Influencing the plan

The program will propose reasonable default choices, and will provide some approximate estimates of the magnitudes where photon noise becomes excessive, and where photon and scintillation noise are comparable. Because the crossover between photon and scintillation noise depends on both zenith distance and azimuth, a set of values will be presented for your inspection. Table shows what a typical crossover table looks like.

  
Table: A sample crossover table

There's a lot of useful information in this table, so let's go over it carefully. First, notice the similar pairs of columns at the left, under the title SCINTILLATION = PHOTON NOISE. The left-hand pair of columns gives crossover magnitudes for an airmass near 2.36; the right-hand pair, for an airmass of 1.10. These are the maximum and minimum airmasses at which the planning program expects to schedule observations of extinction stars. The smaller airmass will be adjusted by the program to provide more or fewer extinction stars, as needed; you can push it back and forth a little if you want.

For each airmass, there is one pair of columns. These contain the magnitudes at which scintillation noise and photon noise are expected to be equal, for two different lines of sight: one looking along the projected wind vector in the upper atmosphere, and the other looking at right angles to the wind. When we look at right angles to the wind, the scintillation shadow pattern moves with the full wind speed across the telescope aperture, and we have the maximum possible averaging of scintillation noise in a given integration time, the least scintillation noise, and thus the brightest possible crossover magnitude. But when we look directly along the wind azimuth, the motion of the shadow pattern is foreshortened by a factor of sec z; then the scintillation noise is maximized (for a given zenith distance), and the crossover does not occur until some fainter magnitude, where the photon noise is big enough to match the increased scintillation.

As we do not know the wind azimuth in advance, we can only say that the scintillation and photon noises will be equal somewhere in the interval between these two extremes. We would generally prefer to have the extinction measurements limited only by scintillation noise, so the initial faint limit for extinction stars is set 1.5 magnitudes brighter than the brightest of the crossover values. This makes the photon noise half as big as scintillation, near the zenith. (Our sample table shows these initial values.) These are conservative values.

However, we may need to set the actual faint limit used in selecting standard and extinction stars (shown in the rightmost column of the table) somewhat fainter. For example, we may be using such a large telescope that we cannot observe such bright stars. (In particular, if you are doing pulse counting, the program will impose a bright limit as well as a faint one.) In this case, both photon and scintillation noise will be quite small, and we can safely use considerably fainter stars without compromising our requested precision.

In the example above, the user has requested an accuracy of 0.01 magnitude. The planning program divides this error budget into four parts: scintillation, photon noise, transformation errors, and instrumental instabilities. If these are uncorrelated, each can have half the size of the allowed total; in our example, that's 0.005 mag. So the table gives the magnitude at which the photon noise reaches its allowed limit (in the next-to-last column), for the adopted integration time (5 seconds, in our example). This magnitude should be regarded as an absolute limit for extinction and standard stars.

Obviously, we could actually push the extinction stars close to this photon-noise limit, without exceeding the requested error tolerance. However, between the photon-noise limit in the right half of the table and the crossover values to the left, there is a substantial contribution of photon noise to the total, and hence a substantial advantage to using brighter stars. If we use this advantage, we provide some ``insurance'' --- a little slack in the error budget.

Whenever the crossover table appears, you will be given an opportunity to change the actual planning limits, whose current values are given in the last column. The columns to its left provide you with the information you need to make a good choice: the crossover magnitudes, and the pure photon limit, for each band.

Although these values are given to 0.1 mag precision, you should be aware that the scintillation noise can fluctuate by a factor of 2 or more within a few minutes, so that only a rough estimate is really possible. Furthermore, the photon-noise estimates are only as good as the estimates available to the program for the transmission of the instrument and the detective quantum efficiency of your detector. So all these numbers are a little ``soft''; you should not take that last digit literally. Just bear in mind that the photon noise varies with magnitude, and that the scintillation varies with airmass and azimuth, by the amounts shown in the table.

Now, let's consider adjusting the circumzenithal airmass. If the high-altitude, low-airmass almucantar is too close to the zenith, only a few standard stars will be available in the small zone it intercepts as the diurnal motion carries the stars past it. Then it may be necessary to choose a larger minimum airmass to expand the region of sky available for choosing extinction stars. Conversely, if too many extinction stars are selected, it makes sense to reduce the zone width a little, thereby getting not only a more reasonable number of stars, but also a little bigger range in airmass for each star.

The planning program will make coarse adjustments in the minimum airmass (i.e., in the width of this zone) to get about the right number of extinction and standard stars, but you can also make fine adjustments yourself. The program gives you this option after making a preliminary selection of standards. When it asks whether you want to adjust the sky area or magnitude limits, reply ``sky,'' and it will make a small change and try again. You may need to make several adjustments to get what you want.

If you expect from past experience that you will have excellent photometric conditions, you may be able to reduce the number of extinction stars a little. However, this is risky: if the weather turns against you, you may need more stars than you expected! Conversely, if you know the observing run is at a place or time of year that usually has mediocre conditions, you will surely want to play it safe and add some extra extinction stars.

You can also alter the number of candidate stars by adjusting the magnitude limits. By adjusting magnitude limits separately in different bands, you can manipulate the range of colors available. For example, because signals tend to be low in ultraviolet passbands, the photon noise is high there, so it often happens that the default faint-magnitude limits do not allow enough very red stars. In this case, making (say) the faint U limit fainter and the V limit brighter biases the selection toward redder standards.

Thus, you can manipulate the region of sky and the magnitude limits to select a reasonable number of standards with a good range of colors. You can make such adjustments iteratively until you are satisfied with the selection. At each stage, the program will show you the distribution of the selected stars in a two-color diagram, as well as on the sky, and ask if its selection is satisfactory. If it is not, you reply ``no'' to the question ``Are these stars OK?'', and then have another chance to manipulate the zone width and magnitude range. When you finally reply ``yes'', the program will make up an observing schedule for each night of the observing run, using the set of stars you approved.

Keep in mind the possibility that a star previously certified as a photometric standard can still turn out to be variable! A surprising number of bright eclipsing binaries continue to be discovered every year. Furthermore, stars of extremely early or late spectral type, and stars of high luminosity, tend to be intrinsically variable by small amounts. Therefore, it is important to use a few more standards than would otherwise be absolutely necessary, just in case of trouble. A little redundancy is cheap insurance against potential problems. We also need some redundancy to find data that should be down-weighted (see section to see why.)