A preliminary search for shells

How can we find expanding shells of gas within a galaxy? Simply looking at the moment maps does not reveal this kind of feature. Since our data resolves the different velocities of the gas, however, we can look for characteristic signatures in the velocity data. A position-velocity (p-v) diagram - a sequence of RA-velocity plots at varying declinations - can be useful. (These can be created by applying the AIPS task kntr, with parameter docont=1, to a cube which has been transformed so that it has velocity along the first axis, RA along the second, and DEC along the third.) An expanding shell may appear as a bend in a p-v diagram. An example is shown below in Fig. 4.

Fig. 4. Position-velocity diagram for a limited region of IC10. Dark pixels represent high column densities of HI. If all the gas in the region is moving at the same velocity, then we will see a straight vertical line of dark pixels. If some gas is moving a bit slower (that is, away from us, in a relative sense), then the line will have a bend at that position in right ascension. If the slow-moving gas extends far in declination, then the kink will persist for several panels in the image. A smooth, localized peak in velocity suggests a region of outflow of gas: perhaps an expanding shell. This feature (denoted "A") is located in a particularly dense cloud at the lower edge of the galaxy (see Figure 5).

From p-v diagrams, we located three other likely regions of outflow. Fig. 5. Locations (on first and second moment maps) of three features with expanding-shell-like signatures.

The maximum velocity of an outflow can be estimated from the extremum of the emission in the p-v diagram, as in Figure 4. The maximum velocities of the three features are listed in Table 1.

We would like to know how much mass is flowing out of these regions. We can estimate this by isolating the pixels in the kink to the side of the main strip of emission (that is, the gas moving faster or slower than the surrounding gas). We then sum up the values of these pixels and convert to mass as before. The outflow masses of the three features are listed in Table 1.

Feature	Max. outflow vel. (km/s)	Outflow mass (kg)
A	32	2 * 10^6
B	-26, -35	1 * 10^6
C	26	4 * 10^5

Table 1.

A note: We might expect that a spherical shell would appear as a two-sided kink: one portion of gas moving toward us and another moving away. However, we were unable to find any such features. The one-sided shells could be explained by the gas in front already having been blown away completely, or by the rear of the shell being obscured by the front.

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Note on Computing

Around this time, the Wisconsin REU ended and I continued work at Duke University as an independent study with the guidance of Prof. Mark Kruse at Duke and Prof. Eric Wilcots at Wisconsin. I installed AIPS and KARMA on a computer in Prof. Kruse's cluster. Troubleshooting the installation and resolving file permission issues took a few weeks, but my understanding of Linux improved drastically in the process. Thanks to Jimmy Dorff at Duke and Stephan Jansen at Wisconsin for help!

A more systematic search for features...

...using p-v diagrams and velocity profiles

My first task in the fall was to search the p-v diagrams more closely for features. I created p-v diagrams of the entire galaxy, zoomed in so that each panel showed about 17 seconds of right ascension and with increments of 4 arcseconds in declination. This should allow us to observe features near the size of a beam (2"). The full set of maps are linked below. Each file contained a subset of declination (1/8 of the full range) and steps through the full range of right ascension in 8 pages. The file for DEC: 59h 18m 08s - 59h 20m 16s is linked here .

I visually searched these maps for interesting features, keeping a fairly low threshold for feature "believability" in order not to miss small or faint features. I noted the positions of apparent holes in the gas (breaks in the vertical emission strip), shells (kinks in the strip), and regions of increased gas chaos or turbulence (broadening or chaos in the strip). It is likely that I saw many false positives, since when I located the possible features on a moment 1 map, many fell outside the visible gas (see Figure 9).

Fig. 9. Map of features observed from p-v diagrams. Larger version here .

However, one feature (a bend in the vertical emission strip seen in panels 1073-1161 of this plot; numbered 27 on the large map) falls directly on the dense lower-central cloud of the galaxy.

This seemed like a believable feature, so I investigated it further using a velocity profile (an array of panels containing velocity histograms for each point in space), shown here . The histograms have been smoothed along the velocity axis to decrease noise. The panels are sequenced with an increment of about 5" (10 pixels) in declination and 2s (30 pixels) in right ascension. In such a diagram, the signature of an expanding shell would be a ring of panels with velocity peaks offset from the systemic velocity of the galaxy, with the encircled panels either having peaks at the systemic velocity or having little total emission. In this figure, it does appear that some of the panels near the edge have velocity peaks nearer to -320 km/s than the systemic -345 km/s, but it is difficult to discern a clear shell.

...using computer analysis tools

The software package KARMA contains a tool called "kshell" for finding expanding spherical shells of gas. Given a center position, the program steps outward in radius, azimuthally averaging the emission at each frequency around a circle at each radius. In the resulting plot of frequency (i.e. gas velocity) against "angular offset" (i.e. radius), an expanding shell should appear as the top half of an ellipse. In other words, if you start at the center of a shell and move outward, gas velocity should peak at the radius of the shell and decrease on either side.

Unfortunately, trying out kshell on some likely shell locations did not produce any clear shell signatures. Some outputs are below.
output of kshell:
1
2
3
4

...based on locations of star clusters

Perhaps a better approach to finding shells in the HI would be to start where there are known to be high rates of star formation. Hunter (2001)^[3] locates several star clusters formed during the recent starburst in IC10 and determines their initial mass functions (IMF). I used KARMA's tool kvis to place these clusters on the zeroth moment map of IC10. Hunter states sizes of the clusters; using her assumption of a distance of 0.95 Mpc and using s=r*theta, I estimated the sizes on the sky of the clusters. The marks on the map are very roughly to scale.

Fig. 8. Clusters from Hunter (2001) overlaid on 0th moment map.

I then created P-V diagrams for small regions (100 pixels on a side) around each of Hunter's clusters, in order to investigate the dynamics of the nearby HI. They are listed below, with comments on each diagram in parentheses. (In defining the regions, I used kvis to match pixel positions with RA/DEC positions and then fed the pixel positions into AIPS to produce the plots.)

CLUSTERS
1-1 (Hole just below cluster in declination)
1-2 (Hole just below cluster in declination)
1-3 (Slight kink at RA=00 20 24-32, DEC=914-939(pix) [SHELL?]. Small dark spot (negative emission?) right in the middle of the strip of positive emission at RA=00 20 27, DEC=944. Several frames, including DEC=944,949,954,969 have dark spots outside emission strip.) 1-3b is zoomed in on dark spot.
1-4 (No distinct features except dark spot at RA=00 20 27, DEC=945 (visible in 1-3 also).

2-1 (Hole just below cluster in declination)
2-2 (Emission strip looks smooth; some dark dots)

4-1 (Slight kink at RA=00 20 23-28, DEC=927-937(pix) [SHELL?])
4-2 (Dark spot in emission strip at RA=00 20 27, DEC=946)
4-3 (No distinct features, but emission strip is somewhat bent.) 4-3b is zoomed out in RA but shows nothing much more interesting.
4-4 (Emission is somewhat chaotic at DEC=900. Dark spot in emission strip at RA=00 20 27, DEC=945.
4-5 (Very smooth, no features.)
4-6 (No distinct features.)
4-7 (No distinct features.)

There is some uncertainty in the placement of these clusters and the regions of the corresponding p-v diagrams. Hunter's paper gives the locations in hours/minutes/seconds of RA and degrees/arcminutes/arcseconds of DEC, whereas AIPS reckons locations in pixels. There are two possible ways to locate the features on an AIPS-made map of the galaxy. The tool kvis displays the position of the mouse cursor on a loaded image in both RA/DEC and pixel position. Thus, by simply moving the mouse to the correct RA/DEC position, one can read off the corresponding pixel position.

Alternatively, we could convert manually from units of time to units of arc. An hour at a high declination subtends a smaller arc than an hour at a low declination; to convert from seconds of time to seconds of arc, we divide by 15*cos(DEC), where DEC is in hours.

I decided to do the latter in order to check the first method. The AIPS image header for the data cube claims that the coordinates of the center of the galaxy are:

RA	00h 20m 23s	1024
DEC	59d 18' 08"	1025

Furthermore, one pixel corresponds to an increment of -0.5" in RA and +0.5" in DEC. From this, we can convert from units of time and units of arc to pixels in the AIPS image. I wrote a matlab script to perform this calculation. The results are summarized in Table 2. The pixel locations from my calculations differ from those given by kvis by a mean of 3 pixels and a maximum of 6 pixels in RA and a mean of 3 pixels and maximum of 5 pixels in DEC. Since I am not sure which method should be more accurate (my calculations could be off, but on the other hand, there could be some small offset in kvis' positions), I used the positions obtained from kvis.

Cluster	RA (in time units, from Hunter)	RA (in pixels, calculated)	RA (in pixels, from kvis)	DEC (in arc units, from Hunter)	DEC (in pixels, calculated	DEC (in pixels, from kvis)
1-1	00 20 25.13	992	989	59 18 07.81	1023	1019
1-2	00 20 24.62	1000	997	59 18 12.53	1033	1028
1-3	00 20 24.95	995	991	59 17 39.97	968	964
1-4	00 20 23.92	1010	1007	59 17 45.29	978	975
2-1	00 20 26.90	964	962	59 18 17.22	1042	1039
2-2	00 20 24.28	1005	1002	59 19 10.54	1149	1146
4-1	00 20 27.77	951	949	59 17 38.65	965	962
4-2	00 20 28.16	943	943	59 17 35.63	959	956
4-3	00 20 26.58	969	967	59 17 02.53	893	890
4-4	00 20 27.47	959	953	59 17 07.92	904	900
4-5	00 20 28.55	939	936	59 17 21.81	931	928
4-6	00 20 26.51	970	968	59 16 36.26	840	837
4-7	00 20 27.58	954	952	59 16 36.49	841	838

Table 2. Verification of kvis' calculation of the pixel locations of the star clusters.

Structure of the HI

The following are zoomed-in moment maps (zeroth, first, and second) for five of the largest HI clouds in the galaxy:
Cloud #1: Lower central - moment 0, with contours | 1 | 2
Cloud #2: Left side - moment 0, with contours | 1 | 2
Cloud #3: Upper - moment 0, with contours | 1 | 2
Cloud #4: Lower right - moment 0, with contours | 1 | 2
Cloud #5: Upper right - moment 0, without contours; note small holes | 0, with contours | 1 | 2
(all contours at levels 10%,25%,40%,55%,70%,85)

The HI in the dense lower cloud (#1) is surprisingly smooth.

A region of interest might be cloud #5, which has several small holes.

Other miscellaneous contour maps:
Lower central cloud -- Levels: 10%,25%,40%,55%,70%,85%
Left hand cloud -- Levels: 10%,25%,40%,55%,70%,85%
Upper cloud -- Levels: 10%,25%,40%,55%,70%,85%
Whole galaxy. Levels: 5,20,40,60,75
Whole galaxy. Levels: 5,20,40,50,60,85

Conclusions

As yet, I have not definitively located expanding shells. While p-v diagrams suggest some possible locations, velocity profiles and kshell plots do not bear out the existence of shells there. Two of the star clusters (1-3 and 4-1) located by Hunter coincide with shell-like signatures in the p-v diagrams; it will be informative to look more closely at these regions.

Here is a pdf of the poster, which was presented at the January 2007 meeting of the American Astronomical Society.

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