3 All-sky spatial, kinematic, and column density properties of the CHVC ensemble

We show in this section the basic observational data for the all-sky properties of the CHVCs; specifically, the deployment in position and velocity as well as the perceived size and H  I column density distributions. These basic properties constitute the observables against which the simulations described in the following sections are tested.

Figure 11:  Average velocity field in the Local Group entering the simulations described in Sect. 4. The velocity at each grid point is given by the average velocity of all the test particles located in a box centered on the grid point and with a width of 10 kpc. Squares are drawn if the velocity dispersion of the ensemble of particles exceeds $100\rm\;km\;s^{-1}$. The length of the thick line in the upper left corresponds to a velocity of  $200\rm\;km\;s^{-1}$. The image corresponds to a simulation with a Local Group mass of $4.3\times10^{12}\;M_\odot$. The Milky Way and M 31 are located at $(x = -0.47, y = 0.0 {\rm\;Mpc})$ and $(x = 0.23, y = 0.0 {\rm\;Mpc})$, respectively. The contours show the relative density levels of a combination of two Gaussian distributions with 200 kpc dispersion, centered on the Milky Way and M 31 at 1, 5, 10, 20, 40, and 80% of the peak. (This figure is available in color in electronic form.)

Figure 12:  Properties of the CHVCs entering the simulations described in Sect. 4. Plotted as a function of H  I mass, the images show the FWHM of the H  I distribution, the central H  I volume density, the velocity dispersion of the gas, and the peak column density. Details of the relation between the H  I masses and cloud properties depend on the dark-matter fraction via the power-law slope of the H  I mass distribution of the CHVC population being modeled: the dashed lines in the images correspond to a slope $\beta =-1.2$; the solid lines, to a slope of -1.6; and the dotted lines, to a slope of -2.0.

  
3.1 Distribution of CHVCs on the sky

Figure 5 shows the all-sky distribution of the cataloged CHVCs superimposed on the integrated H  I emission observed in the range -450 < $V_{\rm LSR}$< +400 km s^-1, but with $V_{\rm DEV}$ >70 km s^-1. The LDS catalog and data are used in the north and the HIPASS catalog and data in the south, with a solid line marking the demarcation at $\delta=0^\circ$ separating the LDS from the HIPASS material. Red symbols indicate positive LSR velocities and black symbols negative velocities The much higher object density observed in the southern hemisphere is quite striking, as is the absence of diffuse emission in the HIPASS MINMED5 data. We comment further below on the extent to which the CHVC density is a consequence of the differing observational parameters, especially that of sensitivity.

To get a better impression of the CHVC clustering and distribution on the sky, an average density field is constructed; this smoothed field is more appropriate for comparison with simulated fields, which, as indicated below, are similarly smoothed. A field of delta functions at the CHVC locations was convolved with a Gaussian with a dispersion of $20^\circ$. The total flux of each delta function is set to unity for the LDS sources and to the value of the likelihood that such a particular CHVC would be observed in an LDS-like survey for the HIPASS sources. Changes in the likelihood relation do not change the overall picture of the CHVC concentrations; only the contrasts of the overdensity regions with respect to the average changes.

Figure 5 shows that the projected density of CHVCs displays a number of local enhancements. The three most prominent of these occur in the southern hemisphere, and were previously noted by Putman et al. (2002) as Groups 1 through 3. Group 1 is concentrated at the south Galactic pole and extends from about $b=-60\hbox{$^\circ$ }$ to $-90^\circ$. It is remarkable for possessing a local velocity dispersion in excess of 150 km s^-1, about twice that seen in any other part of the sky. This region is bisected by a portion of the Magellanic Stream and is also spatially coextensive with the nearest members of the Sculptor group of galaxies (with $D\sim1.5$ Mpc). Group 2 is located near $(l,b) \sim (280\hbox{$^\circ$ },-15\hbox{$^\circ$ })$, with an extent of about $30\hbox{$^\circ$ }$. This concentration is approximately in the direction of the leading arm of the Magellanic Clouds but is also near the Local Group anti-barycenter direction, where the Blitz et al. (1999) model predicts an enhancement of high-velocity clouds. Group 3 is centered near $(l,b) \sim (30\hbox{$^\circ$ },-15\hbox{$^\circ$ })$, a region that Wakker & van Woerden (1991) have identified with the GCN (Galactic Center Negative velocity) population. The most diffuse concentration, which we label Group 4, is in the northern sky near $(l,b) \sim (115\hbox{$^\circ$ },-30\hbox{$^\circ$ })$, approximately coinciding with the Local Group barycenter. The Blitz et al. (1999) model also predicts an enhancement of high-velocity clouds here, albeit a stronger one than observed. Likewise the mini-halo simulations of Klypin et al. (1999), Moore et al. (1999, 2001), and Putman & Moore (2002) predict a strongly enhanced density of low mass objects around the major galaxies of the Local Group, in particular toward M 31, which lies close to the barycenter direction. We comment further on the expected strength of such an enhancement in the observed distribution below.

Figure 13: Distances out to which simulated CHVCs would be detected in the HIPASS survey. The relation between the H  I masses and maximum observable distance depends on the dark-matter fraction via the slope of the H  I mass distribution of the CHVC population. The three curves refer to clouds with a mass-distribution slope of -2.0, -1.6, and -1.2, as dotted, solid, and dashed lines, respectively. The $\beta =-1.2$ clouds are so diffuse that they fall below the HIPASS detection threshold for log( $M_{\rm HI}) \lesssim 6.4$. The horizontal lines bracket distances to individual Sculptor Group galaxies.

Figure 14: Distances up to which simulated CHVCs of the indicated total H  I masses would be destroyed by ram-pressure stripping in the Galactic halo. As an illustration, the limiting distance is calculated assuming a relative velocity of $200\rm\;km\;s^{-1}$. The relation between the H  I masses and the stripping distance depends on their dark-matter content via the slope of the H  I mass distribution of the CHVC population. The dotted curve corresponds to a slope of $\beta = -2.0$, the solid curve to $\beta = -1.6$, and the dashed one to a slope of -1.2.

  
3.2 Distribution of CHVCs in velocity

The kinematic properties of the CHVC population provide an important constraint that must be reproduced by a successful model of the phenomenon. The kinematic distribution is plotted against Galactic longitude and latitude, for the Local, Galactic, and Local Group kinematic reference frames in Figs. 6 and 7, respectively. The CHVCs are confined within a kinematic envelope narrower in extent than the $V_{\rm LSR}$ spectral coverage of the surveys; we stressed above in Sect. 2.2.3 that this confinement is not a selection effect; it is one of the global kinematic properties of the ensemble which must be accounted for.

Table 2 shows that the ensemble of clouds has a lower velocity dispersion in both the GSR and LGSR systems, compared to that measured in the LSR frame, suggesting that either the Galaxy or the Local Group might be the natural reference system of the CHVCs. By measuring the dispersion in the LSR frame, one introduces the solar motion around the Galactic center into the velocities, which results in a higher dispersion.

The CHVC groups noted in the previous subsection can also be identified in the (l,V) and (b,V) distributions. Group 1 is best seen in Fig. 7 where it gives rise to the very broad velocity extent in both the GSR and LGSR frames for $b<-60^\circ$. Group 2, on the other hand, is best seen in Fig. 6, centered near $l=280^\circ$. This group has a positive mean velocity in the GSR frame. Only by going to the LGSR frame does the mean group velocity approach zero. Group 3 is evident in both Figs. 6 and 7. This concentration is seen near $l = 30^\circ$ and has a remarkably high negative velocity of about -200 km s^-1 in both the GSR and LGSR frames. Group 4 can also be distinguished near $l=115^\circ$ in Fig. 6. This group also retains a large negative velocity in both the GSR and LGSR frames.

Figure 15: Tidal force for different potentials as a function of Galactocentric distance. The dashed line corresponds to a point source with the mass of the Milky Way, the dotted line corresponds to a potential consistent with a rotation curve flat at the level of  $220\rm\;km\;s^{-1}$, while the solid line corresponds to the isochrone potential which is used in the simulations to describe the Milky Way. The dashed horizontal lines correspond to the indicated H  I  mass slopes for a cloud mass of $M_{\rm HI}=10^5\;M_\odot$. Only for this low cloud mass and the low dark-matter fraction implied by $\beta =-2$ are clouds unstable to tidal disruption.

Figure 16: Demonstration of the effects of shot-noise on fit quality, showing the best- and worst-fitting instances from a sequence of 35 simulations with one of the lowest average $\chi ^2$ values. The parameter values are $M_1=10^7~M_\odot$, $\beta =-1.7$, and $\sigma _{\rm d}=200$ kpc, corresponding to model #9 from Table 4. The best-fitting instance is plotted on the right and the worst-fitting on the left. Black lines and symbols are used for the simulations and red for the observations. Values of $\chi ^2$from top to bottom for the best-fitting case are 1.5, 2.2, 3.2, 0.19, and 0.21, respectively; while for the worst-fitting case these are 3.5, 3.3, 5.5, 0.29, and 0.36. (This figure is available in color in electronic form.)

Table 2 gives the all-sky statistical parameters of the CHVC ensemble, calculated by weighting the HIPASS objects with the likelihood that they would be observed in an LDS-like survey. The variation of these parameters with the (flux-dependent) relative weighting of the HIPASS sub-sample is explored by considering both 25% higher and lower relative sensitivity. Although the dispersion is not affected strongly by the weighting given to the HIPASS sub-sample, the mean velocity becomes increasingly negative as the fainter HIPASS sub-sample receives a higher relative weight.

Figure 17: Overview of the spatial and kinematic properties of one of the best fitting Local Group models from the simulations of Sect. 4. The simulation, model #9 in Table 4, has the following parameters: $M_1 = 10^7\;M_\odot$, $\beta =-1.7$, and $\sigma_{\rm d} = 200\rm\;kpc$. The quality of the fit to the various observables is given by $\chi ^2 ({\rm size}) = 2.3$, $\chi ^2 ({N_{\rm HI}}) = 2.9$, $\chi ^2\ ({\it FWHM}) = 4.1$, $\chi ^2 (l,b) = 0.28$, $\chi ^2 (l,V_{\rm GSR}) = 0.24$, and $\chi ^2 (V_{\rm GSR},b) = 0.29$. The panels provide the same information as the panels in Fig. 9 for the observed data. The simulation was sampled with the observational parameters of the LDS and HIPASS surveys, depending on the declination of the test cloud, as discussed in the text. The thick-line histograms indicate the LDS (northern hemisphere) contributions to the total detections.

Figure 18: Overview of the spatial and kinematic properties of one of the best fitting Local Group models from the simulations of Sect. 4. The simulation, model #3 in Table 4, has the following parameters: $M_1 = 10^{7.5}\;M_\odot$, $\beta =-1.7$, and $\sigma_{\rm d} = 150\rm\;kpc$. The quality of the fit is characterized by $\chi ^2 ({\rm size}) = 2.6$, $\chi ^2 ({\rm N_{HI}}) = 2.7$, $\chi ^2\ ({\it FWHM}) = 3.9$, $\chi ^2 (l,b) = 0.25$, $\chi ^2 (l,V_{\rm GSR}) = 0.21$, and $\chi ^2 (V_{\rm GSR},b) = 0.25$. The panels provide the same information as the panels in Fig. 9 for the observed data. The thick-line histograms indicate the LDS (northern hemisphere) contributions to the total detections.

CHVCs near the galactic equator display the horizontal component of their space motion. Figure 7 shows that the radial motions at low |b| are at least as large as those at high latitudes, and furthermore that the CHVC distribution does not avoid the Galactic equator, and that substantial positive-velocity amplitudes, as well as negative-velocity ones, are observed. Large horizontal motions as well as high positive velocities are difficult to account for in terms of a galactic fountain model (e.g. Shapiro & Field 1976; Bregman 1980). Similarly, CHVCs located near the galactic poles offer unambiguous information on the vertical, z, component of their space motion. The vertical motions are substantial, with positive velocities approximately equal in number and amplitude to negative velocities; the vertical motions are of approximately the same amplitude as the horizontal ones. This situation also is incompatible with the precepts of the fountain model, which predicts negative V_z velocities for material returning in a fountain flow. Furthermore, the values of V_z are predicted to not exceed the velocity of free fall, of some 200 km s^-1. In fact, $V_{\rm LSR}$ amplitudes substantially larger than the free-fall value are observed.

Figure 19: Overview of the spatial and kinematic properties of one of the best fitting Local Group models before including the effects of foreground obscuration and SGP exclusion. The simulation, model #9 in Table 4, is shown in Fig. 17 after applying these effects. The panels provide the same information as the panels in Fig. 9 for the observed data.

Several aspects of the spatial and kinematic topology of the class are difficult to account for if the CHVCs are viewed as a Milky Way population, in particular if they are viewed as consequences of a galactic fountain; these same aspects would seem to discourage a revival of several of the mechanisms suggested earlier for a Milky Way population of high-velocity clouds (reviewed, for example, by Oort 1966), including ejection from the Galactic nucleus, association with a Galactic spiral arm at high latitude, and ejection following a nearby supernova explosion. We note that the spatial deployment plotted Fig. 5 shows no preference for the Galactic equator, nor for the longitudes of the inner Galaxy expected to harbor most of the disruptive energetic events. CHVCs do not contaminate the H  I terminal-velocity locus in ways which would be expected if they pervaded the Galactic disk; this observation constrains the clouds either to be an uncommon component of the Milky Way disk, confined to the immediate vicinity of the Sun, or else to be typically at large distances beyond the Milky Way disk. We note also that the lines of sight in the directions of each of the low |b|CHVCs traverse some tens of kpc of the disk before exiting the Milky Way: unless one is prepared to accept these CHVCs as boring through the conventional disk at hypersonic speeds (for which there is no evidence), and atypical in view of the cleanliness of the terminal-velocity locus, then their distance is constrained to be large. We note further that some of the CHVC objects are moving with velocities in excess of a plausible value of the Milky Way escape velocity (cf. Oort 1926).

Figure 20: Three-dimensional distribution of synthetic clouds in the model #9 simulation of a CHVC population in the Local Group. The Galaxy and M 31 are indicated with the large black dots, with the Galaxy at (x,y,z)=(0,0,0). The axes are labeled in units of Mpc. The smaller circles indicate all of the objects in the model, whose parameters are given in Table 4. Not all of the clouds survive the simulated environment, and not all of those that do survive would be detected in the LDS and HIPASS observations. The filled black circles indicated those input clouds that are destroyed by tidal and ram-pressure stripping influences of M 31 and the Galaxy. The filled grey circles indicate clouds that are too faint to be detected by the LDS or by HIPASS, respectively, depending on their declination as viewed from the origin. The open red circles are the objects that are obscured by the foreground Galactic H  I . Only the filled red circles would be detected in the combined LDS and HIPASS CHVC sample. (This figure is available in color in electronic form.)

Figure 8 shows the average velocity field and velocity dispersion field, which is constructed in the same way as the average density field. A field of delta functions was convolved with a Gaussian with a dispersion of $20^\circ$. The flux of each delta function was set equal to the measured CHVC velocity and multiplied by the likelihood that the CHVC would be observed in an LDS-like survey. The convolved image was then normalized by the density field. For the velocity dispersion field, a gridded distribution of squared velocity was similarly generated and the velocity dispersion was calculated from the square root of the mean squared velocity less the mean velocity squared, $\sigma=\sqrt{(<V^2>-<V>^2)}$. The velocity dispersion field was blanked where the normalized density was below the mean, since insufficient objects otherwise contribute to the measurement of local dispersion.

 

 

Table 2: Average velocity and velocity dispersion for the CHVC ensemble and for the dwarf galaxies in the Local Group, expressed for three different kinematic reference frames. To correct for the difference in sensitivity between the LDS and the HIPASS compilations, the HIPASS CHVCs were weighted by the likelihood that they would be observed in an LDS-like survey. The three values given for the average velocity and for the dispersion for the CHVC ensemble for each reference frame, pertain to an LDS sensitivity 25% lower than the one shown in Fig. 11 of Paper I, to the same sensitivity, and to a sensitivity that is 25% higher, respectively. The Local Group data refer to 27 dwarf galaxies with known radial velocities, from the tabulation of Mateo (1998).

	CHVCs	CHVCs	L.G. galaxies	L.G. galaxies
reference frame	<velocity>	dispersion	<velocity>	dispersion
	(km s-1)	(km s-1)	(km s-1)	(km s-1)
	-33	253
LSR	-45	238	-57	196
	-59	240
	-58	128
GSR	-63	128	-22	104
	-69	126
	-57	114
LGSR	-60	112	+4	79
	-65	110

Kinematic patterns in the LSR velocity field are dominated by the contribution of Galactic rotation. After removing the contribution of Galactic rotation by changing to the GSR reference frame, the following characteristics of the kinematics of the groups are evident. Relative minima of $V_{\rm GSR} =-100$ to -175 km s^-1 are seen in the directions of Groups 3 and 4, and a relative maximum of $V_{\rm GSR} = +45\rm\;km\;s^{-1}$ is seen in the vicinity of Group 2. Transforming to the LGSR frame generally lowers the magnitude of these kinematic properties (except in the case of Group 3 which becomes more negative in velocity) although they are all still present. The relative velocities of Groups 2, 3, and 4 fit into a coherent global pattern shared by much of the CHVC population, consisting of a strong gradient in the GSR and LGSR velocity that varies from strongly negative below the Galactic plane in the first and second quadrants to near zero in the third and fourth quadrants near the plane.

The distribution of velocity dispersion is not as strongly effected by the choice of reference frame since it is a locally defined quantity. The exception to this rule is near $l=0\hbox{$^\circ$ }$, where there are large gradients in the velocity field, leading to larger apparent dispersions when sampled with our smoothing kernel. Group 1 is remarkable for its extremely high velocity dispersion, exceeding that of Groups 2-4 by a factor of two or more. It is plausible that the Group 1 concentration represents a somewhat different phenomenon than the remainder of the CHVC sample, as we discuss further below.

  
3.3 Summary of the basic observables of the CHVC ensemble

In the preceding sub-sections we have attempted to correct for the differing detection levels in the northern and southern hemisphere data to produce a spatially unbiased estimate of the CHVC distributions in position and velocity. However, when making comparisons with model calculations it is possible to explicitly take account of the differing resolutions and sensitivity of the data in the north and south, obviating the need to re-weight portions of our sample in advance. The basic observables from our all-sky sample of CHVCs, without re-weighting, are shown in Fig. 9 relative to the GSR frame. The top row of panels represents the density, velocity, and velocity-dispersion fields, just as in Figs. 5 and 8, except that the HIPASS sub-sample has not been re-weighted relative to the LDS. Smoothed versions of the (l,V) and (V,b) plots shown in Figs. 6 and 7 are shown in the middle panels of Fig. 9 to facilitate comparison with the model distributions discussed below. The distribution of delta functions was convolved with a Gaussian with a dispersion of $20^\circ$ in angle and 20 km s^-1 in velocity. Composite histograms of the peak column density and angular size distributions for the whole sky are shown in the lower panels of Fig. 9. Since the LDS and HIPASS survey resolutions are different (as discussed above in Sect. 2.2.2) these observables have a different physical implication in the two hemispheres, but again, these differences can be accounted for explicitly in the comparison with model distributions.

Figure 21:  Velocities plotted against galactic longitude for the ensemble of synthetic clouds corresponding to model #9 of a CHVC population in the Local Group, whose sky deployment is plotted in Fig. 17. The red symbols indicate unobscured clouds which are sufficiently bright to be detected by the Leiden/Dwingeloo or Parkes surveys, depending on the object declination. Black symbols refer to simulated clouds which are either too faint to be detected or obscured. As in the observed velocity, longitude plots of Fig. 6, the kinematic distributions for the simulated situation are indicated for three different kinematic reference frames, namely the LSR (upper), the GSR (middle), and the LGSR (lower panel). (This figure is available in color in electronic form.)

Figure 22:  Velocities plotted against galactic latitude for the ensemble of synthetic clouds corresponding to model #9 of a CHVC population in the Local Group. The kinematic distributions are indicated for three different kinematic reference frames, namely the LSR (upper), the GSR (middle), and the LGSR (lower panel). As in the simulated (l,V) distribution of Fig. 21, red symbols indicate unobscured clouds which are sufficiently bright to be detected by the Leiden/Dwingeloo or Parkes surveys, depending on the object declination, while black symbols refer to simulated clouds which are either too faint to be detected or obscured. The simulated (b,V) plot may be compared with the observed situation plotted in Fig. 7. (This figure is available in color in electronic form.)