Magnitude Calibration of BATC Photomeric System



1, BATC magnitude of standard stars 7, Iteration
2, Photometry 8, Running program
3, The information from head of image 9, Applications
4, Extinction curve 10, Test by TA03 field
5, Variation of the extinction 11, New TEST Quality of calibration by TA03 field
6, Fitting of variation of extinction 12, diferencial check of standard zero point

Because  left of Zheng Zhong-yuan  and I am not familiar with system of IRAF, we need to develop a new software to treat the data of photometric night used for BATC flux calibration. The method

1, BATC magnitude of standard stars

4 standard star of Oke & Gunn(1983) are used for BATC flux calibration. They are: BD+17d4708, BD+26d2606, HD19445, and HD84937. The absolute fluxes of these stars are taken from Fukugita et al.(1996). The definition of BATC magnitude and the method for get the magnitudes from absolute flux was described by Yan et al. (1999). Table 1 of gives the magnitude of the 4 standards (Yan et al. 1999).
No filter wavelength HD19445 
1 a 3360 9.234 9.486 10.933 10.726
2 b 3890 8.653 8.800 10.299 10.057
3 c 4210 8.447 8.626 10.095 9.841
4 d 4550 8.294 8.505 9.962 9.693
5 e 4920 8.187 8.429 9.848 9.592
6 f 5270 8.072 8.338 9.743 9.488
7 g 5795 7.969 8.259 9.652 9.396
8 h 6075 7.935 8.232 9.617 9.365
9 i 6660 7.885 8.205 9.576 9.318
10 j 7050 7.851 8.171 9.541 9.273
11 k 7490 7.826 8.165 9.522 9.255
12 m 8020 7.800 8.150 9.501 9.238
13 n 8480 7.790 8.144 9.489 9.226
14 o 9190 7.784 8.149 9.489 9.226
15 p 9745 7.801 8.173 9.507 9.244

2, Photometry

As we done before (Yan,1999), a radius of 15 pixel aperture is used for make aperture photometry. Bertin's photometric code, Source Extractor is used for calculation. The parameter set are listed in dingbiao.set. The file bindbiao.param gives the contents in output catalogs "". Note: The output catalogue "" is a temporary file, it is deleted after it being used. In the output catalog, the central brightest star is regard as standard stars. It will be used for comparing with standard BATC magnitude of standards. Before do that, the instrumental magnitudes are normalized to the magnitude with exposure time of 300 second.

3, The information from head of image

By reading head of the image treated, we can get coordinates (RA and DEC), observation date and time and exposure duration. The RA, DEC and observing time are used for calculate the Air mass of the image. exposure time is used for normalize the instrumental magnitude.

4, Extinction curve

The diagrams of magnitude vs airmass shows the extinction curves. The magnitude is the difference of instrumental magnitude M_inst and BATC magnitude of different standards.
By fitting a straight line we can get the extinction coefficient of the filter K and the instrumental zero point:

M_inst-M_batc = K X + C

here X is airmass of the image.
K and C is derived by median fitting of the data points with straight line. A program from Numerical Recipe, "medfit" is used for fitting.

5, Variation of the extinction

As supposed the changing of the instrumental zero point is very small within a short time (in scale of few hours), the main variation in calibration with time is variation of the weather. We need a time dependent item to trace the variation of the condition of the earth atmosphere. As our previous works, a correction on zero point C, named f(ut) was used. It independent from airmass and color of the filters bands. It can be regard as mean variation of all possible reason with the time. As shown in paper of Yan et al.(1999), it can much reduce the fitting error and gives K and C good enough for BATC propose.

In my present work, for make things better, I considered the difference of wavelength and airmass. I use a variation item on extinction coefficient K instead of zero point. Two kind of variation is given in my programs. One is variation of the extinction coefficient of single filter band dK_band. the other is mean variation of all filter bands, dk_mean.

6, Fitting of variation of extinction

Different from we have done before, I used a smoothed continue curve to trace the variation instead of several jointed straight lines. Each fit point is the mean value of all observing points with 2 hours. I give a higher weight to nearby points in time.


here T_fit is fitting time point and T_obs is times of each observation point. They are in unit of hour.

7, Iteration

A good trace of extinction variation need a set of good estimation of mean extinction coefficient K and instrumental zero point C. And a good estimation of K and C need information of the variation. Few iterations are done on determination of K, C and variation. Fortunately, almost all the nights, the iteration can be convergent within 4 iterations. For security, 10 iterations are run before stop.

8, Running program

Two similar codes, dingbiao_ds and dingbiao_qs are used for situation of single band variation and mean variation respectively. Here we use dingbiao_ds to show how to use the two codes.
Tape dingbiao_ds without any arguments, we can see a simple one line help:

This shows the 4 function of the program. The program can distinct the different functions by the input arguments.

i, Read original data and make calculation of K, C and variation

dingbiao_ds image-directory figur-format


there are two argument in this case. The first is the directory where the piplined images locate. The another argument is figure display window or output figure format. There 3 kind of format usually used:

  • xw : output the figures to a new x-window
  • gif : Output figure in gif format same as the figure files of this web page.
  • ps : Output the figures as postscript files. It can be used for printing or called by latex. If "xw" is selected, we need to click the figure window to change figure and go to next step of calculation. The intermediate result are written in file of result.dat and stdxxxx.dat. xxxx is Julian date of the observation.
  • First column is the filter name. The second column is time of the image in UT. The third column is airmass and the 4'th column is differential magnitude between instrumental and BATC standard magnitude.

    ii, Checking the Processing and the Result

    For checking, several figures will shown during calculation. We can also check again the calculation from result of photometry "result.dat" by

    dingbiao_ds plot figure-format

    In this case only figure-format can be changed. Five kind of figure are shown during the calculation.

    First figure is primary fitting of extinction curves (figures/pf11127.gif)

    Second figure is variation of extinction on zero point as f(ut) of Yan(1999) (figures/rC91127.gif)

    Third figure is variation of extinction processed (figures/rK91127.gif)

    The 4'th figure is variation of extinction with fitting curve (figures/rKf91127.gif)

    the Last figure is the next fitting of extinction curve (figures/nf91127.gif)

    In the same time of figure showing, the result of calculation of each iteration is listed.

    iii, Get K and C of indicated filter and time

    From the result of photometry stdxxxx.dat (again, xxxx is Julian date), we make calculation and give the extinction coefficient and the zero point of indicated filter band and time (in UT).

    dingbiao_ds filter-band Julian-date UT

    Still, used JD1127 as an example. After run:

    dingbiao_ds d 1127 16.35

    we get:

    iv, Get calibrated magnitude

    By the given parameters of filter band, Julian date, observing time (UT), airmass, exposure time and instrumental magnitude, the program can give the calibrated magnitude.

    dingbiao_ds Filter U.T. AirMs Exposur M_inst

    Again, used JD1127 as an example. After run:

    dingbiao_ds d 1127 16.35 1.20 600 17.3

    we get "M_batc" as calibrated magnitude :

    9, Applications

    By using the new calibration codes, I have checked all the BATC data CDs. There are 77 days from JD0 9648 to JD1 1525 make standard observations. (The period is 11525-9648=1877days or 15/year). From these 77 days data, I found 58 days (about 12/year) are useful for BATC calibration by using code "dingbiao_ds" and "dingbiao_qs". All good days are listed in following table. By click on day of the table, we can find the figures of the fitting.
    TABLE of Useful Photometric Nights 
    1 0024  1 0049  1 0058  1 0063  1 0072  1 0081  1 0091  1 0092  1 0113  1 0175 
    1 0245  1 0365  1 0372  1 0382  1 0400  1 0402  1 0455  1 0462  1 0466  1 0490 
    1 0499  1 0555  1 0669  1 0670  1 0694  1 0757  1 0770  1 0797  1 0849  1 0850 
    1 1072  1 1127  1 1186  1 1199  1 1208  1 1213  1 1214  1 1217  1 1237  1 1239 
    1 1401  1 1512  1 1514  1 1518  1 1523  1 1525  0 9681  0 9741  0 9742  0 9753 
    0 9764  0 9774  0 9781  0 9783  0 9833  0 9971  0 9972  0 9987 

    There are 1849 image of BATC field were obtained during these 58 photometric nights. I get the zero magnitude ( M_zero ) and fitting error (RMS) for all these images. The result are listed in img2cali.dat . The zero magnitude means the BATC magnitude for a star of 0 instrumental magnitude.
    A program developed for do this work:

    apply image-list-file

    Separately, there are two table for TA03 field and T329 field.

    10, Test by TA03 field

    TA03 field was used for check new codes by JIANG Zhao-ji. His works were done in following steps:
    In fact,

    M_pip2-ap-Mag_zero is zero magnitude of combined image


    11, New TEST Quality of calibration by TA03 field