THE DESTRUCTION OF THIN STELLAR DISKS VIA COSMOLOGICALLY COMMON SATELLITE ACCRETION EVENTS

A solid majority of observed galaxies have disk-dominant morphology; despite wide variance in methods of sampling and classification, roughly 70% of Galaxy-sized dark matter halos in the universe host late-type systems (Weinmann et al. 2006; van den Bosch et al. 2007; Ilbert et al. 2006; Choi et al. 2007; Park et al. 2007). Moreover, Kautsch et al. (2006) find that about one-third of all local disk galaxies have no observable pressure-supported component (whether a "classical" bulge formed by the central starburst associated with a merger event, or a "pseudobulge" having arisen from the secular transport of angular momentum toward the galactic center), and another one-third host systems with only pseudobulges, a conclusion supported by spheroid-disk decomposition of large galaxy samples (Allen et al. 2006; Barazza et al. 2008). The vast majority of disk stars in the Milky Way reside in the thin disk component, with an exponential scale height of z_d ≃ 300 ± 60 pc (Jurić et al. 2008, and references therein) and a total velocity dispersion of σ_tot ≃ 35 km s⁻¹ (Nordström et al. 2004). Whether the scale height of the Galactic disk is typical for galaxies of its size is a topic of vital interest. Unfortunately, firm measurements for a statistical sample of galaxies have been limited by dust obscuration which presents a problem even in K-band imaging (Kregel et al. 2005; Yoachim & Dalcanton 2006).

Aside from the considerable challenges associated with forming disk galaxies in ΛCDM cosmologies (e.g., Mayer et al. 2008), hierarchical models must also self-consistently maintain thin, rotationally supported systems against the constant barrage of merging subhalos. Though the former endeavor has enjoyed some recent advances (Abadi et al. 2003; Sommer-Larsen et al. 2003; Brook et al. 2004; Robertson et al. 2004; Governato et al. 2007), the survival of disk galaxies during the often violent mass accretion history of their dark host remains a concern (Toth & Ostriker 1992; Quinn et al. 1993; Walker et al. 1996; Wyse 2001) and has been the target of numerous studies aimed at quantifying the resilience of galactic disks to satellite accretion events (Quinn & Goodman 1986; Toth & Ostriker 1992; Quinn et al. 1993; Walker et al. 1996; Huang & Carlberg 1997; Sellwood et al. 1998; Velazquez & White 1999; Ardi et al. 2003; Gauthier et al. 2006; Hayashi & Chiba 2006; Kazantzidis et al. 2008; Read et al. 2008; Villalobos & Helmi 2008; Hopkins et al. 2008).

Both numerical simulations (Stewart et al. 2008) and purely analytic calculations (Purcell et al. 2007; Zentner 2007) indicate that mass delivery into dark matter halos of mass M_host is dominated by the accretion of objects with mass ∼(0.05–0.15)M_host. Stewart et al. (2008) find that ∼70% of 10¹² M_☉ Galaxy-sized halos have accreted a system of mass M_sat ≃ 10¹¹ M_☉ ≃ 3M_disk into their virial radii in the last 10 Gyr, with associated disk impacts within the last 8 Gyr. Stewart et al. (2008) also find that less massive accretions are virtually ubiquitous, and that the merger fraction falls off quickly for satellites larger than M_sat ≃ 2 × 10¹¹ M_☉. Overall, these results suggest that ∼1:10 satellite accretion events represent the primary concern for disk survival in ΛCDM. Along these lines, recent analytic work by Hopkins et al. (2008) suggests that orbital energy deposition via merger is less destructive to a disk than was often previously surmised (Toth & Ostriker 1992; Quinn et al. 1993; Walker et al. 1996), claiming that the Galaxy could have undergone ∼5–10 independent mergers of this kind since z ∼ 2 while maintaining a thin disk.

Recently, Kazantzidis et al. (2008) utilized dissipationless N-body simulations to investigate the response of thin galactic disks subject to a ΛCDM-motivated satellite accretion history. These authors showed that the thin disk component survives, though it is strongly perturbed by the violent gravitational encounters with substructure. However, Kazantzidis et al. (2008) focused on infalling systems with masses in the range 0.2M_disk ≲ M_sat ≲ M_disk, ignoring the most massive accretion events expected over a galaxy's lifetime. In this Letter, we expand upon this initiative by investigating the morphological and dynamical evolution of initially thin Galaxy-type disks during cosmologically common ∼1:10 accretion events involving two-component (stars and dark matter) satellites of mass M_sat ≃ 10¹¹ M_☉ ≃ 3M_disk.

Working in a similar mass regime, Villalobos & Helmi (2008) simulated the formation of thick disks via the infall of satellite galaxies with virial masses ∼10–20% that of the host, using both a z = 0 Galactic primary system and a scaled version at z = 1 in order to show that realistic thick disks result from these impacts. Though our preparation is similar, our goals and techniques are different. We aim to determine whether any thin, dynamically cold component can survive such an event, and conservatively use a primary disk that is as massive as the Milky Way disk today.

Past investigations into the stability of galactic disks against the infall of satellites have often suffered from the necessities of numerical limitations or from analytic axioms later deemed incompatible with standard cosmological models; for example, the modeling of one or more structural components as rigid potentials (Quinn & Goodman 1986; Quinn et al. 1993; Sellwood et al. 1998; Ardi et al. 2003; Hayashi & Chiba 2006), the initialization of a disk much thicker than the old, thin stellar disk of the Galaxy (Quinn et al. 1993; Walker et al. 1996; Huang & Carlberg 1997; Velazquez & White 1999; Font et al. 2001; Villalobos & Helmi 2008), the infall of satellites with only a concentrated baryonic component (Quinn et al. 1993; Walker et al. 1996; Huang & Carlberg 1997; Velazquez & White 1999), and the imposition of subhalo infalls with orbital parameters inconsistent with ΛCDM cosmological models (Quinn et al. 1993; Walker et al. 1996; Huang & Carlberg 1997). Analytic arguments, meanwhile, have historically been forced to assume simplifications such as the local deposition of a satellite's orbital energy (Toth & Ostriker 1992), or the absence of global heating modes (Benson et al. 2004; Hopkins et al. 2008) which are analytically shown to dominate disk heating by Sellwood et al. (1998), although the latter authors employ a rigid satellite model and perfectly radial polar orbits for their simulated experimental tests. Fortunately, advances both in computational power and in our understanding of ΛCDM expectations allow us to address these concerns directly.

Our contribution improves upon earlier studies in several important respects. First and foremost, we examine the response of galactic disks to accretion events that represent the primary concern for disk survival in ΛCDM cosmologies. Secondly, we employ galaxy and satellite models that are constructed in equilibrium from fully self-consistent distribution functions and which have the resolution in force and mass to study the heating of a disk that is as thin as the old thin stellar disk of the Milky Way (z_d ≃ 300 pc); in synergy with the high mass and force resolution we adopt, this quality allows us to construct equilibrium N-body models of disk galaxies that are as thin as the old, thin stellar disk of the Galaxy. Lastly, the masses, density structure, stellar content, and orbital configurations of our infalling satellites are directly motivated by the prevailing ΛCDM paradigm of structure formation.

All simulations are performed using the multi-stepping, parallel, tree N-body code PKDGRAV (Stadel 2001), in which we set the gravitational softening length to = 100 pc and 50 pc for dark matter and stellar particles, respectively.

2.1. Primary and Satellite Galaxy Models

We construct N-body realizations of primary disk galaxies and satellites using the method of Widrow et al. (2008). This technique produces self-consistent, multi-component galaxy models that are ideal for studying complex dynamical processes associated with the intrinsic fragility of galactic disks such as gravitational interactions with infalling subhalos. We explore two initial models for the primary galaxy in our satellite–disk encounter simulations: Galaxy 1 (hereafter G1), a Milky Way-analog system drawn from the set of self-consistent equilibrium models that best fit Galactic observational parameters as produced by Widrow et al. (2008), and Galaxy 2 (hereafter G2), an identical system save for the absence of a central bulge, i.e., the two models have stellar disks and dark halos with equivalent initial properties. In each case, the dark matter halo of the primary galaxy was populated by 4 × 10⁶ particles following the Navarro et al. (1996, hereafter NFW) density profile with scale radius r_s = 14.4 kpc, and the bulge in G1 (comprised of 5 × 10⁵ particles) contained a stellar mass M_bulge = 9.5 × 10⁹ M_☉ following a Sérsic profile with effective radius R_e = 0.58 kpc and index n = 1.118. The stellar disks, comprised of 10⁶ particles each, contained a mass M_disk = 3.6 × 10¹⁰ M_☉ following an exponential distribution in cylindrical radius with scale length R_d = 2.84 kpc, while the vertical distribution of stars was described by a sech² function with z_d = 0.43 kpc being the vertical scale height. We note that the choice of numerical and physical parameters minimizes secular evolution (e.g., strong bar formation, artificial heating through interactions with massive halo particles) on the timescales of relevance to our investigation which could interfere with the interpretation of our results. In the left panel of Figure 1, we show the edge-on surface brightness map for both primary galaxy models, having assumed a stellar mass-to-light ratio M_⋆/L = 3. The satellite galaxy in each case was initialized with 9 × 10⁵ dark particles representing a mass M_sat = 1.0 × 10¹¹ M_☉ within the virial radius of a halo which is well fitted by an NFW profile with a concentration c_vir ≃ 14 at z = 0.5. We populate this satellite with a stellar mass M_⋆ = 2.2 × 10⁹ M_☉, roughly corresponding to the upper 1σ limit derived by Conroy & Wechsler (2008) for M_⋆/M_sat(z ∼ 0.5) at our subhalo's virial mass, and we distribute these 10⁵ stellar particles in a central spheroid with Sérsic index n ∼ 0.5 according to the distribution of shape parameters versus dwarf elliptical galaxy magnitudes found by van Zee et al. (2004) in their survey of Virgo cluster members.

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2.2. Satellite Galaxy Orbits

Edge-on surface brightness profiles for remnants of the θ = 30° and 90° impacts are shown in the middle and left panels of Figure 1, where the upper and lower renderings correspond to primary cases G1 and G2, respectively (with and without initial bulge). It is clear from these images that the resultant disks are considerably thicker than the initial case. We note that while the stars in the accreted satellite end up in the final disk remnant (see Villalobos & Helmi 2008), primary disk stars dominate these images, even high above the plane.

Figure 2 shows the minor-axis surface brightness profiles for the G1 simulations using M_⋆/L = 3. The left panel shows a vertical slice at a projected radius of R_☉ = 8 kpc and the right panel shows a similar slice at radius 2 R_☉. Black solid lines show the initial disk and different color/line types represent the remnants as indicated. Clearly, the resultant disks are dramatically thicker than the initial galaxy model in each case. In order to conservatively compare our disks to the Milky Way, we allow for thick and thin components by fitting a double sech² profile at R_☉. The fitted scale heights are shown in Table 1 and compared directly in Figure 3 to the Galactic values obtained by Jurić et al. (2008)³. Though we initially employ a disk that is thicker (z_thin = 0.43 kpc) and therefore conservatively more robust to accretion events (S. Kazantzidis et al. 2009, in preparation) than the Galactic value of z_thin = 0.34 kpc from Jurić et al. (2008), the final systems all have thin disk components with z_thin larger by a factor of ∼3–5 than the Milky Way. Moreover, the low-surface-brightness thick component in our remnant disks is also considerably thicker than the Galactic thick disk, with scale heights so large (z_thick ≃ 4–10 kpc) that this material would likely be considered a stellar halo component.

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A second relevant measure of disk survival is the stellar velocity dispersion; we therefore compare the velocity ellipsoid of our final disks to that observed in the solar neighborhood by the Geneva–Copenhagen Survey (Nordström et al. 2004; see also Seabroke & Gilmore 2007). In Figure 4, we show these values for velocity dispersion in each coordinate, where the indicated range spans the stellar population age, and the point is placed at the median age t ∼ 2–3 Gyr according to Nordström et al. (2004) for this local sample. Shown also are the corresponding dispersion components for our initial and final stellar disks measured within a 0.3 kpc box centered on the disk plane at R_☉ = 8 kpc. As summarized in Table 2, each of our simulated merger remnants is substantially enhanced in all three components of velocity dispersion (σ_R,ϕ,z corresponding to σ_U,V,W). The total dispersion σ_tot = (σ²_R + σ²_ϕ + σ²_z)^1/2 increases by a factor of ∼1.5–2 compared to that of the initial disk.

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Using fully self-consistent N-body simulations of satellite–disk interactions we have quantitatively demonstrated for the first time that cosmologically common accretion events of mass ratio ∼1:10 do not preserve thin, dynamically cold stellar disks like the old, thin stellar disk of the Milky Way. This has potentially serious ramifications for models of galaxy formation and evolution. It is possible that our benchmark case of the Milky Way is not representative, and that the Galaxy sits within a rare halo that has not experienced in the last ∼8 Gyr a disk impact associated with a significant accretion event, as posited in the observationally motivated suggestion of Hammer et al. (2007), in which the Galaxy is shown to have remarkably low angular momentum and stellar mass compared to local spiral galaxies in host halos of similar mass. Future investigations may help quantify the range of thin disk scale heights in the local universe.

Otherwise, the addition of gas physics may play a role in explaining the apparent discrepancy. Gas can cool and reform a thin disk, and its presence may stabilize the stellar disk (e.g., Robertson et al. 2006). The regrowth of the massive thin disk after a satellite accretion may cause heated stars to contract and lose kinetic energy. Accurate treatment of the various aspects of hydrodynamics will therefore play a crucial role in the capacity of simulated galaxy evolution to reproduce thin disks such as those that dominate observed galaxy catalogs.

In a recent paper Hopkins et al. (2008) have argued that disk heating is less effective than previously thought and that the expected merger histories of ΛCDM halos are compatible with the high thin disk fraction seen in the universe. It is important, therefore, to investigate this point of disagreement. Their result, a reshaping of the arguments presented in Toth & Ostriker (1992; updated to reflect the more realistically radialized orbits of a ΛCDM cosmology), relied primarily on an analytic formula, normalized to simulations with much lower mass and force resolution than those explored here, to map the ratio (M_sat/M_host) to a disk heating parameter ΔH/R, where H is the median scale height of the resultant disk and R is the radius where the height is measured (and must be within a factor of 2 of the disk half-mass radius R_e). For the ∼1:10 mass-ratio accretion events we explore here, the Hopkins et al. (2008) formula predicts a disk thickening of ΔH/R ≃ 0.015. Our simulations typically exhibit significantly more heating; at R = R_e we measure ΔH/R ≃ (0.03–0.09) and, because of the impact-induced flaring, we measure even larger values ΔH/R ≃ (0.05–0.11) at R = 2R_e.

It is perhaps not surprising that our results disagree with first-order analytic expectations. In addition to direct heating, the resultant disk structure is affected by global modes such as bending and density waves excited in the disk as the interaction occurs (Sellwood et al. 1998), and not included in the simple analytic scalings is a dependence on the orbital inclination of the encounter that is likely associated with resonant coupling. Finally, though Hopkins et al. (2008) normalized their results to numerical simulations, those initial disks were significantly thicker than the Galactic-type disk we have simulated, and were therefore more robust to tidal perturbations. Direct numerical experiments involving satellite–disk encounters indicate that mass ratio, orbital inclination, initial disk scale height, and relative dark matter fraction are all crucial in determining the degree to which galactic disks are perturbed by infalling subhalos (Figures 3, 4, and S. Kazantzidis et al. (2009, in preparation)). More detailed analysis is forthcoming of the morphological and dynamical effects experienced by our disks; among other concerns, we defer for future work the issues of stellar halo/thick disk distinguishability and the reinforcement of central bulges by accreted stars.

We thank Joachim Stadel for providing the PKDGRAV code. We thank Charlie Conroy, Phil Hopkins, Kyle Stewart, and Andrew Zentner for useful discussions as well as Larry Widrow and John Dubinski for kindly making available the software used to set up the primary galaxy models. C.W.P. and J.S.B. are supported by National Science Foundation (NSF) grants AST-0607377 and AST-0507816, and the Center for Cosmology at UC Irvine. S.K. is supported by the Center for Cosmology and Astro-Particle Physics at The Ohio State University. The numerical simulations were performed on the IA-64 cluster at the San Diego Supercomputing Center.