# Posts Tagged core

## Recent Postings from core

### 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 [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).

### 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).

### 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 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.

### 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 [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.

### 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)

### 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.

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

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.

### Persistent crust-core spin lag in neutron stars [Replacement]

It is commonly believed that the magnetic field threading a neutron star provides the ultimate mechanism (on top of fluid viscosity) for enforcing long-term corotation between the slowly spun down solid crust and the liquid core. We show that this argument fails for axisymmetric magnetic fields with closed field lines in the core, the commonly used twisted torus' field being the most prominent example. The failure of such magnetic fields to enforce global crust-core corotation leads to the development of a persistent spin lag between the core region occupied by the closed field lines and the rest of the crust and core. We discuss the repercussions of this spin lag for the evolution of the magnetic field, suggesting that, in order for a neutron star to settle to a stable state of crust-core corotation, the bulk of the toroidal field component should be deposited into the crust soon after the neutron star's birth.

### Persistent crust-core spin lag in neutron stars

It is commonly believed that the magnetic field threading a neutron star provides the ultimate mechanism (on top of fluid viscosity) for enforcing long-term corotation between the slowly spun down solid crust and the liquid core. We show that this argument fails for axisymmetric magnetic fields with closed field lines in the core, the commonly used twisted torus' field being the most prominent example. The failure of such magnetic fields to enforce global crust-core corotation leads to the development of a persistent spin lag between the core region occupied by the closed field lines and the rest of the crust and core. We discuss the repercussions of this spin lag for the evolution of the magnetic field, suggesting that, in order for a neutron star to settle to a stable state of crust-core corotation, the bulk of the toroidal field component should be deposited into the crust soon after the neutron star's birth.

### Multi-epoch, multi-frequency VLBI study of the parsec-scale jet in the blazar 3C 66A

We present the observational results of the Gamma-ray blazar, 3C 66A, at 2.3, 8.4, and 22 GHz at 4 epochs during 2004-05 with the VLBA. The resulting images show an overall core-jet structure extending roughly to the south with two intermediate breaks occurring in the region near the core. By model-fitting to the visibility data, the northmost component, which is also the brightest, is identified as the core according to its relatively flat spectrum and its compactness. As combined with some previous results to investigate the proper motions of the jet components, it is found the kinematics of 3C 66A is quite complicated with components of inward and outward, subluminal and superluminal motions all detected in the radio structure. The superluminal motions indicate strong Doppler boosting exists in the jet. The apparent inward motions of the innermost components last for at least 10 years and could not be caused by new-born components. The possible reason could be non-stationarity of the core due to opacity change.

### Extragalactic sources in Cosmic Microwave Background maps [Replacement]

We discuss the potential of a next generation space-borne CMB experiment for studies of extragalactic sources with reference to COrE+, a project submitted to ESA in response to the M4 call. We consider three possible options for the telescope size: 1m, 1.5m and 2m (although the last option is probably impractical, given the M4 boundary conditions). The proposed instrument will be far more sensitive than Planck and will have a diffraction-limited angular resolution. These properties imply that even the 1m telescope option will perform substantially better than Planck for studies of extragalactic sources. The source detection limits as a function of frequency have been estimated by means of realistic simulations. The most significant improvements over Planck results are presented for each option. COrE+ will provide much larger samples of truly local star-forming galaxies, making possible analyses of the properties of galaxies (luminosity functions, dust mass functions, star formation rate functions, dust temperature distributions, etc.) across the Hubble sequence. Even more interestingly, COrE+ will detect, at |b|> 30 deg, thousands of strongly gravitationally lensed galaxies. Such large samples are of extraordinary astrophysical and cosmological value in many fields. Moreover, COrE+ high frequency maps will be optimally suited to pick up proto-clusters of dusty galaxies, i.e. to investigate the evolution of large scale structure at larger redshifts than can be reached by other means. Thanks to its high sensitivity COrE+ will also yield a spectacular advance in the blind detection of extragalactic sources in polarization. This will open a new window for studies of radio source polarization and of the global properties of magnetic fields in star forming galaxies and of their relationships with SFRs.

### Extragalactic sources in Cosmic Microwave Background maps

We discuss the potential of a next generation space-borne CMB experiment for studies of extragalactic sources with reference to COrE+, a project submitted to ESA in response to the M4 call. We consider three possible options for the telescope size: 1m, 1.5m and 2m (although the last option is probably impractical, given the M4 boundary conditions). The proposed instrument will be far more sensitive than Planck and will have a diffraction-limited angular resolution. These properties imply that even the 1m telescope option will perform substantially better than Planck for studies of extragalactic sources. The source detection limits as a function of frequency have been estimated by means of realistic simulations. The most significant improvements over Planck results are presented for each option. COrE+ will provide much larger samples of truly local star-forming galaxies, making possible analyses of the properties of galaxies (luminosity functions, dust mass functions, star formation rate functions, dust temperature distributions, etc.) across the Hubble sequence. Even more interestingly, COrE+ will detect, at |b|> 30 deg, thousands of strongly gravitationally lensed galaxies. Such large samples are of extraordinary astrophysical and cosmological value in many fields. Moreover, COrE+ high frequency maps will be optimally suited to pick up proto-clusters of dusty galaxies, i.e. to investigate the evolution of large scale structure at larger redshifts than can be reached by other means. Thanks to its high sensitivity COrE+ will also yield a spectacular advance in the blind detection of extragalactic sources in polarization. This will open a new window for studies of radio source polarization and of the global properties of magnetic fields in star forming galaxies and of their relationships with SFRs.

### Efficient star cluster formation in the core of a galaxy cluster: The dwarf irregular NGC 1427A in Fornax

Gas-rich galaxies in dense environments such as galaxy clusters and massive groups are affected by a number of possible types of interactions with the cluster environment, which make their evolution radically different than that of field galaxies. The dIrr galaxy NGC 1427A, presently infalling towards the core of the Fornax galaxy cluster, offers a unique opportunity to study those processes in a level of detail not possible to achieve for galaxies at higher redshits. Using HST/ACS and auxiliary VLT/FORS ground-based observations, we study the properties of the most recent episodes of star formation in this gas-rich galaxy, the only one of its type near the core of the Fornax cluster. We study the structural and photometric properties of young star cluster complexes in NGC 1427A, identifying 12 bright such complexes with exceptionally blue colors. The comparison of our broadband near-UV/optical photometry with simple stellar population models yields ages below ~4x10^6 yr and stellar masses from a few thousand up to ~3x10^4 Msun, slightly dependent on the assumption of cluster metallicity and IMF. Their grouping is consistent with hierarchical and fractal star cluster formation. We use deep Halpha imaging data to determine the current Star Formation Rate (SFR) in NGC 1427A and estimate the ratio, Gamma, of star formation occurring in these star cluster complexes to that in the entire galaxy. We find Gamma to be exceptionally large, even after conservatively accounting for the possibility of contamination from intra-cluster light and other modelling uncertainties, implying that recent star formation predominantly occurred in star cluster complexes. This is the first time such high star cluster formation efficiency is reported in a dwarf galaxy within the confines of a galaxy cluster, strongly hinting at the possibility that is being triggered by its passage through the cluster environment.

### Efficient star cluster formation in the core of a galaxy cluster: The dwarf irregular NGC 1427A in Fornax [Replacement]

Gas-rich galaxies in dense environments such as galaxy clusters and massive groups are affected by a number of possible types of interactions with the cluster environment, which make their evolution radically different than that of field galaxies. The dIrr galaxy NGC 1427A, presently infalling towards the core of the Fornax galaxy cluster, offers a unique opportunity to study those processes in a level of detail not possible to achieve for galaxies at higher redshifts. Using HST/ACS and auxiliary VLT/FORS ground-based observations, we study the properties of the most recent episodes of star formation in this gas-rich galaxy, the only one of its type near the core of the Fornax cluster. We study the structural and photometric properties of young star cluster complexes in NGC 1427A, identifying 12 bright such complexes with exceptionally blue colors. The comparison of our broadband near-UV/optical photometry with simple stellar population models yields ages below ~4x10^6 yr and stellar masses from a few thousand up to ~3x10^4 Msun, slightly dependent on the assumption of cluster metallicity and IMF. Their grouping is consistent with hierarchical and fractal star cluster formation. We use deep Ha imaging data to determine the current Star Formation Rate (SFR) in NGC 1427A and estimate the ratio, Gamma, of star formation occurring in these star cluster complexes to that in the entire galaxy. We find Gamma to be exceptionally large, even after conservatively accounting for the possibility of contamination from intra-cluster light and other modelling uncertainties, implying that recent star formation predominantly occurred in star cluster complexes. This is the first time such high star cluster formation efficiency is reported in a dwarf galaxy within the confines of a galaxy cluster, strongly hinting at the possibility that is being triggered by its passage through the cluster environment.

### A starburst in the core of a galaxy cluster: The dwarf irregular NGC 1427A in Fornax [Replacement]

Gas-rich galaxies in dense environments such as galaxy clusters and massive groups are affected by a number of possible types of interactions with the cluster environment, which make their evolution radically different than that of field galaxies. The dIrr galaxy NGC 1427A, presently infalling towards the core of the Fornax galaxy cluster, offers a unique opportunity to study those processes in a level of detail not possible to achieve for galaxies at higher redshifts. Using HST/ACS and auxiliary VLT/FORS ground-based observations, we study the properties of the most recent episodes of star formation in this gas-rich galaxy, the only one of its type near the core of the Fornax cluster. We study the structural and photometric properties of young star cluster complexes in NGC 1427A, identifying 12 bright such complexes with exceptionally blue colors. The comparison of our broadband near-UV/optical photometry with simple stellar population models yields ages below ~4x10^6 yr and stellar masses from a few thousand up to ~3x10^4 Msun, slightly dependent on the assumption of cluster metallicity and IMF. Their grouping is consistent with hierarchical and fractal star cluster formation. We use deep Ha imaging data to determine the current Star Formation Rate (SFR) in NGC 1427A and estimate the ratio, Gamma, of star formation occurring in these star cluster complexes to that in the entire galaxy. We find Gamma to be among the largest such values available in the literature, consistent with starburst galaxies. Thus a large fraction of the current star formation in NGC 1427A is occurring in star clusters, with the peculiar spatial arrangement of such complexes strongly hinting at the possibility that the starburst is being triggered by the passage of the galaxy through the cluster environment.

### G305.136+0.068: A massive and dense cold core in an early stage of evolution

We report molecular line observations, made with ASTE and SEST, and dust continuum observations at 0.87 mm, made with APEX, towards the cold dust core G305.136+0.068. The molecular observations show that the core is isolated and roughly circularly symmetric and imply that it has a mass of $1.1\times10^3~M_\odot$. A simultaneous model fitting of the spectra observed in four transitions of CS, using a non-LTE radiative transfer code, indicates that the core is centrally condensed, with the density decreasing with radius as $r^{-1.8}$, and that the turbulent velocity increases towards the center. The dust observations also indicate that the core is highly centrally condensed and that the average column density is 1.1 g cm$^{-2}$, value slightly above the theoretical threshold required for the formation of high mass stars. A fit to the spectral energy distribution of the emission from the core indicates a dust temperature of $17\pm2$ K, confirming that the core is cold. Spitzer images show that the core is seen in silhouette from 3.6 to 24.0 $\mu$m and that is surrounded by an envelope of emission, presumably tracing an externally excited photo-dissociated region. We found two embedded sources within a region of 20" centered at the peak of the core, one of which is young, has a luminosity of $66~L_\odot$ and is accreting mass with a high accretion rate, of $\sim1\times10^{-4}~M_\odot$ yr$^{-1}$. We suggest that this object corresponds to the seed of a high mass protostar still in the process of formation. The present observations support the hypothesis that G305.136+0.068 is a massive and dense cold core in an early stage of evolution, in which the formation of a high mass star has just started.

### Vacuum currents induced by a magnetic flux around a cosmic string with finite core [Cross-Listing]

We evaluate the Hadamard function and the vacuum expectation value of the current density for a massive complex scalar field in the generalized geometry of a straight cosmic string with a finite core enclosing an arbitrary distributed magnetic flux along the string axis. For the interior geometry, a general cylindrically symmetric static metric tensor is used with finite support. In the region outside the core, both the Hadamard function and the current density are decomposed into the idealized zero-thickness cosmic string and core-induced contributions. The only nonzero component corresponds to the azimuthal current. The zero-thickness part of the latter is a periodic function of the magnetic flux inside the core, with the period equal to the quantum flux. As a consequence of the direct interaction of the quantum field with the magnetic field inside the penetrable core, the core-induced contribution, in general, is not a periodic function of the flux. In addition, the vacuum current, in general, is not a monotonic function of the distance from the string and may change the sign. For a general model of the core interior, we also evaluate the magnetic fields generated by the vacuum current. As applications of the general results, we have considered an impenetrable core modeled by Robin boundary condition, a core with the Minkowski-like interior and a core with a constant positive curvature space. Various exactly solvable distributions of the magnetic flux are discussed.

### Vacuum currents induced by a magnetic flux around a cosmic string with finite core [Cross-Listing]

We evaluate the Hadamard function and the vacuum expectation value of the current density for a massive complex scalar field in the generalized geometry of a straight cosmic string with a finite core enclosing an arbitrary distributed magnetic flux along the string axis. For the interior geometry, a general cylindrically symmetric static metric tensor is used with finite support. In the region outside the core, both the Hadamard function and the current density are decomposed into the idealized zero-thickness cosmic string and core-induced contributions. The only nonzero component corresponds to the azimuthal current. The zero-thickness part of the latter is a periodic function of the magnetic flux inside the core, with the period equal to the quantum flux. As a consequence of the direct interaction of the quantum field with the magnetic field inside the penetrable core, the core-induced contribution, in general, is not a periodic function of the flux. In addition, the vacuum current, in general, is not a monotonic function of the distance from the string and may change the sign. For a general model of the core interior, we also evaluate the magnetic fields generated by the vacuum current. As applications of the general results, we have considered an impenetrable core modeled by Robin boundary condition, a core with the Minkowski-like interior and a core with a constant positive curvature space. Various exactly solvable distributions of the magnetic flux are discussed.

### Vacuum currents induced by a magnetic flux around a cosmic string with finite core

We evaluate the Hadamard function and the vacuum expectation value of the current density for a massive complex scalar field in the generalized geometry of a straight cosmic string with a finite core enclosing an arbitrary distributed magnetic flux along the string axis. For the interior geometry, a general cylindrically symmetric static metric tensor is used with finite support. In the region outside the core, both the Hadamard function and the current density are decomposed into the idealized zero-thickness cosmic string and core-induced contributions. The only nonzero component corresponds to the azimuthal current. The zero-thickness part of the latter is a periodic function of the magnetic flux inside the core, with the period equal to the quantum flux. As a consequence of the direct interaction of the quantum field with the magnetic field inside the penetrable core, the core-induced contribution, in general, is not a periodic function of the flux. In addition, the vacuum current, in general, is not a monotonic function of the distance from the string and may change the sign. For a general model of the core interior, we also evaluate the magnetic fields generated by the vacuum current. As applications of the general results, we have considered an impenetrable core modeled by Robin boundary condition, a core with the Minkowski-like interior and a core with a constant positive curvature space. Various exactly solvable distributions of the magnetic flux are discussed.