HALOGAS: H i OBSERVATIONS AND MODELING OF THE NEARBY EDGE-ON SPIRAL GALAXY NGC 4565

NGC 4565 is classified as an SAb galaxy (de Vaucouleurs et al. 1991) with an SFR of 0.67 M_☉ yr⁻¹ calculated in Heald et al. (2012) using total infrared (TIR) flux measurements. This places it near the low star-forming end of the HALOGAS sample. However, based on its rotation curve, it is among the most massive, which would presumably hinder gas being ejected to large heights above the disk. This combination gives it substantial importance in determining overall trends involving extraplanar H i and star formation.

At a distance of 10.8 Mpc (Heald et al. 2011), NGC 4565 is relatively nearby, and among the best studied edge-on spirals. It has been observed in optical continuum (e.g., Kormendy & Barentine 2010), Hα (Rand et al. 1992), radio continuum (Kodilkar et al. 2008), CO line emission (Neininger et al. 1996), and X-rays (Vogler et al. 1996).

In the optical, NGC 4565 is seen to have a box-shaped bulge indicating a bar (Kormendy & Barentine 2010). Additionally, Neininger et al. (1996) found radial motions in CO emission along the minor axis, which they suggested could be due to a bar or a spiral density wave. We see evidence for the bar in H i, as will be discussed in Section 3.

Kodilkar et al. (2008) detected a radio continuum halo extending up to 3 kpc. In contrast, Rand et al. (1992) found that NGC 4565 was lacking a smooth DIG halo, which is consistent with its low SFR.

Unexpectedly, substantial X-ray emission, generally not seen in galaxies without enhanced star formation activity, was detected both within and above the disk (Vogler et al. 1996). The nature of this X-ray emission is still unknown.

Finally, H i observations of NGC 4565 were previously performed using the Very Large Array, but detailed models were not created from those data (Rupen 1991). However, a comprehensive description was provided in that paper, mentioning several features we now see in greater detail, and with a higher level of confidence. Additional WSRT data were taken (Dahlem et al. 2005), which were further interpreted in van der Hulst & Sancisi (2005). These WSRT data are supplemented with the HALOGAS data to produce the final data set presented here. Table 1 summarizes parameters for NGC 4565.

Table 1. NGC 4565 Parameters

Parameter	Value	Reference
Distance (Mpc)	10.8a	Heald et al. (2011)
Systemic velocity (km s−1)	1220	This work
Inclination	875	This work
SFR (M☉ yr−1)	0.67	Heald et al. (2011)
Morphological type	SAbb	de Vaucouleurs et al. (1991)
Kinematic center α (J2000.0)	12h36m21s	This work
Kinematic center δ (J2000.0)	25d59m10s	This work
D25 (kpc)	16.2	de Vaucouleurs et al. (1991)
Total atomic gas mass (109M☉)	9.9 c	This work

Notes. ^aDistance is the median value of distances found on the NED database, excluding those obtained using the Tully–Fisher relation. ^bThe A classification indicating no bar is likely erroneous based on Neininger et al. (1996), Kormendy & Barentine (2010), and this work. ^cIncludes neutral He via a multiplying factor of 1.36.

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Several basic models are initially considered. These include a simple one-component (i.e., single disk with a constant exponential scale height and no warp or flare), flare, a substantial warp component along the line of sight, and a model with a second, thickened disk simulating an extended global halo. The one-component and flare models are labeled as 1C and F in figures.

Upon examination of the zeroth-moment map (Figure 1) as well as the vertical profile (Figure 5), the latter two models (not shown) may be eliminated quickly due to a lack of thickening of the gas layer at small to intermediate radii that is a feature of these models as well as poor fits to position–velocity diagrams and channel maps. The observed vertical profile is almost entirely devoid of wing structure, making it difficult to fit while maintaining the correct curvature and width near the center with such models. A substantial warp component along the line of sight places flux high above the midplane on the systemic side of the bv diagrams as is seen in the data. However, it also creates indentations along the major axis at large radii in channel maps as well as on the systemic side of bv diagrams. These are not seen in the data. As for a halo model, adding a second thicker component not only increases the width of bv diagrams on the systemic side, but also increases the width closer to the terminal side. Again, this is not seen in the data. For these reasons, only the 1C and F models are considered further and described below.

Although multiple types of models are considered, some parameters remain fixed. These include the central position ($12^{\rm h} 36^{\rm m} 20\mbox{$.\!\!^{\mathrm s}$}63$, $25^{\rm d} 59^{\rm m} 16\mbox{$.\!\!^{\mathrm s}$}8$), systemic velocity (1220 km s⁻¹), velocity dispersion (10 km s⁻¹), the run of the position angle and inclination, the surface brightness profile, and the rotation curve. All models include a bar and a small-scale feature that are discussed in Sections 4.1.3 and 4.1.4.

Due to asymmetries, the disk is divided into two halves along the minor axis, and each half is independently modeled in what follows.

4.1.1. One-component Model

A model consisting of a single component with an exponential scale height of 470 pc was created. This model is a reasonable approximation to the data, but with deficiencies. The first of these may be seen in the vertical profile (Figure 5) where the 1C model is too flat near the top compared to the data. If the scale height is decreased to match the data near the center, then the model becomes too narrow in the wings. No other combination of scale height and inclination improves the fit. In the bv diagrams shown in Figure 3, the 1C model is too thick at terminal and intermediate velocities when compared to the data. Furthermore, an excess of emission in the 1C model can be seen at major axis offsets within ±5' of the center offsets of the lv diagrams corresponding to −16'' and −32'' in Figures 6(a) and (b). Finally, in Figure 7, one may note that, while the minor axis thickness is well matched at velocities close to systemic, the 1C model is too thick at small and intermediate major axis offsets. As will be shown, these issues are all remedied by allowing the scale height to vary in the form of a flare.

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4.1.2. Flaring Model

Instead of using a single exponential scale height throughout the disk, if we allow the disk to flare (scale height = 4'' (200 pc) near the center, increasing to scale height = 12'' (600 pc) in outer radii), the issues mentioned above are all but eliminated, as may be seen in the third columns of Figures 6(a) and (b). Other variations in the scale height were tested, but this was found to be the best fit to the data. Figure 8 shows the radial variation of scale height used in our flaring models. Note that the scale height increases in steps rather than a straight line. A smoothed version would produce nearly identical results, but arbitrarily smoothing the scale height distribution could imply that the models are better constrained than they are in reality. Thus, we include the steps as they are a better representation of the modeling process and limitations. Nevertheless, the scale height is seen to rise in a nearly linear fashion.

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Although some improvements with the flare model are seen in lv diagrams where the excess emission in the 1C model is not seen, the most convincing evidence for improvement is also seen in bv diagrams and channel maps (Figures 3 and 7). In Figure 3, one may note a widening on the systemic relative to the terminal side of the data best seen in panels within ±3', which is significantly better matched by adding a flare. Additionally, in Figure 7 it is seen that there is a thickening at large major axis offsets in the channel maps that is best reproduced via the addition of the flare (e.g., the panel corresponding to 1381 km s⁻¹).

Key parameters for the models described above, with the 1C and F models differing only in scale height behavior, are shown in Figure 8.

Up to this point, we have discussed modeling only global features found throughout the disk. Now we will discuss the modeling of more localized features such as a bar and adding further refinements such as radial motions. Given that Figures 3–5 provide the most detailed representation of the models, these figures all include the features that will be described below. Abbreviated representations of the models excluding them will be shown in order to show their effects.

4.1.3. Including a Bar

As mentioned in Sections 1 and 3 there are indications of a bar in NGC 4565, which we will show can also explain the large velocity spread in panels near the center in Figures 3 and 10. The effects of adding a bar are most clearly seen in the latter figure, which shows no bar and bar models side by side. We model this bar by adding a series of one-dimensional Gaussian emission components starting at the center and moving outward radially along some azimuthal direction in the disk. The dispersion of the Gaussian component is specified along the azimuthal angle and is 15'' in our models. The amplitude is also specified. Additionally, parameters which are specified in rings as described above may also be set, notably the azimuthal position and radial velocity. It should be noted that these parameters allow for an approximation of a bar, and do not account for more complex streaming motions or morphology. Figure 9 shows how this bar appears in a face-on view of our best model.

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We examine several orientations with respect to the line of sight, keeping in mind that Kormendy & Barentine (2010) assume a line-of-sight (i.e., end-on) orientation due to the boxy bulge seen in the optical, while Athanassoula (2005) states that such boxy bulges are indicative of components across the line of sight (i.e., side-on), but possibly only as little as 10° from the end-on view. From the clear indications of radial motions described below, we can be certain that the bar is at least partially end-on, although it is difficult to gauge how much. We explore this in our models.

First we examine a line-of-sight or end-on orientation and assume that the half-length of the bar roughly extends to 125 (4 kpc), or just within a ring of higher density in the disk (Figure 8). A linearly increasing rotation curve is used, which matches the rest of the disk at radii larger than 45''. (Note: aside from the bar, no H i is included in the main disk interior to this radius.) Adding a bar in this way allows for some spread in the velocity range (Figure 10, column 3), while remaining in a narrow range along the minor axis. However, the full velocity spread seen in the data is not achieved. Such a model is improved by adding radial motions of ±20 km s⁻¹ (Figure 10, column 4). Due to projection effects and limited spatial resolution, we cannot discern whether this is inflow or outflow.

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For ±30° and ±45° offsets from the line of sight (positive corresponds to the near side of the bar being in the NW quadrant), we achieve a somewhat improved fit with radial motions of ±40 km s⁻¹. Finally, increasing the offset to ±60° from the line of sight requires increasing the radial motions to ±60 km s⁻¹. These results ignore any additional radial motions in the disk beyond the bar, which are shown to be necessary in Section 4.1.5. These motions in the disk render constraining the orientation and radial motions of the bar even more difficult.

The length of the bar and the dispersion of the Gaussian distortions remain constant in all cases. For the figures in this paper we display a −30° offset bar with a radial motion of −20 km s⁻¹. It should be noted that +30° offset bar paired with +20 km s⁻¹ radial motion produces the same results. The disk radial motions decrease the amplitude of the optimal bar radial motion; hence we choose −20 km s⁻¹ for the latter instead of −40 km s⁻¹ as mentioned above.

4.1.4. Additional Morphological Modifications

4.1.5. Radial Motions in the Disk

There are several indications of radial motions beyond the bar. This is most readily seen in Figure 3 as well as in Figure 10. Note first the slope of the highest contours on the systemic side of the approaching half, particularly evident in the panels corresponding to 0' and 1'. This is appropriately reversed for the receding half. These are indicative of radial inflow at small to intermediate radii. This is modeled by introducing an inflow starting with an extreme value of −50 ± 5 km s⁻¹ at 175 (5.5 kpc) and quickly decreasing with radius before becoming undetectable beyond 275 (8.6 kpc). This inflow is symmetric in both halves and is very likely associated with the ring of higher density. The model in the fourth column of Figure 3 (Fi) includes all of these motions. Arrows in Figure 3 indicate the significant but often subtle effects of adding such inflow. The directions of the arrows correspond to the direction in which emission is displaced due to radial motions. Additional isolated regions of inflow are seen in each half, but these are not symmetric and are likely associated with spiral structure. It should be noted that a more modest inflow of 10–15 km s⁻¹ spread over a larger radial range could not reproduce what is seen in the data.

In addition to the indications of radial inflow in the inner parts of the galaxy, indications of outflow are seen at large radii. This is best seen as the overall negative slope on the systemic side, opposite in direction from that produced by the inflow, ±40''–80'' off the plane of the disk in panels between −5' and +5' (once again indicated by arrows). This is modeled by allowing a radial outflow of 10 km s⁻¹ beginning at 675 (21.2 kpc), and extending outward to the edge of the disk in each half (Figure 3, column 5 (Fio)).

The distribution of radial motions in the models may be seen in Figure 11.

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It is difficult to tell with certainty if the observed radial motions are due to streaming along spiral arms or another source. However, the substantial inflow located within and just outside the ring of higher density indicates that the inflow in this region may be true axisymmetric inflow or associated with the bar rather than spiral arms.

4.1.6. The Addition of a Lag

As previously discussed in Section 4.1.1 and seen in the bv diagrams in Figure 3, the data are relatively thin near the terminal side compared to the systemic. This is somewhat remedied by the addition of a flare (Section 4.1.2), but improvements may still be made through adding changes in rotational velocity with height above the disk. This causes observed velocities of emission at high z to be displaced toward the systemic side in the bv diagrams, resulting in a thinning in the width near the terminal side and a thickening on the systemic side. This is best seen in the bv diagrams closer to the center, as shown in Figures 12(a) and (b) where the contours on the terminal side become more rounded to better match the data with the addition of a lag. This is also evident at the terminal edge of lv diagrams, where emission is displaced to lower velocities. It should be noted that these effects are subtle but cannot be reproduced by changing the flare parameters. If a lag is present in the data, then we should see some or all of these features, provided there is sufficient resolution. However, given how thin and far away the disk is, our resolution is lacking, so our error bars are large. We find an optimal lag peaking at −40⁺⁵ _{− 20} km s⁻¹ kpc⁻¹ between 125 and 475 (3.9 and 14.9 kpc) in the approaching half, and −30⁺⁵ _{− 30} km s⁻¹ kpc⁻¹ between 125 and 425 (3.9 and 13.4 kpc) in the receding half. These quickly decrease in magnitude within the specified range in both halves, as shown in Figure 13. This lag distribution is again represented in Figure 14 as an azimuthal velocity that rises more steeply at high z.

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For completeness we also include a model with a constant global lag throughout the galaxy in the sixth column of Figure 3. Such a lag overestimates the rounding on the terminal side in panels corresponding to ±5' and ±7', emphasizing the need for radial variation in the lag.

A rigorous statistical analysis of the fitting of tilted ring models is generally omitted from the literature (e.g., Barbieri et al. 2005; Oosterloo et al. 2007; Rand & Benjamin 2008). Such studies employ a simple model focusing on the quantification of certain features in observed galactic disks, driven by a specific scientific question. In our case the main aim is to constrain the vertical structure of the H i disk, which means giving significant weight to faint emission. If fitting were fully automated, a goodness-of-fit criterion such as a χ² (which TiRiFiC provides) could be used to distinguish models by significantly downweighting the bright emission that would otherwise dominate the statistic and render it meaningless for our purposes. In principle, a reduced χ² with such a weighting could also account for the varying number of free parameters among models. However, it is generally much more efficient to use the judgment of the modeler and adjust certain parameters manually. But this makes an accurate accounting of the degrees of freedom in each model difficult. For instance, the radial scale height dependence (Figure 8) shows eight values and eight inflections, indicating sixteen values were varied. However, for this and other parameters, finer variations may have been considered and discarded as providing insignificant improvement. Likewise, initially most parameters for the approaching and receding models are the same, and then some parameters varied as needed, but some deviations between halves may have been tested and discarded to keep the models simple. If so, the number of parameters allowed to vary was larger than the final model would suggest.

We therefore rely on fitting by eye to guide our choice of models. A visual comparison of data and models provides a powerful method for deciding how models must be altered to fit the data, easily allowing attention to be focused on regions of interest. One statistic we could examine, regardless of the number of degrees of freedom, is the rms of the residual cube, downweighting regions of bright emission. In fact, when we examine this statistic, using only emission above 3σ, we indeed find a significant 7% reduction for models which include a flare (all models beginning with "F") rather than a constant scale height (1C). However, among the flaring models, the numerical difference due to the addition of radial motions, a bar, or a lag is negligible. Nevertheless, improvement is clearly seen in Figures 3, 10, and 12(b), respectively. In spite of such limitations, we address the need for such features here.

First, the additional arc in the receding half (Section 4.1.4), which is included in all models presented in this paper, can be justified rather simply. There are clear indications that a feature of higher flux density exists in this region, but only in one quadrant of the disk (Figure 3, panel corresponding to 5'). The feature could be reproduced with an overall change in position angle, allowing flux to be redistributed at high z, but as this feature is seen only in a select region of the disk, such a change would worsen the fit in other parts of the disk. Additionally, a change in position angle for only this region would be unphysical and was seen to be a less desirable match during the modeling process (not shown).

The addition of radial motions duplicates slants, slopes, and curves in the data (Figure 3) that are otherwise not reproducible. One could argue for changes in the position angle near the center to reproduce these slants, but through modeling we see that such a change would not fit the data as well. Furthermore, warping near the center, as well as both the positive and negative changes in position angle required to reproduce the correct slanting, would be uncharacteristic of warping typically seen in other galaxies (Briggs 1990).

It is clear that a bar exists in NGC 4565, both from previous works at other wavelengths (Kormendy & Barentine 2010; Neininger et al. 1996) as well as our models. Substantial improvement can be seen in Figure 10 although, due to projection effects, the uniqueness of this bar is difficult to constrain. Thus we provide generous uncertainties for the quantities involved (Section 4.1.3).

Finally, the lag is best constrained using faint emission, high above the plane of the disk. For this reason, improvements due to a lag do not exhibit substantial changes in the rms of the residuals. Nonetheless, subtle improvements are seen in Figures 6(a) and (b), as well as Figures 12(a) and (b). The characteristics of the lag may initially be interpreted as H i that appears (at least in projection) above the plane of the disk that is rotating more slowly than H i in the midplane. The issue of projection effects could hinder the uniqueness of our models if such effects are not considered carefully. However, signatures in both bv diagrams and channel maps described at the beginning of Section 4.1 allow us to successfully rule out inclination effects in this case. From this we may conclude that the observed effects are extremely likely due to a lag. A range of possible values for this lag is given in Figure 13.

The warp in NGC 4565 is highly asymmetric, not only extending further and reaching higher values in position angle on the receding half, but also flattening at large radii on that side as well (Figure 8). There was a hint of this flattening in a few channels as noted by Rupen (1991), most prominent in the channel corresponding to v_hel = 1459 km s⁻¹. Here we see it from v_hel = 1440 to 1473 km s⁻¹. A similar flattening is also seen in NGC 5907 (Sancisi 1983).

Additionally, there is a slight rise in inclination for radii larger than 875 (27.5 kpc), causing the galaxy to become more edge-on. This is only seen in radii beyond the extent of the emission in the approaching half and thus it is only seen in the receding half.

It is difficult to determine the exact cause of the asymmetries in the warp, but it is possible that the companion galaxies play some role. NGC 4565 is clearly interacting with IC 3571, as can be seen in Figure 1 by the bridge of material between them. Additionally, material closer to the plane of the disk appears to be displaced above the plane, toward IC 3571 (Figure 1). Given the location of IC 3571, it may contribute to the asymmetry in the component of the warp across the line of sight. This was also noted by van der Hulst & Sancisi (2005).

Emission likely tied to IC 3571 as part of the bridge between the two galaxies could not be reproduced in the models, which is unsurprising. The velocity range associated with this emission is reasonably close to that of the main disk of NGC 4565 (Figure 15), and is likely only a disturbance of gas within the disk as opposed to accretion from IC 3571.

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The exponential scale height in NGC 4565 begins to increase in both halves from an initial 4'' (200 pc) near a radius of 3' (9.4 kpc), eventually reaching a value of 12'' (600 pc) at a radius of 7' (22.8 kpc). This is just within the optical radius (81 or 25.5 kpc).

Flares are seen in other galaxies, including M 31 (Brinks & Burton 1984) and the Milky Way (Kalberla et al. 2007, and references therein). However, there exist galaxies for which extensive H i modeling has been done that do not show flaring gas layers, including NGC 5746 (Rand & Benjamin 2008) and NGC 4559 (Barbieri et al. 2005), indicating that flares are common although not ubiquitous.

Our models yield no evidence for a massive, extended H i halo in NGC 4565. This is shown by the vertical profile in Figure 5 where there are no indications of a second, extended component that exists globally throughout the data. Furthermore, a second component is not seen to improve position–velocity diagrams or channel maps (not shown).

We return to the issue discussed in Section 1 of whether there is any connection between H i halos and disk star formation activity. It is difficult to extract any concrete trends regarding H i halos with such a small number of galaxies having been observed to this depth and subsequently modeled in detail. The situation is in the process of being remedied via the HALOGAS survey and Expanded Very Large Array observations involving some HALOGAS team members. In Table 3 we compare properties including total H i mass, TIR luminosity per unit area, scale heights, and lags of NGC 4565 with those of previously modeled edge-on galaxies.

The TIR luminosity per unit area for each galaxy is calculated in this work unless otherwise stated. These calculations are done based on equations found in Dale et al. (2009), and involve the optical area (de Vaucouleurs et al. 1991 in most cases; additional references are provided in the table). Spitzer MIPS data are used if available for a given galaxy, otherwise IRAS data are used.

Immediately apparent is the pattern of higher infrared luminosity per unit area (i.e., SFR per unit area) and the presence of extraplanar H i in the form of a halo. The obvious exception is UGC 7321. NGC 5775 could be considered an exception, since a global H i halo is absent. However, in that case, prominent extraplanar features including extensions and arcs are present.

Still, we must emphasize that this result is based on only a few galaxies and modeling methods differ among them. Further analysis of the HALOGAS sample, in which individual galaxies are modeled in a fashion consistent from galaxy to galaxy, will provide a stronger test of this trend.

We do not detect substantial extraplanar H i in the form of a global halo, which indicates that there is no strong disk–halo cycling in NGC 4565. However, the H i has some vertical velocity dispersion and experiences a lag when it rises above the plane of the disk. The lag we detect is within the innermost 475 (14.9 kpc) and 425 (13.4 kpc) in the approaching and receding halves, respectively. As is the case for UGC 1281 (Kamphuis et al. 2011) and NGC 4244 (Zschaechner et al. 2011), this indicates that substantial extraplanar gas need not be present in order for a lag to be observed. (Although for UGC 1281, a larger line-of-sight warp component is favored over a lag, yet a lag cannot be ruled out.)

The H i lag detected in NGC 4565 is very steep. This would be consistent with the Heald et al. (2007) trend in which DIG lags are seen to steepen with decreasing SFR, provided that H i and DIG lags share a common origin. Although the DIG lag in NGC 4565 is unknown, modeling of the DIG within the HALOGAS project is currently underway (Wu et al. 2012).

A radially varying lag is seen in NGC 4565, which we will now discuss. The onset of this shallowing is at 275 (8.6 kpc) in the approaching half and 225 (7 kpc) in the receding half. Given the large uncertainty associated with the lag in general, it is difficult to constrain the manner in which it shallows, although outside of 475 (14.9 kpc) in the approaching half, and 425 (13.4 kpc) in the receding half, it appears to be zero.

An entirely geometric interpretation of the shallowing of a lag at large radii, without any consideration of effects such as extraplanar pressure gradients, drag, or magnetic fields, considers the relationship between the rotational velocity and the gravitational potential: gas rotating high above the plane of the disk is further from the gravitational center than the gas at the same radius in the midplane, resulting in a slower rotational velocity. This effect is more pronounced at smaller radii, where a certain height above the disk is comparable to the radial distance from the center, resulting in a larger relative change in the gravitational potential, and thus a steeper lag. This effect may be seen in Figure 3 of Collins et al. (2002) and may in part be why a lag is only seen in the inner third of the disk in NGC 4565. However, it should again be noted that such purely ballistic models have underpredicted observed lag magnitudes (Fraternali & Binney 2006; Heald et al. 2007), indicating that additional factors must be considered.

This radial variation could also be affected by an extraplanar pressure gradient if the cycling gas does not orbit purely ballistically and is subject to hydrodynamic influences. According to Benjamin (2002), a pressure gradient directed radially inward may cause a steeper global lag. An outward pressure gradient may result in a shallower global lag, or even an increase in rotation velocity. If such pressure gradients vary radially themselves, then a radial change in the lag may occur. Given how little is currently known of halo pressure gradients, as well as the potentially substantial impacts even small pressure gradients may have, it is difficult to say to what degree these will alter the characteristics of any given lag.

In H i, radially shallowing lags are also seen in NGC 4244 (Zschaechner et al. 2011) and NGC 891 (Oosterloo et al. 2007), and the Milky Way Marasco & Fraternali (2011). In NGC 4244 the lag decreases from −9 km s⁻¹ kpc⁻¹ to −5 km s⁻¹ kpc⁻¹ and −4 km s⁻¹ kpc⁻¹ in the approaching and receding halves, respectively. This would correspond to a shallowing of 2–2.5 km s⁻¹ kpc⁻² (although, as stated in that paper, and is the case for NGC 4565, the uncertainties in the radial variation are large). In NGC 891, the gradient in the inner regions is −43 km s⁻¹ kpc⁻¹ and decreases to −14 km s⁻¹ kpc⁻¹ in outer radii, corresponding to a shallowing of 2.5 km s⁻¹ kpc⁻². In the Milky Way, the lag starts with a magnitude of approximately −45 km s⁻¹ kpc⁻¹ and reaches a value of −15 km s⁻¹ kpc⁻¹ near 4.5 kpc, resulting in a more rapid shallowing of 6.7 km s⁻¹ kpc⁻². The lag in NGC 4565 also decreases rapidly with radius. Considering the onset of the shallowing of the lag in each half and their respective lag magnitudes (Figure 13), this corresponds to a shallowing of 6.4 km s⁻¹ kpc⁻² and 4.8 km s⁻¹ kpc⁻² in each half for our optimal models. Judging by the minimum and maximum lag models, the shallowing could be between 6.4 and 38 km s⁻¹ kpc⁻² in the approaching half (although the latter value is very unlikely as it would imply that a very rapid drop of −60 km s⁻¹ kpc⁻¹ occurs in a very narrow annulus of 1.6 kpc, which does not seem physically realistic) and between 4 and 7.6 km s⁻¹ kpc⁻² in the receding half. Thus, the lag in NGC 4565 appears to shallow more rapidly than in NGC 4244 and NGC 891, but at a similar rate to that of the Milky Way.

In NGC 4244, the onset of the shallowing of the lag is seen just within the optical radius, whereas the shallowing of the lag in NGC 891 is closer to its center. In the Milky Way, the lag begins to shallow immediately at the center, and reaches a constant value near 4.5 kpc. In NGC 4565, the shallowing of the lag begins at approximately 25 (7.9 kpc), which is less than half the optical radius of 81 (25.5 kpc). The lag then reaches a constant value of zero near 5' (15.7 kpc). Thus, there does not yet appear to be a characteristic radius at which the lags begin to shallow, or where the lags reach constant values.

In addition to these edge-on examples, NGC 4559, a moderately inclined galaxy, also shows evidence for a radially decreasing lag (Barbieri et al. 2005). Although a true velocity gradient in height above the plane of the disk cannot be measured in this case, Barbieri et al. (2005) find a decrease in the rotational velocity of the thick halo component compared to the thin disk of roughly −60 km s⁻¹ near the center of the galaxy and −20 km s⁻¹ at large radii. As long as the vertical extent of the lagging halo does not fall in a similar way, this drop would indicate a true radially decreasing lag. However, because of its inclination, NGC 4559 does not yield an unambiguous case of a radially varying lag.

This small sample shows evidence for discrepancies in the nature of the radial variations in lags in each galaxy, including differences in the radius of the onset of shallowing and the rate of shallowing. Although three edge-on external galaxies as well as the Milky Way clearly show a shallowing lag with increasing radius, a larger sample must be studied in order to extract reliable trends.

We find kinematic evidence for radial motions, which we associate with a bar. Given the inclination of NGC 4565, we only observe a rather limited two-dimensional projection—not nearly enough to determine its length and thickness using only spatial information, so we must rely on its kinematics. However, observations at other wavelengths are considered in order to help constrain morphological properties. In the optical, the bar is seen as a boxy bulge (Kormendy & Barentine 2010). Additionally, a ring may be seen in higher resolution 24 μm MIPS (NASA/IPAC Infrared Science Archive) data (Figure 16), as well as CO and 1.2 mm continuum emission (Neininger et al. 1996; Kijeong Yim et al. 2012, in preparation). The radius of the ring (1'–17 in the 24 μm data, and peaking from 1' to 15 with an outer radius of 3' in the CO data) is consistent with the ring of higher density seen in H i, and is thus consistent with the length of the bar we have modeled.

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Parameters related to the bar are difficult to constrain; thus we will only state what may be reliably extracted from these data. We can say that the bar exists with a half-length of approximately 125 (4 kpc). According to Neininger et al. (1996), the bar's orientation is between 0° and ±45° from end-on. Due to limited resolution and projection effects, we cannot improve upon this. In fact, by adjusting the rotation curve along the bar and radial motions within the disk, these data allow for an even larger azimuthal range.

There appear to be radial motions up to ±60 km s⁻¹ within the bar. For these radial motions we cannot discern between inflow and outflow, largely because we cannot determine the sign of the orientation due to projection effects, although within the length of the bar a net inflow is expected (e.g., Athanassoula 1992). Furthermore, even without changing the sign of the orientation, changing the direction of radial motions produces too small an effect at most orientations to determine which is correct. This may be further complicated by radial motions that vary in magnitude along the bar: there is some indication of this in that further from the center there appears to be less need for such motions, but this is complicated by projection effects and is not enough to make meaningful constraints. These properties are extremely interconnected, and our spatial resolution limited, hence the large ranges presented here. Fortunately, as may be seen in Figure 10, the effects from radial motions outside the bar far outweigh any contributions from the bar itself. Thus, we must stress that the conclusions we draw from our final models that are not directly about the bar are unaffected by the bar itself.

Observations of purely axisymmetric inflows, not associated with motions along a bar or spiral structure, have been ambiguous (Wong et al. 2004, and references therein). Our work does not break this ambiguity, but rather provides additional constraints.

We see clear indications of a net inflow beginning around the ring of higher density (175 or 5.5 kpc) and extending out to 275 (8.6 kpc). The extreme value of this inflow is −50 ± 5 km s⁻¹. Unlike the issues related to constraining the bar, the signatures for this inflow are clear and appear to be unique. There are additional regions in which the models are improved by inflow, but these are almost certainly due to spiral arms. Since this inflow is associated with the ring, it could be associated with the bar potential. Finally, there exists evidence for a net outflow of 10 km s⁻¹ beginning near a radius of 675 (21.2 kpc) and extending outward in both halves.

The observed effects of the outflow are primarily seen above the plane of the disk at a height of 40''–80'' (2–4 kpc). A range of inclinations corresponding to a warp component along the line of sight were tested, but none could replicate the asymmetric slant in the data. Furthermore, if the apparent offset from the plane of the disk were due to projection effects alone, then these would correspond to radii between 50 and 70 kpc, placing them well outside the disk. Therefore, these motions likely do exist above the plane of the disk, rather than being due to such effects. It is also possible that any outflow could be caused by material being pulled outward due to tidal interactions.

Both NGC 4559 (Barbieri et al. 2005) and NGC 2403 (Schaap et al. 2000; Fraternali et al. 2002) have shown similar indications of radial inflows, estimated between 10 and 20 km s⁻¹. In each case, the authors note that the inflow is high above the plane of the disk. As mentioned above, our data and models indicate that most of the outflow in NGC 4565 is in the thicker, flaring layer. The inflow, however, is close to the plane of the disk and is significantly higher than these values.