# Posts Tagged core

## Recent Postings from core

### The Next Generation Virgo Cluster Survey (NGVS). XIII. The Luminosity and Mass Function of Galaxies in the Core of the Virgo Cluster and the Contribution from Disrupted Satellites

We present measurements of the galaxy luminosity and stellar mass function in a 3.71 deg$^2$ (0.3 Mpc$^2$) area in the core of the Virgo cluster, based on $ugriz$ data from the Next Generation Virgo Cluster Survey (NGVS). The galaxy sample consists of 352 objects brighter than $M_g=-9.13$ mag, the 50% completeness limit of the survey. Using a Bayesian analysis, we find a best-fit faint end slope of $\alpha=-1.33 \pm 0.02$ for the g-band luminosity function; consistent results are found for the stellar mass function as well as the luminosity function in the other four NGVS bandpasses. We discuss the implications for the faint-end slope of adding 92 ultra compact dwarfs galaxies (UCDs) -- previously compiled by the NGVS in this region -- to the galaxy sample, assuming that UCDs are the stripped remnants of nucleated dwarf galaxies. Under this assumption, the slope of the luminosity function (down to the UCD faint magnitude limit, $M_g = -9.6$ mag) increases dramatically, up to $\alpha = -1.60 \pm 0.06$ when correcting for the expected number of disrupted non-nucleated galaxies. We also calculate the total number of UCDs and globular clusters that may have been deposited in the core of Virgo due to the disruption of satellites, both nucleated and non-nucleated. We estimate that ~150 objects with $M_g\lesssim-9.6$ mag and that are currently classified as globular clusters, might, in fact, be the nuclei of disrupted galaxies. We further estimate that as many as 40% of the (mostly blue) globular clusters in the core of Virgo might once have belonged to such satellites; these same disrupted satellites might have contributed ~40% of the total luminosity in galaxies observed in the core region today. Finally, we use an updated Local Group galaxy catalog to provide a new measurement of the luminosity function of Local Group satellites, $\alpha=-1.21\pm0.05$.

### A detailed mass distribution of a high-density core in Taurus with ALMA

We present the results of ALMA observations of dust continuum emission and molecular rotational lines, including the ALMA Compact Array, toward a dense core MC27 (a.k.a. L1521F) in Taurus, which is considered to be at very early stage of star formation. Detailed column density distribution with a size scale from a few tens AU to ~10000 AU scale are revealed by combining the ALMA data and the single-dish data. The high angular resolution observation at 0.87 mm reveals that a protostellar source, MMS-1, is still not spatially resolved without gas association and a starless high-density core, MMS-2, has substructures both in dust and molecular emission. The averaged radial column density distribution of the inner part (r < 3000 AU) is N_H2 ~r^-0.4, clearly flatter than that of the outer part, ~r^-1.0. We found the complex velocity/spatial structure obtained with previous ALMA observations is located inside the inner flatter region, which may reflect the dynamical status of the dense core.

### Deep Chandra study of the truncated cool core of the Ophiuchus cluster

We present the results of a deep (280 ks) Chandra observation of the Ophiuchus cluster, the second-brightest galaxy cluster in the X-ray sky. The cluster hosts a truncated cool core, with a temperature increasing from kT~1 keV in the core to kT~9 keV at r~30 kpc. Beyond r~30 kpc the intra-cluster medium (ICM) appears remarkably isothermal. The core is dynamically disturbed with multiple sloshing induced cold fronts, with indications for both Rayleigh-Taylor and Kelvin-Helmholtz instabilities. The sloshing is the result of the strongly perturbed gravitational potential in the cluster core, with the central brightest cluster galaxy (BCG) being displaced southward from the global center of mass. The residual image reveals a likely subcluster south of the core at the projected distance of r~280 kpc. The cluster also harbors a likely radio phoenix, a source revived by adiabatic compression by gas motions in the ICM. Even though the Ophiuchus cluster is strongly dynamically active, the amplitude of density fluctuations outside of the cooling core is low, indicating velocities smaller than ~100 km/s. The density fluctuations might be damped by thermal conduction in the hot and remarkably isothermal ICM, resulting in our underestimate of gas velocities. We find a surprising, sharp surface brightness discontinuity, that is curved away from the core, at r~120 kpc to the southeast of the cluster center. We conclude that this feature is most likely due to gas dynamics associated with a merger and not a result of an extraordinary active galactic nucleus (AGN) outburst. The cooling core lacks any observable X-ray cavities and the AGN only displays weak, point-like radio emission, lacking lobes or jets, indicating that currently it may be largely dormant. The lack of strong AGN activity may be due to the bulk of the cooling taking place offset from the central supermassive black hole.

### Magnetic field evolution of accreting neutron stars

The flow of a matter, accreting onto a magnetized neutron star, is accompanied by an electric current. The closing of the electric current occurs in the crust of a neutron stars in the polar region across the magnetic field. But the conductivity of the crust along the magnetic field greatly exceeds the conductivity across the field, so the current penetrates deep into the crust down up to the super conducting core. The magnetic field, generated by the accretion current, increases greatly with the depth of penetration due to the Hall conductivity of the crust is also much larger than the transverse conductivity. As a result, the current begins to flow mainly in the toroidal direction, creating a strong longitudinal magnetic field, far exceeding an initial dipole field. This field exists only in the narrow polar tube of $r$ width, narrowing with the depth, i.e. with increasing of the crust density $\rho$, $r\propto \rho^{-1/4}$. Accordingly, the magnetic field $B$ in the tube increases with the depth, $B\propto \rho^{1/2}$, and reaches the value of about $10^{17}$ Gauss in the core. It destroys super conducting vortices in the core of a star in the narrow region of the size of the order of ten centimeters. Because of generated density gradient of vortices they constantly flow into this dead zone and the number of vortices decreases, the magnetic field of a star decreases as well. The attenuation of the magnetic field is exponential, $B=B_0(1+t/\tau)^{-1}$. The characteristic time of decreasing of the magnetic field $\tau$ is equal to $\tau\simeq 10^3$ years. Thus, the magnetic field of accreted neutron stars decreases to values of $10^8 - 10^9$ Gauss during $10^7-10^6$ years.

### Chemical and physical characterization of collapsing low-mass prestellar dense cores

The first hydrostatic core, also called the first Larson core, is one of the first steps in low-mass star formation, as predicted by theory. With recent and future high performance telescopes, details of these first phases become accessible, and observations may confirm theory and even bring new challenges for theoreticians. In this context, we study from a theoretical point of view the chemical and physical evolution of the collapse of prestellar cores until the formation of the first Larson core, in order to better characterize this early phase in the star formation process. We couple a state-of-the-art hydrodynamical model with full gas-grain chemistry, using different assumptions on the magnetic field strength and orientation. We extract the different components of each collapsing core (i.e., the central core, the outflow, the disk, the pseudodisk, and the envelope) to highlight their specific physical and chemical characteristics. Each component often presents a specific physical history, as well as a specific chemical evolution. From some species, the components can clearly be differentiated. The different core models can also be chemically differentiated. Our simulation suggests some chemical species as tracers of the different components of a collapsing prestellar dense core, and as tracers of the magnetic field characteristics of the core. From this result, we pinpoint promising key chemical species to be observed.

### VLT/SPHERE deep insight of NGC 3603's core: Segregation or confusion?

We present new near-infrared photometric measurements of the core of the young massive cluster NGC 3603 obtained with extreme adaptive optics. The data were obtained with the SPHERE instrument mounted on ESO Very Large Telescope, and cover three fields in the core of this cluster. We applied a correction for the effect of extinction to our data obtained in the J and K broadband filters and estimated the mass of detected sources inside the field of view of SPHERE/IRDIS, which is 13.5"x13.5". We derived the mass function (MF) slope for each spectral band and field. The MF slope in the core is unusual compared to previous results based on Hubble space telescope (HST) and very large telescope (VLT) observations. The average slope in the core is estimated as -1.06^{+0.26}_{-0.26} for the main sequence stars with 3.5 Msun < M < 120 Msun.Thanks to the SPHERE extreme adaptive optics, 814 low-mass stars were detected to estimate the MF slope for the pre-main sequence stars with 0.6 Msun< M < 3.5 Msun , Gamma = -0.54^{+0.11}_{-0.11} in the K-band images in two fields in the core of the cluster. For the first time, we derive the mass function of the very core of the NGC 3603 young cluster for masses in the range 0.6 - 120 Msun. Previous studies were either limited by crowding, lack of dynamic range, or a combination of both.

### Did Jupiter's core form in the innermost parts of the Sun's protoplanetary disk? [Replacement]

Jupiter's core is generally assumed to have formed beyond the snow line. Here we consider an alternative scenario, that Jupiter's core may have accumulated in the innermost parts of the protoplanetary disk. A growing body of research suggests that small particles ("pebbles") continually drift inward through the disk. If a fraction of drifting pebbles is trapped at the inner edge of the disk a several Earth-mass core can quickly grow. Subsequently, the core may migrate outward beyond the snow line via planet-disk interactions. Of course, to reach the outer Solar System Jupiter's core must traverse the terrestrial planet-forming region. We use N-body simulations including synthetic forces from an underlying gaseous disk to study how the outward migration of Jupiter's core sculpts the terrestrial zone. If the outward migration is fast (Tmig~10^4 years), the core simply migrates past resident planetesimals and planetary embryos. However, if its migration is slower (Tmig~10^5 years) the core removes solids from the inner disk by shepherding objects in mean motion resonances. In many cases the disk interior to 0.5-1 AU is cleared of embryos and most planetesimals. By generating a mass deficit close to the Sun, the outward migration of Jupiter's core may thus explain the absence of terrestrial planets closer than Mercury. Jupiter's migrating core often stimulates the growth of another large (~Earth-mass) core -- that may provide a seed for Saturn's core -- trapped in exterior resonance. The migrating core also may transport a fraction of terrestrial planetesimals, such as the putative parent bodies of iron meteorites, to the asteroid belt.

### Did Jupiter's core form in the innermost parts of the Sun's protoplanetary disk?

Jupiter's core is generally assumed to have formed beyond the snow line. Here we consider an alternative scenario, that Jupiter's core may have accumulated in the innermost parts of the protoplanetary disk. A growing body of research suggests that small particles ("pebbles") continually drift inward through the disk. If a fraction of drifting pebbles is trapped at the inner edge of the disk a several Earth-mass core can quickly grow. Subsequently, the core may migrate outward beyond the snow line via planet-disk interactions. Of course, to reach the outer Solar System Jupiter's core must traverse the terrestrial planet-forming region. We use N-body simulations including synthetic forces from an underlying gaseous disk to study how the outward migration of Jupiter's core sculpts the terrestrial zone. If the outward migration is fast (Tmig~10^4 years), the core simply migrates past resident planetesimals and planetary embryos. However, if its migration is slower (Tmig~10^5 years) the core removes solids from the inner disk by shepherding objects in mean motion resonances. In many cases the disk interior to 0.5-1 AU is cleared of embryos and most planetesimals. By generating a mass deficit close to the Sun, the outward migration of Jupiter's core may thus explain the absence of terrestrial planets closer than Mercury. Jupiter's migrating core often stimulates the growth of another large (~Earth-mass) core -- that may provide a seed for Saturn's core -- trapped in exterior resonance. The migrating core also may transport a fraction of terrestrial planetesimals, such as the putative parent bodies of iron meteorites, to the asteroid belt.

### Thermal evolution of hybrid stars within the framework of a nonlocal Nambu--Jona-Lasinio model [Cross-Listing]

We study the thermal evolution of neutron stars containing deconfined quark matter in their core. Such objects are generally referred to as quark-hybrid stars. The confined hadronic matter in their core is described in the framework of non-linear relativistic nuclear field theory. For the quark phase we use a non-local extension of the SU(3) Nambu Jona-Lasinio model with vector interactions. The Gibbs condition is used to model phase equilibrium between confined hadronic matter and deconfined quark matter. Our study indicates that high-mass neutron stars may contain between 35 and 40 % deconfined quark-hybrid matter in their cores. Neutron stars with canonical masses of around $1.4\, M_\odot$ would not contain deconfined quark matter. The central proton fractions of the stars are found to be high, enabling them to cool rapidly. Very good agreement with the temperature evolution established for the neutron star in Cassiopeia A (Cas A) is obtained for one of our models (based on the popular NL3 nuclear parametrization), if the protons in the core of our stellar models are strongly paired, the repulsion among the quarks is mildly repulsive, and the mass of Cas A has a canonical value of $1.4\, M_\odot$.

### Thermal evolution of hybrid stars within the framework of a nonlocal Nambu--Jona-Lasinio model [Cross-Listing]

We study the thermal evolution of neutron stars containing deconfined quark matter in their core. Such objects are generally referred to as quark-hybrid stars. The confined hadronic matter in their core is described in the framework of non-linear relativistic nuclear field theory. For the quark phase we use a non-local extension of the SU(3) Nambu Jona-Lasinio model with vector interactions. The Gibbs condition is used to model phase equilibrium between confined hadronic matter and deconfined quark matter. Our study indicates that high-mass neutron stars may contain between 35 and 40 % deconfined quark-hybrid matter in their cores. Neutron stars with canonical masses of around $1.4\, M_\odot$ would not contain deconfined quark matter. The central proton fractions of the stars are found to be high, enabling them to cool rapidly. Very good agreement with the temperature evolution established for the neutron star in Cassiopeia A (Cas A) is obtained for one of our models (based on the popular NL3 nuclear parametrization), if the protons in the core of our stellar models are strongly paired, the repulsion among the quarks is mildly repulsive, and the mass of Cas A has a canonical value of $1.4\, M_\odot$.

### Thermal evolution of hybrid stars within the framework of a nonlocal Nambu--Jona-Lasinio model

We study the thermal evolution of neutron stars containing deconfined quark matter in their core. Such objects are generally referred to as quark-hybrid stars. The confined hadronic matter in their core is described in the framework of non-linear relativistic nuclear field theory. For the quark phase we use a non-local extension of the SU(3) Nambu Jona-Lasinio model with vector interactions. The Gibbs condition is used to model phase equilibrium between confined hadronic matter and deconfined quark matter. Our study indicates that high-mass neutron stars may contain between 35 and 40 % deconfined quark-hybrid matter in their cores. Neutron stars with canonical masses of around $1.4\, M_\odot$ would not contain deconfined quark matter. The central proton fractions of the stars are found to be high, enabling them to cool rapidly. Very good agreement with the temperature evolution established for the neutron star in Cassiopeia A (Cas A) is obtained for one of our models (based on the popular NL3 nuclear parametrization), if the protons in the core of our stellar models are strongly paired, the repulsion among the quarks is mildly repulsive, and the mass of Cas A has a canonical value of $1.4\, M_\odot$.

### Equivalence Principles, Spacetime Structure and the Cosmic Connection

After reviewing the meaning of various equivalence principles and the structure of electrodynamics, we give a fairly detailed account of the construction of the light cone and a core metric from the equivalence principle for the photon (no birefringence, no polarization rotation and no amplification/attenuation in propagation) in the framework of linear electrodynamics using cosmic connections/observations as empirical support. The cosmic nonbirefringent propagation of photons independent of energy and polarization verifies the Galileo Equivalence Principle [Universality of Propagation] for photons/electromagnetic wave packets in spacetime. This nonbirefringence constrains the spacetime constitutive tensor to high precision to a core metric form with an axion degree and a dilaton degree of freedom. Thus comes the metric with axion and dilation. Constraints on axion and dilaton from astrophysical/cosmic propagation are reviewed. E\"otv\"os-type experiments, Hughes-Drever-type experiments, redshift experiments then constrain and tie this core metric to agree with the matter metric, and hence a unique physical metric and universality of metrology. We summarize these experiments and review how the Galileo equivalence principle constrains the Einstein Equivalence Principle (EEP) theoretically. In local physics this physical metric gives the Lorentz/Poincar\'e covariance. Understanding that the metric and EEP come from the vacuum as a medium of electrodynamics in the linear regime, efforts to actively look for potential effects beyond this linear scheme are warranted.

### Extended objects in nonperturbative quantum field theory and the cosmological constant

We consider a gravitating extended object constructed from vacuum fluctuations of nonperturbatively quantized non-Abelian gauge fields. An approximate description of such an object is given by two gravitating scalar fields. The object has a core filled with a constant energy density of the vacuum fluctuations of the quantum fields. The core is located inside a cosmological event horizon. An exact analytical solution of the Einstein equations for such a core is presented. The value of the energy density of the vacuum fluctuations is connected with the cosmological constant.

### Mapping the Three-Dimensional "X-Shaped Structure" in Models of the Galactic Bulge

Numerical simulations have shown that the X-shaped structure in the Milky Way bulge can naturally arise from the bar instability and buckling instability. To understand the influence of the buckling amplitude on the morphology of the X-shape, we analyze three self-consistent numerical simulations of barred galaxies with different buckling amplitudes (strong, intermediate and weak). We derive the three-dimensional density with an adaptive kernel smoothing technique. The face-on iso-density surfaces are all elliptical, while in the edge-on view, the morphology of buckled bars transitions with increasing radius, from a central boxy core to a peanut bulge and then to an extended thin bar. Based on these iso-density surfaces at different density levels, we find no clear evidence for a well-defined structure shaped like a letter X. The X-shaped structure is more peanut-like, whose visual perception is probably enhanced by the pinched inner concave iso-density contours. The peanut bulge can reproduce qualitatively the observed bimodal distributions which were used as evidence for the discovery of the X-shape. The central boxy core is shaped like an oblong tablet, extending to $\sim$ 500 pc above and below the Galactic plane ($|b| \sim 4^\circ$). From the solar perspective, lines of sight passing through the central boxy core do not show bimodal distributions. This generally agrees with the observations that the double peaks merge at $|b| \sim 4^\circ - 5^\circ$ from the Galactic plane, indicating the presence of a possibly similar structure in the Galactic bulge.

### Tangled up in Spinning Cosmic Strings [Cross-Listing]

It is known for a long time that the space time around a spinning cylindrical symmetric compact object such as the cosmic string, show un-physical behavior, i.e., they would possess closed time like curves (CTC). This controversy with Hawking's chronology protection conjecture is unpleasant but can be understood if one solves the coupled scalar-gauge field equations and the matching conditions at the core of the string. A new interior numerical solution is found of a self gravitating spinning cosmic string with a U(1) scalar gauge field and the matching on the exterior space time is revealed. It is conjectured that the experience of CTC's close to the core of the string is exceedingly unlikely. It occurs when the causality breaking boundary, $r_\mu$, approaches the boundary of the cosmic string, $r_{CS}$. Then the metric components become singular and the proper time on the core of the string stops flowing. Further, we expect that the angular momentum $J$ will decrease due to the emission of gravitational energy triggered by the scalar perturbations. When a complete loop is taken around the string, the interior time jumps by a factor $2\pi J$. The proper time it takes to make a complete loop becomes infinite and will be equal to the period that $g_{\varphi\varphi}$ remains positive. In this time interval the angular momentum will be reduced to zero by emission of wave energy. The physical situation of an observer who experience $r_{\mu}\rightarrow r_{CS}$ is very unpleasant: the energy-momentum tensor components diverge.

### Tangled up in Spinning Cosmic Strings

It is known for a long time that the space time around a spinning cylindrical symmetric compact object such as the cosmic string, show un-physical behavior, i.e., they would possess closed time like curves (CTC). This controversy with Hawking's chronology protection conjecture is unpleasant but can be understood if one solves the coupled scalar-gauge field equations and the matching conditions at the core of the string. A new interior numerical solution is found of a self gravitating spinning cosmic string with a U(1) scalar gauge field and the matching on the exterior space time is revealed. It is conjectured that the experience of CTC's close to the core of the string is exceedingly unlikely. It occurs when the causality breaking boundary, $r_\mu$, approaches the boundary of the cosmic string, $r_{CS}$. Then the metric components become singular and the proper time on the core of the string stops flowing. Further, we expect that the angular momentum $J$ will decrease due to the emission of gravitational energy triggered by the scalar perturbations. When a complete loop is taken around the string, the interior time jumps by a factor $2\pi J$. The proper time it takes to make a complete loop becomes infinite and will be equal to the period that $g_{\varphi\varphi}$ remains positive. In this time interval the angular momentum will be reduced to zero by emission of wave energy. The physical situation of an observer who experience $r_{\mu}\rightarrow r_{CS}$ is very unpleasant: the energy-momentum tensor components diverge.

### Giant planet formation via pebble accretion

In the standard model of core accretion, the formation of giant planets occurs by two main processes: first, a massive core is formed by the accretion of solid material; then, when this core exceeds a critical value (typically greater than 10 Earth masses) a gaseous runaway growth is triggered and the planet accretes big quantities of gas in a short period of time until the planet achieves its final mass. Thus, the formation of a massive core has to occur when the nebular gas is still available in the disk. This phenomenon imposes a strong time-scale constraint in giant planet formation due to the fact that the lifetimes of the observed protoplanetary disks are in general lower than 10 Myr. The formation of massive cores before 10 Myr by accretion of big planetesimals (with radii > 10 km) in the oligarchic growth regime is only possible in massive disks. However, planetesimal accretion rates significantly increase for small bodies, especially for pebbles, particles of sizes between mm and cm, which are strongly coupled with the gas. In this work, we study the formation of giant planets incorporating pebble accretion rates in our global model of planet formation.

### Internal rotation of the red-giant star KIC 4448777 by means of asteroseismic inversion

In this paper we study the dynamics of the stellar interior of the early red-giant star KIC 4448777 by asteroseismic inversion of 14 splittings of the dipole mixed modes obtained from {\it Kepler} observations. In order to overcome the complexity of the oscillation pattern typical of red-giant stars, we present a procedure which involves a combination of different methods to extract the rotational splittings from the power spectrum. We find not only that the core rotates faster than the surface, confirming previous inversion results generated for other red giants (Deheuvels et al. 2012,2014), but we also estimate the variation of the angular velocity within the helium core with a spatial resolution of $\Delta r=0.001R$ and verify the hypothesis of a sharp discontinuity in the inner stellar rotation (Deheuvels et al. 2014). The results show that the entire core rotates rigidly with an angular velocity of about $\langle\Omega_c/2\pi\rangle=748\pm18$~nHz and provide evidence for an angular velocity decrease through a region between the helium core and part of the hydrogen burning shell; however we do not succeed to characterize the rotational slope, due to the intrinsic limits of the applied techniques. The angular velocity, from the edge of the core and through the hydrogen burning shell, appears to decrease with increasing distance from the center, reaching an average value in the convective envelope of $\langle\Omega_s/2\pi\rangle=68\pm22$~nHz. Hence, the core in KIC~4448777 is rotating from a minimum of 8 to a maximum of 17 times faster than the envelope. We conclude that a set of data which includes only dipolar modes is sufficient to infer quite accurately the rotation of a red giant not only in the dense core but also, with a lower level of confidence, in part of the radiative region and in the convective envelope.

### Internal structure of Pluto and Charon with an iron core

Pluto has been observed by the New Horizons space probe to have some relatively fresh ice on the old ices covering most of the surface. Pluto was thought to consist of only a rocky core below the ice. Here I show that Pluto can have an iron core, as can also its companion Charon, which has recently been modelled to have one. The presence of an iron core means the giant impact origin calculations should be redone to include iron and thus higher temperatures. An iron core leads to the possibility of a different geology. An originally molten core becomes solid later, with contraction and a release of latent heat. The space vacated allows the upper rock layers to flow downwards at some locations at the surface of the core, and some of the ice above the rock to descend, filling the spaces left by the rock motion downwards. These phenomena can lead to the forces recently deforming the icy surface of Pluto, and in a lesser way, of Charon.

### Hierarchical gravitational fragmentation. I. Collapsing cores within collapsing clouds

We investigate the Hierarchical Gravitational Fragmentation scenario through numerical simulations of the prestellar stages of the collapse of a marginally gravitationally unstable isothermal sphere immersed in a strongly gravitationally unstable, uniform background medium. The core developes a Bonnor-Ebert (BE)-like density profile, while at the time of singularity (the protostar) formation the envelope approaches a singular-isothermal-sphere (SIS)-like $r^-2$ density profile. However, these structures are never hydrostatic. In this case, the central flat region is characterized by an infall speed, while the envelope is characterized by a uniform speed. This implies that the hydrostatic SIS initial condition leading to Shu's classical inside-out solution is not expected to occur, and therefore neither should the inside-out solution. Instead, the solution collapses from the outside-in, naturally explaining the observation of extended infall velocities. The core, defined by the radius at which it merges with the background, has a time-variable mass, and evolves along the locus of the ensemble of observed prestellar cores in a plot of $M/M_{BE}$ vs. $M$, where $M$ is the core's mass and $M_{BE}$ is the critical Bonnor-Ebert mass, spanning the range from the "stable" to the "unstable" regimes, even though it is collapsing at all times. We conclude that the presence of an unstable background allows a core to evolve dynamically from the time when it first appears, even when it resembles a pressure-confined, stable BE-sphere. The core can be thought of as a ram-pressure confined BE-sphere, with an increasing mass due to the accretion from the unstable background.

### A Semi-Analytic dynamical friction model that reproduces core stalling

We present a new semi-analytic model for dynamical friction based on Chandrasekhar's formalism. The key novelty is the introduction of physically motivated, radially varying, maximum and minimum impact parameters. With these, our model gives an excellent match to full N-body simulations for isotropic background density distributions, both cuspy and shallow, without any fine-tuning of the model parameters. In particular, we are able to reproduce the dramatic core-stalling effect that occurs in shallow/constant density cores, for the first time. This gives us new physical insight into the core-stalling phenomenon. We show that core stalling occurs in the limit in which the product of the Coulomb logarithm and the local fraction of stars with velocity lower than the infalling body tends to zero. For cuspy backgrounds, this occurs when the infalling mass approaches the enclosed background mass. For cored backgrounds, it occurs at larger distances from the centre, due to a combination of a rapidly increasing minimum impact parameter and a lack of slow moving stars in the core. This demonstrates that the physics of core-stalling is likely the same for both massive infalling objects and low-mass objects moving in shallow density backgrounds. We implement our prescription for dynamical friction in the direct summation code NBODY6 as an analytic correction for stars that remain within the Roche volume of the infalling object. This approach is computationally efficient, since only stars in the inspiralling system need to be evolved with direct summation. Our method can be applied to study a variety of astrophysical systems, including young star clusters orbiting near the Galactic Centre; globular clusters moving within the Galaxy; and dwarf galaxies orbiting within dark matter halos.

### Application of supersymmetric quantum mechanics to study bound state properties of exotic hypernuclei

Bound state properties of few single and double-$\Lambda$ hypernuclei is critically examined in the framework of core-$\Lambda$ and core+$\Lambda+\Lambda$ few-body model applying hyperspherical harmonics expansion method (HHEM). The $\Lambda\Lambda$ potential is chosen phenomenologically while the core-$\Lambda$ potential is obtained by folding a phenomenological $\Lambda N$ interaction into the density distribution of the core. The depth of the effective $\Lambda N$ potential is adjusted to reproduce the experimental data for the core-$\Lambda$ subsystem. The three-body Schr\"odinger equation is solved by hyperspherical adiabatic approximation (HAA) to get the ground state energy and wave function. The ground state wavefunction is used to construct the supersymmetric partner potential following prescription of supersymmetric quantum mechanics (SSQM) algebra. The newly constructed supersymmetric partner potential is used to solve the three-body Schr\"odinger equation to get the energy and wavefunction for the first excited state of the original potential. The method is repeated to predict energy and wavefunction of the next higher excited states. The possible number of bound states is found to increase with the increase in mass of the core of the hypernuclei. The Root Mean Squared (RMS) matter radius and some other relevant geometrical observables are also predicted.

### The cooling of the Cassiopeia A neutron star as a probe of a triplet neutron pairing in the core [Cross-Listing]

The observed rapid cooling of the Cassiopeia A neutron star (Cas A NS) can be interpreted as being triggered by the onset of neutron superfluidity in the core of the star, causing enhanced neutrino emission from neutron Cooper pair breaking and formation (PBF). This provides a unique possibility for probing the neutron condensate in the core. Using consistent neutron star core and crust equation of state and composition, I explore the sensitivity of this interpretation to the phase state of the triplet superfluid condensate. Modeling cooling within an expected range of neutron star masses and envelope compositions, I found that the fast cooling of the Cas A NS can not be explained by the PBF processes in the conventional one-component $^3$P$_2$ condensate with $m_{j}=0$. The best-fit solutions are obtained for the multicomponent superfluid phases listed in Table. The $O_1$ solution yields $M=1.52M_{Sun}$ (carbon envelope with $10^{-15}M_{Sun}$). The $O_2$ solution yield $M=1.47M_{Sun}$ (carbon envelope with $5\times 10^{-15}M_{Sun}$), and the $O_{\pm 3}$ solution $M=1.49M_{Sun}$ (iron envelope).

### The cooling of the Cassiopeia A neutron star as a probe of a triplet neutron pairing in the core [Replacement]

The observed rapid cooling of the Cassiopeia A neutron star (Cas A NS) can be interpreted as being triggered by the onset of neutron superfluidity in the core of the star, causing enhanced neutrino emission from neutron Cooper pair breaking and formation (PBF). This provides a unique possibility for probing the neutron condensate in the core. Using consistent neutron star core and crust equation of state and composition, I explore the sensitivity of this interpretation to the phase state of the triplet superfluid condensate. Modeling cooling within an expected range of neutron star masses and envelope compositions, I found that the fast cooling of the Cas A NS can not be explained by the PBF processes in the conventional one-component $^3$P$_2$ condensate with $m_{j}=0$. The best-fit solutions are obtained for the multicomponent superfluid phases listed in Table. The $O_1$ solution yields $M=1.52M_{Sun}$ (carbon envelope with $10^{-15}M_{Sun}$). The $O_2$ solution yield $M=1.47M_{Sun}$ (carbon envelope with $5\times 10^{-15}M_{Sun}$), and the $O_{\pm 3}$ solution $M=1.49M_{Sun}$ (iron envelope).

### The cooling of the Cassiopeia A neutron star as a probe of a triplet neutron pairing in the core [Replacement]

The observed rapid cooling of the Cassiopeia A neutron star (Cas A NS) can be interpreted as being triggered by the onset of neutron superfluidity in the core of the star, causing enhanced neutrino emission from neutron Cooper pair breaking and formation (PBF). This provides a unique possibility for probing the neutron condensate in the core. Using consistent neutron star core and crust equation of state and composition, I explore the sensitivity of this interpretation to the phase state of the triplet superfluid condensate. Modeling cooling within an expected range of neutron star masses and envelope compositions, I found that the fast cooling of the Cas A NS can not be explained by the PBF processes in the conventional one-component $^3$P$_2$ condensate with $m_{j}=0$. The best-fit solutions are obtained for the multicomponent superfluid phases listed in Table. The $O_1$ solution yields $M=1.52M_{Sun}$ (carbon envelope with $10^{-15}M_{Sun}$). The $O_2$ solution yield $M=1.47M_{Sun}$ (carbon envelope with $5\times 10^{-15}M_{Sun}$), and the $O_{\pm 3}$ solution $M=1.49M_{Sun}$ (iron envelope).

### The cooling of the Cassiopeia A neutron star as a probe of a triplet neutron pairing in the core [Replacement]

The observed rapid cooling of the Cassiopeia A neutron star (Cas A NS) can be interpreted as being triggered by the onset of neutron superfluidity in the core of the star, causing enhanced neutrino emission from neutron Cooper pair breaking and formation (PBF). This provides a unique possibility for probing the neutron condensate in the core. Using consistent neutron star core and crust equation of state and composition, I explore the sensitivity of this interpretation to the phase state of the triplet superfluid condensate. Modeling cooling within an expected range of neutron star masses and envelope compositions, I found that the fast cooling of the Cas A NS can not be explained by the PBF processes in the conventional $^3$P$_2$ condensate with $m_{j}=0$.

### The cooling of the Cassiopeia A neutron star as a probe of a triplet neutron pairing in the core [Replacement]

The observed rapid cooling of the Cassiopeia A neutron star (Cas A NS) can be interpreted as being triggered by the onset of neutron superfluidity in the core of the star, causing enhanced neutrino emission from neutron Cooper pair breaking and formation (PBF). This provides a unique possibility for probing the neutron condensate in the core. Using consistent neutron star core and crust equation of state and composition, I explore the sensitivity of this interpretation to the phase state of the triplet superfluid condensate. Modeling cooling within an expected range of neutron star masses and envelope compositions, I found that the fast cooling of the Cas A NS can not be explained by the PBF processes in the conventional $^3$P$_2$ condensate with $m_{j}=0$.

### The cooling of the Cassiopeia A neutron star as a probe of a triplet neutron pairing in the core

The observed rapid cooling of the Cassiopeia A neutron star (Cas A NS) can be interpreted as being triggered by the onset of neutron superfluidity in the core of the star, causing enhanced neutrino emission from neutron Cooper pair breaking and formation (PBF). This provides a unique possibility for probing the neutron condensate in the core. Using consistent neutron star core and crust equation of state and composition, I explore the sensitivity of this interpretation to the phase state of the triplet superfluid condensate. Modeling cooling within an expected range of neutron star masses and envelope compositions, I found that the fast cooling of the Cas A NS can not be explained by the PBF processes in the conventional one-component $^3$P$_2$ condensate with $m_{j}=0$. The best-fit solutions are obtained for the multicomponent superfluid phases listed in Table. The $O_1$ solution yields $M=1.52M_{Sun}$ (carbon envelope with $10^{-15}M_{Sun}$). The $O_2$ solution yield $M=1.47M_{Sun}$ (carbon envelope with $5\times 10^{-15}M_{Sun}$), and the $O_{\pm 3}$ solution $M=1.49M_{Sun}$ (iron envelope).

### On the age and formation mechanism of the core of the Quadrantid meteoroid stream

The Quadrantid meteor shower is among the strongest annual meteor showers, and has drawn the attention of scientists for several decades. The stream is unusual, among others, for several reasons: its very short duration around maximum activity (~12 - 14 hours) as detected by visual, photographic and radar observations, its recent onset (around 1835 AD) and because it had been the only major stream without an obvious parent body until 2003. Ever since, there have been debates as to the age of the stream and the nature of its proposed parent body, asteroid 2003 EH1. In this work, we present results on the most probable age and formation mechanism of the narrow portion of the Quadrantid meteoroid stream. For the first time we use data on eight high precision photographic Quadrantids, equivalent to gram - kilogram size, to constrain the most likely age of the core of the stream. Out of eight high-precision photographic Quadrantids, five pertain directly to the narrow portion of the stream. In addition, we also use data on five high-precision radar Quadrantids, observed within the peak of the shower. We performed backwards numerical integrations of the equations of motion of a large number of 'clones' of both, the eight high-precision photographic and five radar Quadrantid meteors, along with the proposed parent body, 2003 EH1. According to our results, from the backward integrations, the most likely age of the narrow structure of the Quadrantids is between 200 - 300 years. These presumed ejection epochs, corresponding to 1700 - 1800 AD, are then used for forward integrations of large numbers of hypothetical meteoroids, ejected from the parent 2003 EH$_1$, until the present epoch. The aim is to constrain whether the core of the Quadrantid meteoroid stream is consistent with a previously proposed relatively young age (~ 200 years).}

### Limits on thermal variations in a dozen quiescent neutron stars over a decade

In quiescent low-mass X-ray binaries (qLMXBs) containing neutron stars, the origin of the thermal X-ray component may be either release of heat from the core of the neutron star, or continuing low-level accretion. In general, heat from the core should be stable on timescales $<10^4$ years, while continuing accretion may produce variations on a range of timescales. While some quiescent neutron stars (e.g. Cen X-4, Aql X-1) have shown variations in their thermal components on a range of timescales, several others, particularly those in globular clusters with no detectable nonthermal hard X-rays (fit with a powerlaw), have shown no measurable variations. Here, we constrain the spectral variations of 12 low mass X-ray binaries in 3 globular clusters over $\sim10$ years. We find no evidence of variations in 10 cases, with limits on temperature variations below 11% for the 7 qLMXBs without powerlaw components, and limits on variations below 20% for 3 other qLMXBs that do show non-thermal emission. However, in 2 qLMXBs showing powerlaw components in their spectra (NGC 6440 CX 1 & Terzan 5 CX 12) we find marginal evidence for a 10% decline in temperature, suggesting the presence of continuing low-level accretion. This work adds to the evidence that the thermal X-ray component in quiescent neutron stars without powerlaw components can be explained by heat deposited in the core during outbursts. Finally, we also investigate the correlation between hydrogen column density (N$_H$) and optical extinction (A$_V$) using our sample and current models of interstellar X-ray absorption, finding $N_H ({\rm cm}^{-2}) = (2.81\pm0.13)\times10^{21} A_V$.

### A new period of activity in the core of NGC660

The core of the nearby galaxy NGC660 has recently undergone a spectacular radio outburst; using a combination of archival radio and Chandra X-ray data, together with new observations, the nature of this event is investigated. Radio observations made using e-MERLIN in mid-2013 show a new compact and extremely bright continuum source at the centre of the galaxy. High angular resolution observations carried out with the European VLBI Network show an obvious jet-like feature to the north east and evidence of a weak extension to the west, possibly a counter-jet. We also examine high angular resolution HI spectra of these new sources, and the radio spectral energy distribution using the new wide-band capabilities of e-MERLIN. We compare the properties of the new object with possible explanations, concluding that we are seeing a period of new AGN activity in the core of this polar ring galaxy.

### Too big to be real? No depleted core in Holm 15A

Partially depleted cores, as measured by core-Sersic model "break radii", are typically tens to a few hundred parsecs in size. Here we investigate the unusually large (cusp radius of 4.57 kpc) depleted core recently reported for Holm 15A, the brightest cluster galaxy of Abell 85. We model the 1D light profile, and also the 2D image (using GALFIT-CORSAIR, a tool for fitting the core-Sersic model in 2D). We find good agreement between the 1D and 2D analyses, with minor discrepancies attributable to intrinsic ellipticity gradients. We show that a simple Sersic profile (with a low index n and no depleted core) plus the known outer exponential "halo" provide a good description of the stellar distribution. We caution that while almost every galaxy light profile will have a radius where the negative logarithmic slope of the intensity profile equals 0.5, this alone does not imply the presence of a partially depleted core within this radius.

### Internal Structure of Asteroids Having Surface Shedding due to Rotational Instability

Surface shedding of an asteroid is a failure mode where surface materials fly off due to strong centrifugal forces beyond the critical spin period, while the internal structure does not deform significantly. This paper proposes a possible structure of an asteroid interior that leads to such surface shedding due to rapid rotation rates. A rubble pile asteroid is modeled as a spheroid composed of a surface shell and a concentric internal core, the entire assembly called the test body. The test body is assumed to be uniformly rotating around a constant rotation axis. We also assume that while the bulk density and the friction angle are constant, the cohesion of the surface shell is different from that of the internal core. First, developing an analytical model based on limit analysis, we provide the upper and lower bounds for the actual surface shedding condition. Second, we use a Soft-Sphere Discrete Element Method (SSDEM) to study dynamical deformation of the test body due to a quasi-static spin-up. In this paper we show the consistency of both approaches. Additionally, the SSDEM simulations show that the initial failure always occurs locally and not globally. In addition, as the core becomes larger, the size of lofted components becomes smaller. These results imply that if there is a strong enough core in a progenitor body, surface shedding is the most likely failure mode.

### Observational constraints on neutron star crust-core coupling during glitches

We demonstrate that observations of glitches in the Vela pulsar can be used to investigate the strength of the crust-core coupling in a neutron star, and suggest that recovery from the glitch is dominated by torque exerted by the re-coupling of superfluid components of the core that were decoupled from the crust during the glitch. Assuming that the recoupling is mediated by mutual friction between the superfluid neutrons and the charged components of the core, we use the observed magnitudes and timescales of the shortest timescale components of the recoveries from two recent glitches in the Vela pulsar to infer the fraction of the core that is coupled to the crust during the glitch, and hence spun up by the glitch event. Within the framework of a two-fluid hydrodynamic model of glitches, we analyze whether crustal neutrons alone are sufficient to drive the glitch activity observed in the Vela pulsar. We use two sets of neutron star equations of state (EOSs), both of which span crust and core consistently and cover a range of the slope of the symmetry energy at saturation density $30 < L <120$ MeV. One set produces maximum masses $\approx$2.0$M_{\odot}$, the second $\approx$2.6$M_{\odot}$. We also include the effects of entrainment of crustal neutrons by the superfluid lattice. We find that for medium to stiff EOSs, observations imply $>70\%$ of the moment of inertia of the core is coupled to the crust during the glitch, though for softer EOSs $L\approx 30$MeV as little as $5\%$ could be coupled. No EOS is able to reproduce the observed glitch activity with crust neutrons alone, but extending the region where superfluid vortices are strongly pinned into the core by densities as little as 0.016fm$^{-3}$ above the crust-core transition density restores agreement with the observed glitch activity.

### Unusual A2142 supercluster with a collapsing core: distribution of light and mass [Replacement]

We study the distribution, masses, and dynamical properties of galaxy groups in the A2142 supercluster. We analyse the global luminosity density distribution in the supercluster and divide the supercluster into the high-density core and the low-density outskirts regions. We find galaxy groups and filaments in the regions of different global density, calculate their masses and mass-to-light ratios and analyse their dynamical state with several 1D and 3D statistics. We use the spherical collapse model to study the dynamical state of the supercluster. We show that in A2142 supercluster groups and clusters with at least ten member galaxies lie along an almost straight line forming a 50 Mpc/h long main body of the supercluster. The A2142 supercluster has a very high density core surrounded by lower-density outskirt regions. The total estimated mass of the supercluster is M_est = 6.2 10^{15}M_sun. More than a half of groups with at least ten member galaxies in the supercluster lie in the high-density core of the supercluster, centered at the rich X-ray cluster A2142. Most of the galaxy groups in the core region are multimodal. In the outskirts of the supercluster, the number of groups is larger than in the core, and groups are poorer. The orientation of the cluster A2142 axis follows the orientations of its X-ray substructures and radio halo, and is aligned along the supercluster axis. The high-density core of the supercluster with the global density D8 > 17 and perhaps with D8 > 13 may have reached the turnaround radius and started to collapse. A2142 supercluster with luminous, collapsing core and straight body is an unusual object among galaxy superclusters. In the course of the future evolution the supercluster may be split into several separate systems.

### Unusual A2142 supercluster with a collapsing core: distribution of light and mass

We study the distribution, masses, and dynamical properties of galaxy groups in the A2142 supercluster. We analyse the global luminosity density distribution in the supercluster and divide the supercluster into the high-density core and the low-density outskirts regions. We find galaxy groups and filaments in the regions of different global density, calculate their masses and mass-to-light ratios and analyse their dynamical state with several 1D and 3D statistics. We use the spherical collapse model to study the dynamical state of the supercluster. We show that in A2142 supercluster groups and clusters with at least ten member galaxies lie along an almost straight line forming a 50 Mpc/h long main body of the supercluster. The A2142 supercluster has a very high density core surrounded by lower-density outskirt regions. The total estimated mass of the supercluster is M_est = 6.2 10^{15}M_sun. More than a half of groups with at least ten member galaxies in the supercluster lie in the high-density core of the supercluster, centered at the rich X-ray cluster A2142. Most of the galaxy groups in the core region are multimodal. In the outskirts of the supercluster, the number of groups is larger than in the core, and groups are poorer. The orientation of the cluster A2142 axis follows the orientations of its X-ray substructures and radio halo, and is aligned along the supercluster axis. The high-density core of the supercluster with the global density D8 > 17 and perhaps with D8 > 13 may have reached the turnaround radius and started to collapse. A2142 supercluster with luminous, collapsing core and straight body is an unusual object among galaxy superclusters. In the course of the future evolution the supercluster may be split into several separate systems.

### Angular momentum redistribution by mixed modes in evolved low-mass stars. II. Spin-down of the core of red giants induced by mixed modes

The detection of mixed modes in subgiants and red giants by the CoRoT and \emph{Kepler} space-borne missions allows us to investigate the internal structure of evolved low-mass stars. In particular, the measurement of the mean core rotation rate as a function of the evolution places stringent constraints on the physical mechanisms responsible for the angular momentum redistribution in stars. It showed that the current stellar evolution codes including the modelling of rotation fail to reproduce the observations. An additional physical process that efficiently extracts angular momentum from the core is thus necessary. Our aim is to assess the ability of mixed modes to do this. To this end, we developed a formalism that provides a modelling of the wave fluxes in both the mean angular momentum and the mean energy equations in a companion paper. In this article, mode amplitudes are modelled based on recent asteroseismic observations, and a quantitative estimate of the angular momentum transfer is obtained. This is performed for a benchmark model of 1.3 $M_{\odot}$ at three evolutionary stages, representative of the evolved pulsating stars observed by CoRoT and Kepler. We show that mixed modes extract angular momentum from the innermost regions of subgiants and red giants. However, this transport of angular momentum from the core is unlikely to counterbalance the effect of the core contraction in subgiants and early red giants. In contrast, for more evolved red giants, mixed modes are found efficient enough to balance and exceed the effect of the core contraction, in particular in the hydrogen-burning shell. Our results thus indicate that mixed modes are a promising candidate to explain the observed spin-down of the core of evolved red giants, but that an other mechanism is to be invoked for subgiants and early red giants.

### Sound-Triggered Collapse of Stably Oscillating Low-Mass Cores in a Two-Phase Interstellar Medium

Inspired by Barnard 68, a Bok globule, that undergoes stable oscillations, we perform multi-phase hydrodynamic simulations to analyze the stability of Bok globules. We show that a high-density soft molecular core, with an adiabatic index $\gamma$ = 0.7 embedded in a warm isothermal diffuse gas, must have a small density gradient to retain the stability. Despite being stable, the molecular core can still collapse spontaneously as it will relax to develop a sufficiently large density gradient after tens of oscillations, or a few $10^7$ years. However, during its relaxation, the core may abruptly collapse triggered by the impingement of small-amplitude, long-wavelength ($\sim$ 6 $-$ 36 pc) sound waves in the warm gas. This triggered collapse mechanism is similar to a sonoluminescence phenomenon, where underwater ultrasounds can drive air bubble coalescence. The collapse configuration is found to be different from both inside-out and outside-in models of low-mass star formation; nonetheless the mass flux is close to the prediction of the inside-out model. The condition and the efficiency for this core collapse mechanism are identified. Generally speaking, a broad-band resonance condition must be met, where the core oscillation frequency and the wave frequency should match each other within a factor of several. A consequence of our findings predicts the possibility of propagating low-mass star formation, for which collapse of cores, within a mass range short of one order of magnitude, takes place sequentially tracing the wave front across a region of few tens of pc over $10^7$ years.

### Effects of Ohmic and ambipolar diffusion on the formation and evolution of the first cores, protostars and circumstellar discs [Replacement]

We investigate the formation and evolution of a first core, protostar, and circumstellar disc with a three-dimensional non-ideal (including both Ohmic and ambipolar diffusion) radiation magnetohydrodynamics simulation. We found that the magnetic flux is largely removed by magnetic diffusion in the first core phase and that the plasma $\beta$ of the centre of the first core becomes large, $\beta>10^4$. Thus, proper treatment of first core phase is crucial in investigating the formation of protostar and disc. On the other hand, in an ideal simulation, $\beta\sim 10$ at the centre of the first core. The simulations with magnetic diffusion show that the circumstellar disc forms at almost the same time of protostar formation even with a relatively strong initial magnetic field (the value for the initial mass-to-flux ratio of the cloud core relative to the critical value is $\mu=4$). The disc has a radius of $r \sim 1$ AU at the protostar formation epoch. We confirm that the disc is rotationally supported. We also show that the disc is massive ($Q\sim 1$) and that gravitational instability may play an important role in the subsequent disc evolution.

### Effects of Ohmic and ambipolar diffusion on the formation and evolution of the first core, protostar and circumstellar disc

We investigate the formation and evolution of the first core, protostar, and circumstellar disc with a three-dimensional non-ideal (including both Ohmic and ambipolar diffusion) radiation magnetohydrodynamics simulation. We found that the magnetic flux is largely removed by magnetic diffusion in the first core phase and that the plasma $\beta$ of the centre of the first core becomes large, $\beta>10^4$. On the other hand, in an ideal simulation, $\beta\sim 10$ at the centre of the first core. Even though $\beta$ inside the first core thus differs significantly between the resistive and ideal model, the angular momentum of the first core does not. The simulations with magnetic diffusion show that the circumstellar disc forms at almost the same time of protostar formation even with a relatively strong initial magnetic field (the value for the initial mass-to-flux ratio of the cloud core relative to the critical value is $\mu=4$). The disc has a radius of $r \sim 1$ AU at the protostar formation epoch. We confirm that the disc is rotationally supported. We also show that the disc is massive ($Q\sim 1$) and that gravitational instability may play an important role in the subsequent disc evolution.

### Effects of Ohmic and ambipolar diffusion on the formation and evolution of the first cores, protostars and circumstellar discs [Replacement]

We investigate the formation and evolution of a first core, protostar, and circumstellar disc with a three-dimensional non-ideal (including both Ohmic and ambipolar diffusion) radiation magnetohydrodynamics simulation. We found that the magnetic flux is largely removed by magnetic diffusion in the first core phase and that the plasma $\beta$ of the centre of the first core becomes large, $\beta>10^4$. Thus, proper treatment of first core phase is crucial in investigating the formation of protostar and disc. On the other hand, in an ideal simulation, $\beta\sim 10$ at the centre of the first core. The simulations with magnetic diffusion show that the circumstellar disc forms at almost the same time of protostar formation even with a relatively strong initial magnetic field (the value for the initial mass-to-flux ratio of the cloud core relative to the critical value is $\mu=4$). The disc has a radius of $r \sim 1$ AU at the protostar formation epoch. We confirm that the disc is rotationally supported. We also show that the disc is massive ($Q\sim 1$) and that gravitational instability may play an important role in the subsequent disc evolution.

### ALMA Observations of the IRDC Clump G34.43+00.24 MM3: DNC/HNC Ratio

We have observed the clump G34.43+00.24 MM3 associated with an infrared dark cloud in DNC $J$=3--2, HN$^{13}$C $J$=3--2, and N$_2$H$^+$ $J$=3--2 with the Atacama Large Millimeter/submillimeter Array (ALMA). The N$_2$H$^+$ emission is found to be relatively weak near the hot core and the outflows, and its distribution is clearly anti-correlated with the CS emission. This result indicates that a young outflow is interacting with cold ambient gas. The HN$^{13}$C emission is compact and mostly emanates from the hot core, whereas the DNC emission is extended around the hot core. Thus, the DNC and HN$^{13}$C emission traces warm regions near the protostar differently. The DNC emission is stronger than the HN$^{13}$C emission toward most parts of this clump. The DNC/HNC abundance ratio averaged within a $15^{\prime\prime} \times 15^{\prime\prime}$ area around the phase center is higher than 0.06. This ratio is much higher than the value obtained by the previous single-dish observations of DNC and HN$^{13}$C $J$=1--0 ($\sim$0.003). It seems likely that the DNC and HNC emission observed with the single-dish telescope traces lower density envelopes, while that observed with ALMA traces higher density and highly deuterated regions. We have compared the observational results with chemical-model results in order to investigate the behavior of DNC and HNC in the dense cores. Taking these results into account, we suggest that the low DNC/HNC ratio in the high-mass sources obtained by the single-dish observations are at least partly due to the low filling factor of the high density regions.

### Analytical Model of Tidal Distortion and Dissipation for a Giant Planet with a Viscoelastic Core

We present analytical expressions for the tidal Love numbers of a giant planet with a solid core and a fluid envelope. We model the core as a uniform, incompressible, elastic solid, and the envelope as a non-viscous fluid satisfying the $n=1$ polytropic equation of state. We discuss how the Love numbers depend on the size, density, and shear modulus of the core. We then model the core as a viscoelastic Maxwell solid and compute the tidal dissipation rate in the planet as characterized by the imaginary part of the Love number $k_2$. Our results improve upon existing calculations based on planetary models with a solid core and a uniform ($n=0$) envelope. Our analytical expressions for the Love numbers can be applied to study tidal distortion and viscoelastic dissipation of giant planets with solid cores of various rheological properties, and our general method can be extended to study tidal distortion/dissipation of super-earths.

### Relativistic effects on tidal disruption kicks of solitary stars

Solitary stars that wander too close to their galactic centres can become tidally disrupted, if the tidal forces due to the supermassive black hole (SMBH) residing there overcome the self-gravity of the star. If the star is only partially disrupted, so that a fraction survives as a self-bound object, this remaining core will experience a net gain in specific orbital energy, which translates into a velocity "kick" of up to $\sim 10^3$ km/s. In this paper, we present the result of smoothed particle hydrodynamics (SPH) simulations of such partial disruptions, and analyse the velocity kick imparted on the surviving core. We compare $\gamma$ = 5/3 and $\gamma$ = 4/3 polytropes disrupted in both a Newtonian potential, and a generalized potential that reproduces most relativistic effects around a Schwarzschild black hole either exactly or to excellent precision. For the Newtonian case, we confirm the results of previous studies that the kick velocity of the surviving core is virtually independent of the ratio of the black hole to stellar mass, and is a function of the impact parameter $\beta$ alone, reaching at most the escape velocity of the original star. For a given $\beta$, relativistic effects become increasingly important for larger black hole masses. In particular, we find that the kick velocity increases with the black hole mass, making larger kicks more common than in the Newtonian case, as low-$\beta$ encounters are statistically more likely than high-$\beta$ encounters. The analysis of the tidal tensor for the generalized potential shows that our results are robust lower limits on the true relativistic kick velocities, and are generally in very good agreement with the exact results.

### Relativistic effects on tidal disruption kicks of solitary stars [Replacement]

Solitary stars that wander too close to their galactic centres can become tidally disrupted, if the tidal forces due to the supermassive black hole (SMBH) residing there overcome the self-gravity of the star. If the star is only partially disrupted, so that a fraction survives as a self-bound object, this remaining core will experience a net gain in specific orbital energy, which translates into a velocity "kick" of up to $\sim 10^3$ km/s. In this paper, we present the result of smoothed particle hydrodynamics (SPH) simulations of such partial disruptions, and analyse the velocity kick imparted on the surviving core. We compare $\gamma$ = 5/3 and $\gamma$ = 4/3 polytropes disrupted in both a Newtonian potential, and a generalized potential that reproduces most relativistic effects around a Schwarzschild black hole either exactly or to excellent precision. For the Newtonian case, we confirm the results of previous studies that the kick velocity of the surviving core is virtually independent of the ratio of the black hole to stellar mass, and is a function of the impact parameter $\beta$ alone, reaching at most the escape velocity of the original star. For a given $\beta$, relativistic effects become increasingly important for larger black hole masses. In particular, we find that the kick velocity increases with the black hole mass, making larger kicks more common than in the Newtonian case, as low-$\beta$ encounters are statistically more likely than high-$\beta$ encounters. The analysis of the tidal tensor for the generalized potential shows that our results are robust lower limits on the true relativistic kick velocities, and are generally in very good agreement with the exact results.

### Rotation of Giant Stars [Replacement]

The internal rotation of post-main sequence stars is investigated, in response to the convective pumping of angular momentum toward the stellar core, combined with a tight magnetic coupling between core and envelope. The spin evolution is calculated using model stars of initial mass 1, 1.5 and $5\,M_\odot$, taking into account mass loss on the giant branches. We also include the deposition of orbital angular momentum from a sub-stellar companion, as influenced by tidal drag along with the excitation of orbital eccentricity by a fluctuating gravitational quadrupole moment. A range of angular velocity profiles $\Omega(r)$ is considered in the envelope, extending from solid rotation to constant specific angular momentum. We focus on the back reaction of the Coriolis force, and the threshold for dynamo action in the inner envelope. Quantitative agreement with measurements of core rotation in subgiants and post-He core flash stars by Kepler is obtained with a two-layer angular velocity profile: uniform specific angular momentum where the Coriolis parameter ${\rm Co} \equiv \Omega \tau_{\rm con} \lesssim 1$ (here $\tau_{\rm con}$ is the convective time); and $\Omega(r) \propto r^{-1}$ where ${\rm Co} \gtrsim 1$. The inner profile is interpreted in terms of a balance between the Coriolis force and angular pressure gradients driven by radially extended convective plumes. Inward angular momentum pumping reduces the surface rotation of subgiants, and the need for a rejuvenated magnetic wind torque. The co-evolution of internal magnetic fields and rotation is considered in Kissin & Thompson, along with the breaking of the rotational coupling between core and envelope due to heavy mass loss.

### Spin and Magnetism of White Dwarfs

The magnetism and rotation of white dwarf (WD) stars are investigated in relation to a hydromagnetic dynamo operating in the progenitor during shell burning phases. We find that the downward pumping of angular momentum in the convective envelope can, by itself, trigger dynamo action near the core-envelope boundary in an isolated intermediate-mass star. A solar-mass star must receive additional angular momentum following its rotational braking on the main sequence, either by a merger with a planet, or by tidal interaction in a stellar binary. Several arguments point to the outer core as the source for a magnetic field in the WD remnant: i) the outer third of a ~0.55$M_\odot$ WD is processed during the shell burning phases of the progenitor; ii) escape of magnetic helicity through the envelope mediates the growth of (compensating) helicity in the core, as is needed to maintain a stable magnetic field in the remnant; and iii) intense radiation flux at the core boundary facilitates magnetic buoyancy within a relatively thick tachocline layer. The helicity flux into the core is dominated by a persistent magnetic twist, which maintains solid rotation in the core against a latitude-dependent convective stress. The magnetic field deposited in an isolated massive WD can reach ~10MG, and is enhanced in strength if the star experiences an interaction with a brown dwarf or low-mass star. A buried toroidal field experiences moderate ohmic decay above an age ~1 Gyr, which may lead to growth or decay of the external magnetic field. The final WD spin period is related to a critical Coriolis parameter below which magnetic activity shuts off, and core and envelope decouple; it generally sits in the range of hours to days. A wider range of spin periods is possible when the star spins rapidly enough that core and envelope remain magnetically coupled, ranging from less than a day up to a year. (abridged)

### Spin and Magnetism of White Dwarfs [Replacement]

The magnetism and rotation of white dwarf (WD) stars are investigated in relation to a hydromagnetic dynamo operating in the progenitor during shell burning phases. We find that the downward pumping of angular momentum in the convective envelope can, by itself, trigger dynamo action near the core-envelope boundary in an isolated intermediate-mass star. A solar-mass star must receive additional angular momentum following its rotational braking on the main sequence, either by a merger with a planet, or by tidal interaction in a stellar binary. Several arguments point to the outer core as the source for a magnetic field in the WD remnant: i) the outer third of a ~0.55$M_\odot$ WD is processed during the shell burning phases of the progenitor; ii) escape of magnetic helicity through the envelope mediates the growth of (compensating) helicity in the core, as is needed to maintain a stable magnetic field in the remnant; and iii) intense radiation flux at the core boundary facilitates magnetic buoyancy within a relatively thick tachocline layer. The helicity flux into the core is dominated by a persistent magnetic twist, which maintains solid rotation in the core against a latitude-dependent convective stress. The magnetic field deposited in an isolated massive WD can reach ~10MG, and is enhanced in strength if the star experiences an interaction with a brown dwarf or low-mass star. A buried toroidal field experiences moderate ohmic decay above an age ~1 Gyr, which may lead to growth or decay of the external magnetic field. The final WD spin period is related to a critical Coriolis parameter below which magnetic activity shuts off, and core and envelope decouple; it generally sits in the range of hours to days. A wider range of spin periods is possible when the star spins rapidly enough that core and envelope remain magnetically coupled, ranging from less than a day up to a year. (abridged)

### Spin and Magnetism of White Dwarfs [Replacement]

The magnetism and rotation of white dwarf (WD) stars are investigated in relation to a hydromagnetic dynamo operating in the progenitor during shell burning phases. The downward pumping of angular momentum in the convective envelope, in combination with the absorption of a planet or tidal spin-up from a binary companion, can trigger strong dynamo action near the core-envelope boundary. Several arguments point to the outer core as the source for a magnetic field in the WD remnant: the outer third of a $\sim 0.55\,M_\odot$ WD is processed during the shell burning phase(s) of the progenitor; the escape of magnetic helicity through the envelope mediates the growth of (compensating) helicity in the core, as is needed to maintain a stable magnetic field in the remnant; and the intense radiation flux at the core boundary facilitates magnetic buoyancy within a relatively thick tachocline layer. The helicity flux into the growing core is driven by a dynamical imbalance with a latitude-dependent rotational stress. The magnetic field deposited in an isolated massive WD is concentrated in an outer shell of mass $\lesssim 0.1\,M_\odot$ and can reach $\sim 10\,$MG. A buried toroidal field experiences moderate ohmic decay above an age $\sim 0.3$ Gyr, which may lead to growth or decay of the external magnetic field. The final WD spin period is related to a critical spin rate below which magnetic activity shuts off, and core and envelope decouple; it generally sits in the range of hours to days. WD periods ranging up to a year are possible if the envelope re-expands following a late thermal pulse.

### Supernova Seismology: Gravitational Wave Signatures of Rapidly Rotating Core Collapse

Gravitational waves (GW) generated during a core-collapse supernova open a window into the heart of the explosion. At core bounce, progenitors with rapid core rotation rates exhibit a characteristic GW signal which can be used to constrain the properties of the core of the progenitor star. We investigate the dynamics of rapidly rotating core collapse, focusing on hydrodynamic waves generated by the core bounce and the GW spectrum they produce. The centrifugal distortion of the rapidly rotating proto-neutron star (PNS) leads to the generation of axisymmetric quadrupolar oscillations within the PNS and surrounding envelope. Using linear perturbation theory, we estimate the frequencies, amplitudes, damping times, and GW spectra of the oscillations. Our analysis provides a qualitative explanation for several features of the GW spectrum and shows reasonable agreement with nonlinear hydrodynamic simulations, although a few discrepancies due to non-linear/rotational effects are evident. The dominant early postbounce GW signal is produced by the fundamental quadrupolar oscillation mode of the PNS, at a frequency $0.70 \, {\rm kHz} \lesssim f \lesssim 0.80\,{\rm kHz}$, whose energy is largely trapped within the PNS and leaks out on a $\sim\!10$ ms timescale. Quasi-radial oscillations are not trapped within the PNS and quickly propagate outwards until they steepen into shocks. Both the PNS structure and Coriolis/centrifugal forces have a strong impact on the GW spectrum, and a detection of the GW signal can therefore be used to constrain progenitor properties.