We present a new self-consistent method for incorporating dark matter annihilation feedback (DMAF) in cosmological N-body simulations. The power generated by DMAF is evaluated at each dark matter (DM) particle which allows for flexible energy injection into the surrounding gas based on the specific DM annihilation model under consideration. Adaptive, individual time steps for gas and DM particles are supported and a new time-step limiter, derived from the propagation of a Sedov--Taylor blast wave, is introduced. We compare this donor-based approach with a receiver-based approach used in recent studies and illustrate the differences by means of a toy example. Furthermore, we consider an isolated halo and a cosmological simulation and show that for these realistic cases, both methods agree well with each other. The extension of our implementation to scenarios such as non-local energy injection, velocity-dependent annihilation cross-sections, and DM decay is straightforward.
We derive cosmological constraints on the annihilation cross section of dark matter with velocity-dependent structure, motivated by annihilating dark matter models through Sommerfeld or Breit-Wigner enhancement mechanisms. In models with annihilation cross section increasing with decreasing dark matter velocity, big-bang nucleosynthesis and cosmic microwave background give stringent constraints.
Traditionally, incorporating additional physics into existing cosmological simulations requires re-running the cosmological simulation code, which can be computationally expensive. We show that conditional Generative Adversarial Networks (cGANs) can be harnessed to predict how changing the underlying physics alters the simulation results. To illustrate this, we train a cGAN to learn the impact of dark matter annihilation feedback (DMAF) on the gas density distribution. The predicted gas density slices are visually difficult to distinguish from their real brethren and the peak counts differ by …
Assisted annihilation generates thermal sub-GeV dark matter through a novel annihilation between a pair of dark matter and standard-model-like states, called the "assister". We show that, depending on the mass hierarchy between the assister and dark matter, there can be either a suppression or a boost of the effective cross section. This augmentation enables the possibility of $\mathcal{O}(100)$ MeV scale dark matter with perturbative coupling that saturates the relic density estimates while being relatively insulated from cosmological constraints like big bang nucleosynthesis and cosmic micro…
We describe and test a novel Dark Matter Annihilation Feedback (DMAF) scheme that has been implemented into the well known cosmological simulation code \textsf{GADGET-2}. In the models considered here, dark matter can undergo self-annihilation/decay into radiation and baryons. These products deposit energy into the surrounding gas particles and then the dark matter/baryon fluid is self-consistently evolved under gravity and hydrodynamics. We present tests of this new feedback implementation in the case of idealised dark matter halos with gas components for a range of halo masses, concentration…
We review theoretical models of Population III.1 star formation, focusing on the protostellar feedback processes that are expected to terminate accretion and thus set the mass of these stars. We discuss how dark matter annihilation may modify this standard feedback scenario. Then, under the assumption that dark matter annihilation is unimportant, we predict the mass of stars forming in 12 cosmological minihalos produced in independent numerical simulations. This allows us to make a simple estimate of the Pop III.1 initial mass function and how it may evolve with redshift.
Cosmological observations and cold dark matter N-body simulations indicate that our Universe is populated by numerous halos, where dark matter particles annihilate, potentially producing Standard Model particles. In this paper we calculate the contribution to the diffuse neutrino background from dark matter annihilations in halos at all redshifts and we estimate the future sensitivity to the annihilation cross section of neutrino telescopes such as IceCube or ANTARES. We consider various parametrizations to describe the internal halo properties and for the halo mass function in order to bracke…
We revisit constraints on annihilating dark matter based on the global 21cm signature observed by EDGES. For this purpose, we used the numerical data of the latest N-body simulation performed by state-of-the-art standard in order to estimate the boost factor at high redshifts ($z$ = 10 - 100), which enhances the annihilation of dark matter in course of structure formation. By taking into account to what fraction injected energy from dark matter annihilation contributes to ionization, excitation and heating of intergalactic medium during dark ages, we estimated how large the global 21cm absorpt…
Residual late-time dark matter particle annihilations during and after Big Bang Nucleosynthesis (BBN) may alter the predicted cosmological abundances of the light elements. Within the constrained minimal supersymmetric extension of the Standard Model (the CMSSM) with a neutralino LSP, we find negligible effects on the abundances of Deuterium, He3, He4 and Li7 predicted by homogeneous BBN, but potentially a large enhancement in the predicted abundance of Li6. This enhancement may be as much as two orders of magnitude in the focus-point WMAP strip and in the coannihilation and funnel regions for…
We use the suite of Milky Way-like galaxies in the Auriga simulations to determine the contribution to annihilation radiation from dark matter subhalos in three velocity-dependent dark matter annihilation models: Sommerfeld, p-wave, and d-wave models. We compare these to the corresponding distribution in the velocity-independent s-wave annihilation model. For both the hydrodynamical and dark-matter-only simulations, only in the case of the Sommerfeld-enhanced annihilation does the total annihilation flux from subhalos exceed the total annihilation flux from the smooth halo component within the…
Feedback processes are thought to solve some of the long-standing issues of the numerical modelling of galaxy formation: over-cooling, low angular momentum, massive blue galaxies, extra-galactic enrichment, etc. The accretion of gas onto super-massive black holes in the centre of massive galaxies can release tremendous amounts of energy to the surrounding medium. We show, with cosmological Adaptive Mesh Refinement simulations, how the growth of black holes is regulated by the feedback from Active Galactic Nuclei using a new dual jet/heating mechanism. We discuss how this large amount of feedba…
We compute the cosmological boost factor at high redshifts of $z=10$-$100$ by integrating the non-linear matter power spectrum measured from high-resolution cosmological $N$-body simulations. An accurate boost factor is required to estimate the energy injection from dark matter annihilation, which may affect the cosmological re-ionization process. We combined various box-size simulations (side lengths of $1 \, {\rm kpc}$-$10 \, {\rm Mpc}$) to cover a wide range of scales, i.e. $k=1$-$10^7 \, {\rm Mpc}^{-1}$. The boost factor is consistent with the linear theory prediction at $z \gtrsim 50$ but…
We derive constraints on dark matter (DM) annihilation cross section and decay lifetime from cross-correlation analyses of the data from Fermi-LAT and weak lensing surveys that cover a wide area of $\sim660$ squared degrees in total. We improve upon our previous analyses by using an updated extragalactic $γ$-ray background data reprocessed with the Fermi Pass 8 pipeline, and by using well-calibrated shape measurements of about twelve million galaxies in the Canada-France-Hawaii Lensing Survey (CFHTLenS) and Red-Cluster-Sequence Lensing Survey (RCSLenS). We generate a large set of full-sky mock…
In this paper we consider the re-processing of high frequency photons emitted by HeII and HeI during the epoch of cosmological recombination by HeI and HI. We demonstrate that, in comparison to computations which neglect all feedback processes, the number of cosmological recombination photons that are related to the presence of helium in the early Universe could be increased by ~40%-70%. Our computations imply that per helium nucleus ~3-6 additional photons could be produced. Therefore, a total of ~12-14 helium-related photons are emitted during cosmological recombination. This is an important…
We introduce the Making Galaxies in a Cosmological Context (MaGICC) program of smoothed particle hydrodynamics (SPH) simulations. We describe a parameter study of galaxy formation simulations of an L* galaxy that uses early stellar feedback combined with supernova feedback to match the stellar mass--halo mass relationship. While supernova feedback alone can reduce star formation enough to match the stellar mass--halo mass relationship, the galaxy forms too many stars before z=2 to match the evolution seen using abundance matching. Our early stellar feedback is purely thermal and thus operates …
We determine the dark matter pair-wise relative velocity distribution in a set of Milky Way-like halos in the Auriga and APOSTLE simulations. Focusing on the smooth halo component, the relative velocity distribution is well-described by a Maxwell-Boltzmann distribution over nearly all radii in the halo. We explore the implications for velocity-dependent dark matter annihilation, focusing on four models which scale as different powers of the relative velocity: Sommerfeld, s-wave, p-wave, and d-wave models. We show that the J-factors scale as the moments of the relative velocity distribution, an…
We investigate a model where the dark matter particle is a chiral fermion field charged under a global $U(1)$ symmetry which is assumed to be spontaneously broken, leading to a pseudo-Goldstone boson (PGB). We argue that the dark matter annihilation into PGBs determine the dark matter relic abundance. Besides, we also note that experimental searches for PGBs allow either for a very long lived PGB, with a lifetime much longer than the age of the Universe, or a relatively short lived PGB, with a lifetime shorter than one minute. Hence, two different scenarios arise, producing very different sign…
The inhibition of the total HI $n\leftrightarrow 1$ transition rate by delayed resonant reabsorption of HI $(n+1)\to 1$ photons by HI $n\to 1$ line which is possible due to cosmological redshift is considered semi-analytically. The method taking into account this effect in the frame of simple three-level approximation model of recombination is suggested. It is confirmed that the resonant feedbacks affect ionization fraction at the level about 0.2% for the epoch of last scattering. Similar consideration of HeI $2^1P\leftrightarrow 1^1S$ $\Rightarrow$ HeI $2^3P\leftrightarrow 1^1S$ feedback for …
We investigate the observable effects of feedback from Active Galactic Nuclei (AGN) on non-thermal components of the intracluster medium (ICM). We have modelled feedback from AGN in cosmological simulations with the adaptive mesh refinement code ENZO, investigating three types of feedback that are sometimes called quasar, jet and radio mode. Using a small set of galaxy clusters simulated at high resolution, we model the injection and evolution of Cosmic Rays, as well as their effects on the thermal plasma. By comparing, both, the profiles of thermal gas to observed profiles from the ACCEPT sam…
Alternative cosmologies, based on extensions of General Relativity, predict modified thermal histories in the Early Universe during the pre Big Bang Nucleosynthesis (BBN) era, epoch which is not directly constrained by cosmological observations. When the expansion rate is enhanced with respect to the standard case, thermal relics typically decouple with larger relic abundances. The correct value of the relic abundance is therefore obtained for larger annihilation cross--sections, as compared to standard cosmology. A direct consequence is that indirect detection rates are enhanced. Extending pr…
If dark matter (DM) annihilation accounts for the tantalizing excess of cosmic ray electron/positrons, as reported by the PAMELA, ATIC, HESS and FERMI observatories, then the implied annihilation cross section must be relatively large. This results, in the context of standard cosmological models, in very small relic DM abundances that are incompatible with astrophysical observations. We explore possible resolutions to this apparent conflict in terms of non-standard cosmological scenarios; plausibly allowing for large cross sections, while maintaining relic abundances in accord with current obs…
Dark matter self-annihilation holds promise as one of the most robust mechanisms for the identification of the particle responsible for the Universe's missing mass. In this work, I examine the evolution of the dark matter annihilation power produced by smooth and collapsed structures over cosmic time, taking into account uncertainties in the structure of dark matter halos. As we search for observational signatures of annihilation, an understanding of this time evolution will help us to best direct our observational efforts, either with local measurements or investigation of the effects of anni…
In this paper we explore the potential effects of DM annihilations on the cosmological recombination spectrum. With this example we want to demonstrate that the cosmological recombination spectrum in principle is sensitive to details related to possible extra energy release during recombination. We restrict ourselves to DM models which produce a negligible primordial distortion of the CMB energy spectrum. However, since during the epoch of cosmological recombination a large fraction of the deposited energy can directly go into ionizations and excitations of neutral atoms, both the cosmological…
We develop a simple evolutionary scenario for the growth of supermassive black holes (BHs), assuming growth due to accretion only, to learn about the evolution of the BH mass function from $z=3$ to 0 and from it calculate the energy budgets of different modes of feedback. We tune the parameters of the model by matching the derived X-ray luminosity function (XLF) with the observed XLF of active galactic nuclei. We then calculate the amount of comoving kinetic and bolometric feedback as a function of redshift, derive a kinetic luminosity function and estimate the amount of kinetic feedback and $…
We analyze the basic properties of Brightest Cluster Galaxies (BCGs) produced by state of the art cosmological zoom-in hydrodynamical simulations. These simulations have been run with different sub-grid physics included. Here we focus on the results obtained with and without the inclusion of the prescriptions for supermassive black hole (SMBH) growth and of the ensuing Active Galactic Nuclei (AGN) feedback. The latter process goes in the right direction of decreasing significantly the overall formation of stars. However, BCGs end up still containing too much stellar mass, a problem that increa…
We include an energy term based on Dark Matter (DM) self-annihilation during the cooling and subsequent collapse of the metal-free gas, in halos hosting the formation of the first stars in the Universe. We have found that the feedback induced on the chemistry of the cloud does modify the properties of the gas throughout the collapse. However, the modifications are not dramatic, and the typical Jeans mass within the halo is conserved throughout the collapse, for all the DM parameters we have considered. This result implies that the presence of Dark Matter annihilations does not substantially mo…
Annihilation of cosmologically distributed dark matter is predicted to produce a potentially observable flux of high energy photons. Neglecting the contribution from local structure, this signal is predicted to be virtually uniform on the sky and, in order to be identified, must compete with various extragalactic backgrounds. We focus here on unresolved blazars and discuss several techniques for separating the dark matter signal from this background. First, the spectral shapes of the signal and background are expected to differ, a feature which can be exploited with the Fisher Matrix formalism…
We present an optimized variant of the halo model, designed to produce accurate matter power spectra well into the non-linear regime for a wide range of cosmological models. To do this, we introduce physically motivated free parameters into the halo-model formalism and fit these to data from high-resolution $N$-body simulations. For a variety of $Λ$CDM and $w$CDM models the halo-model power is accurate to $\simeq 5$ per cent for $k\leq 10h\,\mathrm{Mpc}$ and $z\leq 2$. An advantage of our new halo model is that it can be adapted to account for the effects of baryonic feedback on the power spec…
We develop a new sub-grid model for the growth of supermassive Black Holes (BHs) and their associated Active Galactic Nuclei (AGN) feedback in hydrodynamical cosmological simulations. Assuming that BHs are created in the early stages of galaxy formation, they grow by mergers and accretion of gas at a Eddington-limited Bondi accretion rate. However this growth is regulated by AGN feedback which we model using two different modes: a quasar-heating mode when accretion rates onto the BHs are comparable to the Eddington rate, and a radio-jet mode at lower accretion rates. In other words, our feedba…
Massive galaxies today typically are not forming stars despite being surrounded by hot gaseous halos with short central cooling times. This likely owes to some form of "quenching feedback" such as merger-driven quasar activity or radio jets emerging from central black holes. Here we implement heuristic prescriptions for these phenomena on-the-fly within cosmological hydrodynamic simulations. We constrain them by comparing to observed luminosity functions and color-magnitude diagrams from SDSS. We find that quenching from mergers alone does not produce a realistic red sequence, because 1 - 2 Gy…
Galaxy clusters are valuable cosmological probes. However, cluster mass estimates rely on observable quantities that are affected by complicated baryonic physics in the intracluster medium (ICM), including feedback from active galactic nuclei (AGN). Cosmological simulations have started to include AGN feedback using subgrid models. In order to make robust predictions, the systematics of different implementations and parametrizations need to be understood. We have developed an AGN subgrid model in FLASH that supports a few different black hole accretion models and feedback models. We use this m…
The annihilation or decay of Dark Matter (DM) particles could affect the thermal history of the universe and leave an observable signature in Cosmic Microwave Background (CMB) anisotropies. We update constraints on the annihilation rate of DM particles in the smooth cosmological background, using WMAP7 and recent small-scale CMB data. With a systematic analysis based on the Press-Schechter formalism, we also show that DM annihilation in halos at small redshift may explain entirely the reionization patterns observed in the CMB, under reasonable assumptions concerning the concentration and forma…
We investigate the implications of dark matter annihilations for cosmological parameter constraints using the causal entropic principle. In this approach cosmologies are weighted by the total entropy production within a causally connected region of spacetime. We calculate the expected entropy from dark matter annihilations within the causal diamond and investigate the preferred values of the cosmological constant and the mass and annihilation cross section of the annihilating dark matter and their dependence on the assumptions in the models. For realistic values of the cross section we typical…
We present a numerical scheme, implemented in the cosmological adaptive mesh refinement code ENZO, to model the injection of Cosmic Ray (CR) particles at shocks, their advection and their dynamical feedback on thermal baryonic gas. We give a description of the algorithms and show their tests against analytical and idealized one-dimensional problems. Our implementation is able to track the injection of CR energy, the spatial advection of CR energy and its feedback on the thermal gas in run-time. This method is applied to study CR acceleration and evolution in cosmological volumes, with both fix…
Indirect searches for the cosmological dark matter have become ever more competitive during the past years. Here, we report the first full calculation of leading electroweak corrections to the annihilation rate of supersymmetric neutralino dark matter. We find that these corrections can be huge, partially due to contributions that have been overlooked so far. Our results imply a significantly enhanced discovery potential of this well motivated dark matter candidate with current and upcoming cosmic ray experiments, in particular for gamma rays and models with somewhat small annihilation rates a…
We consider the propagation and energy losses of protons and anti-protons produced by dark matter annihilation at redshifts 100<z<~2000. In the case of dark matter annihilations into quarks, gluons and weak gauge bosons, protons and anti-protons carry about 20% of the energy injected into e^\pm and γ's, but their interactions are normally neglected when deriving cosmic microwave background bounds from altered recombination histories. Here, we follow numerically the energy-loss history of typical protons/antiprotons in the cosmological medium. We show that about half of their energy is channele…
We consider a modification to the standard cosmological history consisting of introducing a new species $ϕ$ whose energy density red-shifts with the scale factor $a$ like $ρ_ϕ\propto a^{-(4+n)}$. For $n>0$, such a red-shift is faster than radiation, hence the new species dominates the energy budget of the universe at early times while it is completely negligible at late times. If equality with the radiation energy density is achieved at low enough temperatures, dark matter can be produced as a thermal relic during the new cosmological phase. Dark matter freeze-out then occurs at higher tempera…
We show that feedback from active galactic nuclei (AGN) plays an essential role in reproducing the down-sizing phenomena, namely: the colour-magnitude relation; specific star formation rates; and the $α$ enhancement of early type galaxies. In our AGN model, black holes originate from Population III stars, in contrast to the merging scenario of previous works. In this paper, we show how the properties of present-day galaxies in cosmological chemo-hydrodynamical simulations change when we include our model for AGN feedback. Massive galaxies become redder, older, less massive, less compact, and s…
We show that the relic abundance of the minority component of asymmetric dark matter can be very sensitive to the expansion rate of the Universe and the temperature of transition between a non-standard pre-Big Bang Nucleosynthesis cosmological phase and the standard radiation dominated phase, if chemical decoupling happens before this transition. In particular, because the annihilation cross section of asymmetric dark matter is typically larger than that of symmetric dark matter in the standard cosmology, the decrease in relic density of the minority component in non-standard cosmologies with …
We present a new version of a semi-analytic model of cosmological galaxy formation, incorporating a star formation law with a feedback depending on the galaxy-scale mean dust opacity and metallicity, motivated by recent observations of star formation in nearby galaxies and theoretical considerations. This new model is used to investigate the effect of such a feedback on shaping the galaxy luminosity function and its evolution. Star formation activity is significantly suppressed in dwarf galaxies by the new feedback effect, and the faint-end slope of local luminosity functions can be reproduced…
In this study we quantify the properties of the gas and dark matter around active galactic nuclei (AGN) in simulated galaxy groups and clusters and analyze the effect of AGN feedback on the surrounding intra-cluster (group) medium. Our results suggest downsizing of AGN luminosity with host halo mass, supporting the results obtained from clustering studies of AGN. By examining the temperature and density distribution of the gas in the vicinity of AGN we show that due to feedback from the central engine, the gas gets displaced from the centre of the group/cluster resulting in a reduction of the …
We investigate the dark matter annihilation in the brane-world and quintessence scenarios, in which the modified cosmological expansion rate can enhance the thermal relic density of dark matter. According to the observed dark matter abundance, we constrain the thermally averaged annihilation cross section <σv> in these two scenarios. In addition, the big bang nucleosynthesis and the partial-wave unitarity are also used to place bounds on <σv>. It is found that both scenarios can lead to a large annihilation cross section, so they can be used to explain the recent PAMELA, ATIC and PPB-BETS anom…
We use 500 pc resolution cosmological simulations of a Virgo-like galaxy cluster to study the properties of the brightest cluster galaxy (BCG) that forms at the center of the halo. We compared two simulations; one incorporating only supernovae feedback and a second that also includes prescriptions for black hole growth and the resulting AGN feedback from gas accretion. As previous work has shown, with supernovae feedback alone we are unable to reproduce any of the observed properties of massive cluster ellipticals. The resulting BCG is rotating quickly, has a high Sersic index, a strong mass e…
(Context) We calculate constraints from current and future cosmic microwave background (CMB) measurements on annihilating dark matter (DM) with masses below the electroweak scale: m_{DM}=5-100 GeV. In particular, we focus our attention on the lower end of this mass range, as DM particles with masses m_{DM} ~ 10 GeV have been recently claimed to be consistent with the CoGeNT and DAMA/LIBRA results, while also providing viable DM candidates to explain the measurements of Fermi and WMAP haze. (Aims) We study the model (in)dependence of CMB spectrum on particle physics DM models, large scale struc…
Thermal dark matter at the MeV scale faces stringent bounds from a variety of cosmological probes. Here we perform a detailed evaluation of BBN bounds on the annihilation cross section of dark matter with a mass $1\,\text{MeV} \lesssim m_χ\lesssim 1\,\text{GeV}$. For $p-wave suppressed annihilations, constraints from BBN turn out to be significantly stronger than the ones from CMB observations, and are competitive with the strongest bounds from other indirect searches. We furthermore update the lower bound from BBN on the mass of thermal dark matter using improved determinations of primordial …
Cosmic microwave background (CMB) constraints on dark matter annihilation are a uniquely powerful tool in the quest to understand the nature of dark matter. Annihilation of dark matter to Standard Model particles between recombination and reionization heats baryons, ionizes neutral hydrogen, and alters the CMB visibility function. Surprisingly, CMB bounds on dark matter annihilation are not expected to improve significantly with the dramatic improvements in sensitivity expected in future cosmological surveys. In this paper, we will present a simple physical description of the origin of the CMB…
We show that dark matter annihilation around the time of recombination can lead to growing ionization fraction perturbations, that track the linear collapse of matter over-densities. This amplifies small scale cosmological perturbations to the free electron density by a significant amount compared to the usual acoustic oscillations. Electron density perturbations distort the CMB, inducing secondary non-gaussianity. We calculate the CMB bispectrum from recombination, that is marginally observable by Planck. Even though electron perturbations can be markedly boosted compared with the Standard Mo…
We investigate black hole-host galaxy scaling relations in cosmological simulations with a self-consistent black hole growth and feedback model. The sub-grid accretion model captures the key scalings governing angular momentum transport from galactic scales down to parsec scales, while our kinetic feedback implementation enables the injection of outflows with properties chosen to match observed nuclear outflows. We show that "quasar mode" feedback can have a large impact on the thermal properties of the intergalactic medium and the growth of galaxies and massive black holes for kinetic feedbac…
Numerous particle models for the cosmological dark matter feature a pair-annihilation rate that scales with powers of the relative velocity between the annihilating particles. As a result, the annihilation rate in the central regions of a dark matter halo can be significantly lower than at the halo's periphery for particular ambient gravitational potentials. While this might be offset by an increasing dark matter pair number density in the inner halo, it raises the question: what angular region for dark matter models with velocity-suppressed annihilation rates optimizes signal-to-noise? Here, …
We study the impact of the dark matter velocity distribution modelling on signals from velocity-dependent dark matter annihilation in Milky Way dwarf spheroidal galaxies. Using the high resolution APOSTLE simulations, we identify analogues corresponding to Milky Way dwarf spheroidal galaxies, and from these directly determine the dark matter pair-wise relative velocity distribution, and compare to best-fitting Maxwell-Boltzmann distribution models. For three velocity-dependent annihilation models, p-wave, d-wave, and the Sommerfeld model, we quantify the errors introduced when using the Maxwel…
We investigate how the way galaxies acquire their gas across cosmic time in cosmological hydrodynamic simulations is modified by a comprehensive physical model for baryonic feedback processes. To do so, we compare two simulations -- with and without feedback -- both evolved with the moving mesh code AREPO. The feedback runs implement the full physics model of the Illustris simulation project, including star formation driven galactic winds and energetic feedback from supermassive blackholes. We explore: (a) the accretion rate of material contributing to the net growth of galaxies and originatin…
We present a series of high-resolution cosmological simulations of galaxy formation to z=0, spanning halo masses ~10^8-10^13 M_sun, and stellar masses ~10^4-10^11. Our simulations include fully explicit treatment of both the multi-phase ISM (molecular through hot) and stellar feedback. The stellar feedback inputs (energy, momentum, mass, and metal fluxes) are taken directly from stellar population models. These sources of stellar feedback, with zero adjusted parameters, reproduce the observed relation between stellar and halo mass up to M_halo~10^12 M_sun (including dwarfs, satellites, MW-mass…
