Optical H II Regions in M81 and M83

Using Ha, R, B, and V images gathered from the NASA/IPAC Extragalactic Database (NED), the luminosity function of H II regions in M83 and M81 is examined. 296 H II regions were catalogued in M83 by Rumstay & Kaufman (1983), while 492 regions were catalogued of M81 by Petit, Sivan, and Karachentsev (1988). The goal of this project is to investigate a number of these regions to confirm that the respective luminosity function is, in fact, best fit with a power law. Also, using these regions, it can be seen whether or not Van den Bergh's Law holds true for the frequency distribution of the diameters of these regions.

1. Introduction

One interesting aspect of these H II regions is that a luminosity function is a measurable property of them. The H II luminosity function of different galaxies has been measured since Kennicutt & Hodge (1980). It shows a power law relation between the number of measured H II regions and their luminosity. The constant for the power law seems to be standard throughout past experiments, though the power itself is actually variable between them. With a wealth of data from many of the 492 PSK (Petit Sivan Karachentsev) regions in M81 and 296 H II regions of M83, we should reduce a value near a = 1.87 for M81, where a is the power of N(F) = kF^-a with k = 10^5.80 (Petit et al. 1988). One can see the linear relation that is derived from a plot of both the log functions, showing the resultant power law in Figure 1 (Figure 5 of Petit et al. 1988). Figure 2 (Figure 1 of Rumstay & Kaufman 1983) shows the flux readings of M83 with S(Ha) > S(0). The plot is not representative of a complete sampling, and if only the highly luminous regions are taken into consideration, a power law can be found that fits in agreement with NGC 628 (Kennicut & Hodge 1980), M33 (Rumstay & Kaufman 1983), and M81 (Petit et al. 1988).

Figure 1. This logarithmic graph of the Luminosity Function of M81 was taken from Petit et al. (1988). The x-axis has the flux in erg s-1 cm-2 and the y-axis shows the number of occurrences of the respective flux that was recorded from M81's PSK regions.

Figure 2. This is another logarithmic plot of flux vs occurrences (Rumstay & Kaufman 1983). However, this one shows a couple power law fits for M83 due to detection rates and incomplete data. Its highly luminous regions do, in fact, agree with the single power law fit. The axes are labeled with the number of occurrences on the y-axis and the flux (for only S(Ha) > S(0) on the x-axis.

Another relation that can be addressed when observing the H II regions in M81 and M83 is Van den Bergh's "Frequency Distribution of H II Region Diameters" (1981). This relation should also be a power law fit and has been observed and verified in numerous galaxies. To accomplish this in our project, the image must be cleaned enough so that only the H II regions remain. Even more importantly, the regions will have to be clean enough to be separated individually. This data will be used to verify the Petit et al. work that was done on their PSK regions, as well as Rumstay & Kaufman's work with their H II regions in M83. Each of these investigations involved both the luminosity function and the frequency distribution of diameters of their respective galaxies.

   This project will be using narrowband Ha to find the H II regions of the grand-design spiral galaxy M81 (NGC 3031) and M83 (NGC 5236). M81 is a very large galaxy, of approximately 27 arcminutes by 14 arcminutes. The size of this galaxy makes it a prime choice for Ha investigation, as the H II regions are more sporadically spread as one leaves the core of the galaxy. The regions also dissipate in the far reaches of the spiral arms, so not all of the galaxy will be required for observation. These characteristics can be seen in Figure 3a (Figure 1b of Petit et al. 1998) which can also be used as a finding chart. M83 (NGC 5236) is an intermediate spiral galaxy. It is also relatively close to our galaxy, at 15 million light years away, with dimensions of 13 arcminutes by 12 arcminutes. Its proximity and brightness make it a prime candidate for the second part of this investigation. Figure 3b is a similar finding chart that was used for M83.

Figure 3a. To the left is a catalogue of the PSK regions of M81. This chart from Petit et al. was used as a finding chart for our Ha - R image. The different axes are simply J2000 coordinates of the galaxy. Stars are labeled as well to try to avoid confusion within the Ha image.

Figure 3b. To the left is a catalogue of the H II regions of M83. This chart from Petit et al. was used as a finding chart for our Ha - R image. The coordinates on these axes are in kilo-parsecs, which were useful for Rumstay and Kaufman when it came to defining the size of the H II regions. Despite our differing purpose, this was still useful for locating different sized H II regions.

The Ha flux readings will be compared to works done by both Petit et al. (1988) and Rumstay & Kaufman (1983) to find similarities and discrepancies in the reductions. One objective will be to find a power law fit to the frequency and luminosity of the H II regions, with a goal of getting a similar a value as Petit et al. and a similar plot as Rumstay & Kaufman. Another goal will be to check for the power law fit of Van den Bergh's "Frequency Distribution of H II Region Diameters" (1981), which was also confirmed in both of the aforementioned works.

2. Observations

As these images were put onto NASA's database, it is assumed that the zeroes and flats were taken already and utilized by each observer. It is noted that Cheng et al. used IRAF to compose his image, though the Danish observers did not specify their method. After this, we proceeded to do the sky subtraction on our own.

For comparison, the narrow-band Ha image of M81 taken by Courtes et al. (1987) was used, as was the case from Petit et al. This image was taken by the 6m Soviet Special Astrophysical Observatory in Zalentchuk, and was used to create the finding chart of the H II regions of M81. Likewise, the catalogue compiled by Rumstay & Kaufman was created using UBVRHa surface photometry by Talbot, Jensen, and Dofour (1979).

3. Reductions

The registered and sky-subtracted B and V images were divided using 'imexpression.' This resulted in a color map of the galaxy. Figure 4a shows the color map for M81, and Figure 4b shows the color map for M83.

Figure 4a. This color map of M81 was made by dividing B and V filters from each other after registering the images and taking sky subtraction into account.

Figure 4b. This color map of M83 was made by dividing B and V filters from each other after registering the images together and taking sky subtraction into account.

A fraction of the R image was subtracted from the Ha image using 'imexpression.' This eliminated the starlight near the H II bandpass, leaving the H II regions of the galaxy easily visible. The Ha filter compared to the subtracted Ha - R is displayed in Figure 5a and 5b for M81. The same comparison can be seen for M83 in 6a and 6b. Regions for the late-type M81 are very numerous, but scattered and small, while the regions in SBc spiral M83 are fewer, but large. These regions were defined using the 'polymark' task in the 'apphot' package with polygons that would be compatible with the 'polyphotometry' task. From 'polyphot' we were able to get the area, flux, and magnitude of each region. The 'polymark' task called for the polygon region boundaries to coincide with pixel boundaries, so small, faded regions could not be catalogued. Because of this, Van den Bergh's "Frequency Distribution of H II Region Diameters" (1981), which required separating each H II region individually, could not be duplicated.

Figure 5a. The original Ha image of M81 after sky subrtraction and registration to the R image. Originally looks rather similar to the R image as well due to the H II bandpass' location within the R filter. The image was taken from NED and was provided by Cheng et al. (1997).

Figure 5b. This is the final Ha M81 image used for our H II flux reductions. It was created by subtracting 0.33 of the R band image from the original Ha image seen above. Much of the starlight from the original image was filtered out due to this process.

Figure 6a. Another original Ha image, this time of M83. This image was also found on NED and was provided by Danish observers. Again, the Ha image can be seen to be similar to what would be expected from an R filtered image.

Figure 6b. This is the result of subtracting 1.5 of the R band image from the above Ha image. This was the final Ha image that was used for defining the H II regions of M83. Due to the brightness of the galaxy and the large H II regions, more subtraction was needed to pinpoint the H II regions, which is why the image is so dark in all other places.

Our photometric data was sufficient for computing a luminosity function. The 'pconvert' task in 'ptools' allowed us to convert our 'apphot' data file into a clean table containing only the desired data, the flux of each region. These values were further divided into flux bins and graphed using 'graph' in 'plot.'

4. Results

Displayed below is a false color image of the H II regions that we used for our final calculations of the luminosity function. There are 159 regions highlighted for M81 and 139 regions specified for M83. The obvious danger of manually selecting these regions is that the result will tend to be slightly biased. We tried our best to take a selection of all different sizes and fluxes of the regions, as seen below.

Figure 7. The scale adjusted image of the Ha - R filters used here has the H II regions within M81 clearly identified. The regions were selected by hand using a finding chart as a guide. A sample of 159 regions was taken from a number of different region sizes and fluxes. These regions are very numerous, yet scattered and smaller in size compared to M83 below. This image is approximately 20x25 arcminutes.

Figure 8. This is another scale adjusted image from the Ha - R filters. M83 is seen to the left as having large, luminous H II regions. We have selected 139 of these regions, which have been highlighted for further data reduction of the luminosity function. This image is approximately 11x10 arcminutes.

   We were able to find out a number of different things about these regions. With starlight not being a factor, the most important details that were obtained were the fluxes. These fluxes were separated into bins of varying sizes to study the relation between the luminosity and the frequency of occurrence in certain ranges. Below is the final list of the data for M81 and M83 respectively. The bin size is shown as well as the numbers of fluxes in that bin, and the average per 50 arbitrary units, due to flux calibration being impossible.

Table 1. Listed to the left are the flux bins for M81. The first column shows the size of each bin in arbitrary units while the second column shows the physical number of regions that we had with the respective flux. In the final column, the average of that number was taken over a 50 arbitrary unit range.

Table 2. Listed to the left are the flux bins for M83. Again, the first column shows the size of each bin in arbitrary units while the second column shows the physical number of regions that we had with the respective flux. Because of M83's giant H II regions, the maximum flux was much larger. In the final column, the average of the physical number was taken over a 50 arbitrary unit range.

These data were used to create a log-log graph of the Flux vs. Frequency of occurrence. The power law relationship that was discovered was one very similar to that of Peit et al. (1988), with only slight differences. These differences were due possibly to incomplete and human biased data selection or to the low quality of the IRAF image which made small, faint regions lost or blocky. Shown below are the luminosity functions for each galaxy. It can be seen that M81 has a power law fit as expected with the previous data. M83 seems to have a double, similar fit, which is what was expected due to what Figure 2 illustrated. This makes sense due to the fact that the small, faint regions that had thrown off the Figure 2 fit from other examples would have been made even more faint, as well as dimming some regiosn that would have been brighter. These were the regions Rumstay & Kaufman (1983) had predicted as throwing off their power law, and in ignoring these regions, we can see that there is a very clear power law present, which is exactly what had been said in their research.

Figure 11. A log-log graph of the luminosity function of M81. The data collected from the flux frequencies within the bins shows the power law that is represented by the best fit curve imposed on the graph. This was the same relationship that we set out to discover from the beginning of the project. The graph has occurrences on the y-axis and flux in arbitrary units on the x-axis.

Figure 12. A log-log graph of a similar luminosity function for M83. The data collected from its flux frequencies per bin shows another power law relationship. This was also similar to the initial relationship that we set out to discover from the beginning of the project. The y-axis contains the number of occurences of each bin while the x-axis shows the related flux in arbitrary units.

As can be seen above, the graphs are slightly different than those of the past experiments, though still very similar. The best fit line that shows the power law fits well ignoring the fainter regions. Due to our small sampling, there are a number of bins above and below the fit, which lead us to believe that on average the result was very close. Also, the faint regions throw the fit line off, which is something that Petit et al. (1988) and Rumstay & Kaufman (1983) had both noticed as well. They ignored the faintest of the regions, which turns off for us around 250-300 arbitrary units for M81 and around 3500-4000 arbitrary units for M83. These are the regions where our sample becomes incomplete due to faintness.

5. Discussion

We did see a power law in our luminosity function, similar to that of that of Petit et al. (1988) for M81 and Rumstay & Kaufman (1983) for M83. M83's power law was just as we had expected it to be, very similar to that of M81's when the faint regions are ignored. We attribute this to the fact that we were able to account for even less decently luminous regions than Rumstay & Kaufman were able to account for. This enhanced the second power law that they hypothesized seeing. Other differences are credited both to the fact that they had used 492 and 296 H II regions respectively, as well as the fact that the image quality was greatly reduced in the IRAF version which made small regions either blocky or nonexistent. Despite these difficulties, the end result did verify that there is a power law relationship between the flux of H II regions and the frequencies of those fluxes.

Because of this same problem in image clarity, we were unable to attempt to verify Van den Bergh's Law of "Frequency Distribution of H II Region Diameters" (1981). The blockiness of the regions, mixed with loss of smaller regions, as well as the limitations of 'polyphot', would mix the region sizes together due to the small, blocky image quality.

In conclusion, it is clear that there is a power law relationship between the luminosity of the H II regions in M81 and M83 compared to the occurrence of these regions. The experiments and reductions done by Petit et al. and Rumstay & Kaufman on the subject have been verified to be true, with results strikingly consistent with our own. Van den Bergh's Law was not able to be verified as true or false. Though we were unable to use the Great Ohio telescope to duplicate these projects that were done by a 6m Soviet Telescope and Talbot, Jensen, and Dofour's observations (1979), we were able to use data taken from Kitt Peak as well as Denmark, while getting very similar results by simply staying in Clippinger Labs.

Aknowledgements

References