Spiral and Bar Instabilities Provoked by Dark Matter Satellites
John Dubinski, Jean-Rene Gauthier, Larry Widrow, Sarah Nickerson
aa r X i v : . [ a s t r o - ph ] F e b Formation and Evolution of Disk GalaxiesASP Conference Series, Vol. XXX, 2008J.G. Funes and E.M. Corsini
Spiral and Bar Instabilities Provoked by Dark MatterSatellites
John Dubinski , Jean-Ren´e Gauthier , , Larry Widrow , and SarahNickerson Abstract.
We explore the secular dynamical evolution of an N-body modelof M31 in the presence of a population of 100 dark matter satellites over 10 Gyr.The satellite population has structural and kinematic characteristics modelled tofollow the predictions of ΛCDM cosmological simulations. Vertical disk heatingis a small effect despite many interactions with the satellite population with onlya 20% increase in vertical velocity dispersion σ z and the disk scale height z d atthe equivalent solar radius R = 2 . R d . However, the stellar disk is noticeablyflared after 10 Gyr with z d nearly doubling at the disk edge. Azimuthal diskheating is much larger with σ R and σ z both increasing by 1 . × . However, ina control experiment without satellites dispersion increases by 1 . × suggestingthat most of the effect is due to heating through scattering off of spiral structureexcited by swing-amplified noise. Surprisingly, direct impacts of satellites onthe disk can excite spiral structure with a significant amplitude and in somecases impacts close to the disk center also induce the bar instability. The largenumber of dark matter satellite impacts expected over a galaxy’s lifetime may bea significant source of external perturbations for driving disk secular evolution.
1. Introduction
Cosmological simulations in ΛCDM show that the dark matter halos of galax-ies contain hundreds to thousands of subhalos or dark satellites (Moore et al.1999; Gao et al. 2004; Diemand et al. 2007). The existence of subhalos raisesinteresting questions about the dynamical evolution of disk galaxies. Whilethis population is under-represented in the observed satellites (Klypin et al.1999), the recent success of ΛCDM in accounting for many properties of theuniverse from the CMB to the large-scale structure leads us to take this pre-diction seriously. Cosmological infall of a large number of dark satellites ontoa typical spiral galaxy could be a major source of disk heating and thickening(T´oth & Ostriker 1992; Font et al. 2001; Benson et al. 2004; Kazantzidis et al.2007) beyond known astrophysical processes so it important to quantify the effectand see if the observed galaxy population is morphologically consistent. A maindifficulty with numerical studies is that N-body disks are prone to self-heating Department of Astronomy and Astrophysics, University of Toronto, Toronto, ON M4S 3H4,Canada [email protected]; [email protected] Department of Astronomy and Astrophysics, Kavli Institute for Cosmological Physics, TheUniversity of Chicago, Chicago, IL 60637, USA [email protected] Department of Physics, Queen’s University, Kingston, ON K7L 3N6, [email protected] DUBINSKI et al. by two-body relaxation with inadequate resolution so that any perturbations bysatellites can easily be masked by numerical effects. Ad hoc assumptions aboutthe structure of satellites also make the interpretation of results difficult in lightof the predictions of ΛCDM.In this study, we attempt to overcome these problems using new galaxysimulations with sufficient resolution to measure the heating directly due to acosmologically inspired model population of dark matter satellites. These simu-lations reveal the importance of satellite impacts – i.e direct passage of satellitesthrough the stellar disk – in exciting both spiral and bar instabilities. Darksatellite interactions may therefore be an essential driver of secular dynamicalevolution of disk galaxies (see also Kazantzidis et al. (2007)).
2. Methods
For the study here, we use the stable, equilibrium axisymmetric model of M31derived from a distribution function as described in Widrow & Dubinski (2005).We model M31 with an exponential disk, a Hernquist model bulge, and a cuspydark halo with an NFW profile. Model parameters are determined that fit therotation curve and surface brightness profile for M31 with an assumed
M/L ratio for the stellar components such that the disk remains stable against barformation for 10 Gyr.The method for generating a satellite population is described in detail inGauthier et al. (2006). The satellite properties reflect cosmological numericalpredictions for the subhalo mass function, radial distribution, tidal radii as wellas internal density structure. To summarize, 10% of the dark matter halo mass isinitially in 100 subhalos spanning a mass range of 10 − M ⊙ selected from amass function dN/dM ∼ M − . . The radial number density of satellites are setaccording to the formulae presented in Gao et al. (2004). Our highest resolutiongalaxy model contains the following numbers of particles: 10M disk, 5M bulge,and 20M smooth halo for a total of 35M. The 100 dark satellites each contain100K particles for a total of 10M. We run the simulation using a parallelizedtreecode (Dubinski 1996) with a fixed Plummer softening length ǫ = 15 pc and20000 equal timesteps with δt = 0 .
49 Myr. Total binding energy is conserved towithin 0.3% and total angular momentum is conserved to within 2%. We alsouse models with 10 times fewer particles in some additional studies.
3. Disk Heating
We first ran a control simulation at 35M particles to understand numerical ef-fects (Fig. 1). Vertical disk heating is negligible over most of the disk withalmost no change in σ z and the vertical scale height at this resolution. However,the radial and azimuthal velocity dispersions grow by 50% due to spiral instabil-ities arising from swing amplified Poisson noise in the disk particle distribution.We then added satellites in two different runs with statistically similar distribu-tions. In our first simulation, the disk developed a bar half way through the run(Gauthier et al. 2006) and so introduces an unwanted additional source of heat-ing (see Movie 1). The formation of a bar was unexpected and we will discuss theorigin of this instability shortly. Fortunately in the second run, no bar formed PIRAL, BARS AND DARK SATELLITES Figure 1. The evolution of the disk velocity ellipsoid for the control simu-lation (no subhalos) and the simulation with 100 dark satellites with no barinstability. Also, the evolution of the vertical scale-height as measured by thevariance in z at different radii. so we could directly measure heating effects by the satellite population (Fig. 1).Vertical heating is still small with roughly a 20% increase in σ z even under thebombardment of satellites. The increase in σ r and σ θ is also only 20% over andabove the heating caused by intrinsic spiral instabilities. However, there is anoticeable flaring of the disk in the presence of satellites with the scale heightnearly doubling from 2 disk scale lengths to the disk edge. Kazantzidis et al.(2007) also see this effect in similar work. Similar features are seen in the outerdisk of M31 (Ibata et al. 2007).
4. Spiral and Bar Instabilities from Satellite Impacts
An unexpected feature of these simulations is the induced bar instability inour first run as well as easily distinguished multi-armed global spiral structure.The main cause of these features are satellite impacts. The passage of a satel-lite through the disk induces a localized disturbance that presumably grows byToomre’s swing amplification mechanism (Toomre 1981). Note that the tidaleffects of the satellites are generally small and so this mechanism is quite dif-ferent than the tidal interactions responsible for grand-design spiral galaxieslike M51. The mechanism is closer to the original ideas suggested by bothGoldreich & Lynden-Bell (1965) and Julian & Toomre (1966) where a mass per-turbation appearing within the disk – a giant molecular cloud or massive starforming region – is the source of a disturbance that is subsequently amplified.A virtual fly by of the evolving galaxy clearly shows episodes of spiral struc-ture excitation immediately after satellites pass through the disk (see Movie 2).In the case of model with the bar instability, there appears to be a single strongencounter with one of the more massive satellites near the center of disk justbefore the onset of the bar. It seems likely the disturbance caused by the passingsatellite disrupts the center of the galaxy enough to make it susceptible to theswing-amplifier feedback loop (Toomre 1981).We are testing these ideas further with more experiments and idealizedperturbations representing satellite passages throught the disk. We performed 10additional experiments with 4.5M particle models and statistically independent
DUBINSKI et al. but consistent satellite populations in orbit around M31 (see Movie 3). Five outof ten of these models develop a bar instability during their lifetime apparentlydue to chance central encounter with a massive satellite. Those models that donot suffer strong central encounters with satellites avoid bar formation. In allcases, spiral perturbations of significant amplitude are observed due to satelliteinteractions.We are now doing a quantitative study of the effect of satellite impactson disks using a transient mass perturbation appearing within the plane of thedisk. Preliminary results suggest that even satellite masses as small as 10 M ⊙ or roughly 5-10% the mass of the LMC are large enough to induce obvious spiralstructure while the passage of a LMC-sized satellite creates a strong response(see Movie 4). A typical galaxy will experience dozens of impacts with satel-lites more massive than 10 M ⊙ during its life according to the predictions ofΛCDM. Dark satellite impacts may then play an important role in maintainingthe multi-armed, global spiral patterns seen in the disk galaxies. At this stage,we need to quantify the response of a disk as a function of satellite impactormass and impact radius on the disk. The orbital statistics of ΛCDM subhalosfrom cosmological simulations will allow us to determine the frequency, massdistribution and distribution of impact radii expected on a galactic disk overits history. By combining these two results, we should be able to quantify theeffect of dark satellites on disk secular evolution and so address observations ofthe morphological appearance of galaxies including the bar fraction (Jogee et al.2004) throughout cosmic history. Acknowledgments.
The authors acknowledge supercomputing time on ma-chines supported by SHARCNET and CITA. We also acknowledge funding byNSERC.