Random Angular Momentum Research Articles

Numerical simulations of the random angular momentum in convection – II. Delayed explosions of red supergiants following ‘failed’ supernovae

ABSTRACT When collapse of the iron core in a massive red or yellow supergiant does not lead to an energetic supernova, a significant fraction of the convective hydrogen envelope will fall in towards the black hole formed from the collapsing core. The random velocity field in the convective envelope results in finite specific angular momentum in each infalling shell. Using 3D hydrodynamical simulations, we follow the infall of this material to small radii, resolving the circularization radii of the flow. We show that infall of the convective envelope leads to nearly complete envelope ejection in a ≳1048 erg explosion with outflow speeds of ≳200 km s−1. The light curve of such an explosion would show a characteristic, red plateau as the ejecta cools and a hydrogen recombination front recedes through the expanding ejecta. Adopting supernova IIp scalings, the event would have a plateau luminosity of ≳1040 erg s−1 and a duration of several hundreds of days. These events would appear quite similar to luminous red novae with red or yellow supergiant progenitors; some luminous red novae may, in fact, be signposts of black hole formation. The mechanism studied here produces more energetic explosions than the weak shock generated from radiation of neutrino energy during the protoneutron star phase. Because we cannot simulate all the way to the horizon, our results are likely lower limits on the energy and luminosity of transients produced during the collapse of a red or yellow supergiant to form a black hole.

Splashback Radius in a Spherical Collapse Model

It was shown several years ago that dark matter halo outskirts are characterized by very steep density profiles in a very small radial range. This feature has been interpreted as a pile-up of different particle orbits at a similar location, namely, splashback material at half an orbit after collapse. Adhikari et al. (2014) obtained the location of the splashback radius through a very simple model by calculating a dark matter shell trajectory in the secondary infall model while it crosses a growing NFW profile-shaped dark matter halo. Because they imposed a halo profile instead of calculating it from the trajectories of the shells of dark matter, they were not able to find the dark matter profile around the splashback radius. In the present paper, we use an improved spherical infall model taking into account shell crossing as well as several physical effects such as ordered and random angular momentum, dynamical friction, adiabatic contraction, etc. This allows us to determine the density profile from the inner to the outer region and to study the behavior of the outer density profile. We compare the density profiles and their logarithmic slope of with the simulation results of Diemer and Kravtsov (2014), finding a good agreement between the prediction of the model and the simulations.

Numerical simulations of the random angular momentum in convection: Implications for supergiant collapse to form black holes

ABSTRACT During the core collapse of massive stars that do not undergo a canonical energetic explosion, some of the hydrogen envelope of a red supergiant (RSG) progenitor may infall on to the newborn black hole (BH). Within the athena++ framework, we perform 3D, hydrodynamical simulations of idealized models of supergiant convection and collapse in order to assess whether the infall of the convective envelope can give rise to rotationally supported material, even if the star has zero angular momentum overall. Our dimension-less, polytropic models are applicable to the optically thick hydrogen envelope of non-rotating RSGs and cover a factor of 20 in stellar radius. At all radii, the specific angular momentum due to random convective flows implies associated circularization radii of 10–1500 times the innermost stable circular orbit of the BH. During collapse, the angular momentum vector of the convective flows is approximately conserved and is slowly varying on the time-scale relevant to forming discs at small radii. Our results indicate that otherwise failed explosions of RSGs lead to the formation of rotationally supported flows that are capable of driving outflows to large radii and powering observable transients. When the BH is able to accrete most of the hydrogen envelope, the final BH spin parameter is ∼ 0.5, even though the star is non-rotating. For fractional accretion of the envelope, the spin parameter is generally lower and never exceeds 0.8. We discuss the implications of our results for transients produced by RSG collapse to a black hole.

Mass-temperature relation in ΛCDM and modified gravity

We derive the mass-temperature relation using an improved top-hat model and a continuous formation model which takes into account the effects of the ordered angular momentum acquired through tidal-torque interaction between clusters, random angular momentum, dynamical friction, and modifications of the virial theorem to include an external pressure term usually neglected. We show that the mass-temperature relation differs from the classical self-similar behavior, $M \propto T^{3/2}$, and shows a break at $3--4$ keV, and a steepening with a decreasing cluster temperature. We then compare our mass-temperature relation with those obtained in the literature with $N$-body simulations for $f(R)$ and symmetron models. We find that the mass-temperature relation is not a good probe to test gravity theories beyond Einstein's general relativity, because the mass-temperature relation of the $\Lambda$CDM model is similar to that of the modified gravity theories.

Black hole accretion discs and luminous transients in failed supernovae from non-rotating supergiants

ABSTRACT We show that for supergiants, net angular momentum is not a necessary condition for forming accretion discs during core collapse. Even absent net rotation, convective motions in the outer parts of supergiants generate mean horizontal flows at a given radius with velocities of ${\sim } 1 \, {\rm km \, s}^{-1}$; the direction of the mean flow will vary as a function of height through the convection zone. We confirm these analytic estimates using Cartesian Boussinesq convection simulations. These mean horizontal flows lead to a random angular momentum in supergiant convection zones that exceeds that of the last stable circular orbit of a black hole by a factor of ∼10. As a result, failed explosions of supergiants – in which the accretion shock on to the neutron star does not revive, leading to black hole formation – may often produce accretion discs that can power day–week (blue supergiants) or week–year (yellow and red supergiants) non-thermal and thermal transients through winds and jets. These transients will be especially time variable because the angular momentum of the accreting material will vary substantially in time. Observed sources such as Swift J1644+57, iPTF14hls, and SN 2018cow, as well as energetic Type II supernovae (OGLE-2014-SN-073), may be produced by this mechanism.

Cusps and cores in the presence of galactic bulges

In this paper, we study how the presence of bulge formation in galaxies influence their inner density profile, by means of an extended version of the Del Popolo (2009) semi-analytical model. As in Del Popolo (2009), the model takes into account the effect of baryons adiabatic contraction, ordered and random angular momentum, dynamical friction, and adds to the previous the effect of gas cooling, star formation, supernova feedback, and reionization. Our model shows that dwarf galaxies are bulgeless, in agreement with observations showing that the large majority of them has no stellar bulges, and are characterized by a flat profile well described by a Burkert profile. We then studied the effect of a bulge, added to the cored DM halo, on the density profile. In the case of a galaxy having a mass 1011M⊙ the inner density profile has a slope α ≃ 0.65, for a bulge of 4.5 × 109M⊙ , while if bulge formation is not considered, the slope would be α ≃ 0.55. If the bulge is larger, 6.5 × 109M⊙ the slope is α ≃ 0.7. In the case of a larger galaxy with 1012M⊙ the slope is α ≃ 0.85, while in absence of bulge it is α ≃ 0.75. We finally study how the inner slope α changes with the bulge mass, and we find a correlation among the two quantities. The result shows that bulge formation has an important role in shaping the inner DM density profile in agreement with Inoue & Saitoh (2011) result. The result implies that going from Sc to SO Hubble type the slope is slightly steepening due to the bulge formation, and due to the fact that early type galaxies have larger bulges.

Surface density of dark matter haloes on galactic and cluster scales

In this paper, in the framework of the secondary infall model, the correlation between the central surface density and the halo core radius of galaxy, and cluster of galaxies, dark matter haloes was analyzed, this having recently been studied on a wide range of scales. We used Del Popolo (2009) secondary infall model taking into account ordered and random angular momentum, dynamical friction, and dark matter (DM) adiabatic contraction to calculate the density profile of haloes, and then these profiles are used to determine the surface density of DM haloes. The main result is that $r_\ast$ (the halo characteristic radius) is not an universal quantity as claimed by Donato et al. (2009) and Gentile et al. (2009). On the contrary, we find a correlation with the halo mass $M_{200}$ in agreement with Cardone & Tortora (2010), Boyarsky at al. (2009) and Napolitano et al. (2010), but with a significantly smaller scatter, namely $0.16 \pm 0.05$. We also consider the baryon column density finding this latter being indeed a constant for low mass systems such as dwarfs, but correlating with mass with a slope $\alpha= 0.18 \pm 0.05$. In the case of the surface density of dark matter for a system composed only of dark matter, as in dissipationless simulations, we get $\alpha=0.20 \pm 0.05$. These results leave little room for the recently claimed universality of (dark and stellar) column density.

On the density-profile slope of clusters of galaxies

The present paper extends a previous study of Del Popolo to clusters of galaxies, considering how baryon–dark matter (DM) interplay shapes the density profiles of dwarf galaxies. Cluster density profiles are determined taking into account dynamical friction, random and ordered angular momentum and the response of DM haloes to condensation of baryons. We find that haloes containing only DM are characterized by Einasto’s profiles, and that profiles flatten with increasing content of baryons and increasing values of random angular momentum. The analytical results obtained in the first part of the paper are applied to well-studied clusters, the inner profiles of which have slopes flatter than Navarro, Frenk & White (NFW) predictions (A611, A383) or are characterized by profiles in agreement with the NFW model (MACS J1423.8+2404, RXJ1133). By using an independently measured baryonic fraction and a typical spin parameter value λ≃ 0.03 and adjusting the random angular momentum, we re-obtain the mass and density profiles of the quoted clusters. Finally, we show that the baryonic mass inside ≃10 kpc, Mb, in, is correlated with the total mass of the clusters as ⁠.

Density profile slopes of dwarf galaxies and their environment

In the present paper, we study how the dark matter density profiles of dwarfs galaxies in the mass range $10^8-10^{10} M_{\odot}$ are modified by the interaction of the dwarf in study with the neighboring structures, and by changing baryon fraction in dwarfs. As already shown in Del Popolo (2009), the slope of density profile of inner halos flattens with decreasing halo mass and the profile is well approximated by a Burkert's profile. The analysis shows that dwarfs who suffered a smaller tidal torquing (consequently having smaller angular momentum) are characterized by steeper profiles with respect to dwarfs subject to higher torque, and similarly dwarfs having a smaller baryons fraction have also steeper profiles than those having a larger baryon fraction. In the case tidal torquing is shut down and baryons are not present, the density profile is very well approximated by an Einasto profile, similarly to dwarfs obtained in dissipationless N-body simulations. We then apply the result of the previous analysis to the dark matter halo rotation curves of three different dwarfs, namely NGC 2976, known to have a flat inner core, NGC 5949 having a profile intermediate between a cored and a cuspy one, and NGC 5963 having a cuspy profile. After calculating baryon fraction, which is $\simeq 0.1$ for the three galaxies, we fitted the rotation curves changing the value of angular momentum. NGC 2976, has an higher value of ordered angular momentum ($\lambda \simeq 0.04$) with respect to NGC 5949 ($\lambda \simeq 0.025$) and in the case of NGC 5963 the very steep profile can be obtained with a low value of $\lambda$ ($\lambda \simeq 0.02$) and also decreasing the value of the random angular momentum. In the case of NGC 2976 tidal interaction with M81 could have also influenced the inner part of the density profile.

Non-power law behavior of the radial profile of phase-space density of halos

We study the pseudo phase-space density, ρ(r)/σ3(r), of ΛCDM dark matter halos with and without baryons (baryons+DM, and pure DM), by using the model introduced in Del Popolo (2009), which takes into account the effect of dynamical friction, ordered and random angular momentum, baryons adiabatic contraction and dark matter baryons interplay. We examine the radial dependence of ρ(r)/σ3(r) over 9 orders of magnitude in radius for structures on galactic and cluster of galaxies scales. We find that ρ(r)/σ3(r) is approximately a power-law only in the range of halo radius resolved by current simulations (down to 0.1% of the virial radius) while it has a non-power law behavior below the quoted scale, with inner profiles changing with mass. The non-power-law behavior is more evident for halos constituted both of dark matter and baryons while halos constituted just of dark matter and with angular momentum chosen to reproduce a Navarro-Frenk-White (NFW) density profile, are characterized by an approximately power-law behavior. The results of the present paper lead to conclude that density profiles of the NFW type are compatible with a power-law behavior of ρ(r)/σ3(r), while those flattening to the halo center, like those found in Del Popolo (2009) or the Einasto profile, or the Burkert profile, cannot produce radial profile of the pseudo-phase-space density that are power-laws at all radii. The results argue against universality of the pseudo phase-space density and as a consequence argue against universality of density profiles constituted by dark matter and baryons as also discussed in Del Popolo (2009).

On the universality of density profiles

We use the secondary infall model described in Del Popolo (2009), which takes into account the effect of dynamical friction, ordered and random angular momentum, baryons adiabatic contraction and dark matter baryons interplay, to study how in- ner slopes of relaxed LCDM dark matter (DM) halos with and without baryons (baryons+DM, and pure DM) depend on redshift and on halo mass. We apply the quoted method to structures on galactic scales and clusters of galaxies scales. We find that the inner logarithmic density slope, of dark matter halos with baryons has a significant dependence on halo mass and redshift with slopes ranging from 0 for dwarf galaxies to 0.4 for objects of M = 10^13M_solar and 0.94 for M = 10^15M_solar clusters of galaxies. Structures slopes increase with increasing redshift and this trend reduces going from galaxies to clusters. In the case of density profiles constituted just of dark matter the mass and redshift dependence of slope is very slight. In this last case, we used the Merrit et al. (2006) analysis who compared N-body density profiles with various parametric models finding systematic variation in profile shape with halo mass. This last analysis suggests that the galaxy-sized halos obtained with our model have a different shape parameter, i.e. a different mass distribution, than the cluster-sized halos, obtained with the same model. The results of the present paper argue against universality of density profiles constituted by dark matter and baryons and confirm claims of a systematic variation in profile shape with halo mass, for dark matter halos.

Density profiles of dark matter haloes on galactic and cluster scales

In the present paper, we improve the "Extended Secondary Infall Model" (ESIM) of Williams et al. (2004) to obtain further insights on the cusp/core problem. The model takes into account the effect of ordered and random angular momentum, dynamical friction and baryon adiabatic contraction in order to obtain a secondary infall model more close to the collapse reality. The model is applied to structures on galactic scales (normal and dwarf spiral galaxies) and on cluster of galaxies scales. The results obtained suggest that angular momentum and dynamical friction are able, on galactic scales, to overcome the competing effect of adiabatic contraction eliminating the cusp. The NFW profile can be reobtained, in our model only if the system is constituted just by dark matter and the magnitude of angular momentum and dynamical friction are reduced with respect to the values predicted by the model itself. The rotation curves of four LSB galaxies from de Blok & Bosma (2002) are compared to the rotation curves obtained by the model in the present paper obtaining a good fit to the observational data. On scales smaller than $\simeq 10^{11} h^{-1} M_{\odot}$ the slope $\alpha \simeq 0$ and on cluster scales we observe a similar evolution of the dark matter density profile but in this case the density profile slope flattens to $\alpha \simeq 0.6$ for a cluster of $\simeq 10^{14} h^{-1} M_{\odot}$. The total mass profile, differently from that of dark matter, shows a central cusp well fitted by a NFW model.

THE CUSP/CORE PROBLEM AND THE SECONDARY INFALL MODEL

We study the cusp/core problem using a secondary infall model (SIM) that takes into account the effect of ordered and random angular momentum, dynamical friction and baryons adiabatic contraction. The model is applied to structures on galactic scales (normal and dwarfs spiral galaxies) and on clusters of galaxies scales. Our analysis suggest that angular momentum and dynamical friction are able, on galactic scales, to overcome the competing effect of adiabatic contraction eliminating the cusp. The slope of density profile of inner haloes flattens with decreasing halo mass and the profile is well approximated by a Burkert's profile. In order to obtain the NFW profile, starting from the profiles obtained from our model, the magnitude of angular momentum and dynamical friction must be reduced with respect to the values predicted by the model itself. The rotation curves of four LSB galaxies from Gentile et al. (2004) are compared to the rotation curves obtained by the model in the present paper obtaining a good fit to the observational data. The time evolution of the density profile of a galaxy of $10^8-10^9 M_{\odot}$ shows that after a transient steepening, due to the adiabatic contraction, the density profile flattens to $\alpha \simeq 0$. On cluster scales we observe a similar evolution of the dark matter density profile but in this case the density profile slope flattens to $\alpha \simeq 0.6$ for a cluster of $\simeq 10^{14} M_{\odot}$. The total mass profile, differently from that of dark matter, shows a central cusp well fitted by a NFW model.

Angular momentum transfer in the reactions induced by 166 MeVNe20onCu63

A study has been made of the energy, angular, and charge distribution of products emitted in the reaction of 166-MeV $^{20}\mathrm{Ne}$ ions with $^{63}\mathrm{Cu}$. The first three moments of the $\ensuremath{\gamma}$-ray multiplicity distribution and the out-of-plane $\ensuremath{\gamma}$-ray angular correlations have been measured in coincidence with the projectile-like fragments. Relaxation times of 2.6 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}22}$ s for energy dissipation, 4.1 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}22}$ s for angular momentum transfer, and a charge diffusion coefficient of 0.58 \ifmmode\times\else\texttimes\fi{} ${10}^{22}$ ${(\mathrm{charge}\mathrm{units})}^{2}$ ${\mathrm{s}}^{\ensuremath{-}1}$ have been deduced from these data. A small $\ensuremath{\gamma}$-ray anisotropy and a large width of the multiplicity distribution have been observed. These are interpreted in terms of a random component of transferred angular momentum whose magnitude is comparable to that of the aligned component induced by tangential friction. Thermal excitation of collective modes of motion in the equilibrated dinuclear complex can account quantitatively for these experimental results. Other mechanisms for the generation of a random component of angular momentum are also possible.NUCLEAR REACTIONS $^{63}\mathrm{Cu}(^{20}\mathrm{Ne}, X)$, $X=\mathrm{deeply}\mathrm{inelastic}\mathrm{fragments}$, evaporation residues, $E=166$ MeV, enriched target; measured $\ensuremath{\sigma}(E, \ensuremath{\theta}, Z)$, $\ensuremath{\gamma}$-ray multiplicity, angular correlations; deduced relaxation times, diffusion coefficients, random angular momentum. $^{63}\mathrm{Cu}(^{12}\mathrm{C}, X)$, $X=\mathrm{evaporation}\mathrm{residues}$, $E=133$ MeV, measured $\ensuremath{\gamma}$-ray multiplicity.