Corrections for Multiple Cluster and Radial Profile Plot

So at this point I was interested in correcting the program to account for fields with multiple clusters and to calculate meaningfull radial profiles. The solution I found solved both problems even though it was temporary.
If the density has been calculated in a meaningfull manner then it is reasonable to assume that the sources of highest density will be located in clusters. As such, were we to have a field with two clusters then perhaps the first 5, say, highest density sources will be in one cluster whereas the next 5 will be in the other cluster. Or perhaps the first 10 sources will be equally distributed between the two clusters. As such, it seemed reasonable to use those highest density stars as an indicator as to where the cluster was. The procedure then used was to obtain all the high density sources located in a 1pc radius around the source of highest density and recalculate the cluster center. This recalculated cluster center was then used for the radial profile. Note that in the radial profile calculation all the stars in the field were counted. The following figures show two cluster detections (the program actually performs the above mentioned routine for the first 10 highest density sources) based on this method and their radial profiles.

Figure: IC 348 cluster detected in a 30 arcminute field.

Figure: Radial profile from running the cluster recognition program on a field of IC 348. The first vertical line is the density-weighted cluster radius, the second vertical line just represents the distance at which the furthest (from the chosen center and within a 1pc radius) high density source is located. The horizontal line is at the average on-field source-number density.

The above results were encouraging. The main cluster (the one studied in M03) was detected as was another region of high density. The second region may be one of the regions indicated in M03. The radial profile has also changed drastically and now it doesn`t differ greatly from that given by M03 (see figure 7), in fact, the location where the background counts merge with the radial profile is not much larger than that in M03. Also, M03 chooses 5 arcminutes (close to 0.47pc) as being the radius of the central region of the cluster and just above 10 arcminutes (approximately 0.95pc) as being the outer radius, CRP results show that the cluster radius is approximately 0.35pc (I note again that whereas the first vertical line in the radial profile plots is the density-weighted radius, the second line is just based on a chosen radius). Another point to make is that, for large values of sampling radii (in the radial profile program), the radial profile is forced to decrease since the annulus will be, if the center is not at the field center, partially located out of the field. As such, the number of stars per equal area will be forced to decrease. This just means that it is hard to trust the outer limits of the radial profile, it may artificially decrease to the background level.

Lets now look at one more result obtained at this stage:

Figure: Trapezium cluster detected in a 50 arcminute field.

Figure: Radial profile from running the cluster recognition program on a field of Trapezium in Orion. The first vertical line is the density-weighted cluster radius, the second vertical line just represents the distance at which the furthest (from the chosen center and within a 1pc radius) high density source is located. The horizontal line is at the average on-field source-number density.

Above is just one of the several fields which were studied with this preliminary version of the CRP. Below I present some of these results as compared with values from the literature.

Table: Comparison of some preliminary data. R (Lit.) and Members (Lit.) are the values for the core radius, in parsecs, and the number of cluster members which I obtained from the literature. R (CRP) and Members (CRP) are, respectively, the values obtained with my program.

$Object$	$R (Lit.)$	$R (CRP)$	$Members (Lit)$	$Members (CRP)$	$Origin of Data$
IC 348	0.47	0.35	300	251	M03
NGC 2282	0.19	0.2	51	69	Horner et al 1978
Trapezium	0.47	0.47	1740 / 749	1253	LL03 and M02

We note that the core radii, as calculated with the CRP, roughly agrees with that of the literature and so do the number of members. For the case of Trapezium the number of members is lower than that given by LL03 yet higher than that given by M02. This comparison was important to show that the program was providing physically significant data and, thus, was on the right track.