11.3 Extinction and Night Coefficients

As Table  shows, the SA110-503 field was observed twice every night at different airmasses, typically 1.65 and 1.15. The extinction coefficient, k, can now be determined by fitting the relation m = m₀ + kX to the two (X,m(X)) points for each night and filter. m is the observed magnitude, X is the airmass, and m₀ is the magnitude of the star outside the atmosphere. By the observed magnitude we mean the magnitude that phot outputs, m_phot, which in turn is given by

$$m_{phot} = {\tt zmag} - 2.5 \log \left(\frac{I_{star+sky}-I_{sky}}{t_{exp}} \right).$$ (11.4)

zmag is the arbitrary zero point of the magnitude scale, I_star+sky is the total number of counts (in ADU) from the star and the sky background within the aperture, I_sky is the equivalent number of counts (in ADU) from the sky background alone within the aperture, and t_exp is the exposure time (in seconds, say). zmag = 22 mag was used.

Since there are 8 stars in the SA110-503 field, we get 8 determinations of k for each image. The final k can then be calculated as the mean, with the possibility of rejecting points. This procedure is implemented in the task stars.calext. The package stars is written by IJ.

First, mkimsets was used to create an image set file for each night for the SA110-503 images.

Second, mknobsfile was used to create an observations file for each night for the SA110-503 images. mknobsfile inputs the APPHOT databases (the image.mag.1 files) and the image set file, and outputs the observations file^11.1. In the process of compiling the data of the multiple APPHOT databases into one file, it also does the aperture correction.

calext is given an observations file and a fields file. The first column of the latter contains the star names to be used. Optionally, in the second column it contains a color, e.g. (B-V). One can either fit k as a constant, or as a function of star color, $k = k((B-V)) = c_1 + c_2\cdot(B-V)$, still for the same given filter.

calext was first run without a color term. The stars which seemed to deviate too much were deleted. The deleted stars are shown in Table . No more than 3 of the 8 stars were deleted. Some of the deleted stars were inspected in the images; in some cases, there were cosmic ray events within the aperture, whereas in other cases, noting unusual could be seen. It should be noted, that the star SA110-502, which was deleted in 4 out of 6 cases in Johnson U, is very faint in that filter, U = 17.0 mag (cf. Table ).

 

Table: Deleted Stars When Determining the Extinction

Night	GR	JV	JB	JU
1	-	496	502, 504	502
2	-	-	-	502
3	-	504	-	504
4	-	496	504	497, 504
6	497, 504	497	496	502, 497, 504
7	-	506	504	502

 

Notes: All stars are from the SA110 field. Magnitudes of the stars can be found in Table .

The resulting nightly extinctions coefficients are shown in Figure  and Table . It can be seen, that there are variations from night to night. These variations are qualitatively the same in all the filters.

 

 

Table: The Nightly Extinction Coefficients

Night	GR	JV	JB	JU
1	0.110	0.151	0.250	0.506
2	0.070	0.118	0.192	0.493
3	0.089	0.135	0.221	0.483
4	0.105	0.182	0.276	0.589
6	0.120	0.210	0.313	0.610
7	0.067	0.142	0.219	0.459

 

calext was also run fitting k as a function af (B-V), $k = c_1 + c_2\cdot(B-V)$, with (B-V) taken from Landolt (1992). The stars which were deleted were the same as when fitting k without a color term, with three exceptions (night 1, JB: star 502 & 504 not deleted, night 2, JU: star 502 not deleted), and they were not very clear. The resulting color term coefficients, c₂, averaged over the 6 nights, were $-0.007 \pm 0.003$, $-0.001 \pm 0.003$, $-0.012 \pm 0.009$, and $-0.104 \pm 0.043$, for GR, JV, JB, and JU, respectively. At face value, these are different from zero at the 2.0, 0.5, 1.4, & 2.4 sigma level, respectively. For JU it was noted when doing the fit of $c_1 + c_2\cdot(B-V)$ to the 8 values of k per night, that the scatter was very high, and that the mean c₂ for the given night was very sensitive to which stars were included in the fit, which in turn was not easy to decide. The 6 mean values of c₂ scatter a lot, too, from 0.00 to -0.27, with the latter value being for night 2 where the star 502 was included.

It was concluded, that if there was any color dependence it was small, and that it therefore was appropriate to use the color independent fit of k.

Now having determined the nightly extinction coefficients, we were ready to apply these to all the stars. mkimsets and mknobsfile (including aperture correction) were run on all the stars in the 3 fields, and the names were corrected to what they were in the standard catalog. All the magnitudes were then corrected for extinction (Table ) using the task stars.magcorrect. magcorrect can also apply night coefficients, but that function was not used at this step, the parameter nitecoef was set to "". The above was done separately for the focused and defocused images, and separately for the 6 nights.

Having corrected the magnitudes for extinction, they should in principle be consistent from night to night. However, this is usually not the case, so one brings them to the same relative system by adding so-called night coefficients. The night coefficient for night i with respect to night ref is given by

$$n({\rm night}\,i) = \langle m({\rm night}\,{\sl ref}, {\rm star}\,j) - m({\rm night}\, i, {\rm star}\,j) \rangle,$$ (11.5)

where the mean is taken over all stars j observed on both of the nights. If a star has been observed more than once on a given night, $m({\rm night}\,i,{\rm star}\,j)$ can be taken to be the mean value. Typically, night coefficients are of the order of a few hundredths of a magnitude.

Since night coefficients are relative, it is arbitrary which night is chosen as reference night. One might as well chose the night that would seem to be the most reliable one, e.g. the night with the most observations, or the night with the lowest extinction. Here, night 2 was chosen.

Calculations of night coefficients can be done by the task stars.calnitecoef. It calculates mean magnitudes using the task stars.meanphot (or, alternative, the user can do that directly first, and tell calnitecoef to use these mean magnitude files). The user can do the fitting of the mean of the individual night coefficients (one for each star in common) interactively.

Night coefficients with respect to night 2 were determined for the 6 nights, separately for the focused and the defocused images, using calnitecoef. The result is shown in Figure .

As can be seen, the night coefficients are very large, indicating that something is wrong. It is also striking, that the variation of the night coefficients from night to night (Figure ) is qualitatively the same as the variation of the nightly extinction coefficients from night to night (Figure ). This suggests, that the nightly extinction coefficients are uncorrect.

The weather needs to be photometric in order to be able to determine the extinction coefficient. If the weather is not photometric, the stars will appear too faint.

If it is photometric when observing at low airmass, but not photometric when observing at high airmass, the determined extinction coefficient will be higher than the true value. If it is the other way round, the determined extinction coefficient will be lower than the true value. If it is not photometric neither at low nor at high airmass, anything can happen.

Notes about the weather was written by the observer usually on top of each page of the observations log, see Table . These are the only notes about the weather in the log for the days in question. Only once it was stated, that the weather was not photometric for sure. A few places it was stated, that the weather might not be photometric.

If we assume, that the weather in fact was not photometric where it was stated that it might not be, we would expect, that the extinction coefficients were too high for night 3, and too low for night 6. In Figure  one sees, that the night 3 extinction coefficients are not high compared to the values from the other nights, so it does not seem likely, that the night 3 values are actually too high. One also sees, that the night 6 extinction coefficients are high compared to the values from the other nights, so it does not seem likely, that the night 6 values are actually too low, either.

However, the above assumption might not be correct. It is difficult per se to precisely determine whether the weather is photometric, and since the observer is busy observing, he/she cannot spend all the time monitoring the weather. We will conclude, that it was not photometric all the time, but that we cannot say precisely when.

In any case, the night coefficients based on the nightly extinction coefficients are very large, and the variation does resemble that of the nightly extinction coefficients, so something with the latter must be wrong.

It was concluded, that the nightly extinction coefficients for night 4 and 6 were too high. It was decided to use the mean value of the nightly extinction coefficients for night 1, 2, 3, and 7 as the extinction coefficient for the given filter. Those 4 final extinction coefficients are shown in Table . Also shown are the La Silla mean extinction coefficients. For JV, JB, & JU, the adopted values are 4-10% higher than the La Silla mean values. For GR, the adopted value is 30% higher than the La Silla mean value. However, the adopted value agrees very well (< 4%) with the values of run 1-3 of Jørgensen (1994), in which the very same filter (ESO #460) was used. These comparisons give confidence that the adopted values of the extinction coefficients are reasonable.

 

Table: The Notes in the Observations Log About the Weather

Night	Page	Weather	Standard fields observed
1	1	Photometric - to be checked
1	2	Photometric	M67
1	3	Photometric
1	4	Photometric
1	5	Photometric	PG1633+099, SA110 (high airmass)
1	6	Photometric	SA110 (low airmass)
1	7	Photometric
2	8	Photometric	M67
2	9	Photometric
2	10	Photometric
2	11	Photometric	PG1633+099, SA110 (high airmass)
2	12	Photometric	SA110 (low airmass)
2	13	Photometric	SA110 (low airmass) continued
3	14	[nothing written]
3	15	Photometric	M67
3	16	Photometric
3	17	Photometric
3	17	May not be photometric right now, check this	PG1633+099
3	18	Photometric (?)	SA110 (high airmass)
3	19	Photometric	SA110 (low airmass)
4	20	Photometric
4	21	Photometric	M67
4	22	Photometric
4	22	NON-photometric
4	23	Photometric? check this
4	24	Photometric	SA110 (high airmass)
4	25	Photometric	PG1633+099
4	26	Photometric	SA110 (low airmass)
6	25	Photometric
6	26	Photometric	M67
6	27	Photometric
6	28	Photometric	SA110 (high airmass)
6	29	Photometric (?)	PG1633+099, SA110 (low airmass)
6	30	Photometric (?)
7	31	Photometric	M67
7	32	Photometric
7	33	Photometric	SA110 (high airmass)
7	34	Photometric	SA110 (low airmass)
7	35	Photometric

 

Notes: The weather was noted on top of each page of the log book, except for page 17 and 22, where it was also noted further down. On night 5, the first page number was set to 21 instead of 27 as it should have been, therefore the strange page numbers for night 6 and 7.

 

 

Table: The Final Extinction Coefficients

Filter	GR	JV	JB	JU
Adopted ext. coeff.	0.084	0.137	0.220	0.485
La Silla mean ext. coeff.	0.065	0.125	0.212	0.459

 

Notes: The adopted extinction coefficient for a given filter is the mean of the nightly extinction coefficients for night 1, 2, 3, and 7 (cf. Table  and Figure ). The La Silla mean values are taken from Jørgensen (1994). This author used the exact same filters as in this study, viz. ESO # 460, 451, 450, & 632, respectively.

The observations were extinction corrected using the new extinction coefficients, and the night coefficients were determined again, still with respect to night 2. The result is shown in Figure .

 

Now the night coefficients were of a more reasonable size, although still somewhat large. What is striking is, that the focused and defocused stars do not have the same night coefficients, except for the reference night, night 2, where they per definition are 0. This indicates, that night 2 is not representative - if another night had been chosen as reference night, this offset would have been smaller for more of the nights (and of course for night 2, it would be large and with opposite sign).

It was decided to proceed and to calculate night coefficients for the combined sample of focused and defocused stars. In doing this, the defocused stars were weighted more than the focused, as 59 stars to 13 stars. When fitting, it was sometimes obvious, that there was an offset between the focused and defocused individual night coefficients. Nevertheless, the mean was calculated more or less blindly, only throwing away points which seemed to deviate for other reasons. The result is shown in Figure  and Table .

 

Table: The Night Coefficients Based on the Final Extinction Coefficients

Night	GR	JV	JB	JU
1	-0.009	-0.007	-0.014	-0.020
2	0.0	0.0	0.0	0.0
3	-0.007	-0.001	-0.005	-0.004
4	-0.011	-0.010	-0.021	-0.021
6	-0.011	-0.023	-0.036	-0.044
7	0.001	-0.004	-0.015	-0.018

 

Finally, the night coefficients were applied to the already aperture and extinction corrected observations files using magcorrect again, this time setting extcoef="". These magnitudes are called instrumental magnitudes. In short, they are given by

$$m_{inst} = m_{phot} + {\rm apcor} -kX + n,$$ (11.6)

where k is the extinction coefficients for the given filter, X is the airmass for the given observation, and n is the night coefficient for the given filter and night. m_phot and ${\rm apcor}$ should correspond to the same aperture.