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Dusan Keres

Publications and source records attributed to Dusan Keres.

At least 73 records · Page 4Linked to original sources

Galaxies on FIRE (Feedback In Realistic Environments): Stellar Feedback Explains Cosmologically Inefficient Star Formation

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 disks, and small groups). By extension, this leads to reasonable agreement with the stellar mass function for M_star<10^11 M_sun. We predict weak redshift evolution in the M_star-M_halo relation, consistent with current constraints to z>6. We find that the M_star-M_halo relation is insensitive to numerical details, but is sensitive to the feedback physics. Simulations with only supernova feedback fail to reproduce the observed stellar masses, particularly in dwarf and high-redshift galaxies: radiative feedback (photo-heating and radiation pressure) is necessary to disrupt GMCs and enable efficient coupling of later supernovae to the gas. Star formation rates agree well with the observed Kennicutt relation at all redshifts. The galaxy-averaged Kennicutt relation is very different from the numerically imposed law for converting gas into stars in the simulation, and is instead determined by self-regulation via stellar feedback. Feedback reduces star formation rates considerably and produces a reservoir of gas that leads to rising late-time star formation histories significantly different from the halo accretion history. Feedback also produces large short-timescale variability in galactic SFRs, especially in dwarfs. Many of these properties are not captured by common 'sub-grid' galactic wind models.

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A new population of recently quenched elliptical galaxies in the SDSS

We use the Sloan Digital Sky Survey to investigate the properties of massive elliptical galaxies in the local Universe (z\leq0.08) that have unusually blue optical colors. Through careful inspection, we distinguish elliptical from non-elliptical morphologies among a large sample of similarly blue galaxies with high central light concentrations (c_r\geq2.6). These blue ellipticals comprise 3.7 per cent of all c_r\geq2.6 galaxies with stellar masses between 10^10 and 10^11 h^{-2} {\rm M}_{\sun}. Using published fiber spectra diagnostics, we identify a unique subset of 172 non-star-forming ellipticals with distinctly blue urz colors and young (< 3 Gyr) light-weighted stellar ages. These recently quenched ellipticals (RQEs) have a number density of 2.7-4.7\times 10^{-5}\,h^3\,{\rm Mpc}^{-3} and sufficient numbers above 2.5\times10^{10} h^{-2} {\rm M}_{\sun} to account for more than half of the expected quiescent growth at late cosmic time assuming this phase lasts 0.5 Gyr. RQEs have properties that are consistent with a recent merger origin (i.e., they are strong `first-generation' elliptical candidates), yet few involved a starburst strong enough to produce an E+A signature. The preferred environment of RQEs (90 per cent reside at the centers of < 3\times 10^{12}\,h^{-1}{\rm M}_{\sun} groups) agrees well with the `small group scale' predicted for maximally efficient spiral merging onto their halo center and rules out satellite-specific quenching processes. The high incidence of Seyfert and LINER activity in RQEs and their plausible descendents may heat the atmospheres of small host halos sufficiently to maintain quenching.

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The AGORA High-Resolution Galaxy Simulations Comparison Project

We introduce the AGORA project, a comprehensive numerical study of well-resolved galaxies within the LCDM cosmology. Cosmological hydrodynamic simulations with force resolutions of ~100 proper pc or better will be run with a variety of code platforms to follow the hierarchical growth, star formation history, morphological transformation, and the cycle of baryons in and out of 8 galaxies with halo masses M_vir ~= 1e10, 1e11, 1e12, and 1e13 Msun at z=0 and two different ("violent" and "quiescent") assembly histories. The numerical techniques and implementations used in this project include the smoothed particle hydrodynamics codes GADGET and GASOLINE, and the adaptive mesh refinement codes ART, ENZO, and RAMSES. The codes will share common initial conditions and common astrophysics packages including UV background, metal-dependent radiative cooling, metal and energy yields of supernovae, and stellar initial mass function. These are described in detail in the present paper. Subgrid star formation and feedback prescriptions will be tuned to provide a realistic interstellar and circumgalactic medium using a non-cosmological disk galaxy simulation. Cosmological runs will be systematically compared with each other using a common analysis toolkit, and validated against observations to verify that the solutions are robust - i.e., that the astrophysical assumptions are responsible for any success, rather than artifacts of particular implementations. The goals of the AGORA project are, broadly speaking, to raise the realism and predictive power of galaxy simulations and the understanding of the feedback processes that regulate galaxy "metabolism." The proof-of-concept dark matter-only test of the formation of a galactic halo with a z=0 mass of M_vir ~= 1.7e11 Msun by 9 different versions of the participating codes is also presented to validate the infrastructure of the project.

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Accretion Does Not Drive the Turbulence in Galactic Disks

Rapid accretion of cold gas plays a crucial role in getting gas into galaxies. It has been suggested that this accretion proceeds along narrow streams that might also directly drive the turbulence in galactic gas, dynamical disturbances, and bulge formation. In cosmological simulations, however, it is impossible to isolate and hence disentangle the effect of accretion from internal instabilities and mergers. Moreover, in most cosmological simulations, the phase structure and turbulence in the ISM arising from stellar feedback are treated in a sub-grid manner, so that feedback cannot generate ISM turbulence. In this paper we therefore test the effects of cold streams in extremely high-resolution simulations of otherwise isolated galaxy disks using detailed models for star formation and feedback; we then include or exclude mock cold flows falling onto the galaxies with accretion rates, velocities and geometry set to maximize their effect on the disk. We find: (1) Turbulent velocity dispersions in gas disks are identical with or without the cold flow; the energy injected by the flow is dissipated where it meets the disk. (2) In runs without stellar feedback, the presence of a cold flow has essentially no effect on runaway local collapse, resulting in star formation rates (SFRs) that are far too large. (3) Disks in runs with feedback and cold flows have higher SFRs, but only insofar as they have more gas. (4) Because flows are extended relative to the disk, they do not trigger strong resonant responses and so induce weak morphological perturbation (bulge formation via instabilities is not accelerated). (5) However, flows can thicken the disk by direct contribution of out-of-plane streams. We conclude that while inflows are critical over cosmological timescales to determine the supply and angular momentum of gas disks, they have weak instantaneous dynamical effects on galaxies.

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Resolving The Generation of Starburst Winds in Galaxy Mergers

We study galaxy super-winds driven in major mergers, using pc-resolution simulations with detailed models for stellar feedback that can self-consistently follow the formation/destruction of GMCs and generation of winds. The models include molecular cooling, star formation at high densities in GMCs, and gas recycling and feedback from SNe (I&II), stellar winds, and radiation pressure. We study mergers of systems from SMC-like dwarfs and Milky Way analogues to z~2 starburst disks. Multi-phase super-winds are generated in all passages, with outflow rates up to ~1000 M_sun/yr. However, the wind mass-loading efficiency (outflow rate divided by SFR) is similar to that in isolated galaxy counterparts of each merger: it depends more on global galaxy properties (mass, size, escape velocity) than on the dynamical state of the merger. Winds tend to be bi- or uni-polar, but multiple 'events' build up complex morphologies with overlapping, differently-oriented bubbles/shells at a range of radii. The winds have complex velocity and phase structure, with material at a range of speeds up to ~1000 km/s, and a mix of molecular, ionized, and hot gas that depends on galaxy properties and different feedback mechanisms. These simulations resolve a problem in some 'sub-grid' models, where simple wind prescriptions can dramatically suppress merger-induced starbursts. But despite large mass-loading factors (>~10) in the winds, the peak SFRs are comparable to those in 'no wind' simulations. Wind acceleration does not act equally, so cold dense gas can still lose angular momentum and form stars, while blowing out gas that would not have participated in the starburst in the first place. Considerable wind material is not unbound, and falls back on the disk at later times post-merger, leading to higher post-starburst SFRs in the presence of stellar feedback. This may require AGN feedback to explain galaxy quenching.

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Moving mesh cosmology: tracing cosmological gas accretion

We investigate the nature of gas accretion onto haloes and galaxies at z=2 using cosmological hydrodynamic simulations run with the moving mesh code AREPO. Implementing a Monte Carlo tracer particle scheme to determine the origin and thermodynamic history of accreting gas, we make quantitative comparisons to an otherwise identical simulation run with the smoothed particle hydrodynamics (SPH) code GADGET-3. Contrasting these two numerical approaches, we find significant physical differences in the thermodynamic history of accreted gas in haloes above 10^10.5 solar masses. In agreement with previous work, GADGET simulations show a cold fraction near unity for galaxies forming in massive haloes, implying that only a small percentage of accreted gas heats to an appreciable fraction of the virial temperature during accretion. The same galaxies in AREPO show a much lower cold fraction, <20% in haloes above 10^11 solar masses. This results from a hot gas accretion rate which, at this same halo mass, is an order of magnitude larger than with GADGET, while the cold accretion rate is also lower. These discrepancies increase for more massive systems, and we explain both as due to numerical inaccuracies in the standard formulation of SPH. We also observe that the relatively sharp transition from cold to hot mode dominated accretion, at a halo mass of ~10^11, is a consequence of comparing past gas temperatures to a constant threshold value independent of virial temperature. Examining the spatial distribution of accreting gas, we find that gas filaments in GADGET tend to remain collimated and flow coherently to small radii, or artificially fragment and form a large number of purely numerical "blobs". Similar gas streams in AREPO show increased heating and disruption at 0.25-0.5 virial radii and contribute to the hot gas accretion rate in a manner distinct from classical cooling flows.

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Stellar Feedback & Bulge Formation in Clumpy Disks

We use numerical simulations of isolated galaxies to study the effects of stellar feedback on the formation and evolution of giant star-forming gas 'clumps' in high-redshift, gas-rich galaxies. Such galactic disks are unstable to the formation of bound gas-rich clumps whose properties initially depend only on global disk properties, not the microphysics of feedback. In simulations without stellar feedback, clumps turn an order-unity fraction of their mass into stars and sink to the center, forming a large bulge and kicking most of the stars out into a much more extended stellar envelope. By contrast, strong radiative stellar feedback disrupts even the most massive clumps after they turn ~10-20% of their mass into stars, in a timescale of ~10-100 Myr, ejecting some material into a super-wind and recycling the rest of the gas into the diffuse ISM. This suppresses the bulge formation rate by direct 'clump coalescence' by a factor of several. However, the galactic disks do undergo significant internal evolution in the absence of mergers: clumps form and disrupt continuously and torque gas to the galactic center. The resulting evolution is qualitatively similar to bar/spiral evolution in simulations with a more homogeneous ISM.

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Moving mesh cosmology: characteristics of galaxies and haloes

We discuss cosmological hydrodynamic simulations of galaxy formation performed with the new moving-mesh code AREPO, which promises higher accuracy compared with the traditional SPH technique that has been widely employed for this problem. We use an identical set of physics in corresponding simulations carried out with the well-tested SPH code GADGET, adopting also the same high-resolution gravity solver. We are thus able to compare both simulation sets on an object-by-object basis, allowing us to cleanly isolate the impact of different hydrodynamical methods on galaxy and halo properties. In accompanying papers, we focus on an analysis of the global baryonic statistics predicted by the simulation codes, (Vogelsberger et al. 2011) and complementary idealized simulations that highlight the differences between the hydrodynamical schemes (Sijacki et al. 2011). Here we investigate their influence on the baryonic properties of simulated galaxies and their surrounding haloes. We find that AREPO leads to significantly higher star formation rates for galaxies in massive haloes and to more extended gaseous disks in galaxies, which also feature a thinner and smoother morphology than their GADGET counterparts. Consequently, galaxies formed in AREPO have larger sizes and higher specific angular momentum than their SPH correspondents. The more efficient cooling flows in AREPO yield higher densities and lower entropies in halo centers (and the opposite trend in halo outskirts) leading to higher star formation rates of massive galaxies. While both codes agree to acceptable accuracy on a number of baryonic properties of cosmic structures, our results clearly demonstrate that galaxy formation simulations greatly benefit from the use of more accurate hydrodynamical techniques such as AREPO.

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Moving mesh cosmology: numerical techniques and global statistics

We present the first hydrodynamical simulations of structure formation using the new moving mesh code AREPO and compare the results with GADGET simulations based on a traditional smoothed particle hydrodynamics (SPH) technique. The two codes share the same Tree-PM gravity solver and include identical sub-resolution physics, but employ different methods to solve the equations of hydrodynamics. This allows us to assess the impact of hydro-solver uncertainties on the results of cosmological studies of galaxy formation. We focus on predictions for global baryon statistics, such as the cosmic star formation rate density, after we introduce our simulation suite and numerical methods. Properties of individual galaxies and haloes are examined by Keres et al. (2011), while a third paper by Sijacki et al. (2011) uses idealised simulations to analyse the differences between the hydrodynamical schemes. We find that the global baryon statistics differ significantly between the two simulation approaches. AREPO shows higher star formation rates at late times, lower mean temperatures, and different gas mass fractions in characteristic phases of the intergalactic medium, in particular a reduced amount of hot gas. Although both codes use the same implementation of cooling, more gas cools out of haloes in AREPO compared with GADGET towards low redshifts. We show that this is caused by a higher heating rate with SPH in the outer parts of haloes, owing to viscous dissipation of SPH's inherent sonic velocity noise and SPH's efficient damping of subsonic turbulence injected in the halo infall region, and because of a higher efficiency of gas stripping in AREPO. As a result of such differences, AREPO leads also to more disk-like morphologies compared to GADGET. Our results indicate that inaccuracies in hydrodynamic solvers can lead to comparatively large systematic differences.

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Moving mesh cosmology: the hydrodynamics of galaxy formation

We present a detailed comparison between the well-known SPH code GADGET and the new moving-mesh code AREPO on a number of hydrodynamical test problems. Through a variety of numerical experiments we establish a clear link between test problems and systematic numerical effects seen in cosmological simulations of galaxy formation. Our tests demonstrate deficiencies of the SPH method in several sectors. These accuracy problems not only manifest themselves in idealized hydrodynamical tests, but also propagate to more realistic simulation setups of galaxy formation, ultimately affecting gas properties in the full cosmological framework, as highlighted in papers by Vogelsberger et al. (2011) and Keres et al. (2011). We find that an inadequate treatment of fluid instabilities in GADGET suppresses entropy generation by mixing, underestimates vorticity generation in curved shocks and prevents efficient gas stripping from infalling substructures. In idealized tests of inside-out disk formation, the convergence rate of gas disk sizes is much slower in GADGET due to spurious angular momentum transport. In simulations where we follow the interaction between a forming central disk and orbiting substructures in a halo, the final disk morphology is strikingly different. In AREPO, gas from infalling substructures is readily depleted and incorporated into the host halo atmosphere, facilitating the formation of an extended central disk. Conversely, gaseous sub-clumps are more coherent in GADGET simulations, morphologically transforming the disk as they impact it. The numerical artefacts of the SPH solver are particularly severe for poorly resolved flows, and thus inevitably affect cosmological simulations due to their hierarchical nature. Our numerical experiments clearly demonstrate that AREPO delivers a physically more reliable solution.

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The Role of Dwarf Galaxy Interactions in Shaping the Magellanic System and Implications for Magellanic Irregulars

We present a novel pair of numerical models of the interaction history between the Large and Small Magellanic Clouds (LMC and SMC, respectively) and our Milky Way (MW) in light of recent high precision proper motions (Kallivayalil et al. 2006a,b). Given the new velocities, cosmological simulations of structure formation favor a scenario where the Magellanic Clouds (MCs) are currently on their first infall towards our Galaxy (Boylan-Kolchin et al. 2011, Busha et al. 2011). We illustrate here that the observed irregular morphology and internal kinematics of the MCs (in gas and stars) are naturally explained by interactions between the LMC and SMC, rather than gravitational interactions with the MW. This picture further supports a first infall scenario (Besla et a. 2007). In particular, we demonstrate that the Magellanic Stream, a band of HI gas trailing behind the MCs 150 degrees across the sky, can be accounted for by the action of LMC tides on the SMC before the system was accreted by the MW. We further demonstrate that the off-center, warped stellar bar of the LMC and its one-armed spiral, can be naturally explained by a recent direct collision with the SMC. Such structures are key morphological characteristics of a class of galaxies referred to as Magellanic Irregulars (de Vaucouleurs & Freeman 1972), the majority of which are not associated with massive spiral galaxies. We infer that dwarf-dwarf galaxy interactions are important drivers for the morphological evolution of Magellanic Irregulars and can dramatically affect the efficiency of baryon removal from dwarf galaxies via the formation of extended tidal bridges and tails. Such interactions are important not only for the evolution of dwarf galaxies but also have direct consequences for the buildup of baryons in our own MW, as LMC-mass systems are believed to be the dominant building blocks of MW-type halos.

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Intergalactic Dust Extinction in Hydrodynamic Cosmological Simulations

Recently Menard et al. detected a subtle but systematic change in the mean color of quasars as a function of their projected separation from foreground galaxies, extending to comoving separations of ~10Mpc/h, which they interpret as a signature of reddening by intergalactic dust. We present theoretical models of this remarkable observation, using SPH cosmological simulations of a (50Mpc/h)^3 volume. Our primary model uses a simulation with galactic winds and assumes that dust traces the intergalactic metals. The predicted galaxy-dust correlation function is similar in form to the galaxy-mass correlation function, and reproducing the MSFR data requires a dust-to-metal mass ratio of 0.24, about half the value in the Galactic ISM. Roughly half of the reddening arises in dust that is more than 100Kpc/h from the nearest massive galaxy. We also examine a simulation with no galactic winds, which predicts a much smaller fraction of intergalactic metals (3% vs. 35%) and therefore requires an unphysical dust-to-metal ratio of 2.18 to reproduce the MSFR data. In both models, the signal is dominated by sightlines with E(g-i)=0.001-0.1. The no-wind simulation can be reconciled with the data if we also allow reddening to arise in galaxies up to several x 10^10 Msun. The wind model predicts a mean visual extinction of A_V ~0.0133 mag out to z=0.5, with a sightline-to-sightline dispersion similar to the mean, which could be significant for future supernova cosmology studies. Reproducing the MSFR results in these simulations requires that a large fraction of ISM dust survive its expulsion from galaxies and its residence in the intergalactic medium. Future observational studies that provide higher precision and measure the dependence on galaxy type and environment will allow detailed tests for models of enriched galactic outflows and the survival of IG dust.

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Mergers in Lambda-CDM: Uncertainties in Theoretical Predictions and Interpretations of the Merger Rate

Different methodologies lead to order-of-magnitude variations in predicted galaxy merger rates. We examine and quantify the dominant uncertainties. Different halo merger rates and subhalo 'destruction' rates agree to within a factor ~2 given proper care in definitions. If however (sub)halo masses are not appropriately defined or are under-resolved, the major merger rate can be dramatically suppressed. The dominant differences in galaxy merger rates owe to baryonic physics. Hydrodynamic simulations without feedback and older models that do not agree with the observed galaxy mass function propagate factor ~5 bias in the resulting merger rates. However, if the model matches the galaxy mass function, properties of central galaxies are sufficiently converged to give small differences in merger rates. But variations in baryonic physics of satellites also have dramatic effects. The known problem of satellite 'over-quenching' in most semi-analytic models (SAMs), whereby SAM satellites are too efficiently stripped of gas, could lead to order-of-magnitude under-estimates of merger rates for low-mass, gas-rich galaxies. Fixing the satellite properties to observations tends to predict higher merger rates, but with factor ~2 empirical uncertainties. Choice of mass ratio definition matters: at low masses, most true major mergers (in baryonic/dynamical galaxy mass) will appear to be minor mergers in their stellar or luminosity mass ratio. Observations and models using these criteria may underestimate major merger rates by factors ~5. Orbital parameters and gas fractions also introduce factor ~3 differences in amount of bulge formed by mergers, even for fixed mass ratio encounters.

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Simulations of the Magellanic Stream in a First Infall Scenario

Recent high precision proper motions from the Hubble Space Telescope (HST) suggest that the Large and Small Magellanic Clouds (LMC and SMC, respectively) are either on their first passage or on an eccentric long period (>6 Gyr) orbit about the Milky Way (MW). This differs markedly from the canonical picture in which the Clouds travel on a quasi-periodic orbit about the MW (period of ~2 Gyr). Without a short period orbit about the MW, the origin of the Magellanic Stream, a young (1-2 Gyr old) coherent stream of HI gas that trails the Clouds ~150 degrees across the sky, can no longer be attributed to stripping by MW tides and/or ram pressure stripping by MW halo gas. We propose an alternative formation mechanism in which material is removed by LMC tides acting on the SMC before the system is accreted by the MW. We demonstrate the feasibility and generality of this scenario using an N-body/SPH simulation with cosmologically motivated initial conditions constrained by the observations. Under these conditions we demonstrate that it is possible to explain the origin of the Magellanic Stream in a first infall scenario. This picture is generically applicable to any gas-rich dwarf galaxy pair infalling towards a massive host or interacting in isolation.

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Mergers and Bulge Formation in Lambda-CDM: Which Mergers Matter?

We use a suite of semi-empirical models to predict galaxy merger rates and contributions to bulge growth as functions of merger mass, redshift, and mass ratio. The models use empirical halo occupation constraints to identify mergers, together with high-resolution simulations to quantify how mergers with different properties contribute to the bulge population. We find good agreement with a variety of observational constraints, and provide fitting functions for merger rates and contributions to bulge growth. We identify several robust conclusions. (1) Major mergers dominate formation and assembly of L* bulges and the spheroid mass density, minor mergers contribute ~30%. (2) This is mass-dependent: bulge formation is dominated by more minor mergers in lower-mass systems. At higher masses, bulges form in major mergers near L*, but subsequently assemble in minor mergers. (3) The minor/major contribution is also morphology-dependent: higher B/T systems form in more major mergers, lower B/T systems form in situ from minor mergers. (4) Low-mass galaxies, being gas-rich, require more major mergers to reach the same B/T as high-mass systems. (5) Absolute merger rates increase with galaxy mass. (6) Predicted rates agree well with observations, but suggest that some morphology-selected samples include contamination from minor mergers. (7) Predicted rates agree with integrated growth in bulge mass with cosmic time, but with factor ~2 uncertainty - half the bulge mass density could come from non-mergers. We consider ~1000 model variations and quantify resulting uncertainties. Conclusions regarding the major/minor contribution to bulge growth are very robust, absolute merger rates have systematic factor ~2 uncertainties.

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Substructure depletion in the Milky Way halo by the disk

We employ numerical simulations and simple analytical estimates to argue that dark matter substructures orbiting in the inner regions of the Galaxy can be efficiently destroyed by disk shocking, a dynamical process known to affect globular star clusters. We carry out a set of fiducial high-resolution collisionless simulations in which we adiabatically grow a disk, allowing us to examine the impact of the disk on the substructure abundance. We also track the orbits of dark matter satellites in the high-resolution Aquarius simulations and analytically estimate the cumulative halo and disk shocking effect. Our calculations indicate that the presence of a disk with only 10% of the total Milky Way mass can significantly alter the mass function of substructures in the inner parts of halos. This has important implications especially for the relatively small number of satellites seen within ~30 kpc of the Milky Way center, where disk shocking is expected to reduce the substructure abundance by a factor of ~2 at 10^9 M$_{\odot}$ and ~3 at 10^7 M$_{\odot}$. The most massive subhalos with 10^10 M$_{\odot}$ survive even in the presence of the disk. This suggests that there is no inner missing satellite problem, and calls into question whether these substructures can produce transient features in disks, like multi-armed spiral patterns. Also, the depletion of dark matter substructures through shocking on the baryonic structures of the disk and central bulge may aggravate the problem to fully account for the observed flux anomalies in gravitational lens systems, and significantly reduces the dark matter annihilation signal expected from nearby substructures in the inner halo.

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When Should We Treat Galaxies as Isolated?

Traditionally, secular evolution is defined as evolution of systems where the internal growth of structure and instabilities dominates the growth via external drivers (e.g. accretion/mergers). Most study has focused on 'isolated' galaxies, where seed asymmetries may represent realistic cosmological substructure, but subsequent evolution ignores galaxy growth. Large-scale modes in the disk then grow on a timescale of order a disk rotation period (0.1-1 Gyr). If, however, galaxies evolve cosmologically on a shorter timescale, then it may not be appropriate to consider them 'isolated.' We outline simple scalings to ask whether the timescale for secular evolution is shorter than the timescale for cosmological accretion and mergers. This is the case in a narrow, but important range of perturbation amplitudes corresponding to substructure or mode/bar fractional amplitudes 0.01-0.1, a range of interest for observed strong bars and pseudobulges. At smaller amplitudes <<0.1, systems are not isolated: typical disks will grow by accretion at a comparable level over even a single dynamical time. At larger amplitudes >>0.1, the evolution is no longer secular; direct gravitational evolution of the seed swamps the internal disk response. We derive criteria for when disks can be well-approximated as 'isolated' as a function of mass, redshift, and disk stability. The relevant parameter space shrinks at higher mass, higher disk stability, and higher-z as accretion rates increase. Cosmological rates of galaxy evolution also define a maximum bar/mode lifetime of practical interest, of ~0.1/H(z). Longer-lived modes will de-couple from their drivers (if driven) and encounter cosmological effects.

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