Steep Cusps Research Articles

A photometric in-depth look at the core-collapsed globular cluster NGC 6284

High-resolution Hubble Space Telescope (HST) optical observations have been used to perform the deepest photometric study of the poorly studied Galactic globular cluster NGC 6284. The deep colour-magnitude diagram (CMD) that we obtained reaches 6 mag below the main-sequence turnoff. We provide the first determination of the gravitational centre (Cgrav) and density profile of the system from resolved stars. We note that the gravitational centre is significantly offset (by 1.5 − 3″) from the values in the literature. The density profile shows the presence of a steep central cusp, unambiguously indicating that the cluster experienced the core-collapse phase. Updated values of the structural parameters and relaxation times of the system are provided. We also constructed the first high-resolution reddening map in the cluster direction, which allowed us to correct the evolutionary sequences in the CMD for the effects of differential reddening. Isochrone fitting to the corrected CMD provided us with new estimates of the cluster age, average colour excess, metallicity, and distance. We find an absolute age of 13.3 ± 0.4 Gyr, an average colour excess E(B − V) = 0.32 ± 0.01, a metallicity [Fe/H] = −1.36 ± 0.01, and a true distance modulus (m − M)0 = 15.61 ± 0.04 that sets the cluster distance at 13.2 ± 0.2 kpc from the Sun. The superb quality of the CMD allowed a clear-cut identification of the red giant branch (RGB) bump, which is clearly distinguishable along the narrow RGB. The absolute magnitude of this feature turns out to be ∼0.2 mag fainter than the previous identification.

Phase-space simulations of prompt cusps: simulating the formation of the first haloes without artificial fragmentation

ABSTRACT The first generation of haloes forms from the collapse of the smallest peaks in the initial density field. N-body simulations of this process suggest a prompt formation of a steep power-law cusp, but these calculations are plagued by numerical artefacts that cast some doubt on this result. Here, we develop new simulation methods based on the dark matter phase-space sheet approach and present results that are entirely free of artificial clumps. We find that a cusp with density ρ ∝ r−1.5 is indeed formed promptly, subsequently accreting a more extended halo and participating in the hierarchical growth of later halo generations. However, our simulations also suggest that the presence of artificial clumps just before peak collapse can significantly shallow the inner profiles of the cusps. We use N-body simulations with controlled amounts of small-scale power to place a conservative upper limit on the scales affected by artificial clumps. Finally, we used these results to simulate the collapse of the first generation of peaks of various types and in different cosmologies, finding prompt cusps to form in all cases. We conclude that prompt cusps are a generic feature of the collapse of peaks on the free-streaming scale of the initial density field, and their structure can safely be studied using N-body simulations provided care is taken to excise the region potentially affected by artificial clumps.

Discovery of a Double Sequence of Blue Straggler Stars in the Core-collapsed Globular Cluster NGC 6256

We used a combination of high-resolution optical images acquired with the Hubble Space Telescope and near-IR wide-field data to investigate the stellar density profile and the population of blue straggler stars (BSSs) in the Galactic globular cluster NGC 6256, with the aim of probing its current stage of internal dynamical evolution. We found that the inner stellar density profile significantly deviates from a King model, while it is well reproduced by a steep cusp with a power-law slope α cusp = −0.89, thus implying that the cluster is currently in the post-core-collapse (PCC) phase. This is also confirmed by the very high segregation level of the BSS population measured through the parameter. We also found that the distribution of BSSs in the color–magnitude diagram is characterized by a collimated blue sequence and a red more sparse component, as already observed in three other PCC clusters. A comparison with appropriate collisional models demonstrates that the vast majority of the BSSs lying along the collimated blue sequence is consistent with a generation of coeval (1 Gyr old) stars with different masses originated by an event that highly enhanced the collisional rate of the system (i.e., the core collapse). This study confirms that the segregation level of BSSs is a powerful dynamical diagnostic also of star cluster in a very advanced stage of dynamical evolution. Moreover, it pushes forward the possibility of using the morphology of BSSs in a color–magnitude diagram as a tracer of the core-collapse and subsequent dynamical evolutionary phases.

Analytical analysis of the origin of core-cusp matter density distributions in galaxies

We propose an analytical method to describe a matter density profile near a galaxy center. The description is based on the study of the distribution function of particles over possible trajectories. We establish a relation between the central slope of density profile and the near-origin behavior of the angular momentum distribution function. We consider both a spherically symmetric (on average) matter distribution as well as deviations from it. If the density profile forms in a background of spherical gravitation potential then a core-type distribution arises. A regular matter may behave in such way if the background potential was formed by the dark matter. In the presence of deviation from spherical symmetry the formation of cusp-type distribution is possible. Moreover, a reduction of spherical symmetry to the axial one leads to a less steep cusp profile. The complete symmetry breaking (which corresponds, in particular, to the common setup of numerical simulations), leads to a steeper cusp profile.

Cuspy dark matter density profiles in massive dwarf galaxies

ABSTRACT Rotation curves of galaxies probe their total mass distributions, including dark matter. Dwarf galaxies are excellent systems to investigate the dark matter density distribution, as they tend to have larger fractions of dark matter compared to higher mass systems. The core-cusp problem describes the discrepancy found in the slope of the dark matter density profile in the centres of galaxies (β*) between observations of dwarf galaxies (shallower cores) and dark matter-only simulations (steeper cusps). We investigate β* in six nearby spiral dwarf galaxies for which high-resolution CO J = 1–0 data were obtained with ALMA (Atacama Large Millimeter/submillimeter Array). We derive rotation curves and decompose the mass profile of the dark matter using our CO rotation curves as a tracer of the total potential and 4.5 $\mu$m photometry to define the stellar mass distribution. We find 〈β*〉 = 0.6 with a standard deviation of ±0.1 among the galaxies in this sample, in agreement with previous measurements in this mass range. The galaxies studied are on the high stellar mass end of dwarf galaxies and have cuspier profiles than lower mass dwarfs, in agreement with other observations. When the same definition of the slope is used, we observe steeper slopes than predicted by the FIRE and NIHAO simulations. This may signal that these relatively massive dwarfs underwent stronger gas inflows towards their centres than predicted by these simulations, that these simulations overpredict the frequency of accretion or feedback events, or that a combination of these or other effects are at work.

Methodology investigation: Impact of crown geometry, crown, abutment and antagonist material and thermal loading on the two-body wear of dental materials

ObjectivesTo investigate the impact of crown geometry, crown/abutment/antagonist material and thermal loading on the two-body wear of dental materials caused by chewing simulation. Materials and methodsFor the crown geometry, crowns (polymethylmethacrylate (PMMA), polyetheretherketone (PEEK) and silicate ceramic (SiO2)) were milled with a flat, steep, or medium cusp inclination (CINC). For the crown/abutment material, crowns (PMMA, PEEK and SiO2) were combined with PMMA, polymer-infiltrated-ceramic-network (PICN), cobalt-chrome alloy (CoCr) and natural teeth (ENAM) abutments. For the antagonist material, antagonists were fabricated from PICN, CAD/CAM resin composite (RECO), steatite (STEA), steel (STL) and ENAM and tested against flat specimens (substrates) made of veneering ceramic (VC). For thermal loading, the duration (30 s, 60 s, 120 s) and presence of temperature changes (37 °C versus 5 °C/55 °C) was varied. Material losses were determined by matching scanned specimens before and after aging (400,000 chewing cycles, 50 N, 1.3 Hz). Martens parameters were determined for the antagonists/substrates. Data were analyzed using Kolmogorov-Smirnov-test, Kruskal-Wallis H, Scheffé-Post-Hoc-tests, pairwise comparisons, Bonferroni correction, one-way ANOVA, Mann-Whitney-U and Spearman rho. ResultsPMMA crowns presented the highest and PEEK the lowest material losses. Flat CINC showed the lowest material losses for PEEK and SiO2 crowns. CoCr and ENAM abutments presented material losses in the same range. Antagonist and cumulative material losses for RECO and ENAM were similar. Thermal loading did not influence material losses. SignificanceCrown geometry influences the crown and antagonists wear, with an increased cusp inclination entailing increased wear. For in vitro set-ups, CoCr abutments and RECO antagonists present valid alternatives to natural teeth. For polymers, in vitro chewing simulations may be performed at a constant temperature (37 °C).

The Black Hole Mass of NGC 4151 from Stellar Dynamical Modeling

Abstract The mass of a supermassive black hole (M BH) is a fundamental property that can be obtained through observational methods. Constraining M BH through multiple methods for an individual galaxy is important for verifying the accuracy of different techniques and for investigating the assumptions inherent in each method. However, there exist only a few galaxies where multiple M BH measurement techniques can be applied. NGC 4151 is one of these rare galaxies for which multiple methods can be used: stellar and gas dynamical modeling because of its proximity (D = 15.8 ± 0.4 Mpc from Cepheids), and reverberation mapping because of its active accretion. In this work, we reanalyzed H-band integral field spectroscopy of the nucleus of NGC 4151 from Gemini NIFS, improving the analysis at several key steps. We then constructed a wide range of axisymmetric dynamical models with the new orbit-superposition code Forstand. One of our primary goals is to quantify the systematic uncertainties in M BH arising from different combinations of the deprojected density profile, inclination, intrinsic flattening, and mass-to-light ratio. As a consequence of uncertainties on the stellar luminosity profile arising from the presence of the active galactic nucleus, our constraints on M BH are rather weak. Models with a steep central cusp are consistent with no black hole; however, in models with more moderate cusps, the black hole mass lies within the range of 0.25 × 107 M ⊙ ≲ M BH ≲ 3 × 107 M ⊙. This measurement is somewhat smaller than the earlier analysis presented by Onken et al. but agrees with previous M BH values from gas dynamical modeling and reverberation mapping. Future dynamical modeling of reverberation data, as well as IFU observations with JWST, will aid in further constraining the mass of the central supermassive black hole in NGC 4151.

Self-gravitating Equilibria of Non-minimally Coupled Dark Matter Halos

Abstract We investigate self-gravitating equilibria of halos constituted by dark matter (DM) non-minimally coupled to gravity. In particular, we consider a theoretically motivated non-minimal coupling that may arise when the averaging/coherence length L associated with the fluid description of the DM collective behavior is comparable to the local curvature scale. In the Newtonian limit, such a non-minimal coupling amounts to a modification of the Poisson equation by a term L 2∇2 ρ proportional to the Laplacian of the DM density ρ itself. We further adopt a general power-law equation of state p ∝ ρ Γ r α relating the DM dynamical pressure p to density ρ and radius r, as expected for phase-space density stratification during the gravitational assembly of halos in a cosmological context. We confirm previous findings that, in the absence of non-minimal coupling, the resulting density ρ(r) features a steep central cusp and an overall shape mirroring the outcomes of N-body simulations in the standard ΛCDM cosmology, as described by the classic Navarro–Frenk–White or Einasto profiles. Most importantly, we find that the non-minimal coupling causes the density distribution to develop an inner core and a shape that closely follows the Burkert profile out to several core scale radii. In fact, we highlight that the resulting mass distributions can fit, with an accuracy comparable to Burkert’s one, the coadded rotation curves of dwarf, DM-dominated galaxies. Finally, we show that non-minimally coupled DM halos are consistent with the observed scaling relation between the core radius r 0 and core density ρ 0, in terms of a universal core surface density ρ 0 × r 0 among different galaxies.

Strong constraints on thermal relic dark matter from Fermi-LAT observations of the Galactic Center

The extended excess toward the Galactic Center (GC) in gamma rays inferred from Fermi-LAT observations has been interpreted as being due to dark matter (DM) annihilation. Here, we perform new likelihood analyses of the GC and show that, when including templates for the stellar galactic and nuclear bulges, the GC shows no significant detection of a DM annihilation template, even after generous variations in the Galactic diffuse emission models and a wide range of DM halo profiles. We include Galactic diffuse emission models with combinations of three-dimensional inverse Compton maps, variations of interstellar gas maps, and a central source of electrons. For the DM profile, we include both spherical and ellipsoidal DM morphologies and a range of radial profiles from steep cusps to kiloparsec-sized cores, motivated in part by hydrodynamical simulations. Our derived upper limits on the dark matter annihilation flux place strong constraints on DM properties. In the case of the pure $b$-quark annihilation channel, our limits on the annihilation cross section are more stringent than those from the Milky Way dwarfs up to DM masses of approximately TeV and rule out the thermal relic cross section up to approximately 300 GeV. Better understanding of the DM profile, as well as the Fermi-LAT data at its highest energies, would further improve the sensitivity to DM properties.

The dichotomy of dark matter fraction and total mass density slope of galaxies over five dex in mass

AbstractWe analyse the mass density distribution in the centres of galaxies across five orders of magnitude in mass range. Using high-quality spiral galaxy rotation curves and infrared photometry from SPARC, we conduct a systematic study of their central dark matter (DM) fraction (fDM) and their mass density slope (α), within their effective radius. We show that lower mass spiral galaxies are more DM dominated and have more shallow mass density slopes when compared with more massive galaxies, which have density profiles closer to isothermal. Low-mass (${M_{*}}\lesssim 10^{10}\, {\mathrm{M}_\odot}$) gas-rich spirals span a wide range of fDM values, but systematically lower than in gas-poor systems of similar mass. With increasing galaxy mass, the values of fDM decrease and the density profiles steepen. In the most massive late-type gas-poor galaxies, a possible flattening of these trends is observed. When comparing these results to massive (${M_{*}}\gtrsim 10^{10}\, {\mathrm{M}_\odot}$) elliptical galaxies from SPIDER and to dwarf ellipticals (dEs) from SMACKED, these trends result to be inverted. Hence, the values of both fDM and α, as a function of M*, exhibit a U-shape trend. At a fixed stellar mass, the mass density profiles in dEs are steeper than in spirals. These trends can be understood by stellar feedback from a more prolonged star formation period in spirals, causing a transformation of the initial steep density cusp to a more shallow profile via differential feedback efficiency by supernovae, and by galaxy mergers or AGN feedback in higher mass galaxies.

Globular clusters as probes of dark matter cusp-core transformations

Abstract Bursty star formation in dwarf galaxies can slowly transform a steep dark matter cusp into a constant density core. We explore the possibility that globular clusters (GCs) retain a dynamical memory of this transformation. To test this, we use the nbody6df code to simulate the dynamical evolution of GCs, including stellar evolution, orbiting in static and time-varying potentials for a Hubble time. We find that GCs orbiting within a cored dark matter halo, or within a halo that has undergone a cusp-core transformation, grow to a size that is substantially larger (Reff > 10 pc) than those in a static cusped dark matter halo. They also produce much less tidal debris. We find that the cleanest signal of an historic cusp-core transformation is the presence of large GCs with tidal debris. However, the effect is small and will be challenging to observe in real galaxies. Finally, we qualitatively compare our simulated GCs with the observed GC populations in the Fornax, NGC 6822, IKN, and Sagittarius dwarf galaxies. We find that the GCs in these dwarf galaxies are systematically larger (〈Reff〉 ≃ 7.8 pc), and have substantially more scatter in their sizes than in situ metal-rich GCs in the Milky Way and young massive star clusters forming in M83 (〈Reff〉 ≃ 2.5 pc). We show that the size, scatter, and survival of GCs in dwarf galaxies are all consistent with them having evolved in a constant density core, or a potential that has undergone a cusp-core transformation, but not in a dark matter cusp.

Stellar cusp and warm dust at the heart of NGC 1068

Aims. Establishing precisely how stars and interstellar medium distribute within the central 100 pc area around an AGN, down to the pc scale, is key to understanding the late stages of transfer of matter onto the accretion disc. Methods. Using adaptive optics-assisted (SPHERE-VLT) near-IR images in the H band, Ks band, and several narrow bands of the Seyfert 2 galaxy NGC 1068, we analysed the radial distribution of brightness in the central r < 100 pc area down to the pc scale. The median-averaged radial profiles are fitted by a cusp (power law) plus a central point source. A simple radiative transfer model is also used to interpret the data. Results. We find that the fit of radial brightness profiles beyond 10 pc is done quite precisely at Ks band by a cusp of exponent −2.0 plus a central point source and by a cusp of exponent −1.2 at H. The difference of exponents between H band and Ks band can be explained by differential extinction, provided that the distribution of dust is itself cuspy, with an exponent −1.0. However, the derived stellar density is found to follow a r−4 cusp, which is much steeper than any other cusp, either theoretically predicted around a massive black hole, or observed in the centre of early- and late-type galaxies or in mergers. Introducing a segregation in the stellar population with a central excess of giant stars leads to a somewhat less steep exponent; however, the de-reddened luminosity of the stellar cusp, as well as the mass of dust and gas all appear much too high to be realistic. An alternative scenario, where the Ks-band profile is well fitted by a combination of radiation from a stellar cusp identical to the H-band profile and thermal emission of warm/hot dust heated by the central engine appears much more satisfactory. NGC 1068 is shown to satisfy a relationship between half-light radius, cusp luminosity, and exponent that we established using a sample of luminous infrared galaxies (LIRGs) and ultraluminous infrared galaxies ULIRGs. This suggests that the cusp is the remnant of a recent starburst. We identify the central point-like source with the very hot dust at the internal wall of the putative torus and derive an intrinsic luminosity that requires a central extinction AK ≈ 8, a value consistent with predictions by several torus models. Conclusions. The overall picture revealed by this study is closely consistent with the scheme of a central rather steep stellar cusp, embedded in a diluted medium of warm dust, while a compact and dense structure identified with the putative torus is required to interpret a highly reddened point-like central source of very hot dust.

Formation of LISA Black Hole Binaries in Merging Dwarf Galaxies: The Imprint of Dark Matter

Abstract Theoretical models for the expected merger rates of intermediate-mass black holes (IMBHs) are vital for planned gravitational-wave detection experiments such as the Laser Interferometer Space Antenna (LISA). Using collisionless N-body simulations of dwarf galaxy (DG) mergers, we examine how the orbital decay of IMBHs and the efficiency of IMBH binary formation depend on the central dark matter (DM) density profile of the merging DGs. Specifically, we explore various asymptotic inner slopes γ of the DG’s DM density distribution, ranging from steep cusps (γ = 1) to shallower density profiles (γ < 1), motivated by well-known baryonic-feedback effects as well as by DM models that differ from cold DM at the scales of DGs. We find that the inner DM slope is crucial for the formation (or lack thereof) of an IMBH binary; only mergers between DGs with cuspy DM profiles (γ = 1) are favorable to forming a hard IMBH binary, whereas when γ < 1 the IMBHs stall at a separation of 50–100 pc. Consequently, the rate of LISA signals from IMBH coalescence will be determined by the fraction of DGs with a cuspy DM profile. Conversely, the LISA event rates at IMBH mass scales offer in principle a novel way to place constraints on the inner structure of DM halos in DGs and address the core–cusp controversy. We also show that, with spatial resolutions of ∼0.1 kpc, as often adopted in cosmological simulations, all IMBHs stall, independent of γ. This suggests caution should be taken when employing cosmological simulations of galaxy formation to study BH dynamics in DGs.

Gravitational wave driven mergers and coalescence time of supermassive black holes

Aims. The evolution of supermassive black holes (SMBHs) initially embedded in the centres of merging galaxies realised with a stellar mass function (SMF) is studied from the onset of galaxy mergers until coalescence. Coalescence times of SMBH binaries are of great importance for black hole evolution and gravitational wave detection studies. Methods. We performed direct N-body simulations using the highly efficient and massively parallel phi-GRAPE+GPU code capable of running on high-performance computer clusters supported by graphic processing units (GPUs). Post-Newtonian terms up to order 3.5 are used to drive the SMBH binary evolution in the relativistic regime. We performed a large set of simulations with three different slopes of the central stellar cusp and different random seeds. The impact of a SMF on the hardening rate and the coalescence time is investigated. Results. We find that SMBH binaries coalesce well within one billion years when our models are scaled to galaxies with a steep cusp at low redshift. Here higher central densities provide a larger supply of stars to efficiently extract energy from the SMBH binary orbit and shrink it to the phase where gravitational wave (GW) emission becomes dominant, leading to the coalescence of the SMBHs. Mergers of models with shallow cusps that are representative of giant elliptical galaxies having central cores result in less efficient extraction of the binary’s orbital energy, due to the lower stellar densities in the centre. However, high values of eccentricity witnessed for SMBH binaries in such galaxy mergers ensure that the GW emission dominated phase sets in earlier at larger values of the semi-major axis. This helps to compensate for the less efficient energy extraction during the phase dominated by stellar encounters resulting in mergers of SMBHs in about 1 Gyr after the formation of the binary. Additionally, we witness mass segregation in the merger remnant resulting in enhanced SMBH binary hardening rates. We show that at least the final phase of the merger in cuspy low-mass galaxies would be observable with the GW detector eLISA.

Density Functional Theory under the Bubbles and Cube Numerical Framework.

Density functional theory within the Kohn–Sham density functional theory (KS-DFT) ansatz has been implemented into our bubbles and cube real-space molecular electronic structure framework, where functions containing steep cusps in the vicinity of the nuclei are expanded in atom-centered one-dimensional (1D) numerical grids multiplied with spherical harmonics (bubbles). The remainder, i.e., the cube, which is the cusp-free and smooth difference between the atomic one-center contributions and the exact molecular function, is represented on a three-dimensional (3D) equidistant grid by using a tractable number of grid points. The implementation of the methods is demonstrated by performing 3D numerical KS-DFT calculations on light atoms and small molecules. The accuracy is assessed by comparing the obtained energies with the best available reference energies.

Dark-matter halo profiles of a general cusp/core with analytic velocity and potential

We present useful functions for the profiles of dark-matter (DM) haloes with a free inner slope, from cusps to cores, where the profiles of density, mass-velocity and potential are simple analytic expressions. Analytic velocity is obtained by expressing the mean density as a simple functional form, and deriving the local density by differentiation. The function involves four shape parameters, with only two or three free: a concentration parameter $c$, inner and outer asymptotic slopes $\alpha$ and $\bar{\gamma}$, and a middle shape parameter $\beta$. Analytic expressions for the potential and velocity dispersion exist for $\bar{\gamma}=3$ and for $\beta$ a natural number. We match the models to the DM haloes in cosmological simulations, with and without baryons, ranging from steep cusps to flat cores. Excellent fits are obtained with three free parameters ($c$, $\alpha$, $\bar{\gamma}$) and $\beta=2$. For an analytic potential, similar fits are obtained for $\bar{\gamma}=3$ and $\beta=2$ with only two free parameters ($c$, $\alpha$); this is our favorite model. A linear combination of two such profiles, with an additional free concentration parameter, provides excellent fits also for $\beta=1$, where the expressions are simpler. The fit quality is comparable to non-analytic popular models. An analytic potential is useful for modeling the inner-halo evolution due to gas inflows and outflows, studying environmental effects on the outer halo, and generating halo potentials or initial conditions for simulations. The analytic velocity can quantify simulated and observed rotation curves without numerical integrations.

Testing feedback-modified dark matter haloes with galaxy rotation curves: estimation of halo parameters and consistency with ΛCDM scaling relations

Cosmological $N$-body simulations predict dark matter (DM) haloes with steep central cusps (e.g. NFW, Navarro et al. 1996). This contradicts observations of gas kinematics in low-mass galaxies that imply the existence of shallow DM cores. Baryonic processes such as adiabatic contraction and gas outflows can, in principle, alter the initial DM density profile, yet their relative contributions to the halo transformation remain uncertain. Recent high resolution, cosmological hydrodynamic simulations (Di Cintio et al. 2014, DC14) predict that inner density profiles depend systematically on the ratio of stellar to DM mass (M$_*$/M$_{\text{halo}}$). Using a Markov Chain Monte Carlo approach, we test the NFW and the M$_*$/M$_{\text{halo}}$-dependent DC14 halo models against a sample of 147 galaxy rotation curves from the new {\it Spitzer} Photometry and Accurate Rotation Curves (SPARC) data set. These galaxies all have extended H{\small I} rotation curves from radio interferometry as well as accurate stellar mass density profiles from near-infrared photometry. The DC14 halo profile provides markedly better fits to the data compared to the NFW profile. Unlike NFW, the DC14 halo parameters found in our rotation curve fits naturally fall within two standard deviations of the mass-concentration relation predicted by $\Lambda$CDM and the stellar mass-halo mass relation inferred from abundance matching with few outliers. Halo profiles modified by baryonic processes are therefore more consistent with expectations from $\Lambda$ cold dark matter ($\Lambda$CDM) cosmology and provide better fits to galaxy rotation curves across a wide range of galaxy properties than do halo models that neglect baryonic physics. Our results offer a solution to the decade long cusp-core discrepancy.

Studies on proximity effect in Mo/Bi1.95Sb0.05Se3 hybrid structure

Proximity effect in a mechanically exfoliated Bi1.95Sb0.05Se3 topological insulator (TI) single crystal partially covered with disordered superconducting (SC) Mo thin film is reported. Magneto-transport measurement was performed simultaneously across three different regions of the sample viz. SC, TI and SC / TI junction. Resistance measured across SC shows a TC at 4.3 K concomitantly the resistance measurement on TI showed a metallic trend with a steep upturn at TC. Magneto-resistance (MR) measurement on TI exhibit a positive MR with Shubnikov-de Haas (SdH) oscillations, whereas on SC a positive MR superimposed with steep cusp close to TC is observed. Across SC/TI junction both SdH oscillation and the cusp were observed. The frequency of SdH oscillation on SC / TI junction is found to be lesser (~125 T) as compared to a reference Bi1.95Sb0.05Se3 sample (~174 T). Upper critical field HC2 deduced from WHH fit was found to be 17.14 T for a reference Mo film whereas Mo film deposited on TI showed a decreased HC2 of 4.05 T. The coherence length for the former was found to be 4.38 nm and for the latter 9.01 nm. The interaction between the spin-less Cooper pairs in SC with the spin-momentum locked carriers on the surface of TI is believed to cause such changes in transport properties.

The Biomechanics of Partial Symphyseal Fusion in Hapalemur Examined Using Finite Element Analysis

A wealth of research on primate feeding supports the hypothesis that fused mandibular symphyses, ubiquitous among anthropoids, strengthen the joint against “wishboning” stresses that occur as a result of transversely-oriented muscle forces. However, in mammals that include extensive transverse occlusal movements, fusion has been suggested to increase bite forces in the horizontal plane by more efficiently transferring balancing-side muscle forces to the biting side. Some strepsirrhines, including Hapalemur and Propithecus, exhibit varying degrees of partial fusion. Hapalemur feeds extensively on extremely tough bamboo, so increasing transverse bite forces could be selectively important. However, steep molar cusps limit the potential for transverse occlusal movements. We used finite element analysis to examine symphyseal mechanics in Hapalemur. We constructed one completely fused Hapalemur mandible model and five with “symphyseal plates” assigned increasingly stiff elastic moduli (5MPa – 600MPa). Models were constrained at the second molar and loaded with muscle forces. By comparing nodal displacements, we found that modest increases in symphyseal stiffness (0MPa – 50MPa) drastically reduce wishboning, suggesting partially fused symphyses may be nearly as strong as those that are completely ossified. In contrast, we found that stiff/fused symphyses do not increase transverse bite forces.

Re-examining the too-big-to-fail problem for dark matter haloes with central density cores

Recent studies found the densities of dark matter (DM) subhaloes which surround nearby dwarf spheroidal galaxies (dSphs) to be significantly lower than those of the most massive subhaloes expected around Milky Way sized galaxies in cosmological simulations, the so called "too-big-to-fail" (TBTF) problem. A caveat of previous work has been that dark substructures were assumed to contain steep density cusps in the center of DM haloes even though the central density structure of DM haloes is still under debate. In this study, we re-examine the TBTF problem for models of DM density structure with cores or shallowed cusps. Our analysis demonstrates that the TBTF problem is alleviated as the logarithmic slope of the central cusp becomes shallower. We find that the TBTF problem is avoided if the central cusps of DM haloes surrounding dSphs are shallower than $r^{-0.6}$.