This recipe describes how to calibrate a set of instrumental magnitudes into standard magnitudes. It assumes that you are going to calibrate instrumental magnitudes for a set of programme objects by the usual technique of observing a set of standard stars. Thus, the starting point is a list of standard stars with both instrumental and standard (or catalogue) magnitudes and a list of programme objects with instrumental magnitudes. The techniques for calibrating instrumental magnitudes are discussed in Section 11.
The recipe uses the photometric calibration functions in the CURSA package for manipulating catalogues and tables (see SUN/190[16]) which do not include colour corrections. Thus, the recipe is only appropriate if your instrumental system is well-matched to the target standard system and where very high precision is not required. Nonetheless, with modern instrumentation and good observing conditions it is possible to achieve results accurate to within 0.01 magnitude.
The contents of the two tables are as follows.
In both cases, if you do not have the air mass then the zenith distance can be substituted instead. Note that it is the observed zenith distance, that is, as affected by atmospheric refraction, which is required. You obtain these various items of information as follows.
These various data must be edited into two tables which CURSA can read. The simplest way to format these tables is to use the CURSA Small Text List (STL) format. STL tables are simple text files which can be created with a text editor. If you originally used CURSA to select the standard stars to observe, as described in the recipe in Section 13, you could use the catalogue of standard stars which the recipe produces as a starting point. This approach has the advantage of avoiding have to re-type the catalogue magnitudes. Alternatively, example catalogues are available as starting points and these are used in this recipe. The catalogues of standard stars and programme objects are discussed separately below. You should copy these example catalogues into a convenient directory and make this directory your current directory.
| Standard | Catalogue Colours | Time | Air Mass | Instrumental | |
| Star | (UT) | Magnitudes | |||
| 113Z475 | 09.737 | 1.057 | 19:58 | 1.16 | 16.37 |
| 110Z450 | 11.033 | 0.950 | 20:06 | 2.20 | 17.74 |
| 114Z531 | 11.672 | 0.732 | 20:12 | 1.13 | 18.29 |
| 113Z475 | 09.737 | 1.057 | 21:33 | 1.41 | 16.39 |
| 114Z548 | 10.868 | 1.362 | 21:43 | 1.23 | 17.50 |
| 94Z251 | 10.547 | 1.218 | 00:19 | 1.14 | 17.17 |
| 93Z424 | 11.067 | 1.084 | 00:25 | 1.18 | 17.69 |
| 95Z74 | 10.931 | 1.127 | 00:32 | 1.17 | 17.55 |
| 96Z737 | 10.982 | 1.331 | 00:38 | 1.26 | 17.62 |
| 97Z249 | 11.369 | 0.651 | 03:11 | 1.14 | 17.99 |
| 94Z251 | 10.547 | 1.218 | 03:16 | 1.57 | 17.21 |
| 95Z301 | 10.527 | 1.285 | 03:20 | 1.32 | 17.16 |
| 99Z367 | 10.618 | 1.005 | 05:36 | 1.15 | 17.23 |
| 96Z737 | 10.982 | 1.331 | 05:42 | 1.81 | 17.67 |
Note that the example catalogue does not contain all the columns in Table 4. The catalogue is in the CURSA STL format. This format is probably more-or-less self-explanatory. In case of difficulty there is a short introductory tutorial in the CURSA manual, SUN/190[16]. The most relevant points are:
!’) are comments,
C’ define the
columns in the table. The word immediately following the ‘C’ is the name of the
column, the next item is its data type and the following one its sequence number
in the table of values. Thus in Figure 14 the first column is a character string
called NAME, the second column a double-precision number called MCATetc,
BEGINTABLE’ line.
The catalogue must contain columns containing the instrumental magnitude, the catalogue
magnitude and the air mass (or alternatively the observed zenith distance). It may
optionally contain a column containing a name for each of the standard stars and a column
of ‘include in the fit’ flags. All five columns are included in the example. If supplied, the
star name is listed in the table of residuals produced when the fit is made. Often being able
to identify each standard star will be useful to you. The ‘include in the fit’ flag column
is of data type LOGICAL and determines whether each star is included in the
fit or not. To include or exclude a given star in the fit you simply edit the STL
format catalogue and toggle the value of the flag for the star to ‘T’ (or ‘TRUE’) or
‘F’ (or ‘FALSE’) to include or exclude it as appropriate. This procedure is much
less troublesome and error-prone than deleting and reinserting stars from the
catalogue. Initially set the flags for all the stars to ‘T’ (or ‘TRUE’) so that they are all
included in the fit. In the example all the stars are included in the fit except
99Z367 (the penultimate one in the list). This star is excluded as an illustration.
When preparing your own catalogues you will usually initially include all the
stars.
The zenith distance is an angle and if it is used it must ultimately be presented to the CURSA applications in radians. If you wish you can simply type the values into the STL catalogue in radians. Alternatively, if it is more convenient, you can define the zenith distance column as containing a sexagesimal angle, usually in degrees, and type in the values as sexagesimal degrees. The example catalogue of programme objects in Figure 15 includes a column of zenith distances in this form.
Though both the columns of star names and ‘include in the fit’ flags are optional their use is strongly recommended.
The columns do not have to have the names shown in the example. However, if you use these names you will be able to accept the defaults from the prompts in the CURSA applications.
A useful trick is to enter the observations in the table in chronological order of observation. Then, when the residuals are computed they also will be listed in order of observation, making it easy to spot any systematic trends during the night.
Obviously the catalogue can contain additional columns, though these are not used. For example, if you are calibrating multi-colour photometry you could prepare a single catalogue containing the instrumental and catalogue magnitudes in all the colours observed. Obviously the columns for magnitudes in different colours would have to have different names. If you did not observe all the stars in all the colours simply use the STL mechanism for indicating missing (or ‘null’) values: enter the string ‘<null>’ instead of the missing value (see SUN/190 for further details).
As an illustration this catalogue contains columns of both the air mass and the observed zenith distance. It does not need to contain both, but must contain one or the other. Here the zenith distance has been entered as sexagesimal degrees and minutes.
The columns do not have to have the names shown in the example. However, if you use these names you will be able to accept the defaults from the prompts in the CURSA applications.
The catalogue can contain additional columns; indeed a programme catalogue will often contain celestial coordinates and/or object names. Also, if you are calibrating multi-colour photometry you could prepare a single catalogue containing the instrumental magnitudes in all the colours observed. Obviously the columns for magnitudes in different colours would have to have different names. If you did not observe all the objects in all the colours simply use the STL mechanism for indicating missing (or ‘null’) values: enter the string ‘<null>’ instead of the missing value (see SUN/190 for further details).
A message similar to the following should appear.
Conversely, if the catalogue of standard stars contains observed zenith distances then type:
In both cases you will be prompted for various column names. If you have used the same
column names as the example in Figure 14 you will be able to hit return in response to the
prompts. catphotomfit then displays some details of the fit, writes a file of transformation
coefficients and terminates.
catphotomfitFigure 16 shows the output displayed by catphotomfit. The transformation coefficients are
self-explanatory. The minimum residual vector length is a measure of the goodness of the fit. The
table of residuals is also mostly self-explanatory. The column of star names will be absent if
parameter NAME was specified as ‘NONE’. A ‘Y’ in the ‘Fit’ column indicates that the star was
included in the fit. The residuals are defined in the sense:
| (19) |
The transformation coefficients are shown to six places of decimals and the calculated magnitudes and residuals to three places of decimals. These formats do not imply that the results are this accurate; the actual accuracy will depend on the data used. It is noteworthy, however, that in the example data the largest residual is only slightly larger than 0.01 magnitude, despite the method ignoring colour corrections.
The bar to the right of the residuals is a simple graphic representation of the absolute size of the
residual; the length of the bar is scaled according to the absolute size of the residual for the star.
The scaling is such that the largest absolute residual amongst the stars included in the fit is ten
asterisks long. Stars which are included in the fit are shown as a row of asterisks (‘*’). Stars
which are excluded from the fit are shown as a row of dashes (‘-’). Because excluded stars will
often have larger residuals than the included stars, for excluded stars with residuals larger than
the largest included residual a right chevron (‘>’) is shown beyond the last dash (thus forming an
arrow).
F’ (or ‘FALSE’). Then re-run
catphotomfit. Repeat this process until you get a satisfactory fit. Note that as you
exclude new stars you may well wish to experiment with re-instating ones excluded
previously.
In the example data no additional stars really need excluding. However, you might like to
experiment with re-instating the penultimate star, 99Z367 (edit the table of standards and toggle
the ‘include in the fit’ flag for 99Z367 to ‘T’, or ‘TRUE’).
catphotomfit to calibrate the instrumental magnitudes for the programme objects. If your
table of programme objects contains air masses (the example contains both air masses and zenith
distances) then simply type:
Conversely, if the catalogue of standard stars contains observed zenith distances then type:
In both cases catphotomtrn will prompt you for various items. When prompted for the name of
the output catalogue it is probably best to give a name ending in the file type ‘.TXT’ or
‘.txt’ so that the table is written in the STL format. If you have used the same column
names as the example in Figure 15 the you will be able to hit return in response to the
prompts.
A new table containing the calibrated magnitudes in the standard system, as well as all the
columns in the original table of programme objects, will be written. If you specified the STL
format for this table it will be a simple text file and you will be able to examine it with a text
editor or Unix commands such as more or cat. It can also be examined with the CURSA
catalogue browser xcatview (see Section 13 for an example using xcatview), though
this is probably overkill for a small table of programme objects. Figure 17 shows
an output catalogue written in the STL format by catphotomtrn. In this catalogue
the calibrated magnitudes are column MCAT. Column MCAT, and the other columns,
are defined in the lines beginning with a ‘C’ or ‘:’ in the upper half of the figure.
The values for MCAT are the rightmost column in the table beneath the ‘BEGINTABLE’
line.
catphotomtrn15In this recipe, and more generally in CURSA, the terms ‘catalogue’ and ‘table’ are usually used interchangeably.