PNe8alpha

Generating fake PNe positions from our images' surface brightness - PNe8alpha

Rather than get into the conversions/systems/units/completeness/depth questions of observed PNe data, we can apply the theoretical relationship between light and PNe to generate 'artifical' PNe positional data based on our distributions of light. Basically, we pick values of alpha, the coefficient that relates luminosity to number of PNe, and examine our images to generate, with some Monte Carlo action, a possible distribution of PN. Here's how it works:

Start with the value of a pixel, convert that to Bolometric Luminosity (with 0-point, distance, etc). Convert L_bol to N PNe by alpha (N = alpha*L_bol). This will always turn out (with our images and our selected values of alpha) to be a number between 0 and 1 - essentially a probability. Select a random number between 0 and 1. If the value for N is greater than the random number, we have a PN at this pixel.

Code Outline: clicking on the links will take you to that section of the code - it's online, too, on a separate page.

Code --> PNe8alpha.sm - PNe8alpha   - read fits image, set up running parameters/loops, call PNe8alphaw
                                            PNe8alphaw - loop over all pixels, on each pixel:
                                                                        pick random number to compare with calculated N, decide if it is a PN
                                                                    convert PN coordinates from x,y into RA/DEC, store in in file:
                                                                                                                              8.PNe.3.fits.alpha2523.RADEC.dat
                                                                    write out .reg file of these positions: 8.PNe.3.fits.alpha2523.reg [again, alpha25 means alpha_2.5 and alpha2523 means alpha_{2.5} = 23 x 10^-9
                                                                    use command line ds9 to generate jpg of overlaid coordinates (shown below)

Here are the results - our pretend PNe. These represent, for respective values of alpha_{2.5}, the TOTAL number of PNe predicted to exist in these images.

For all of these images we used a mask comprised of the SExtracted/Monte Carloed object mask and the bright star hand mask. The surface brightness mask (which we have normally been including at this stage) was kept out of this process.

Our alpha_{2.5} values have been selected based on Feldmeier's (?) citation of alpha_{2.5} to be 23 +10/-12 x 10^-9, and are 11, 23, and 33 x 10^-9

Fields          alpha_{2.5} values
3                  11 x 10^-9
                    23 x 10^-9
                    33 x 10^-9
4                  11 x 10^-9
                    23 x 10^-9
                    33 x 10^-9
7                  11 x 10^-9
                    23 x 10^-9
                    33 x 10^-9
Sub            11 x 10^-9
                    23 x 10^-9
                    33 x 10^-9
Core            11 x 10^-9
                    23 x 10^-9
                    33 x 10^-9
LPC           11 x 10^-9
                    23 x 10^-9
                    33 x 10^-9
FCJ           11 x 10^-9
                    23 x 10^-9
                    33 x 10^-9

3mm.fits
alpha_{2.5} = 11 x 10^-9