11.2.2 The Defocused Images

phot was run on 4 well isolated stars (F81, F153, F170, & I27) in the defocused images, with apertures $5,6,\ldots,42$ pixels, and with salgorithm=gauss, annulus=42.0 pixels, and dannulus=14.0 pixels. Even though the defocused stars did not have a peak to define their centers, they were centered well using a somewhat large box, centerpars.cbox=15 pixels, which still was small enough to exclude the neighboring stars.

A large effort went into trying to get mkapfile to fit the profiles of the defocused stars, and compute the aperture correction. This did not succeed.

Instead, aperture corrections at 12 and 15 pixels were manually read from the growth curves that mkapfile produced. These growth curves, one for each image, were based on the above 4 stars. An example of such a curve is shown in Figure . The resulting aperture corrections are shown in Table , and plotted in Figure , the two left panels. In the top right panel, the difference between the two is shown.

 

From the plots it can readily be seen, that the aperture correction is not the same for the 4 filters, and that it is not the same from night to night. Further, the difference between the aperture corrections at the two apertures is not the same for the 4 filters and from night to night.

 

Table: The manually measured aperture corrections, by night

night	filter	image	apcor12	apcor15	delta
1	GR	d1263	-0.032	-0.018	0.015
1	JV	d1262	-0.027	-0.014	0.012
1	JB	d1264	-0.034	-0.019	0.014
1	JU	d1266	-0.048	-0.023	0.025
2	GR	d1388	-0.025	-0.017	0.009
2	JV	d1389	-0.020	-0.012	0.007
2	JB	d1390	-0.032	-0.020	0.012
2	JU	d1391	-0.044	-0.026	0.018
3	GR	d1534	-0.017	-0.012	0.006
3	JV	d1535	-0.015	-0.010	0.005
3	JB	d1536	-0.021	-0.016	0.006
3	JU	d1537	-0.043	-0.030	0.013
4	GR	d1689	-0.021	-0.014	0.007
4	JV	d1690	-0.017	-0.013	0.004
4	JB	d1691	-0.024	-0.015	0.009
4	JU	d1692	-0.040	-0.027	0.013
6	GR	d1948	-0.022	-0.017	0.005
6	JV	d1949	-0.017	-0.012	0.005
6	JB	d1950	-0.023	-0.015	0.008
6	JU	d1951	-0.038	-0.024	0.013
7	GR	d2092	-0.021	-0.015	0.006
7	JV	d2093	-0.016	-0.010	0.005
7	JB	d2094	-0.021	-0.014	0.008
7	JU	d2095	-0.038	-0.027	0.011

 

Notes: apcor12 and apcor15 are the aperture corrections for the defocused images at an aperture of 12 pixels and 15 pixels, respectively, in magnitudes. delta is minus the difference between the two, i.e. delta = -(apcor12-apcor15). The aperture corrections were manually measured from growth curves based on the 4 stars F81, F153, F170, and I27. Uncertainties were estimated from the scatter of the used individual points. Typical values are: GR: 0.002 mag, JV: 0.001 mag, JB: 0.002 mag, JU: 0.006 mag. When doing the eye fit, the JU values from night 4 was noted as uncertain, and a more realistic uncertainty for these values is probably 0.010-0.015 mag.

 

The M67 field of this study had 23 stars in common with the standard stars of Jørgensen (1994). Besides of these standard stars, 36 stars were selected as ``program'' stars on the following three criteria: they should be somewhat bright (we required a peak > 500 ADU in the GR image d1262), they should not be too close to other stars, and they should have a unique name. The reason for including these program stars was: 1) the derived magnitudes for these stars could be useful in another context (they could perhaps serve as tertiary standard stars), and 2) the more stars, the better statistics for the test of the aperture correction, see below.

phot was run on these 59 stars, using two apertures: 12 and 15 pixels. cbox was increased to 20 pixels. The reason for using two apertures was to test the aperture corrections determined above at these two apertures. Since per definition

$$m({\rm total}) m(12{\rm px}) + {\rm apcor}(12{\rm px})$$ = (11.1)

$$m(15{\rm px}) + {\rm apcor}(15{\rm px}),$$ = (11.2)

it follows that

$$m(12{\rm px}) - m(15{\rm px}) = - \left[ {\rm apcor}(12{\rm px}) - {\rm apcor}(15{\rm px}) \right].$$ (11.3)

This only holds in the absence of contributions from neighboring stars and cosmic ray events. $m(12{\rm px}) - m(15{\rm px})$ for the above 59 stars for each image (with one image per night per filter) is shown in Figure  for Gunn r and Johnson V, and Figure  for Johnson B and U. The median value of $m(12{\rm px}) - m(15{\rm px})$ for each of the 24 images is shown in Figure , bottom right panel. In the top right panel of the same figure is shown $- \left[ {\rm apcor}(12{\rm px}) - {\rm apcor}(15{\rm px}) \right]$.

 

Table: Mapping between star names and ID numbers

ID	Name	Type	ID	Name	Type	ID	Name	Type
1	M67-F81	standard	21	M67-F141	standard	41	M67- I56	program
2	M67-F83	program	22	M67-F143	program	42	M67- I60	program
3	M67-F93/ I12	standard	23	M67-F145	program	43	M67- II20	program
4	M67-F94	program	24	M67-F147	program	44	M67- II22	standard
5	M67-F95	standard	25	M67-F149	program	45	M67- II30	program
6	M67-F105	standard	26	M67-F153	standard	46	M67- III1	program
7	M67-F106/ I11	standard	27	M67-F164	program	47	M67- III2	program
8	M67-F108	standard	28	M67-F170	program	48	M67- III7	program
9	M67-F111	standard	29	M67- I1	program	49	M67- III12	program
10	M67-F115	program	30	M67- I5	program	50	M67- IV2	program
11	M67-F117	standard	31	M67- I9	program	51	M67- IV3	program
12	M67-F119	program	32	M67- I14	program	52	M67- IV4	program
13	M67-F124	standard	33	M67- I15	standard	53	M67- IV6	program
14	M67-F127	standard	34	M67- I17	program	54	M67- IV12	program
15	M67-F128/ I198	standard	35	M67- I20	standard	55	M67- IV13	program
16	M67-F129/ I199	standard	36	M67- I24	program	56	M67- IV21	program
17	M67-F130	standard	37	M67- I25	standard	57	M67- IV34	program
18	M67-F132	program	38	M67- I27	standard	58	M67- IV35	program
19	M67-F134	standard	39	M67- I31	program	59	M67- IV59	program
20	M67-F135	standard	40	M67- I49	standard

 

Notes: ID is the identification serial number which phot uses internally. It is also the number used in Figure  and .

 

 

As can be seen, the form of the ``curves'' is qualitatively the same, but there is a small offset. This offset is probably due to contributions from neighboring stars for the sample of 59 stars. This contribution is much less in the sample of 4 stars, since they were selected from being isolated. This can be checked by inspecting these 4 stars in Figure  and . They are almost always in the lower range of the 59 points. The mapping between names and serial ID number for these 4 stars is F81=ID1, F153=ID26, F170=ID28, and I27=ID38. F81 with and ID of 1 is particularly easy to locate. The conclusion is, that the manually determined aperture corrections pass the test of equation ().

The M67 field is quite crowded. For example, F128/ I198 and F129/ I199 are 25 pixels (13'') apart, F129/ I199 and F130 are 23 pixels (12'') apart, and F106/ I11 and its fainter neighbor I10 are only 16 pixels (8'') apart. This also shows up in the magnitude difference plots in Figure  and . The mapping between names and serial ID number for these 4 stars is F128/ I198=ID15, F129/ I199=ID16, F130=ID17, and F106/ I11=ID7. Especially F106/ I11 is very contaminated. The above speaks in favor of a small aperture

Also, the images are quite defocused. Inspection of screen dumps of the images used in Jørgensen (1994) shows, that that these images were less defocused than the images of this study, despite that both used a defocusing of +200 encoder steps. This is probably because the filters are now placed in the DFOSC, instead in the instrument adapter as they previously were.

Jørgensen (1994) used two apertures for her defocused images, 7.52'' and 9.40''.

It was decided to use an aperture of 12 pixels (6.09''), and to use the corresponding aperture corrections listed in Table . As previously mentioned, the background region was 42-56 pixels, i.e. 21.31-28.41''.

Finally, we can compare the aperture corrections for the focused and the defocused images. This in done in Figure . The variation with night is quite similar for the focused and defocused images.