THE VERTICAL X-SHAPED STRUCTURE IN THE MILKY WAY: EVIDENCE FROM A SIMPLE BOXY BULGE MODEL

The edge-on galaxy with a side-on bar is shown in the upper panel of Figure 1, and an X-shaped structure is discernible in the inner region of the boxy bulge. The bar length, defined as the distance between the two end points of the bar (2 R_bar), is about 8 kpc (Shen et al. 2010). After applying a mask to cover the X-shaped structure, we use the IRAF task ELLIPSE to fit the elliptical isophote of this edge-on image. The center is fixed for each isophote, whereas the ellipticity and position angle are free parameters. Then we use the task BMODEL to construct a model based on the extracted elliptical isophotes to properly account for the underlying smooth component of the edge-on galaxy. This model is subtracted from the original image to produce a residual image (lower panel of Figure 1), which more clearly highlights the X-shaped structure. We carried out several tests and found that this residual image is insensitive to the size of the mask used. The four arms of the X-shaped structure are cone-like (with finite thickness). They are narrow toward the GC, and become wider outward. In the X-direction, the end-to-end separation between the inner two edges of the X-shaped structure is ∼2 kpc. For the outer two edges, the end-to-end separation is ∼4 kpc. We estimate the size of the X-shaped structure in the X-direction by averaging the two separations, which yields about ∼3 kpc. This value is less than half of the full length of the bar (8 kpc). Similarly, in the Z-axis, the end-to-end separation between the inner two edges of the X-shaped structure is ∼1.2 kpc. For the outer two edges in the Z-axis, this separation is ∼2.4 kpc. Therefore, the size of the X-shaped structure in the Z-direction is ∼1.8 kpc. Since the boundaries of this structure are not clear-cut, our measurement has an uncertainty of about 0.2 kpc.

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From the image, it is also apparent that the X shape is quite symmetric in the X–Z plane. By summing up the pixels with positive values in the X-shaped region, we estimate that the light fraction of this X-shaped structure relative to the whole boxy bulge region is about 7%.

To further confirm the existence of this X-shaped structure, we smooth the image with a median filter and subtract it from the original image. The residual clearly shows an X-shaped structure in the disk, which is less extended than that in the lower panel of Figure 1. Because the median filter technique is only sensitive to small scale and strong structures, the residual image does not reliably reflect the size of the X-shaped structure. Near the end points of the X-shaped structure, the intensity contrast relative to the local background is low, and the structure becomes quite broad. Therefore, it is not very surprising that the extended faint parts of the X-shaped structure do not stand out in the median filter processed residual image.

It is of great interest to compare our model with the observational evidence of the X-shaped structure in our Milky Way (MZ10; Nataf et al. 2010; S11). First, we need to create the mock image in the solar perspective. The configuration is exactly the same as Shen et al. (2010), where the Sun is 8.5 kpc away from the GC (R_☉ = 8.5 kpc), and the Sun–GC line is 20° away from the major axis of the bar. Note that the half length of the bar (R_bar) is about 4 kpc.

3.2.1. Double Peaks in Distance Histograms

Figure 3 in MZ10 shows the luminosity functions of RC stars in different fields at b = −8°. A bimodal distribution shows up in almost all panels, which was also seen in Nataf et al. (2010). The relative amplitude of the bright to faint RC peaks changes dramatically with the longitude l; the faint RC dominate at negative l and the bright RC are more prominent at positive l. The two RCs at different l actually have similar apparent magnitude in K₀ band, indicating that the distance to both RCs varies little with l. MZ10 found this result hard to understand with a naive straight bar.

Figure 2 shows the distance histograms of particles in different regions at b = −8°. To make a fair comparison, we study the fields identical to those in MZ10. Almost all panels in Figure 2 display a bimodal distribution. Note that the double peaks in the distance histograms actually correspond to those in the magnitude histograms (Figure 3 in MZ10); the brighter RC peak is closer to us, and the fainter RC peak is farther away from us. The relative amplitude of the bright peak to the faint one decreases as the line of sight shifts from positive to negative l. However, at negative l, the front peak is still more prominent than the second peak, which is different from MZ10. This is mainly due to the fact that the front arm of the X-shaped structure in our model is wide in longitude at b = −8°, covering from +9° to −6° in l. Moreover, in each field, particles at the front peak are closer to the Galactic plane than the second peak, therefore the space density at the front peak is higher. The two vertical lines in each panel of Figure 2 mark the position of the double peaks in the field (+ 1, −8), in the same fashion as MZ10. We can find that the positions of the two peaks are roughly constant at different l as in MZ10.

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Figure 3 shows the distance histograms of particles in fields at l = +1° with two vertical lines marking the same positions as in Figure 2 (to be compared to Figure 7 in MZ10). A bimodal distribution again shows up in all panels. For fields closer to the Galactic plane, the separation between the two peaks decreases, which is clear evidence for the X-shaped structure. The distance difference increases from ∼1.8 kpc at b = ±55 to ∼2.5 kpc at b = ±1025. MZ10 also found that at lower latitude, the magnitude difference between the two peaks decreases, meaning the two RCs are getting close to each other. Figure 8 in MZ10 shows that the structure extends to about 3 kpc in the disk and 2 kpc in the vertical direction. The X-shaped structure in our model (Figure 1) has almost the same size.

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So our model, which contains an X-shaped structure created naturally in the buckled bar, is in good agreement with the observational results of MZ10.

3.2.2. Number Density Maps in Latitude and Longitude Slices

We compare the number density maps in latitude and longitude slices of our model to those obtained by S11. Figure 4 shows normalized stellar number densities for slices at different latitudes b. The projected GC is marked with a black cross at the center of each panel. Two overdensities show up in almost all panels, and the separation between them increases with |b|. The connection of the two overdensities tilts in a similar fashion as in S11; this is consistent with the fact that our bar angle (20°) is the same as that found by S11. The two overdensities get closer as |b| decreases toward the disk plane. Due to incompleteness of Two Micron All Sky Survey at lower latitude (|b| ⩽ 35), S11 were unable to measure the number densities in those fields. We produce the stellar number density maps for slices at |b| = 3° and 2° in our model. Our model predicts that the two overdensities are about 1 kpc apart at |b| = 3° (shown in Figure 4), and almost merge together for |b| ⩽ 2°.

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Another feature in Figure 3 of S11 is that the overdensity on the far side fades away faster than the closer overdensity. The same behavior is also seen in our Figure 4. Since the X-shaped structure looks symmetric in Figure 1, this behavior may be caused by the line-of-sight effect. At the same latitude, particles at large distances actually reside in diffuse ends of the X shape, so they fade faster than the closer overdensity region (S11). In Figure 4, the overdensity at larger distance becomes noisier for slices at |b| ⩾ 6° due to the limited number of particles in our model. We hope that future higher resolution simulations will improve particle statistics on this.

Figure 5 shows the stellar number density maps of vertical slices at different l toward the GC. A weak X shape is discernible for |l| ⩽ 2°. This is qualitatively consistent with Figure 4 in S11. For slices at |l| > 2°, the X-shaped structure becomes hard to identify as in S11.

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The formation of the boxy bulge in our self-consistent model naturally produces a vertical X-shaped structure. The bar formation process enhances the radial streaming motion of stars along the bar, making the disk vulnerable to the buckling/firehose instability (Toomre 1966; see also reviews by Sellwood & Wilkinson 1993; Sellwood 2010). As the instability gradually saturates, the thickened bar appears as a BPS bulge when viewed edge-on (Raha et al. 1991).

The backbone orbits of a three-dimensional buckled bar are the x₁ tree, i.e., the x₁ family plus a tree of two-dimensional and three-dimensional families bifurcating from it (Pfenniger & Friedli 1991). The X-shaped structure is probably associated with orbits trapped around the three-dimensional x₁ family, e.g., x1v1, x1v4, etc. (e.g., Patsis et al. 2002; Athanassoula 2005). Note that the radial extent of our X-shaped structure is less than half of the bar length. The length of the bar is determined mainly by the x₁ family or two-dimensional rectangular-like 4:1 resonance orbits, which have a larger radial extent (Patsis et al. 2003). On the other hand, the three-dimensional backbone orbits of the X shape probably extend shorter in the radial direction (e.g., Patsis et al. 2002).

This X-shaped structure does not have a straightforward explanation in classical bulge formation scenarios (Bureau et al. 2006), but it is a natural consequence of the bar buckling mechanism as we show in this Letter. We can qualitatively reproduce the observational signatures of the X shape, such as double peaks in distance histograms (MZ10) and number density maps (S11). The existence of the X-shaped structure in our Milky Way may imply that the Galactic bulge is shaped mainly by internal disk dynamical instabilities instead of mergers.

De Propris et al. (2011) studied the radial velocity and abundances of bright and faint RCs at (l, b) = (0°, −8°), and found no dynamical or chemical differences (also Uttenthaler et al. 2012). Proper motions of the two RCs are also similar (Vieira et al. 2007). These clues suggest that the two RCs indeed belong to the same coherent dynamical structure, which could be naturally made in the formation of the bar/boxy bulge.

In our N-body simulation, the buckling instability gradually saturates and the X-shaped structure becomes increasingly symmetric with time. We also studied the snapshot model at an earlier time of 2.4 Gyr. Unlike our canonical model at 4.8 Gyr, the X-shaped structure at 2.4 Gyr appears quite asymmetric about the disk plane. The observed symmetry (MZ10; S11) probably indicates that the X-shaped structure in the Galactic bulge has been in existence for at least a few billion years.

Although the X-shaped structure in our simple model is qualitatively similar to the observed one, it still cannot match all details of observations. For example, in the panels at negative longitudes in Figure 2, the second peak at larger distances is not as significant as the observed peak of the faint RC stars (Figure 3 of MZ10). Nevertheless, it is encouraging that our simple model matches observations in many aspects, and may help to guide future analyses. Further improvements on this model are clearly desired to completely understand the Galactic bulge structure, its dynamical and chemical histories.

After this Letter was published in the arXiv and submitted to ApJL, Ness et al. (2012) independently reported their study on the split RC based on the ARGOS survey and compared to an N-body boxy bulge model. Their main conclusions are broadly consistent with ours.