High-Resolution Images of Diffuse Neutral Clouds in the Milky Way. I. Observations, Imaging, and Basic Cloud Properties.
A set of diffuse interstellar clouds in the inner Galaxy within a few hundred pc of the Galactic plane has been observed at an angular resolution of combining data from the NRAO Green Bank Telescope and the Very Large Array. At the distance of the clouds the linear resolution ranges from pc to pc. These clouds have been selected to be somewhat out of the Galactic plane and are thus not confused with unrelated emission, but in other respects they are a Galactic population. They are located near the tangent points in the inner Galaxy, and thus at a quantifiable distance: kpc from the Galactic Center, and pc from the Galactic plane. These are the first images of the diffuse neutral H i clouds that may constitute a considerable fraction of the ISM. Peak H i column densities range from cm. Cloud diameters vary between about 10 and 100 pc, and their H i mass spans the range from less than a hundred to a few thousands . The clouds show no morphological consistency of any kind except that their shapes are highly irregular. One cloud may lie within the hot wind from the nucleus of the Galaxy, and some clouds show evidence of two distinct thermal phases as would be expected from equilibrium models of the interstellar medium.
The concept of a diffuse interstellar cloud is more than 50 years old, yet there are few observations that support the most basic aspects of the standard picture. The strongest evidence for discrete clouds is kinematic: there are usually distinct absorption lines at different velocities in spectra toward stars (e.g., Munch (1952); Hobbs (1978); Redfield & Linsky (2008)). But spectral features can be produced not only by spatial structures, i.e., clouds, but in a continuous turbulent medium as well (Lazarian & Pogosyan, 2000). In contrast to the often well-defined clouds of molecular gas like the Infrared-dark Clouds (e.g., Rathborne et al., 2010), there is little support for the existence of discrete clouds in 21cm emission observations, which suggest instead that the atomic interstellar medium (ISM) consists of fragments of filaments and “blobby sheets”, many of which may be a consequence of turbulence (Kulkarni & Heiles, 1987; Dickey & Lockman, 1990; Miville-Deschênes et al., 2003; Heiles & Troland, 2003; Kalberla & Kerp, 2009). In most direction 21cm H i emission maps are highly confused, leading to considerable ambiguity in determining the morphology and boundries of interstellar clouds, even assuming that they do exist. A mammoth study of Na i and Ca ii absorption lines toward nearly 2000 stars within 800 pc of the Sun by Lallement et al. (2003) and Welsh et al. (2010) has revealed the three-dimensional structure of the local interstellar medium, “cell-like cavity structures” a fragmented “wall” of neutral gas, and what appears to be clouds “physically linked to the wall of denser gas”, but it is difficult to know how to generalize this result to the broader ISM.
The situation is quite different, however, in the lower halo of the inner Galaxy, where there is a population of discreet H i clouds whose velocities are consistent with circular rotation, but whose location several hundred pc from the place separates them from unrelated emission (Lockman, 2002, 2004)111First detections of a few prominent representatives of this population date back to Prata (1964), Simonson (1971), and Lockman (1984). A very detailed history and bibliography of both observational and theoretical early studies of interstellar clouds and H i halo can be found in Chapter 1 of Pidopryhora (2006).. Similar clouds can be seen at low Galactic latitude when their random velocity is large enough to remove confusion (Stil et al., 2006); others are detected in the outer Galaxy (Strasser et al., 2007; Stanimirović et al., 2006; Dedes & Kalberla, 2010). The clouds in the inner Galaxy are likely the product of H i supershells as their abundance and scale height are linked to the large-scale pattern of star formation in the disk (Ford et al., 2008, 2010).
While many aspects of these “disk-halo” clouds are poorly understood, they can be used as test particles sensitive to the physical conditions in their surroundings, and thus give information about interstellar processes not easily gotten from the highly blended spectra typical of most observations. The disk-halo clouds in the inner Galaxy are so abundant that a number of them lie near the terminal velocity in their direction, and thus near the tangent point, whose distance is determined from simple geometry. Their location, mass and size can be estimated with quantifiable errors.
There have been numerous theoretical studies of the expected properties of the diffuse ISM as a function of location in the Galaxy, distance from the Galactic plane, sources of heating, etc. Strong theoretical predictions have been made, especially about the existence of two thermal phases in pressure equilibrium (Field et al., 1969; Wolfire et al., 1995a, b; Koyama & Ostriker, 2009). The disk-halo clouds offer the perfect laboratories for testing these predictions.
We selected a set of disk-halo clouds using observations with the Robert C. Byrd Green Bank Telescope (GBT) and measured them with the Very Large Array (VLA) in three different array configurations. The clouds were selected to cover a range of longitude and latitude and to be located near the tangent points of the inner Galaxy, and thus at a known distance.
This paper is the first in a series about these clouds. Here we discuss the observations and data reduction for the GBT and VLA D-array data only, taken at an angular resolution of 09-15 providing a linear resolution of 1.9 to 2.8 pc. We concentrate on understanding all sources of uncertainty.
2 Selection of Targets
Targeted 21cm H i surveys of regions in the inner Galaxy made with the GBT provided a list of diffuse clouds that might be suitable for high-resolution imaging (Lockman, 2002, 2004). From these we selected a set using the following criteria: 1) The clouds have LSR velocities at or beyond the terminal velocity in their direction ensuring that their distance could be determined (see §2.1 ); 2) the clouds cover a range of Galactic longitude and latitude ensuring that different environments were probed, though all are in the first quadrant of Galactic longitude; 3) the clouds are relatively isolated in position and velocity to minimize potential confusion; 4) their 21cm emission as observed with the GBT is bright enough to be detectable with the VLA in a few hours. An example of the GBT observations used to select the clouds is given in Figure 1. Table 1 gives the cloud designation, field centers, and the 21cm line peak brightness temperature, FWHM, and velocity as determined from the GBT observations.
The kinematics of the disk-halo cloud population studied here is dominated by the circular rotation of the Milky Way with a cloud-cloud velocity dispersion km s(Lockman, 2002; Ford et al., 2008, 2010). Toward the inner Galaxy, the maximum velocity permitted by Galactic rotation at is called the terminal velocity, , and arises from the tangent point where the distance from the Galactic center is . Here we use kpc, the IAU recommended value (Kerr & Lynden-Bell, 1986). The terminal velocity can be measured from observations of species such as H i or CO or can be approximated with a rotation curve (e.g., Burton & Liszt (1993); Clemens (1985); McClure-Griffiths & Dickey (2007); Dickey (2013)) . In the first quadrant of Galactic longitude and an object with V must thus lie near the tangent point where its distance is known from geometry. In the current sample all clouds have velocities so we calculate the tangent-point distance projected on the Galactic plane . A cloud’s distance from the Galactic plane is then and the distance to the cloud center .
2.1.1 Distance Uncertainties
An estimate of the uncertainties in a cloud’s distance can be derived from the change in distance that would correspond to a change in the cloud’s of in that particular direction for an assumed rotation curve. As almost all of the clouds have , in some cases by as much as , we conservatively estimate errors by the change in distance were the cloud to have a velocity () or (), whichever produces the larger change in distance. Errors calculated this way using the rotation curves of Burton & Liszt (1993) and Dickey (2013) agree to within a few percent, and are given in Table 1. We note that the greater a cloud’s velocity beyond , the more likely that it lies near the tangent point (Ford et al., 2010). Thus for many of our clouds, especially G which lies nearly 30 km s past , our error estimates are probably overstated.
The final two columns of Table 1 give derived distances and errors as well as the distance of each cloud from the Galactic plane.
3 Observations and Basic Data Reduction
3.1 Green Bank Telescope Observations
The GBT was used to map H i emission around the disk-halo clouds to measure their overall properties, to determine whether they might be suitable for high-resolution imaging, and to provide the short spacing data for image reconstruction (see e. g., Stanimirović et al. (1999)). Maps were made over an area around each cloud of or depending on the extent of the cloud. Spectra were taken every in Galactic longitude and latitude, somewhat finer than the Nyquist sampling interval for the GBT’s beam (FWHM). Observations were repeated several times over a period of a few months. In-band frequency switching gave a useable velocity coverage of 400 km s around zero velocity (LSR) at a channel spacing of 0.16 km s.
3.2 Very Large Array Observations
A sample of 20 H i disk-halo clouds was observed in 21 cm line emission spectroscopy with the Very Large Array (VLA) in D configuration during 2003 and 2004. The spectra had 256 frequency channels separated by km sin equivalent Doppler velocity centered on the peak velocity of each cloud (Pidopryhora et al., 2004; Lockman & Pidopryhora, 2005; Pidopryhora, 2006). Fifteen of the clouds were observed in single pointings, and 5 as mosaics. Two of these were also observed in C configuration with the identical spectroscopic setup (Pidopryhora et al. (2012)) and two more (G and G) were observed in B configuration at both H i and OH frequencies in an attempt to detect absorption against bright background continuum sources. Here we present results on just the ten clouds observed only in D configuration with single pointings, deferring discussion of the others to a later paper. Parameters of the VLA observations are given in Table 2. An example of the -coverage for one of the clouds is given in Fig. 2.
3.3 Green Bank Telescope Data Reduction
The spectra were calibrated and corrected for stray radiation as described in Boothroyd et al. (2011), and a second-order polynomial was fit to emission-free regions of each spectrum to correct for residual instrumental effects. For each cloud the data were assembled into a cube on a 105″ grid. There was occasional narrow-band interference that was stable in frequency, so spectra were interpolated over the affected channels. The final GBT data cubes had a brightness temperature noise K in a 0.16 km s channel.
Each GBT image cube was converted to the same coordinate system as the VLA, cropped to fit the exact VLA field size and interpolated to the matching grid and sequence of spectral channels with the Miriad (Sault et al., 1995) task REGRID. The GBT data were taken while the telescope was moving and thus have an effective resolution of , with the major axis along Galactic longitude, the scanning direction. In the VLA’s equatorial coordinate system this resulted in slightly different beam position angles for each field. In order to smooth out gridding artifacts each GBT image was also convolved with a circular beam function of 200″, approximately 1/3 of the original beam size, so the final GBT angular resolution is approximately 10′ FWHM.
3.4 Very Large Array Data Reduction
After calibration and study of preliminary dirty images of each VLA field, the continuum was subtracted in the domain using AIPS UVLIN task based on selected line-free channels. Naturally-weighted dirty images of continuum-free data were then cleaned channel by channel with AIPS SDCLN with no cleaning mask applied. The residual flux threshold was set to 0.7 mJy/beam for all clouds, corresponding to 0.2–0.3 . In the final step the correction for the VLA primary beam was applied to the clean image cubes with the AIPS task PBCOR. The imaging synthesized beam size was different for each field as described below; their values are given in Table 3.
4 Further Data Processing, Noise Levels and Errors
4.1 Combining the Interferometric and Single-Dish Data
For several reasons we have chosen to use Miriad’s IMMERGE to combine the interferometric and single-dish data: 1) it uses a well understood algorithm that is easy to control; 2) it runs quickly and is easily applied to large image cubes; 3) we have developed a calibration technique described below that ensures accuracy of the results.
Another approach was also tried for two clouds not of the set described in this paper (Pidopryhora et al., 2012): using a maximum entropy (MEM) algorithm (AIPS VTESS task) with the GBT image used as the default, but it was found to be less efficient. For a detailed review of all possible methods see Stanimirović (1999).
Miriad’s task IMMERGE uses a linear method sometimes known as ‘feathering’ to combine interferometric and single-dish data (Sault & Killeen, 2008; Stanimirović, 1999). Essentially this is just merging clean interferometric and single-dish images after Fourier-transforming them into the domain, the result covering the whole combined spatial frequency range. For this procedure to be meaningful the Fourier images of interferometric and single-dish data should match within the overlapping ranges of their common spatial frequencies. Due to the completely different natures of the two original datasets and thus unavoidable discrepancies, this has to be ensured by varying their common calibration scaling factor , which is the main control parameter of the IMMERGE task. In the case that the calibration of both data sets was done properly this factor should be close to unity, but its exact value has to be determined empirically in each particular case. If a compact source of 21cm emission were present in the field of view, both unresolved by the VLA and unconfused with other emission by the GBT, determining would be as simple as dividing the interferometric flux density of this source by its single-dish flux density. Unfortunately, such sources are rare and not present in our data, so a more complex strategy of determining was used.
There is another important control parameter called ‘tapering’. If IMMERGE tapering is applied, the Fourier image of the interferometric data is smoothly continued into the low spatial-frequency region (Sault & Killeen, 2008). This fixes possible edge effects in the Fourier transformation, but introduces an additional non-linear distortion of the data. As well as determining the best value of , it is necessary to decide if tapering should be applied.
4.2 Derivation of the Optimal
IMMERGE has a built-in method of matching the two datasets and deriving , provided that the overlapping range of spatial frequencies is defined. Figure 3 shows examples of application of this method. The interferometric image is convolved with the single-dish beam, then both images are Fourier-transformed and compared to each other within the overlapping spatial frequency range. The value of is selected by scaling the single-dish data until the slope of the line fit to the data is exactly 1. Based on several trials varying IMMERGE parameters with different samples taken from our data, we have determined that: 1) tapering distorts the data and makes a reasonable linear fit impossible; 2) due to a large scatter of the values the best linear fit usually does not characterize the data well and derived from it should be treated only as an estimate. Thus for our purposes we use IMMERGE without tapering and we determine the optimal by other methods.
It should be noted that describing the discrepancy between single-dish and interferometric data with a single linear parameter is only an approximation of very complex behavior. One immediately notices that the optimal seems to be different for different channels (Stanimirović, 1999). In particular, it is sensitive to the signal-to-noise ratio and spatial signal distribution of brightness in each channel. This is understandable as ideally should be determined from a point source unresolved by both telescopes. For a cloud comprised of diffuse gas that smoothly fills the field of view and is detectable by the single-dish but is completely invisible to the interferometer, the estimated approaches zero. In the cloud data we usually have some combination of these two extreme cases, and what seems to be the optimal may fluctuate significantly. But allowing it to vary with frequency would introduce an unknown non-linear distortion. Based on the general assumptions of this model, and as all clouds observed only with the VLA D-array present the same variety of interferometric data (similar beam sizes, noise levels, -coverage etc.), we sought a single value of that would work well not only for every channel of a particular cloud, but for all ten clouds.
One criterion for testing the goodness of a particular value of is that the spectrum of the merged cube averaged over an area somewhat larger than the GBT beam, but small enough not to be effected by the VLA primary beam pattern, should match the average taken over the same region in the single-dish data alone. We have found that averaging over an area at the center of the field works well for all clouds observed with the VLA D-array. Requiring that the average spectrum over this area given by IMMERGE matches the single-dish mean profile is sufficient to derive an optimal = 0.87. In fact, this method may be preferable to any other since it directly preserves the single-dish flux.
Figure 4 shows the comparison of mean line profiles of the VLA, the GBT and the best IMMERGE combined images for all 10 targets using the single value of = 0.87, which was adopted for all subsequent work.
4.3 Testing the Accuracy of the Image Produced by IMMERGE
The average difference between the observed GBT and final IMMERGE line profiles can be calculated
where and are the spectral values for individual channels and the summing is done over velocities of interest for each cloud. Figure 5 shows values of for all 10 clouds. Taking into account the peculiarities of profiles that make their exact match impossible, e. g., the presence of large amounts of Galactic diffuse gas invisible to the interferometer as in clouds G and G, these values set an upper limit to the error possibly introduced by IMMERGE in the process of merging the VLA and GBT data. For most of the clouds this error is only a few per cent, indicating that the resulting cubes are scaled accurately.
4.4 Converting to Galactic Coordinates
The final image cubes were regrided to Galactic coordinates as the last step of the data reduction. To ensure a smooth transformation the pixel size was decreased. The final cubes are with a pixel size of 57 over the 49′ diameter field. The synthesized beam sizes and resulting gains for the data cubes are given in Table 3.
4.5 The Noise Pattern
The detection threshold for the 21-cm line emission depends on the noise and its distribution across the map areas. Examining the noise distribution is also a useful test of the effects of the merger of the GBT and VLA data. We have measured the noise in the cubes at various stages of the analysis. An essential step of the VLA data reduction is the primary beam attenuation correction, PBCOR, which involves scaling the data to correct for the attenuation from the primary beam response of the 25m dishes of the VLA. This correction must be done before using IMMERGE to determine as described in section 4.1. The correction for the primary beam response produces images whose noise is a strong function of radius from the pointing center. This is illustrated in Fig. 6, which shows the VLA+GBT column density map for G. The high noise near the edges of the map shows the effect of the primary beam correction on the interferometer data, which persists after merger with the GBT data. (The GBT maps have nearly uniform sensitivity everywhere.) The noise distribution has a characteristic shape as a function of radius, , from the field center. The noise at the map edge is so high that it dominates the brightness scale of the image.
To set a robust noise threshold for detection of the line, and to determine the errors in measured parameters based on the data, we need to understand the function . The VLA primary beam gain factor is approximated in PBCOR by (Perley, 2000):
where is the frequency of observation in GHz and is the angular radius in arcmin. The coefficients are roughly constant for each VLA band; for our observations their values are:
PBCOR divides the spectrum at each point by from eq. (2), thus amplifying both signal and noise, since . The various clouds have slightly different values of the center frequency, , depending on their radial velocities, and different values of , which are almost entirely due to the noise in the VLA data, as explained in the next section. For setting detection thresholds and computing errors in the column density and mass at different points in each cloud, we use:
Figure 7 shows the measured values of using channels with no line emission as a function of distance from the center of the map shown in Fig. 6. The curve is the prediction of eq. 4, showing the effect of the primary beam correction applied to the VLA data, as it appears after merging with the GBT data. It is clear that noise from the VLA data completely dominates the noise in the final cubes, as the points in Fig. 7 are well described by the curve. For each cube we measure empirically the noise level at the field center, , using off-line channels, and construct a noise function similar to that shown in Fig. 7. These are given in Table 4 in Kelvins and the equivalent error in for a 25 km s wide velocity interval and the channel width of 0.64 km s.
4.6 Noise Amplitude
Because of the angular resolution difference, noise from the GBT has little influence on the noise in the final cube, but rather appears as a systematic error in flux measurement over areas of a size comparable to the GBT beam. Rms noise values in the GBT cubes are 0.08 – 0.14 K, a factor 3-4 times smaller than the noise at the very center of any of the final H i maps. Thus the dominant noise in the final data comes from the VLA, and errors due to the GBT noise can be neglected.
We have processed the data in a number of non-trivial ways so it is important to check that the final noise level is reasonable, and is consistent with the noise in the VLA data at earlier reduction stages. Examination of the noise in line-free channels in the dirty continuum-subtracted cubes and in the clean cubes before PBCOR for four clouds is given in Table 5. Comparing for each cloud from Table 5 with in Table 4 we conclude that despite a significant number of processing steps following the cleaning of the VLA image, the rms noise value remains virtually unchanged, except by the correction for the main beam gain of eq. (4).
Two conclusions can be drawn: 1) because rms noise values are good indicators of the finest scale of the image, the fact that they do not change much from the VLA to the final data cube shows that our procedure of recovering the short spacings from the GBT data has not distorted the small-scale structure of the interferometric data; 2) the values of measured in § 4.5 and the noise pattern of eq. (4) are indeed valid indicators of the rms noise in the final data and can be used with confidence.
4.7 A Noise Threshold
Using eq. (4) we can establish a noise threshold for every pixel in a cube. If there is no emission over the channel range of interest the spectrum is flagged and not used for making column density maps or other types of analysis. Figure 8 shows the same data as Figure 6, only with pixels blanked below the level, leaving only emission detected significantly above the noise.
5.1 Column Density Maps, Mass Profiles, Spectra
Fig. 9 shows in comparison both full and thresholded column density maps of G based separately on the GBT and VLA data, and final VLA+GBT results. Fig. 10 gives the corresponding mass profiles. Finally, Fig. 11 presents a summary of G: thresholded VLA+GBT maps in relation to full GBT images, mass profile of the VLA+GBT image, and spectra toward the peak of the clouds. Caption to the latter figure contains comments about the structure of the cloud.
Measured cloud properties are summarized in Table 6. The values of line brightness temperature, velocity and line width are derived from the Gaussian decomposition, sampled toward the position of the peak . Errors are from the Gaussian fit. Four of the clouds have spectral lines that require two Gaussians. The values of in col. 7 are integrals over the relevant velocity range (given in caption to each Figure) and are always close to the value from the sum of the Gaussian fits. We do not know the optical depth and so we cannot correct for self-absorption in the 21cm line, therefore the column densities and masses calculated in this paper are all lower limits.
The mass profiles were constructed in the following fashion. The mass was sampled over a set of annuli of varying radius increment but equal area, all centered at the main column density peak of the map. With equal areas, the mass in each annulus is proportional to the average with the same proportionality coefficient and thus the points can be plotted simultaneously with two sets of axes: distance-dependent mass vs. linear radius and distance-independent vs. angular radius (see Fig. 10 and its counterparts, upper panels). The vertical error bars show the cumulative error due to noise222Both the mass and the linear radius measurements are also subject to the distance uncertainty (see Table 7) not shown in these plots., the horizontal ones show the average beam radius , with and for the VLA given in column 2 of Table 3. The GBT values are the same for all clouds: 10.2′ 9.7′, slightly increased compared to the original GBT beam due to pre-IMMERGE processing.
Since there is a significant freedom of choice for such annulus sets, we have selected a fixed maximum radius of the sequence, the same for all clouds and equal to 0319, which covers most of the VLA primary beam, with the exception of a small outer portion having the highest noise. Then we required the width of the largest annulus to be equal to , i.e. at the resolution of the map. Designating the number of annuli and the smallest radius of the set, we arrive at the following equations:
Comparing line parameters of the GBT-only observations of Table 1 with the high resolution GBT+VLA results in Table 6 we find identical mean velocities, with a difference of km s. As expected given the small angular structure revealed in the maps, the lines in the final maps are brighter by factors that range from 1.6 to 11 (for the very compact G), with a median value around 4. These ratios are smaller than might occur: hydrogen clouds with sizes should appear times brighter to the VLA than the GBT, so it seems that the major structures in the clouds have been resolved in the current data. The line widths have a much smaller variation with the increased angular resolution. For lines that appear narrow to the GBT it is typical that they are even narrower in the combined data by around 20%, suggesting that the higher resolution observations are revealing colder or less turbulent material. But the broadest lines as measured with the GBT are sometimes even broader in the combined data, clouds G and G being examples.
5.2 Estimating Masses, Sizes and Densities of the Clouds
In most cases the clouds do not display clear boundaries. In order to determine meaningful sizes and masses we have employed contours of constant . In each case a contour was chosen to encompass most of the visible cloud structures in the VLA+GBT maps (bottom left panels of Figures 9, 12 etc.). The resulting contours are shown in the left panels of Figures 39 – 42. The H i masses inside these contours for each cloud are listed in column 4. For comparison we have also drawn contours in the GBT maps at much lower values. The resulting contours are shown in the right panels of Figures 39 – 42 and the derived properties are listed in Table 8.
For each contour the major axis (the longest distance between two contour points) and the minor axis (the longest distance between contour points in the direction, perpendicular to the minor axis) are determined. The length of these axes are listed as in column 5 of Table 7 and column 3 of Table 8.
5.3 Cloud Cores
Table 9 gives estimates of the properties of the cloud cores, the denser regions of each cloud, determined by analyzing the H i emission at a higher value of around the column density peak of each cloud (column 2). The mass, size and number density of the enclosed area is given in cols. 3–5. The FWHM in Table 6 can be used to limit the kinetic temperature — this value, T is given in col. 6. Finally, multiplying values in columns 5 and 6 we can get a rough estimate of the core pressure in each cloud (column 7). For the clouds with two velocity components the total number density was split proportionally to the corresponding column densities.
We have produced high angular-resolution 21cm H i maps of ten clouds that lie in the boundary between the disk and the halo in the inner Galaxy. This paper presents the data and the reduction methods necessary to insure accurate results. We defer a detailed discussion of the cloud properties to a separate publication, but some general comments can be made, for these clouds are unique samples of the neutral interstellar medium.
The disk-halo clouds, with masses of many hundreds of and locations many hundreds of pc from the Galactic plane, are orders of magnitude denser than their surroundings.
The following rough estimates are made with the assumption of a spherical cloud of pure monoatomic hydrogen at constant number density , its mass density . By the cloud “Size” we understand its diameter and take that determined based on the emission line FWHM, represents its true kinetic temperature .
Under these conditions the sound-crossing time can be expressed as:
For clouds’ dense cores of sizes 10 pc this is just a few Myr. But for whole clouds, with sizes 100 pc, may reach 60 Myr.
On the other hand, the free-fall time of gravitational collapse:
For the highest cloud core density cm, Myr, but for other cores it is 20–50 Myr and for whole clouds this time scale often exceeds 100 Myr. So in all cases and thus the clouds are not gravitationally bound.
It is instructive also to compare with the time of vertical fall to the Galactic plane at cloud’s location. Using a simple analytical expression of Wolfire et al. (1995b) for the -component of the Galactic gravitational acceleration , one can see that for pc the acceleration is close to linear: . The values of range from at kpc to at kpc. Since motion with such acceleration is harmonically periodic, the free-fall time is just . For higher where flattens, these values can be used as lower limits:
equal to 8 – 17 Myr for 2.5 kpc 8.5 kpc. In Pidopryhora (2006) a more precise ballistic calculation was done for 2 kpc 5.3 kpc and a much greater distance from the plane kpc using Walter Dehnen’s GalPot package (Dehnen & Binney, 1998), obtaining Myr, which can be used as an upper limit for all the disk-halo clouds.
For the cloud cores the condition is true, so the clouds have time to respond to local physical conditions. The clouds must have come to internal pressure equilibrium, although the pressure may have contributions from turbulence on a range of scales, and possibly magnetic field and cosmic ray pressures as well. But since for the larger cloud structure, the overall density distribution of the cloud does not have time to dissipate in the low pressure of the halo over the time it takes the cloud to rise or to fall back to the disk.
Similarly one can estimate the clouds’ Jeans masses as
which is two to three orders of magnitude larger than their observed gas masses.
All this implies that the clouds are dynamic entities whose properties must reflect their history as well as conditions at their current locations (e.g., Koyama & Ostriker, 2009; Saury et al., 2014). While the appearance of many of the disk-halo clouds suggests that they are interacting with their local environment producing the steep gradients in or asymmetric shapes, we find little correlation between location in the Galaxy and fundamental cloud properties, with one clear exception, G discussed below.
In theories of the interstellar medium the local pressure is often the controlling factor in the structure of neutral clouds, and over a wide range of conditions in the Galaxy it is expected that neutral clouds could consist of two phases, one warm and one cold (Field et al., 1969; McKee & Ostriker, 1977; Wolfire et al., 1995a; Jenkins, 2012). Four of the clouds studied here have line profiles indicating the presence of two components with different temperatures at the location of their peak . It is unlikely that this results from confusion of unrelated material as all two-component clouds are located at pc from the Galactic plane. The components typically have similar but not identical values of . The narrower line component contains between and of the total , about the mass fraction expected from some simulations (Saury et al., 2014). However, clouds may have two phases not easily separable in their emission profiles as the cold gas may have large velocity fluctuations that blend it with the warmer emission (Vázquez-Semadeni, 2012; Saury et al., 2014).
Cloud G is particularly interesting, as it may lie within the area around the Galactic nucleus excavated by a hot wind: the “Fermi Bubble” (e.g., Bland-Hawthorn & Cohen, 2003; Su et al., 2010). The boundaries of the region effected by the wind are not well-defined, especially at low latitudes, but the G cloud has such distinctive properties as to suggest that its environment is different from that of the other clouds. Within the hot wind the pressure is many times larger than the typical ISM (Bland-Hawthorn & Cohen, 2003; Carretti et al., 2013); this is expected to force clouds into a purely cold phase (Field et al., 1969; Gatto et al., 2015). The properties of G, with its high density, narrow line width, and compact structure, are consistent with this interpretation. Moreover, G is notably smaller then the other clouds, but its size is similar to that of the H i clouds found to be entrained in the nuclear wind (McClure-Griffiths et al., 2013). In contrast, the nearby cloud G is nearly indistinguishable from the other clouds studied here. It might be as close as 135 pc to G, but is more likely at least 1 kpc away given the uncertainties in our assignment of distances. Neither cloud shows kinematic anomalies suggesting that they have been accelerated by the nuclear wind (McClure-Griffiths et al., 2013).
We can also compare the properties of our disk-halo clouds with the disk clouds of Stil et al. (2006) observed at similar resolution, but all at . Only one of their clouds, has an analogous morphology and size, with a few times larger mass and average density compared to the clouds of our survey. The properties of all their other clouds are close to our cloud cores, only in some cases displaying a few times larger average density.
These disk-halo H i structures allow us to study unconfused interstellar clouds in a variety of locations; this may lead to a better understanding of physical conditions that have hitherto been manifest only in ensemble averages. When the GASKAP survey (Dickey et al., 2013) is done, and even more when the full SKA is ready, studies like this one will reveal many more such clouds, and the techniques developed here will be useful for understanding their properties.
|Name||T11In assumption of 40 channels of the total width of 25 km s.||V11In assumption of 40 channels of the total width of 25 km s.||FWHM||Distance||z|
|(K)||(km s)||(km s)||(kpc)||(pc)|
|Cloud||11In assumption of 40 channels of the total width of 25 km s.|
|(kpc)||(pc)||(K)||(km s)||(km s)||( cm)|
|Cloud||R||z||11Clouds’ sizes and masses determined based on contours shown in the left panels of Figs. 39–42.||Size11Clouds’ sizes and masses determined based on contours shown in the left panels of Figs. 39–42.22Fractional uncertainties in both dimensions are identical and are given by the value in parentheses.|
|Cloud||11Clouds’ sizes and masses determined based on contours shown in the right panels of Figs. 39–42.||Size11Clouds’ sizes and masses determined based on contours shown in the right panels of Figs. 39–42.22Fractional uncertainties in both dimensions are identical and are given by the value in parentheses.|
|G33Total for the group of three clouds, containing G and G.||(0.19)|
|Cloud||contour||Size11Fractional uncertainties in both dimensions are identical and are given by the value in parentheses.||T||T|
|( cm)||()||(pc)||(cm)||(K)||( K cm)|
|G22A small separate cloud at the high-longitude side of the G field. First velocity component: T = K, = km s, FWHM = ; second velocity component: T = K, = km s, FWHM = .||0.9||(0.18)|
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