TO: 2MASS Team January 28, 1998

FROM: CAB

SUBJECT: K Band Diffraction Spikes

The effects of diffraction spikes are obvious in both the image and point source data. I have analyzed ~20 bright sources to ensure the correct operation of the spike-flagging software and the suitability of the parameters. My conclusion is that the algorithm works very well and that the values need to be adjusted only slightly to ensure high confidence that diffraction spike extractions are flagged with a minimal impact on completeness. In tuning these parameters, I have erred on the side of reliability in the catalog entries.

Figure 1. Diffraction Spike Sources. K=3.5-6.5 mag

Figure 1 shows all the sources tagged as diffraction spikes for sources covering a range of magnitudes from K=3.5 to K=6.5 mag. These sources were examined visually to verify that these are ALL the sources extracted in the vicinity of the diffraction spikes. I removed a few glints at 11:30 and 5:30 o'clock, as well as a few sources that were obviously real stars within the nominal spike window.

There are a number of patterns obvious from visual inspection of the images. The distribution of the diffraction sources around the centerline of the spikes is remarkably narrow with a population sigma of 0.4 arcsec. The Western spike is more complex than the other three spikes and appears to consist of two spikes that flare with increasing distance from the parent star. The most noticeable effect of this structure is that the Western spike is 3 times broader than the N, S, or E spikes. Although a more rigorous model is possible, it will suffice to excise a broader region around the W spike than around the others. There is also a small effect on the length of the Western spike. Because the diffracted energy is divided between the two rays, diffraction sources fall below threshold more rapidly with distance than for the other spikes. This is a 10-20 % effect in the relative lengths of the East and West spikes.

Figure 2. Fit to diffraction spike length.

The derived K-band values for the diffraction spike parameters are listed below. Since excising diffraction spike sources is an important reliability consideration, the length proposed for MAPCOR is 20% larger than the observed values. This length is parameterized according to Length(K)=Length0*10^(-slope*(K-6 mag)). The values in the Table were derived by examining the length of the spikes in 4 separate magnitude bins (Figure 2). The proposed width of the exclusion zone is derived from the absolute value of any offset between the parent star and the spike source, plus 5*sigma_pop. The half width and length of the box are given in units of camera pixels (2") for each cardinal direction.

Examination of the data shows that the spike sources are DeltaMag = 10.2+/-0.6 mag fainter than their parents. Since weak spikes are not detected around faint parent sources, the DeltaMag is reduced for the weakest parents: only the brightest diffraction spikes, DeltaMag = 9 instead of 10.2 mag, are detected for weakest sources. I have ignored this "Malmquist" bias and used DeltaMag in two ways:

• Since the 3-sigma K detection threshold is K~15.6 mag, then to guarantee that no spike sources escape flagging, one must search around sources as faint as K=15.6- DeltaMag +5*sigma_pop= 8.4 mag. If the parent drops below this magnitude, no more spike sources should be detectable. Accordingly, we have added a diffrac_cutoff = 8.5 mag to MAPCOR, below which there is no need to search for diffraction spikes.
• Sources which are 5*sigma_pop times brighter than the predicted spike brightness, Kparent + DeltaMag - 5*sigma_pop = Kparent + 7.2 mag, are probably real sources, albeit ones contaminated by the spike. These will be marked with the diff1 contamination flag.

Finally, it is worth noting that the spike sources fade slowly with distance from the parent star until they drop below the detection threshold. As shown in figure 2, the magnitude difference between the parent star and spike sources declines by about 1.1 mag as the distance increases from 10 to 100 arcseconds. The equation fitted to the data in Figure 3 is given by DeltaMag=1.1*log(Radius)+8.4. The conservative limits described above make consideration of this detail unnecessary at this time.

I will be examining the J and H data in the same manner to derive parameter values for these wavelengths.

Figure 3. Difference between parent and spike source brightness.

Table 1. Properties of Diffraction Spikes at K
	North	South	East	West
Box Half Width (camera pixel, 2")	0.5	0.5	0.5	1.5
Box Length at K=6 mag (camera pixel, 2")	15	15	15	12
Max length (camera pixel, 2")	75	75	75	75
Slope	-0.22
diffrac_cutoff	K= 8.5 mag
Contamination threshold	Kparent + 10.2 -3.0 mag