of major faults in regional tectonics.

Implementing radial anisotropy with self-similar structures

Radial anisotropy in small objects has been linked to exotic optical properties. It can be implemented with a spherical inclusion that manifests self-similarity. We show that, when a self-similar, onion-like structure with alternating layers is homogenized by using an effective material approximation, the homogenized material becomes uniaxially anisotropic with the axis of anisotropy pointed radially outward from the center of the inclusion. This radial anisotropy becomes exact in the limit of a dense set of layers. The exact equivalence of the layered self-similar inclusion and the radially anisotropic inclusion manifests itself both in the effective permittivities of the two inclusions---when homogenized over the entire volumes---and in the internal potentials. Because the layered sphere and the radially anisotropic sphere are analogous, it is possible to study some of the interesting scattering features of radially anisotropic spheres in a realistic configuration. In particular, we show that the outcome of homogenizing the self-similar inclusion, and consequently the electric response, depends on what the core material at the center of the inclusion is and that a continuous transition between the two homogenization models is possible. The findings suggest intriguing applications in nanophotonics.

Subduction of the Indian Plate and the Nature of the Crust Beneath Western Tibet: Insights From Seismic Imaging

AbstractThe northward extent of subducted Indian plate is a fundamental component of hypotheses explaining deformation and magmatism within the Tibetan Plateau. Yet, these aspects of the plate are debated in west Tibet. Here we report a new three‐dimensional lithospheric structure of seismic velocity and radial anisotropy under west Tibet constructed from Rayleigh and Love wave phase velocity maps at periods of 20–167 and 20–125 s, respectively. Our results show the Indian lithospheric mantle to be subhorizontally subducted under west Tibet across the Bangong‐Nujiang suture to the Qiangtang terrane, as indicated by a prominent fast velocity anomaly accompanied with positive radial anisotropy (Vsh &gt; Vsv). We find a positive spatial correlation of this result with information on the distribution of late Cenozoic potassic‐adakitic rocks in western Tibet. Additionally, we show that the midcrust of west Tibet is characterized by an anomalously low shear wave velocity (3.2–3.4 km/s at ~30‐km depth) and positive anisotropy, which is consistent with an estimated ~3% fraction of partial melt. We suggest that the midcrust of this region is capable of flowing and that its three‐dimensional structure shows it to extend south of the Karakoram fault (KKF), a shear zone interpreted as a barrier to crustal flow. Instead, our results are consistent with the KKF embedded in weak middle crust along with several other structures that display a pattern of distributed deformation in the western portion of the Tibetan Plateau.

Study on anisotropic stars in the framework of Rastall gravity

We investigate the existence of high dense compact objects in the light of Rastall gravity theory. The material content is driven by an imperfect fluid distribution and the inner geometry is described by the Tolman–Kuchowicz space–time. The validity of the obtained model is checked by studying the main salient features such as energy–density, radial and tangential pressures and anisotropy factor. Since Einstein gravity theory shares the same vacuum solution with Rastall gravity theory, the interior geometry is joining in a smoothly way with the exterior Schwarzschild’s solution. The equilibrium of the model under different gradients is analyzed by using the modified hydrostatic equilibrium equation, containing the so–called Rastall gradient. The compact structure has a positive anisotropy factor which enhances the balance and stability mechanisms. To check the potentially stable behavior, we employ Abreu’s and adiabatic index criterion. It was found that the model is completely stable. The incidence of the Rastall’s parameter $\gamma $ on all the physical quantities that characterize the model is described by the help of graphical analysis. Concerning the $\gamma $ spectrum we have considered $0.3142\leq \gamma \leq 0.3157$ . All the results are compared with the general relativity case.

Interaction of the Indian and Asian Plates Under the Pamir and Hindu‐Kush Regions: Insights From 3‐D Shear Wave Velocity and Anisotropic Structures

AbstractThe Pamir‐Hindu‐Kush region is widely cited as a best place to study opposing continental subduction on Earth. Yet, subducting slab morphology of the Indian and Asian plates under this region remains elusive. Here we report new shear wave velocity and radial anisotropy models from Rayleigh and Love wave tomography to constrain the geometry of these two slabs. Together with previous tomographic studies, we show that the Indian slab exhibits along‐strike variation with subhorizontally underthrusting into the Pamir and high‐angle subduction under the Hindu‐Kush. We speculate that the Indian slab was probably detached and sank into the mantle transition zone under the Pamir, while break‐off process is ongoing under the Hindu‐Kush. The Asian lithospheric mantle and lower crust are inferred to be subducting southward into the North Pamir. Two opposing subducting slabs could have interacted under the Pamir, resulting in thickening crust, horizontally stretched midcrustal flow, and horizontal mantle flow. These dynamic processes could explain surface geologic observations and potentially constrain the causes of intermediate‐depth seismicity.

Linking Magma Storage and Ascent to Eruption Volume and Composition at an Arc Caldera

AbstractConceptual models of magma storage and transport under calderas favor a connected system of sills and dikes. These features are individually below the resolution of standard seismic tomography, but radial seismic anisotropy can reveal where they exist in aggregate. We model radial anisotropy at Okmok caldera, Alaska, to demonstrate the presence of a caldera‐centered stacked sill complex and surrounding dike system. We show that ascending magma, inferred from seismicity, either intersects the sill complex, resulting in a larger volume eruption of evolved magma, or bypasses the overlying sill complex via dikes, resulting in a low‐volume mafic eruption. Our results exemplify how the locations of magma storage and paths of transport impact eruption size and composition. As this type of crustal storage is likely common to many calderas, this analysis offers a potential new framework for volcano observatories to forecast the size of impending eruptions.

Mesoscale diffusion magnetic resonance imaging of the ex vivo human hippocampus.

Mesoscale diffusion magnetic resonance imaging (MRI) endeavors to bridge the gap between macroscopic white matter tractography and microscopic studies investigating the cytoarchitecture of human brain tissue. To ensure a robust measurement of diffusion at the mesoscale, acquisition parameters were arrayed to investigate their effects on scalar indices (mean, radial, axial diffusivity, and fractional anisotropy) and streamlines (i.e., graphical representation of axonal tracts) in hippocampal layers. A mesoscale resolution afforded segementation of the pyramidal cell layer (CA1‐4), the dentate gyrus, as well as stratum moleculare, radiatum, and oriens. Using ex vivo samples, surgically excised from patients with intractable epilepsy (n = 3), we found that shorter diffusion times (23.7 ms) with a b‐value of 4,000 s/mm2 were advantageous at the mesoscale, providing a compromise between mean diffusivity and fractional anisotropy measurements. Spatial resolution and sample orientation exerted a major effect on tractography, whereas the number of diffusion gradient encoding directions minimally affected scalar indices and streamline density. A sample temperature of 15°C provided a compromise between increasing signal‐to‐noise ratio and increasing the diffusion properties of the tissue. Optimization of the acquisition afforded a system's view of intra‐ and extra‐hippocampal connections. Tractography reflected histological boundaries of hippocampal layers. Individual layer connectivity was visualized, as well as streamlines emanating from individual sub‐fields. The perforant path, subiculum and angular bundle demonstrated extra‐hippocampal connections. Histology of the samples confirmed individual cell layers corresponding to ROIs defined on MR images. We anticipate that this ex vivo mesoscale imaging will yield novel insights into human hippocampal connectivity.

A detailed Monte Carlo evaluation of 192Ir dose enhancement for gold nanoparticles and comparison with experimentally measured dose enhancements

Gold nanoparticles (GNPs) have been studied extensively as promising radiation dose enhancing agents. In the current study, the dose enhancement effect of GNPs for Ir-192 HDR brachytherapy is studied using Monte Carlo N-Particle code, version 6.2 (MCNP6.2) and compared with experimental results obtained using Burlin cavity theory formalism. The Ir-192 source is verified using TG-43 parameters and dose enhancement factors (DEFs) from GNPs are simulated for three different mass percentages of gold in the GNP solution. These results are compared to DEFs previously reported experimentally by our group (Bassiri et al Med. Phys.) for a GNP-containing volume in an apparatus designed in-house to measure dose enhancement with GNPs for high dose rate (HDR) Ir-192 brachytherapy. An HDR Ir-192 Microselectron v2 r HDR brachytherapy source was modeled using MCNP6.2 using the TG-43 formalism in water. Anisotropy and radial dose function were verified against known values. An apparatus designed to measure dose enhancement to a 0.75 cm3 volume of GNPs from an Ir-192 brachytherapy seed with average energy of 0.38 MeV was built in-house and modeled using MCNP6.2. Burlin cavity correction factors were applied to experimental measurements. The macroscopic DEF was calculated for GNPs of size 30 nm at mass percentages of gold of 0.28%, 0.56% and 0.77%, using the repeating structures capability of MCNP6.2. DEF was calculated by dividing dose to the GNP solution by dose to water in the same volume. The radial dose function and anisotropy factor values at varying angles and distances were accurate when compared against known values. DEFs of 1.018 ± 0.003, 1.031 ± 0.003, and 1.041 ± 0.003 for GNP solutions containing mass percent of gold of 0.28%, 0.56% and 0.77%, respectively, were computed. These DEFs were within 2% of experimental values with Burlin cavity correction factors applied for all three mass percentages of gold.

A Middle Crustal Channel of Radial Anisotropy Beneath the Northeastern Basin and Range

AbstractA challenge in interpreting the origins of seismic anisotropy in deformed continental crust is that composition and rheology vary with depth. We investigated anisotropy in the northeastern Basin and Range where prior studies found prevalent depth‐averaged positive radial anisotropy (VSH &gt; VSV). This study focuses on depth‐dependence of anisotropy and potentially distinct structures beneath three metamorphic core complexes (MCCs). Rayleigh and Love wave dispersion were measured using ambient noise interferometry, and Bayesian Markov chain Monte Carlo inversions for VS structure were tested with several (an)isotropic parameterizations. Acceptable data fits with minimal introduction of anisotropy are achieved by models with anisotropy concentrated in the middle crust. The peak magnitude of anisotropy from the mean of the posterior distributions ranges from 3.5–5% and is concentrated at 8–20 km depth. Synthetic tests with one uniform layer of anisotropy best reproduce the regional mean results with 9% anisotropy at 6–22 km depth. Both magnitudes are plausible based on exhumed middle crustal rocks. The three MCCs exhibit ~5% higher isotropic upper crustal VS, likely due to their anomalous levels of exhumation, but no distinctive (an)isotropic structures at deeper depths. Regionally pervasive middle crustal positive radial anisotropy is interpreted as a result of subhorizontal foliation of mica‐bearing rocks deformed near the top of the ductile deformation regime. Decreasing mica content with depth and more broadly distributed deformation at lower stress levels may explain diminished lower crustal anisotropy. Absence of distinctive deep crustal VS beneath the MCCs suggests overprinting by ductile deformation since the middle Miocene.

Orientation anisotropy of quantitative MRI parameters in degenerated human articular cartilage.

Quantitative magnetic resonance (MR) relaxation parameters demonstrate varying sensitivity to the orientation of the ordered tissues in the magnetic field. In this study, the orientation dependence of multiple relaxation parameters was assessed in cadaveric human cartilage with varying degree of natural degeneration, and compared with biomechanical testing, histological scoring, and quantitative histology. Twelve patellar cartilage samples were imaged at 9.4 T MRI with multiple relaxation parameters, including T1 , T2 , CW - T1ρ , and adiabatic T1ρ , at three different orientations with respect to the main magnetic field. Anisotropy of the relaxation parameters was quantified, and the results were compared with the reference measurements and between samples of different histological Osteoarthritis Research Society International (OARSI) grades. T2 and CW - T1ρ at 400 Hz spin-lock demonstrated the clearest anisotropy patterns. Radial zone anisotropy for T2 was significantly higher for samples with OARSI grade 2 than for grade 4. The proteoglycan content (measured as optical density) correlated with the radial zone MRI orientation anisotropy for T2 (r = 0.818) and CW - T1ρ with 400 Hz spin-lock (r = 0.650). Orientation anisotropy of MRI parameters altered with progressing cartilage degeneration. This is associated with differences in the integrity of the collagen fiber network, but it also seems to be related to the proteoglycan content of the cartilage. Samples with advanced OA had great variation in all biomechanical and histological properties and exhibited more variation in MRI orientation anisotropy than the less degenerated samples. Understanding the background of relaxation anisotropy on a molecular level would help to develop new MRI contrasts and improve the application of previously established quantitative relaxation contrasts.

Crustal Deformations of the Central North China Craton Constrained by Radial Anisotropy

AbstractSituated in a transition zone between the western and eastern North China Craton (NCC), the central NCC exhibits complex dynamics features. Significant lithosphere thinning is observed beneath the eastern NCC and the northern segment of the central NCC. To study how the crust responses to the distinct lateral variations of the lithospheric mantle, we develop a method for joint inversion of Rayleigh and Love dispersion curves based on a transverse‐isotropic (or radial anisotropy) medium and obtain a 3‐D crustal radial anisotropy model. The results reveal significant heterogeneities along the Cenozoic Fenhe‐Weihe Rift (FWR). In the northern FWR, the discretely distributed lower crust positive anisotropy and upper crust negative anisotropy suggest the rifting is mainly dominated by the active mantle upwelling resulting in the Datong volcanoes. Similarly, the northern segment of the Taihang Mountain is also strongly affected by the magmatic activities and exhibits different anisotropy properties compared to its central‐to‐southern counterpart. Based on the negative anisotropy observed in the middle‐to‐lower crust beneath most parts of the Taihang Mountain, we speculate that a lower‐crust compression model can be applied to the Taihang Mountain, which is totally different to that of the adjacent Bohai Bay Basin. Possibly, the root of the Taihang Mountain is pushed by the westward moving lower crust coupled with the lateral escaping mantle flow beneath the Bohai Bay Basin. The Taihang Mountain and the Bohai Bay Basin are formed in similar tectonic environments, but are deformed in different ways.

Shear wave velocity structure of the crust and upper mantle in Southeastern Tibet and its geodynamic implications

Southeastern Tibet, which has complex topography and strong tectonic activity, is an important area for studying the subsurface deformation of the Tibetan Plateau. Through the two-station method on 10-year teleseismic Rayleigh wave data from 132 permanent stations in the southeastern Tibetan Plateau, which incorporates ambient noise data, we obtain the interstation phase velocity dispersion data in the period range of 5–150 s. Then, we invert for the shear wave velocity of the crust and upper mantle through the direct 3-D inversion method. We find two low-velocity belts in the mid-lower crust. One belt is mainly in the SongPan-GangZi block and northwestern part of the Chuan-Dian diamond block, whereas the other belt is mainly in the Xiaojiang fault zone and its eastern part, the Yunnan-Guizhou Plateau. The low-velocity belt in the Xiaojiang fault zone is likely caused by plastic deformation or partial melting of felsic rocks due to crustal thickening. Moreover, the significant positive radial anisotropy (VSH>VSV) around the Xiaojiang fault zone further enhances the amplitude of low velocity anomaly in our VSV model. This crustal low-velocity zone also extends southward across the Red River fault and farther to northern Vietnam, which may be closely related to heat sources in the upper mantle. The two low-velocity belts are separated by a high-velocity zone near the Anninghe-Zemuhe fault system, which is exactly in the inner and intermediate zones of the Emeishan large igneous province (ELIP). We find an obvious high-velocity body situated in the crust of the inner zone of the ELIP, which may represent maficultramafic material that remained in the crust when the ELIP formed. In the upper mantle, there is a large-scale low-velocity anomaly in the Indochina and South China blocks south of the Red River fault. The low-velocity anomaly gradually extends northward along the Xiaojiang fault zone into the Yangtze Craton as depth increases. Through our velocity model, we think that southeastern Tibet is undergoing three different tectonic modes at the same time: (1) the upper crust is rigid, and as a result, the tectonic mode is mainly rigid block extrusion controlled by large strike-slip faults; (2) the viscoplastic materials in the middle-lower crust, separated by rigid materials related to the ELIP, migrate plastically southward under the control of the regional stress field and fault systems; and (3) the upper mantle south of the Red River fault is mainly controlled by large-scale asthenospheric upwelling and may be closely related to lithospheric delamination and the eastward subduction and retreat of the Indian plate beneath Burma.

Crustal Deformation in Southern California Constrained by Radial Anisotropy From Ambient Noise Adjoint Tomography

AbstractWe build a new radially anisotropic shear wave velocity model of Southern California based on ambient noise adjoint tomography to investigate crustal deformation associated with Cenozoic evolution of the Pacific‐North American plate boundary. Pervasive positive radial anisotropy (4%) is observed in the crust east of the San Andreas Fault (SAF), attributed to subhorizontal alignment of mica/amphibole foliation planes resulting from significant crustal extension. Substantial negative anisotropy (6%) is revealed in the middle/lower crust west of the SAF, where high shear wave speeds are also observed. The negative anisotropy could result from steeply dipping amphibole schists in a shear zone developed during Laramide flat slab subduction. Alternatively, it could be caused by the crystal preferred orientation (CPO) of plagioclase, whose fast axis aligns orthogonally to a presumed subhorizontal foliation. The latter new mechanism highlights potentially complex CPO patterns resulting from different lithospheric mineralogy, as suggested by laboratory experiments on xenoliths from the region.

Dynamical masses of brightest cluster galaxies I: stellar velocity anisotropy and mass-to-light ratios

ABSTRACT We investigate the stellar and dynamical mass profiles in the centres of 25 brightest cluster galaxies (BCGs) at redshifts of 0.05 ≤ z ≤ 0.30. Our spectroscopy enables us to robustly measure the Gauss–Hermite higher order velocity moments h3 and h4, which we compare to measurements for massive early-type galaxies, and central group galaxies. We measure positive central values for h4 for all the BCGs. We derive the stellar mass-to-light ratio ($\Upsilon _{\star \rm DYN}$), and velocity anisotropy (β) based on a multi-Gaussian expansion (MGE) and axisymmetric Jeans Anisotropic Methods (cylindrically and spherically aligned). We explicitly include a dark matter halo mass component, which is constrained by weak gravitational lensing measurements for these clusters. We find a strong correlation between anisotropy and velocity dispersion profile slope, with rising velocity dispersion profiles corresponding to tangential anisotropy and decreasing velocity dispersion profiles corresponding to radial anisotropy. The rising velocity dispersion profiles can also indicate a significant contribution from the intracluster light (ICL) to the total light (in projection) in the centre of the galaxy. For a small number of BCGs with rising velocity dispersion profiles, a variable stellar mass-to-light ratio can also account for the profile shape, instead of tangential anisotropy or a significant ICL contribution. We note that, for some BCGs, a variable βz(r) (from radial to tangential anisotropy) can improve the model fit to the observed kinematic profiles. The observed diversity in these properties illustrates that BCGs are not the homogeneous class of objects they are often assumed to be.

High mantle seismic P-wave speeds as a signature for gravitational spreading of superplumes.

New passive- and active-source seismic experiments reveal unusually high mantle P-wave speeds that extend beneath the remnants of the world's largest known large igneous province, making up the 120-million-year-old Ontong-Java-Manihiki-Hikurangi Plateau. Sub-Moho Pn phases of ~8.8 ± 0.2 km/s are resolved with negligible azimuthal seismic anisotropy, but with strong radial anisotropy (~10%), characteristic of aggregates of olivine with an AG crystallographic fabric. These seismic results are the first in situ evidence for this fabric in the upper mantle. We show that its presence can be explained by isotropic horizontal dilation and vertical flattening due to late-stage gravitational collapse and spreading in the top 10 to 20 km of a depleted, mushroom-shaped, superplume head on a horizontal length scale of 1000 km or more. This way, it provides a seismic tool to track plumes long after the thermal effects have ceased.

Realizing optical bistability and tristability in plasmonic coated nanoparticles with radial-anisotropy and Kerr-nonlinearity.

We theoretically study the optical bistability and tristability in plasmonic coated nanospheres containing the nonlinear plasmonic shell and the dielectric core with radial anisotropy. Based on self-consistent mean-field approximation, we establish the relationship between the local field in the shell and the applied incident field, taking into account the Lorentz local field. One or two optical bistabilities and even optical tristability can be observed. Especially, there are two critical geometric parameters between which two optical bistabilities exist. Physically, two optical bistablities result from the excitations of two surface plasmonic resonant modes in the inner and outer interfaces of coated nanospheres, which are well reflected from the spectral representation with two poles. Moreover, the involvement of the radial anisotropy is quite essential to realize the optical tristability. Further discussion on the field-induced tuning of the reflectance reveals the macroscopic properties of this nonlinear optical structure, which provides a potential candidate for designing multi-stable optical devices at the nanoscale.

Upper Mantle Deformation of the Terror Rift and Northern Transantarctic Mountains in Antarctica: Insight From P Wave Anisotropic Tomography

AbstractA large number of teleseismic traveltime data are used to determine the first P‐wave radial anisotropy tomography beneath the Terror Rift, the northern Transantarctic Mountains (NTAM) and the Wilkes Subglacial Basin in Antarctica. Our results show that variations of radial anisotropy occur in both horizontal and vertical directions. In the NTAM, a high‐velocity zone with positive radial anisotropy is revealed at shallower depths, which reflects the lithospheric deformation pattern formed during the Ross Orogeny. In contrast, negative radial anisotropy appears at depths &gt;200 km under the NTAM, which is caused by the characterization of olivine fabric rather than foundering lithosphere. Beneath the western Wilkes Subglacial Basin, a two‐layer lithosphere exists that contains rift‐induced cracks. To the east of the NTAM, asthenospheric upwelling occurs at shallow depths beneath the Terror Rift. Then the upwelling asthenosphere flows northward to Mount Melbourne and southward to Mount Erebus.

Direct Surface Wave Radial Anisotropy Tomography in the Crust of the Eastern Himalayan Syntaxis

AbstractA novel method is implemented to invert Rayleigh and Love wave dispersion curves of all paths jointly for 3‐D shear wave velocity and radial anisotropy simultaneously without intermediate steps. We use the method to derive high‐precision crustal shear wave velocity and radial anisotropy models around the eastern Himalayan syntaxis using ambient noise dispersion data (5–40 s). Results show that the crust can be divided into several subregions with different rigidity and preferred mineral alignment orientation depth‐dependently. In the middle crust, combined with other geophysical observations, 3‐D geometry of two continuous branches of eastward channelized weak zones is outlined in detail. Both branches of the weak zone are blocked by the high velocity zone with radial anisotropy of Vsh&gt;Vsv at around 96–97°E. In the upper crust, the radial anisotropy model depicts a complex pattern, which is associated with the ongoing surface uplifting and shear strain rate distribution.

Cosmological insights into the assembly of the radial and compact stellar halo of the Milky Way

ABSTRACT Recent studies using Gaia DR2 have identified a massive merger in the early history of the Milky Way (MW) whose debris is dominated by radial and counterrotating orbits. This event, dubbed the Gaia-Enceladus/Gaia-Sausage (GE/GS), is also hypothesized to have built the majority of the inner stellar halo. We use the cosmological hydrodynamic simulation Illustris to place this merger in the context of galaxy assembly within lambda cold dark matter. From ∼150 MW analogues, $\sim \!80 {{ \rm {per\ cent}}}$ have experienced at least one merger of similar mass and infall time as the GE/GS. Within this sample, 37 have debris as radial as the GE/GS, which we dub the ancient radial mergers (ARMs). Counterrotation is not rare among ARMs, with $43 {{ \rm {per\ cent}}}$ having $\gt 40 {{ \rm {per\ cent}}}$ of their debris in counterrotating orbits. However, the compactness inferred for the GE/GS debris given its large radial orbital anisotropy, β, and its substantial contribution to the stellar halo are difficult to reproduce. The median radius of ARM debris is r*,deb ≃ 45 kpc, while GE/GS is thought to be mostly contained within r ∼ 30 kpc. For most MW analogues, few mergers are required to build the inner stellar halo, and ARM debris only accounts for (median) $\sim \!12 {{ \rm {per\ cent}}}$ of inner accreted stars. Encouragingly, we find one ARM that is both compact and dominates the inner halo of its central, making it our best GE/GS analogue. Interestingly, this merger deposits a significant number of stars (M* ≃ 1.5 × 109 M⊙) in the outer halo, suggesting that an undiscovered section of GE/GS may await detection.