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3. N-BODY MODELING OF STREAMS

We now turn to discussion of what can be learned from the identification and subsequent theoretical modeling of tidal streams in galaxies beyond the Local Group. In many of the examples illustrated in this chapter, we have shown N-body models of disrupting satellites that roughly reproduce the observed morphology of detected streams. For example, for the great-circle tidal stream around NGC 5907 (Figure 3), an N-body model that best replicates the morphology of the observed stream requires a massive Sgr-like galaxy that has spread debris over at least three orbits. If this is the case, then the complex stream structure seen around this galaxy can be entirely explained by a single accretion event. However, due to the difficulty in measuring kinematics for low surface brightness tidal streams (and, indeed, the impossibility of measuring kinematics of individual stars) at several Mpc away, models must be constrained solely by the observed morphology and the stellar density along the stream. While the panoramic perspective we are afforded of these systems offers many constraints on the properties of the progenitors and their orbits, kinematics will ultimately be needed to fully characterize each accretion event.

It is possible that carefully chosen spectroscopic observations can derive bulk kinematics of some tidal debris features around external galaxies. For example, Sanderson & Helmi (2013) outlined a method to do this for tidal caustics (or “shells”) via careful choice of spectroscopic fiber positioning and identification of the tell-tale velocity signature. A much more promising avenue is to use intrinsically brighter point-like tracers such as globular clusters, planetary nebulae, or HII regions to elucidate debris structures. The densities of globular clusters have been used (D'Abrusco et al. 2015) to show large structures in the halos of Virgo cluster galaxies that may be evidence of recent accretion events.

An example of a stream in a distant galaxy for which kinematics have been measured and an orbit derived is that of the Umbrella Galaxy (NGC 4651). Foster et al. (2014) followed up the low surface-brightness imaging of Martínez-Delgado et al. (2010) with even deeper imaging from the Subaru/Suprime-Cam instrument. Figure 5 shows images from this study, which reveal a “stick” feature extending out to its terminus at a broad arc to the left of the main galaxy. On the opposite side of the disk (right side of the upper panel in Figure5), additional shell-like features are clearly seen. Foster et al. (2014) estimated the total stellar mass in the tidal debris to be ∼ 4 × 108 M, constituting about 1/50th the stellar mass of NGC 4651. In addition, Foster et al. (2014) obtained spectra of candidate globular clusters, planetary nebulae, and HII regions that are spatially coincident with the substructures, and distinguished the kinematical signature of the accreted debris (including a possible progenitor core) from the underlying galactic disk motions. The orbit derived from these is rather radial (as expected for an umbrella-like remnant; see Chapter 6 of this volume), with pericenter of only a few kpc, apocenter of ∼ 40 kpc, and period of ∼ 350 Myr. This implies that the ratio of total mass of the progenitor and the whole of NGC 4651 is ∼ 0.15, making this minor merger event analogous to the Sgr accretion in the Milky Way (see Chapter 2) and the Giant Stellar Stream in M31 (Chapter 8). While detailed exploration of parameter space has yet to be achieved for this system, Foster et al. (2014) did adapt an existing N-body model to show that some inferences can be made from analysis of the surface brightness and velocities of the visible features and associated tracers.

Figure 5

Figure 5. The stellar stream in NGC 4651. Top: color image of the extensive tidal features in NGC 4651, including an “umbrella” and several shells of material. The stream has an exceptionally blue color. Bottom left: several globular clusters (yellow circles), planetary nebulae (cyan diamonds), and HII regions (black triangles) are found along the debris. These bright tracers permit kinematical probes that greatly enhance the ability of N-body modeling (bottom right) to elucidate the physical parameters of the accretion event. [Reproduced from Foster et al. (2014).]

As discussed in Chapter 7, the widths and surface brightnesses of streams that are traced over a long portion of their orbits provide constraints on the number and sizes of dark matter subhalos in the host galaxy's halo (see, e.g. Ibata et al. 2002, Johnston et al. 2002, Peñarrubia et al. 2006, Siegal-Gaskins & Valluri 2008). These authors show that the presence of dark matter subhalos in spiral galaxies would result in progressive heating of tidal streams as a result of close encounters, and in fact gaps may be swept out of streams by interactions with subhalos (e.g., Yoon et al. 2011, Carlberg 2013, Erkal & Belokurov 2014, Ngan et al. 2014). As Peñarrubia et al. (2006) pointed out, the average number of dark matter substructures (and, thus, the likelihood of encounters) in a Milky Way-like galaxy decreases monotonically from z ∼ 2 to the present, implying that “old” stream pieces like the ones visible in external galaxies are more likely to reveal perturbations than recently stripped ones. Tidal debris structures can also be used as kinematical tracers of the underlying gravitational potential in which they are produced (e.g., Johnston et al. 2001; see Chapter 7 for detailed discussion). This has been attempted in the Milky Way using the Sgr streams (e.g., Law et al. 2005, Peñarrubia et al. 2005, Law & Majewski 2010a; see Chapter 2 of this volume for more discussion of Sagittarius). The use of streams beyond the Local Group may ultimately become fruitful for this purpose, as they can be traced over multiple wraps, providing much stronger constraints on the level of stream precession due to the flattening of the halo. Finally, old stream pieces stretching over multiple orbital wraps allows us to study metallicity gradients in the stream (and thus within the progenitor galaxy), as has been done for the Sgr tidal stream (e.g., Bellazzini et al. 2006, Chou et al. 2007, Chapter 2 of this volume). All of these techniques, and likely many others, applied to external galaxies provide valuable constraints on the hierarchical process of galaxy growth and evolution beyond what can be gleaned from our embedded perspective in the Milky Way.

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