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Hagai B. Perets

Publications and source records attributed to Hagai B. Perets.

At least 127 records · Page 7Linked to original sources

A triple origin for the lack of tight coplanar circumbinary planets around short-period binaries

Transiting circumbinary planets are more easily detected around short-period than long-period binaries, but none have yet been observed by {\it Kepler} orbiting binaries with periods shorter than seven days. In triple systems, secular Kozai-Lidov cycles and tidal friction (KLCTF) have been shown to reduce the inner orbital period from $\sim 10^4$ to a few days. Indeed, the majority of short-period binaries are observed to possess a third stellar companion. Using secular evolution analysis and population synthesis, we show that KLCTF makes it unlikely for circumbinary transiting planets to exist around short-period binaries. We find the following outcomes. (1) Sufficiently massive planets in tight and/or coplanar orbits around the inner binary can quench the KL evolution because they induce precession in the inner binary. The KLCTF process does not take place, preventing the formation of a short-period binary. (2) Secular evolution is not quenched and it drives the planetary orbit into a high eccentricity, giving rise to an unstable configuration, in which the planet is most likely ejected from the system. (3) Secular evolution is not quenched but the planet survives the KLCTF evolution. Its orbit is likely to be much wider than the currently observed inner binary orbit, and is likely to be eccentric and inclined with respect to the inner binary. These outcomes lead to two main conclusions: (1) it is unlikely to find a massive planet on a tight and coplanar orbit around a short-period binary, and (2) the properties of circumbinary planets in short-period binaries are constrained by secular evolution.

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Secular dynamics of hierarchical quadruple systems: the case of a triple system orbited by a fourth body

We study the secular gravitational dynamics of quadruple systems consisting of a hierarchical triple system orbited by a fourth body. These systems can be decomposed into three binary systems with increasing semimajor axes, binaries A, B and C. The Hamiltonian of the system is expanded in ratios of the three binary separations, and orbit-averaged. Subsequently, we numerically solve the equations of motion. We study highly hierarchical systems that are well described by the lowest-order terms in the Hamiltonian. We find that the qualitative behaviour is determined by the ratio $\mathcal{R}_0$ of the initial Kozai-Lidov (KL) time-scales of the binary pairs AB and BC. If $\mathcal{R}_0\ll 1$, binaries AB remain coplanar if this is initially the case, and KL eccentricity oscillations in binary B are efficiently quenched. If $\mathcal{R}_0\gg 1$, binaries AB become inclined, even if initially coplanar. However, there are no induced KL eccentricity oscillations in binary A. Lastly, if $\mathcal{R}_0\sim 1$, complex KL eccentricity oscillations can occur in binary A that are coupled with the KL eccentricity oscillations in B. Even if binaries A and B are initially coplanar, the induced inclination can result in very high eccentricity oscillations in binary A. These extreme eccentricities could have significant implications for strong interactions such as tidal interactions, gravitational wave dissipation, and collisions and mergers of stars and compact objects. As an example, we apply our results to a planet+moon system orbiting a central star, which in turn is orbited by a distant and inclined stellar companion or planet, and to observed stellar quadruples.

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The History of Tidal Disruption Events in Galactic Nuclei

The tidal disruption of a star by a massive black hole (MBH) is thought to produce a transient luminous event. Such tidal disruption events (TDEs) may play an important role in the detection and characterization of MBHs and probe the properties and dynamics of their nuclear stellar clusters (NSCs) hosts. Previous studies estimated the recent rates of TDEs in the local universe. However, the long-term evolution of the rates throughout the history of the universe has been hardly explored. Here we consider the TDE history, using evolutionary models for the evolution of galactic nuclei. We use a 1D Fokker-Planck approach to explore the evolution of MBH-hosting NSCs, and obtain the disruption rates of stars during their evolution. We complement these with an analysis of TDEs history based on N-body simulation data, and find them to be comparable. We consider NSCs that are built-up from close-in star-formation (SF) or from SF/clusters-dispersal far-out, a few pc from the MBH. We also explore cases where primordial NSCs exist and later evolve through additional star-formation/cluster-dispersal processes. We study the dependence of the TDE history on the type of galaxy, as well as the dependence on the MBH mass. These provide several scenarios, with a continuous increase of the TDE rates over time for cases of far-out SF and a more complex behavior for the close-in SF cases. Finally, we integrate the TDE histories of the various scenarios to provide a total TDE history of the universe, which can be potentially probed with future large surveys (e.g. LSST).

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Micro - tidal disruption events by stellar compact objects and the production of ultra-long GRBs

We explore full/partial tidal disruption events (TDEs) of stars/planets by stellar compact objects (Black holes; BHs; or neutron stars; NSs), which we term micro-TDEs. Disruption of a star/planet with mass $M_{\star}$ may lead to the formation of a debris disk around the BH/NS. Efficient accretion of a fraction $(f_{acc}=0.1$ of the debris may then give rise to bright energetic long ($10^{3}-10^{4}\,s$), X-ray/Gamma-ray flares, with total energies of up to $(f_{acc}/0.1)\times10^{52}\,(M_{\star}/{0.6\,M_{\odot}})\,$ergs, possibly resembling ultra-long GRBs/XRFs. The energy of such flares depends on the poorly constrained accretion processes. Significantly fainter flares might be produced if most of the disk mass is blown away through strong outflows. We suggest three dynamical origins for such disruptions. In the first, a star/planet is tidally disrupted following a close random encounter with a BH/NS in a dense cluster. We estimate the BH (NS) micro-TDE rates from this scenario to be few$\times10^{-6}$ (few$\times10^{-7}$) ${\rm yr}^{-1}$ per Milky-Way galaxy. Another scenario involves the interaction of wide companions due to perturbations by stars in the field, likely producing comparable but lower rates. Finally, a third scenario involves a BH/NS which gain a natal velocity kick at birth, leading to a close encounter with a binary companion and the tidal disruption of that companion. Such events could be associated with a supernova, or even with a preceding GRB/XRF event, and would likely occur hours to days after the prompt explosion; the rates of such events could be larger than those obtained from the other scenarios, depending on the preceding complex binary stellar evolution.

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Second generation stellar disks in Dense Star Clusters and cluster ellipticities

Globular Clusters (GCs) and Nuclear Star Clusters (NSCs) are typically composed by several stellar populations, characterized by different chemical compositions. Different populations show different ages in NSCs but not necessarily in GCs. The youngest populations in NSCs appear to reside in disk-like structures, as observed in our Galaxy and in M31. Gas infall followed by formation of second generation (SG) stars in GCs may similarly form disk-like structures in the clusters nuclei. Here we explore this possibility and follow the long term evolution of stellar disks embedded in GCs, and study their effects on the evolution of the clusters. We study disks with different masses by means of detailed N-body simulations and explore their morphological and kinematic signatures on the GC structures. We find that as a second generation disk relaxes, the old, first generation, stellar population flattens and becomes more radially anisotropic, making the GC structure become more elliptical. The second generation stellar population is characterized by a lower velocity dispersion, and a higher rotational velocity, compared with the primordial older population. The strength of these kinematic signatures depends both on the relaxation time of the system and on the fractional mass of the second generation disk. We therefore conclude that SG populations formed in flattened configurations will give rise to two systematic trends: (1) Positive correlation between GC ellipticity and fraction of SG population (2) Positive correlation between GC relaxation time and ellipticity. Thereby GC ellipticities and rotation could be related to the formation of SG stars and their initial configuration.

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Supernovae from direct collisions of white dwarfs and the role of helium shell ignition

Models for supernovae (SNe) arising from thermonuclear explosions of white dwarfs (WDs) have been extensively studied over the last few decades, mostly focusing on the single degenerate (accretion of material of a WD) and double degenerate (WD-WD merger) scenarios. In recent years it was suggested that WD-WD direct collisions provide an additional channel for such explosions. Here we extend the studies of such explosions, and explore the role of Helium-shells in affecting the thermonuclear explosions. We study both the impact of low-mass helium ($\sim0.01$ M$_{\odot})$ shells, as well as high mass shells ($\ge0.1$ M$_{\odot}$). We find that detonation of the massive helium layers precede the detonation of the WD Carbon-Oxygen (CO) bulk during the collision and can change the explosive evolution and outcomes for the cases of high mass He-shells. In particular, the He-shell detonation propagates on the WD surface and inefficiently burns material prior to the CO detonation that later follows in the central parts of the WD. Such evolution leads to larger production of intermediate elements, producing large yields of $^{44}{\rm Ti}$ and $^{48}{\rm Cr}$ relative to the pure CO-CO WD collisions. Collisions of WDs with a low-mass He-shell do not give rise to helium detonation, but helium burning does precede the CO bulk detonation. Such collisions produce a high velocity, low-mass of ejected burned material enriched with intermediate elements, with smaller changes to the overall explosion outcomes. The various effects arising from the contribution of low/high mass He layers change the kinematics and the morphological structure of collision-induced SNe and may thereby provide unique observational signatures for such SNe, and play a role in the chemical enrichment of galaxies and the production of intermediate elements and positrons from their longer-term decay.

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Application of Gas Dynamical Friction for Planetesimals: II. Evolution of Binary Planetesimals

One of first the stages of planet formation is the growth of small planetesimals and their accumulation into large planetesimals and planetary embryos. This early stage occurs much before the dispersal of most of the gas from the protoplanetary disk. At this stage gas-planetesimal interactions play a key role in the dynamical evolution of \emph{single} intermediate-mass planetesimals ($m_{p}\sim10^{21}-10^{25}g$) \emph{through gas dynamical friction} (GDF). A significant fraction of all Solar system planetesimals (asteroids and Kuiper-belt objects) are known to be binary planetesimals (BPs). Here, we explore the effects of GDF on the evolution of \emph{binary} planetesimals embedded in a gaseous disk using an N-body code with a fiducial external force accounting for GDF. We find that GDF can induce binary mergers on timescales shorter than the disk lifetime for masses above $m_{p}\gtrsim10^{22}g$ at 1AU, independent of the binary initial separation and eccentricity. Such mergers can affect the structure of merger-formed planetesimals, and the GDF-induced binary inspiral can play a role in the evolution of the planetesimal disk. In addition, binaries on eccentric orbits around the star may evolve in the supersonic regime, where the torque reverses and the binary expands, which would enhance the cross section for planetesimal encounters with the binary. Highly inclined binaries with small mass ratios, evolve due to the combined effects of Kozai-Lidov cycles with GDF which lead to chaotic evolution. Prograde binaries go through semi-regular Kozai-Lidov evolution, while retrograde binaries frequently flip their inclination and $\sim50\%$ of them are destroyed.

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Tidal capture formation of Low Mass X-Ray Binaries from wide binaries in the field

We present a potentially efficient dynamical formation scenario for Low Mass X-ray Binaries (LMXBs) in the field, focusing on black-hole (BH) LMXBs. In this formation channel LMXBs are formed from wide binaries $(>1000$ AU) with a BH component and a stellar companion. The wide binary is perturbed by fly-by's of field stars and its orbit random-walks and changes over time. This diffusion process can drive the binary into a sufficiently eccentric orbit such that the binary components tidally interact at peri-center and the binary evolves to become a short period binary, which eventually evolves into an LMXB. The formation rate of LMXBs through this channel mostly depends on the number of such BH wide binaries progenitors, which in turn depends on the velocity kicks imparted to BHs (or NSs) at birth. We consider several models for the formation and survival of such wide binaries, and calculate the LMXB formation rates for each model. We find that models where BHs form through direct collapse with no/little natal kicks can give rise to high formation rates comparable with those inferred from observations. This formation scenario had several observational signatures: (1) the number density of LMXBs generally follows the background stellar density and (2) the mass function of the BH stellar companion should be comparable to the mass function of the background stellar population, likely peaking at $0.4-0.6$ M$_{\odot}$. The latter aspect, in particular, is unique to this model compared with previously suggested LMXB formation models following common envelope binary stellar evolution. We note that NS LMXBs can similarly form from wide binaries, but their formation rate through this channel is likely significantly smaller due to their much higher natal kicks.

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Application of gas dynamical friction for planetesimals: I. Evolution of single planetesimals

The growth of small planetesimals into large planetary embryos occurs much before the dispersal of the gas from the protoplanetary disk. The planetesimal - gaseous-disk interactions give rise to migration and orbital evolution of the planetesimals/planets. Small planetesimals are dominated by aerodynamic gas drag. Large protoplanets, $m\sim0.1M_{\oplus}$, are dominated by type I migration \emph{differential} torque. There is an additional mass range, $m\sim10^{21}-10^{25}g$ of \emph{intermediate mass} planetesimals (IMPs), where gravitational interactions with the disk dominate over aerodynamic gas drag, but for which such interactions were typically neglected. Here we model these interactions using the \emph{gas dynamical friction} (GDF) approach, previously used to study the disk-planet interactions at the planetary mass range. We find the critical size where GDF dominates over gas drag, and then study the implications of GDF on single IMPs. We find that planetesimals with small inclinations rapidly become co-planar. Eccentric orbits circularize within a few Myrs, provided the the planetesimal mass is large, $m\gtrsim10^{23}g$ and that the initial eccentricity is low, $e\lesssim0.1$. Planetesimals of higher masses, $m\sim10^{24}-10^{25}g$ inspiral on a time-scale of a few Myrs, leading to \emph{an embryonic migration} to the inner disk. This can lead to an over-abundance of rocky material (in the form of IMPs) in the inner protoplanetary disk ($<1$AU) and induce rapid planetary growth. This can explain the origin of super-Earth planets. In addition, GDF damps the velocities of IMPs, thereby cooling the planetesimal disk and affecting its collisional evolution through quenching the effects of viscous stirring by the large bodies.

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On the existence of regular and irregular outer moons orbiting the Pluto-Charon system

The dwarf planet Pluto is known to host an extended system of five co-planar satellites. Previous studies have explored the formation and evolution of the system in isolation, neglecting perturbative effects by the Sun. Here we show that secular evolution due to the Sun can strongly affect the evolution of outer satellites and rings in the system, if such exist. Although precession due to extended gravitational potential from the inner Pluto-Charon binary quench such secular evolution up to $a_{crit}\sim0.0035$ AU ($\sim0.09$ $R_{Hill}$ the Hill radius; including all of the currently known satellites), outer orbits can be significantly altered. In particular, we find that \emph{co-planar} rings and satellites should not exist beyond $a_{crit}$; rather, satellites and dust particles in these regions secularly evolve on timescales ranging between $10^{4}-10^{6}$ yrs, and quasi-periodically change their inclinations and eccentricities through secular evolution (Lidov-Kozai oscillations). Such oscillations can lead to high inclinations and eccentricities, constraining the range where such satellites (and dust particles) can exist without crossing the orbits of the inner satellites, or crossing the outer Hill stability range. Outer satellites, if such exist are therefore likely to be \emph{irregular} satellites, with orbits limited to be non-circular and/or highly inclined. These could be potentially detected and probed by the New-Horizon mission, possibly providing direct evidence for the secular evolution of the Pluto satellite system, and shedding new light on its origins.

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Short and long term evolution of a stellar disk around a massive black hole: The role of binaries, the cusp and stellar evolution

We study the dynamical evolution of a stellar disk orbiting a massive black hole. We explore the role of two-body relaxation, mass segregation, stellar evolution and binary heating in affecting the disk evolution, and consider the impact of the nuclear cluster structure and the stellar-disk mass-function. We use analytic arguments and numerical calculations, and apply them to study the evolution of a stellar disk (similar to that observed in the Galactic center; GC), both on the short (few Myr) and longer (100 Myr) evolutionary timescales. We find the dominant processes affecting the disk evolution are two-body relaxation and mass segregation where as binary heating have only a little contribution. Massive stars play a dominant role in kinematically heating low mass stars, and driving them to high eccentricities/inclinations. Multi-mass models with realistic mass-functions for the disk stars show the disk structure to be mass stratified, with the most massive stars residing in thinner structures. Stellar evolution plays an important role in decreasing the number of massive stars with time, thereby leading to slower relaxation, where the remnant compact objects of these stars are excited to higher eccentricities/inclinations. At these later evolutionary stages dynamical heating by the nuclear cluster plays a progressively more important role. We conclude that the high eccentricities of the disk-stars in the Galactic Center suggest that the disk formed with initially high eccentricities, or that collective or secular processes dominate the disk evolution. Finally, we find that the disk structure is expected to keep a thin structure even after 100 Myrs. It therefore suggests earlier disks now containing only older, lower mass stars might still be observed in the Galactic center, unless destroyed/smeared by other non-two-body relaxation processes.

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A primordial origin for the composition similarity between the Earth and the Moon

Most of the properties of the Earth-Moon system can be explained by a collision between a planetary embryo and the growing Earth late in the accretion process. Simulations show that most of the material that eventually aggregates to form the Moon originates from the impactor. However, analysis of the terrestrial and lunar isotopic composition show them to be highly similar. In contrast, the compositions of other solar system bodies are significantly different than the Earth and Moon. This poses a major challenge to the giant impact scenario since the Moon-forming impactor is then thought to also have differed in composition from the proto-Earth. Here we track the feeding zones of growing planets in a suite of simulations of planetary accretion, in order to measure the composition of Moon-forming impactors. We find that different planets formed in the same simulation have distinct compositions, but the compositions of giant impactors are systematically more similar to the planets they impact. A significant fraction of planet-impactor pairs have virtually identical compositions. Thus, the similarity in composition between the Earth and Moon could be a natural consequence of a late giant impact.

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Star-formation in nuclear clusters and the origin of the Galactic Center apparent core distribution

Nuclear stellar cluster (NSCs) are known to exist around massive black holes (MBHs) in galactic nuclei. Two formation scenarios were suggested for their origin: Build-up of NSCs and Continuous in-situ star-formation. Here we study the effects of star formation on the build-up of NSCs and its implications for their long term evolution and their resulting structure. We show that continuous star-formation can lead to the build-up of an NSC with properties similar to those of the Milky-way NSC. We also find that the general structure of the old stellar population in the NSC with in-situ star-formation could be very similar to the steady-state Bahcall-Wolf cuspy structure. However, its younger stellar population do not yet achieve a steady state. In particular,formed/evolved NSCs with in-situ star-formation contain differential age-segregated stellar populations which are not yet fully mixed. Younger stellar populations formed in the outer regions of the NSC have a cuspy structure towards the NSC outskirts, while showing a core-like distribution inwards; with younger populations having larger core sizes.

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Photometric Amplitude Distribution of Stellar Rotation of Kepler KOIs-Indication for Spin-Orbit Alignment of Cool Stars and High Obliquity for Hot Stars

The observed amplitude of the rotational photometric modulation of a star with spots should depend on the inclination of its rotational axis relative to our line of sight. Therefore, the distribution of observed rotational amplitudes of a large sample of stars depends on the distribution of their projected axes of rotation. Thus, comparison of the stellar rotational amplitudes of the Kepler KOIs with those of Kepler single stars can provide a measure to indirectly infer the properties of the spin-orbit obliquity of Kepler planets. We apply this technique to the large samples of 993 KOIs and 33,614 single Kepler stars in temperature range of 3500-6500 K. We find with high significance that the amplitudes of cool KOIs are larger, on the order of 10%, than those of the single stars. In contrast, the amplitudes of hot KOIs are systematically lower. After correcting for an observational bias, we estimate that the amplitudes of the hot KOIs are smaller than the single stars by about the same factor of 10%. The border line between the relatively larger and smaller amplitudes, relative to the amplitudes of the single stars, occurs at about 6000K. Our results suggest that the cool stars have their planets aligned with their stellar rotation, while the planets around hot stars have large obliquities, consistent with the findings of Winn et al. (2010) and Albrecht et al. (2012). We show that the low obliquity of the planets around cool stars extends up to at least 50 days, a feature that is not expected in the framework of a model that assumes the low obliquity is due to planet-star tidal realignment.

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Formation and evolution of nuclear star clusters with in-situ star-formation: Nuclear cores and age segregation

Nuclear stellar cluster (NSCs) are known to exist around massive black holes (MBHs) in galactic nuclei. Two formation scenarios were suggested for their origin: (1) Build-up of NSCs from consecutive infall of stellar cluster and (2) Continuous in-situ star-formation. Though the cluster-infall scenario has been extensively studied in recent years, the in-situ formation scenario have been hardly explored. Here we use Fokker-Planck (FP) calculations to study the effects of star formation on the build-up of NSCs and its implications for their long term evolution and their resulting structure. We use the FP equation to describe the evolution of several stellar populations, and add appropriate source terms to account for the effects of newly formed stars. We show that continuous star-formation even 1-2 pc away from the MBH can lead to the build-up of an NSC with properties similar to those of the Milky-way NSC. We also find that the general structure of the old stellar population in the NSC with in-situ star-formation could be very similar to the steady-state Bahcall-Wolf cuspy structure. However, its younger stellar population do not yet achieve a steady state. In particular, formed/evolved NSCs with in-situ star-formation contain differential age-segregated stellar populations which are not yet fully mixed. Younger stellar populations formed in the outer regions of the NSC have a cuspy structure towards the NSC outskirts, while showing a core-like distribution inwards; with younger populations having larger core sizes. In principal, such a structure can give rise to an apparent core-like radial distribution of younger (up to 2-3 Gyrs) stars, as observed in the Galactic center. Such an NSC still preserves an underlying stellar cusp of older stars, that can be potentially be missed by current observations of red-giants.

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Secular Evolution Of Binaries Near Massive Black Holes: Formation of compact binaries, merger/collision products and G2-like objects

Here we discuss the evolution of binaries around MBH in nuclear stellar clusters. We focus on their secular evolution due to the perturbation by the MBH, while simplistically accounting for their collisional evolution. Binaries with highly inclined orbits in respect to their orbit around the MBH are strongly affected by secular processes, which periodically change their eccentricities and inclinations (e.g. Kozai--Lidov cycles). During periapsis approach, dissipative processes such as tidal friction may become highly efficient, and may lead to shrinkage of a binary orbit and even to its merger. Binaries in this environment can therefore significantly change their orbital evolution due to the MBH third-body perturbative effects. Such orbital evolution may impinge on their later stellar evolution. Here we follow the secular dynamics of such binaries and its coupling to tidal evolution, as well as the stellar evolution of such binaries on longer time-scales. We find that stellar binaries in the central parts of NSCs are highly likely to evolve into eccentric and/or short period binaries, and become strongly interacting binaries either on the main sequence (at which point they may even merge), or through their later binary stellar evolution. The central parts of NSCs therefore catalyze the formation and evolution of strongly interacting binaries, and lead to the enhanced formation of blue stragglers, X-ray binaries, gravitational wave sources and possible supernova progenitors. Induced mergers/collisions may also lead to the formation of G2-like cloud-like objects such as the one recently observed in the Galactic center.

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Effects of Intermediate Mass Black Holes on Nuclear Star Clusters

Nuclear star clusters (NSCs) are dense stellar clusters observed in galactic nuclei, typically hosting a central massive black hole. Here we study the possible formation and evolution of NSCs through the inspiral of multiple star clusters hosting intermediate mass black holes (IMBHs). Using an N-body code we examine the dynamics of the IMBHs and their effects on the NSC. We find that IMBHs inspiral to the core of the newly formed NSC and segregate there. Although the IMBHs scatter each other and the stars, none of them is ejected from the NSC. The IMBHs are excited to high eccentricities and their radial density profile develops a steep power-law cusp. The stars also develop a power-law cusp (instead of the central core that forms in their absence), but with a shallower slope. The relaxation rate of the NSC is accelerated due to the presence of IMBHs, which act as massive-perturbers. This in turn fills the loss-cone and boosts the tidal disruption rate of stars both by the MBH and the IMBHs to a value excluded by rate estimates based on current observations. Rate estimates of tidal disruptions can therefore provide a cumulative constraint on the existence of IMBHs in NSCs.

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Origin of the Galactic 511 keV emission from positrons produced in irregular supernovae

Gamma ray emission of 511 keV lines arising from electron-positron annihilation has been detected from the Galaxy since the 70s. Spatially resolved observations using the INTEGRAL satellite have shown its full sky distribution to be strongly concentrated in the Galactic bulge, with a smaller contribution from the disk, unlike the situation in any other wavelength. The puzzling distribution of the positrons gave rise to various suggestions, including stellar nucleosynthesis in core-collapse (CC) and type Ia thermonuclear supernovae (SNe), accreting compact objects, and more "exotic" explanations of annihilation of dark-matter particles. However, such models encounter difficulties in reproducing the total Galactic 511 keV flux as well as its peculiar bulge-centered distribution. Theoretical models of SNe from thermonuclear Helium detonations on white dwarfs (WDs) were suggested as potential additional sources of positrons, contributing to the Galactic Gamma-ray emission. Here, we show that the recently discovered class of faint, calcium-rich type Ib SNe (with the prototype SN 2005E), thought to arise from such explosions, also called ".Ia" SNe, can explain both the 511 keV flux and its distribution, and can eliminate the need for non-astrophysical (e.g., dark matter annihilation) sources. Such SNe comprise a fraction of only ~2% of all SNe, but they currently inject hundreds of times more positrons (from $^{44}$Ti decay) to the ISM than injected by CC SNe, enough to reproduce the total Galactic 511 keV line emission. They exclusively explode in old environments, and their contribution to the 511 keV emission therefore follows the old (>10 Gyrs) Galactic stellar population, dominated by the bulge, thereby reproducing the observed large bulge-to-disk ratio.

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