Bars are present in more than 2/3 of all disk galaxies and were already present in disk galaxies at about the same frequency at z = 1. Bars represent the strongest, most robust and long-lived equilibrium departure from axisymmetry. A consequence of this is that the angular momentum of stars is not conserved, making bars efficient drivers of evolution by angular momentum transport.
NGC 2950 (figure 1) is a nearby and undisturbed SB0 galaxy hosting two nested stellar bars. Interest in nested bars is motivated by the hypothesis that their secondary bars drive gas to small radii, feeding super-massive black holes and AGN activity. Our observations permitted us to establish unambiguously, for the first time, that the pattern speeds of the primary and secondary bars are decoupled.
The pattern speed of a bar is the angular frequency with which it rotates about the center. The pattern speeds of bars determine the orbits of stars, and therefore also the morphology and evolution of bars. Until recently, very few direct measurements of pattern speeds had been made. In collaboration with J.A.L. Aguerri and E.M. Corsini, I have been observing barred galaxies of various strength, luminosity and environment to measure their bar pattern speeds. The pattern speed of a bar is usually parametrized by the ratio of the corotation radius (Dl, where the centrifugal and gravitational forces cancel out in a frame rotating with the bar) to bar semi-major axis (aB). This ratio cannot be smaller than 1; values between 1.0 and 1.4 correspond to "fast" bars. All our observed galaxies have fast bars, as can be seen in figure 2.
References: Debattista, Corsini, & Aguerri (2002), Aguerri, Debattista, & Corsini (2003), Corsini, Debattista, & Aguerri (2003), Debattista (2003).
Also to measure the bar pattern speed, in collaboration with T.B. Williams, I obtained 2-D Fabry-Perot absorption-line spectroscopy of NGC 7079. The reduced velocity field is shown in figure 3. This is the first successful application of Fabry-Perot absorption-line spectroscopy in galaxies. One result of this 2-D spectroscopy of NGC 7079 is that the Tremaine-Weinberg method is rather sensitive to small errors in disk position angle (PA), which I subsequently confirmed with N-body simulations. Moreover, this same method permits a crude estimate of the maximum typical density ellipticity of early-type barred galaxies, which turns out to be about 0.07.
Reference: Debattista & Williams (2004).
Theory and Simulations
In all cases in which the bar pattern speed has been measured, fast bars, (i.e., ones with corotation radii slightly past the end of the bar) have been found. However, if the bar is surrounded by a dense halo, dynamical friction will slow the bar down considerably on quite short time-scales. In collaboration with J.A. Sellwood, I have used N-body simulations to study the evolution of bar pattern speeds for various halo
masses. We start out with initially axisymmetric disks which unstable to bar formation.
We find that, in the presence of a dense halo, an initially fast bar slows down very rapidly, as predicted by theory. On the other hand, when the disk is dominant a bar takes a very long time to slow down. Since real bars are fast, we concluded that real barred galaxies, and by extension unbarred disk galaxies, dominate their rotation curves.
References: Debattista & Sellwood (1998, 2000), Sellwood & Debattista (2006).
In collaboration with C.M Carollo, L. Mayer and B. Moore, I carried out simulations of the bending instability in bars. Bending instabilities arise when bars are much cooler in the vertical direction than they are in the horizontal direction. As a result of this instability, the bar bends above and below the plane and produces a peanut-shaped central structure. We examined the claim that this instability destroys bars and found that, while the bar can certainly be weakened, it is not destroyed. An example of the buckling instability is shown in figure 4. We have also made an animation of this simulation (285Mb). The animation of figure 4 shows the buckling of a bar. The animation consists of four panels with time indicated at bottom right. The top right panel shows the system face-on as seen in the observer's frame. The bottom left (main) panel shows the system face-on in the bar's rest frame. The contours show the density while colors indicate the mean height of particles, with 0.05 being the rms thickness of the initial system. The top left and bottom right panels show the edge-on views, side-on and end-on, respectively. The side on view develops a clear peanut shape after buckling and the end-on view shows the extent to which the center thickens. The animation starts shortly after the bar forms and shows three strong episodes of bending. The paper describing this simulation is Debattista, et al. (2006).
Reference: Debattista, et al. (2004, 2006).
Animation 1 and Animation 2 show the effect of inclination on the s4 moment signature of a peanut-shaped bulge in two simulations (referred to as B1 and B3 in Debattista, et al. 2005). In each case only a single time snapshot is used and this is projected onto the sky plane as indicated at the top. Both simulations include a classical bulge such as would form via mergers. Model B1 did not form a peanut while a strong peanut formed in model B3.
In model B1, the system has no peanut and s4 does not show the characteristic double minimum along the bar's major axis up to an inclination of 30°. Negative s4 on the bar major axis occurs for some orientations, but this is not a signature of a peanut. At an inclination of 40° with the bar close to the minor axis, shallow minima in s4 unrelated to a peanut are evident. At the same inclination, when the bar is close to the major axis, the s4 diagnostic is still viable.
In model B3, the peanut is evident as a prominent double minimum in s4 along the major axis of the bar. As the inclination increases, the double minima become unequal as the bar's orientation approaches the minor axis, but can still be recognized. At an inclination of 40°, the peanut can no longer be recognized when the bar is close to the disk's minor axis, although it can when the bar is close to the major axis.
Reference: Debattista, et al. 2005
Bulges and disks are the main components of galaxies. More than half of the stellar luminosity in the universe comes from disks and a further 25% is due to bulges. It is therefore vital to understand how these two components form and evolve.
The bulges of about 45% of edge-on galaxies are box- or peanut- (B/P) shaped. Edge-on studies have established a connection between B/P-shaped bulges and bars, and may form via the action of the bar. These are then refered to as pseudo-bulges.
A classical example of a peanut-shaped bulge is that of NGC 4565 shown in figure 5.
I devised a way to recognize B/P-shaped pseudo-bulges kinematically at low inclinations even when gas is present. In the past these were identified by their box/peanut-shape when viewed edge-on; since edge-on galaxies cannot be uniquely deprojected, the ability to identify pseudo-bulges at low inclinations will improve our understanding of them. The diagnostic is based on the fact that peanut shapes are associated with a flat density distribution in the vertical direction. We showed that the kinematic signature corresponding to such a distribution is a minimum in the fourth-order Gauss-Hermite moment s4.
We used high resolution N-body models to study the kinematic signatures of face-on B/P-shaped pseudo bulges. The simulations shown in figure 6 all started with classical bulges and formed bars which in the case of B2 and B3 then caused a B/P-shape to form. The middle row shows the Gauss-Hermite moment d4 of the vertical density distribution while the bottom row shows s4 for the kinematics.
Reference: Debattista, et al. (2005).
When gas can cool in a gas rich disk, the gaseous disk becomes violently gravitationally unstable and the gas fragments into clumps that sink to the center, dragging an associated stellar clump (figure 7). Such clump instabilities build central bulge-like objects directly. In order for the resulting bulge to sit on the M•-σ, less than 0.3% of the central gas needs to collapse into a black hole.
Disk galaxies are often characterized by an exponential surface brightness profile. However, this is typically valid only over a limited range in radii. At large galacto-centric radii most disk galaxies reveal a truncation in their surface brightness profile. Originally these truncations were interpreted as marking the outer edges of the stellar disks. It has now become clear that they rather indicate a sharp break between an inner and outer exponential profile. About 70% of late-type galaxies have this type of double-exponential breaks. My simulations showed that angular momentum redistribution within galaxies leads to realistic breaks in the surface density of disks. The breaks that result in these simulations are in very good agreement with observations, not only in terms of the break radii in units of inner disk scale length but also outer scale-lengths and the difference between central surface brightnesses of the two exponentials. This is true both in the face-on view and in the edge-on view (figure 8).
Reference: Debattista, et al. (2006).
Dwarf elliptical galaxies are the most common type of galaxy observed. In a hierarchical model, dwarf galaxies are expected to form first and to later merge to form larger galaxies. Thus understanding how they form and evolve is crucial for understanding galaxy formation in general (indeed the study of dwarf galaxies has been called "near field cosmology".)
A sizeable fraction of dwarf elliptical (dE) galaxies contain nuclei. These nuclei are sometimes observed to be offset from the center of the galaxy. In collaboration with S. De Rijcke, I studied the counter-streaming instability as a source of lopsided nuclei in dwarf elliptical galaxies. This instability results when some fraction of a galaxy's stars are counter-rotating with respect to the rest of the galaxy. We considered the case of FCC 046 (figure 9), a prototypical dE with a lopsided nucleus. We showed that simulations of the counter-streaming instability produced systems which are in broad agreement with observations of this galaxy. We also showed that low resolution spectra of FCC 046 seem to suggest the presence of counter-streaming, as required by our model. Higher resolution spectra with less noise are required, however, to confirm this result.
Figure 10 shows the absorption-line spectrum of FCC 046 along the major axis (top 3 panels, left and right) with the prediction from the N-body model overlaid in the gray line. Despite the low S/N, there is an indication that the line-of-sight velocity distribution (LOSVD) is split. The bottom panel shows the spectrum along the minor axis, the split is now absent, exactly as the model predicts.
Reference: De Rijcke & Debattista (2004).
The Milky Way
The Milky Way Galaxy (MWG or the Galaxy) is our home galaxy. Because we live in it, we know less about it than many external galaxies. Nevertheless, in recent years we have learned a lot about the Galaxy, including the fact that it is a barred galaxy. Figure 11 shows the view of the Milky Way disk and bulge as seen in the infrared by the COBE satellite.
In collaboration with O. Gerhard and M.N. Sevenster, we measured the pattern speed of the inner MWG as traced by OH/IR stars, using a modified version of the Tremaine-Weinberg method. OH/IR stars are very useful for such studies because they are old objects (> 1 Gyr) and because their dusty circumstellar envelope absorbs the stellar radiation and re-emits it in the infrared, pumping OH masers. The maser emission at 1612.23 MHz makes these objects easy to identify and is free from dust extinction, so that an unbiased survey is possible. We selected a sample of some 250 OH/IR stars from the survey of Sevenster et al. (1997, 1997, 2001), from which we obtained the pattern speed of the inner Milky Way. The resulting pattern speed was about 59 km/s/kpc, in excellent agreement with other, independent measurements. However, unlike previous measurements, our's is completely model-independent. Moreover, and perhaps more interestingly, we showed how, with future astrometric missions (such as ESA's GAIA) providing both distance and radial velocity data, it will be possible to use this method to accurately measure the MWG spiral pattern speed as a function of radius.
References: Debattista, Gerhard, & Sevenster (2002, 2003).
In collaboration with N. Bissantz and Gerhard, I developed a dynamical model of the Milky Way. Previous dynamical models of the Milky Way were unable to match the long duration wing of the microlensing event timescale distribution (ETD). We started from a well motivated density model which had previously been tested against gas kinematics in the inner Milky Way and the microlensing optical depth. To construct this model, we implemented for the first time the new and efficient algorithm of Syer & Tremaine (1997). This algorithm allowed us to construct a dynamical model which matched the full microlensing event timescale distribution. A figure with the ETD and its decomposition by source and lens distance from the Galactic center is shown in figure 12. In the top panel, the solid line shows the cumulative distribution of event timescales for our best fitting model while the stepped distribution shows the observational data of Alcock et al. (2000). The bottom panel shows the decompostion of the best distribution (solid line) and the contributions of lenses within 4 kpc of the sun (dashed line), lenses further than 4 kpc (dotted line), and sources between 6 kpc and 10 kpc from the sun (dot-dashed line).
Reference: Bissantz, Debattista, & Gerhard (2004).
Dynamical modeling involves trying to recover the phase space distribution of a galaxy's stars. This is useful for a variety of reasons. Because phase space is conserved, it helps constrain the formation of galaxies. More practically, such models can constrain the dark matter content of galaxies and the masses of black holes. Several approaches are possible for generating such models. The first is to fit analytic distribution functions to observables of galaxies. The principal drawback is that these methods are not robust enough to handle all cases of interest. A more robust and widely used method is the Schwarzschild method. In this method, stellar orbits are superposed with non-negative weights such that galaxy observables are reproduced. The main disadvantage of this method is that such models are generally computationally expensive and they require that the orbit space is specified a priori, which is generally complicated especially in the presence of chaos.
Recently a new algorithm was introduced by Syer & Tremaine (1997). This "made-to-measure" algorithm produces dynamical models much more efficiently that does the Schwarzschild method. Together with F. De Lorenzi and O. Gerhard, I have successfully implemented this algorithm for the first time. We used the method to construct a dynamical model of the Milky Way (figure 13). We were able to use almost 4 million particles (orbits) in our model, almost 400 times more than previous dynamical models of the Milky Way. We used the model to explore the event timescale distribution of microlensing events. Previous dynamical models of the Milky Way were unable to match the long duration wing of the microlensing event timescale distribution (ETD). The ETD and its decomposition by source and lens distance from the Galactic center is shown in figure 12. In the top panel, the solid line shows the cumulative distribution of event timescales for our best fitting model while the stepped distribution shows the observational data of Alcock et al. (2000). The bottom panel shows the decompostion of the best distribution (solid line) and the contributions of lenses within 4 kpc of the sun (dashed line), lenses further than 4 kpc (dotted line), and sources between 6 kpc and 10 kpc from the sun (dot-dashed line).
Reference: Bissantz, Debattista, & Gerhard (2004).