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Register a new userFluctuations of the gravitational field generated by a random population of extended substructures
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Jorge Pe~narrubia
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A large population of extended substructures generates a stochastic gravitational field that is fully specified by the function $p({bf F})$, which defines the probability that a tracer particle experiences a force $bf F$ within the interval ${bf F},{bf F}+ dbf F$. This paper presents a statistical technique for deriving the spectrum of random fluctuations directly from the number density of substructures with known mass and size functions. Application to the subhalo population found in cold dark matter simulations of Milky Way-sized haloes shows that, while the combined force distribution is governed by the most massive satellites, the fluctuations of the {it tidal} field are completely dominated by the smallest and most abundant subhaloes. In light of this result we discuss observational experiments that may be sufficiently sensitive to Galactic tidal fluctuations to probe the dark low-end of the subhalo mass function and constrain the particle mass of warm and ultra-light axion dark matter models.
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This paper presents $N$-body and stochastic models that describe the motion of tracer particles in a potential that contains a large population of extended substructures. Fluctuations of the gravitational field induce a random walk of orbital velocities that is fully specified by drift and diffusion coefficients. In the impulse and local approximations the coefficients are computed analytically from the number density, mass, size and relative velocity of substructures without arbitrary cuts in forces or impact parameters. The resulting Coulomb logarithm attains a well-defined geometrical meaning, $ln(Lambda)=ln (D/c)$, where $D/c$ is the ratio between the average separation and the individual size of substructures. Direct-force and Monte-Carlo $N$-body experiments show excellent agreement with the theory if substructures are sufficiently extended ($c/Dgtrsim 10^{-3}$) and not spatially overlapping ($c/Dlesssim 10^{-1}$). However, close encounters with point-like objects ($c/Dll 10^{-3}$) induce a heavy-tailed, non-Gaussian distribution of high-energy impulses that cannot be described with Brownian statistics. In the point-mass limit ($c/Dapprox 0$) the median Coulomb logarithm measured from $N$-body models deviates from the theoretical relation, converging towards a maximum value $langle ln(Lambda)rangle approx 8.2$ independently of the mass and relative velocity of nearby substructures.
Gravitating systems surrounded by a dynamic sea of substructures experience fluctuations of the local tidal field which inject kinetic energy into the internal motions. This paper uses stochastic calculus techniques to describe `tidal heating as a random walk of orbital velocities that leads to diffusion in a 4-dimensional energy--angular momentum space. In spherical, static potentials we derive analytical solutions for the Greens propagators directly from the number density and velocity distribution of substructures with known mass & size functions without arbitrary cuts in forces or impact parameters. Furthermore, a Monte-Carlo method is presented, which samples velocity kicks from a probability function and can be used to model orbital scattering in fully generic potentials. For illustration, we follow the evolution of planetary orbits in a clumpy environment. We show that stochastic heating of (mass-less) discs in a Keplerian potential leads to the formation, and subsequent `evaporation of Oort-like clouds, and derive analytical expressions for the escape rate and the fraction of comets on retrograde orbits as a function of time. Extrapolation of the subhalo mass function of Milky Way-like haloes down to the WIMP free-streaming length suggests that objects in the outer Solar system experience repeated interactions with dark microhaloes on dynamical time-scales.
We investigate the gravitational wave (GW) signal generated by a population of double neutron-star binaries (DNS) with eccentric orbits caused by kicks during supernova collapse and binary evolution. The DNS population of a standard Milky-Way type galaxy has been studied as a function of star formation history, initial mass function (IMF) and metallicity and of the binary-star common-envelope ejection process. The model provides birth rates, merger rates and total numbers of DNS as a function of time. The GW signal produced by this population has been computed and expressed in terms of a hypothetical space GW detector (eLISA) by calculating the number of discrete GW signals at different confidence levels, where `signal refers to detectable GW strain in a given frequency-resolution element. In terms of the parameter space explored, the number of DNS-originating GW signals is greatest in regions of recent star formation, and is significantly increased if metallicity is reduced from 0.02 to 0.001, consistent with Belczynski10a. Increasing the IMF power-law index (from --2.5 to --1.5) increases the number of GW signals by a large factor. This number is also much higher for models where the common-envelope ejection is treated using the $alpha-$mechanism (energy conservation) than when using the $gamma-$mechanism (angular-momentum conservation). We have estimated the total number of detectable DNS GW signals from the Galaxy by combining contributions from thin disc, thick disc, bulge and halo. The most probable numbers for an eLISA-type experiment are 0-1600 signals per year at S/N$geqslant$1, 0-900 signals per year at S/N$geqslant$3, and 0-570 at S/N$geqslant$5, coming from about 0-65, 0-60 and 0-50 resolved DNS respectively.
We present the widest-field resolved stellar map to date of the closest ($Dsim3.8$ Mpc) massive elliptical galaxy NGC 5128 (Centaurus A; Cen A), extending out to a projected galactocentric radius of $sim150$ kpc. The dataset is part of our ongoing Panoramic Imaging Survey of Centaurus and Sculptor (PISCeS) utilizing the Magellan/Megacam imager. We resolve a population of old red giant branch stars down to $sim1.5$ mag below the tip of the red giant branch, reaching surface brightness limits as low as $mu_{V,0}sim32$ mag arcsec$^{-2}$. The resulting spatial stellar density map highlights a plethora of previously unknown streams, shells, and satellites, including the first tidally disrupting dwarf around Cen A (CenA-MM-Dw3), which underline its active accretion history. We report 13 previously unknown dwarf satellite candidates, of which 9 are confirmed to be at the distance of Cen A (the remaining 4 are not resolved into stars), with magnitudes in the range $M_V=-7.2$ to $-13.0$, central surface brightness values of $mu_{V,0}=25.4-26.9$ mag arcsec$^{-2}$, and half-light radii of $r_h=0.22-2.92$ kpc. These values are in line with Local Group dwarfs but also lie at the faint/diffuse end of their distribution; interestingly, CenA-MM-Dw3 has similar properties to the recently discovered ultra-diffuse galaxies in Virgo and Coma. Most of the new dwarfs are fainter than the previously known Cen A satellites. The newly discovered dwarfs and halo substructures are discussed in light of their stellar populations, and they are compared to those discovered by the PAndAS survey of M31.
What gravitational field is generated by a massive quantum system in a spatial superposition? Despite decades of intensive theoretical and experimental research, we still do not know the answer. On the experimental side, the difficulty lies in the fact that gravity is weak and requires large masses to be detectable. However, it becomes increasingly difficult to generate spatial quantum superpositions for increasingly large masses, in light of the stronger environmental effects on such systems. Clearly, a delicate balance between the need for strong gravitational effects and weak decoherence should be found. We show that such a trade off could be achieved in an optomechanics scenario that allows to determine whether the gravitational field generated by a quantum system in a spatial superposition is in a coherent superposition or not. We estimate the magnitude of the effect and show that it offers perspectives for observability.
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