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JD 2445067.0+

Fig. 2.2 RADS differential photometry. Differential V RADS light curve 44i Bootis on JD 2445067 published by Robb and Milone (1982)

JD 2445067.0+

Fig. 2.2 RADS differential photometry. Differential V RADS light curve 44i Bootis on JD 2445067 published by Robb and Milone (1982)

the duty cycles and time delay determines the chopping frequency, which may be as high as 20 or 30 Hz; the system is usually operated closer to 1 Hz, however, because of the overhead caused by image motion and the delays at each station. The chopping line of the mirror may be rotated to coincide with the line between two stars. Two of the channels are usually consigned to observe the sky near the stars (near cities, "cloudy skies" usually also means "bright skies," so the flux spatially and temporally near the stars must be sampled also). The pulse-counting electronics are gated to the position of the mirror, and auxiliary controls permit the programming of filter changes. RADS works for stars which are separated by up to 45 arc-min. It thus may be superior to imaging devices with typical fields of view of a few arc-minutes for observations of objects in sparse areas of the sky, because it is highly desirable to have stars of similar spectral energy distribution and brightness to avoid systematic effects. Schiller & Milone (1990) discuss a study in which single-channel photoelectric and CCD photometry were carried out simultaneously on similar sized telescopes at McDonald Observatory of a star (the 5 Scuti star DY Herculis) in a sparse CCD frame. The photoelectric light curve was far superior because the small chip size allowed no bright comparison star to be imaged simultaneously.

Two-star systems such as RADS are insensitive to first-order extinction, and even to "second-order" extinction (many astronomers prefer to use the more strictly correct term "color-dependent extinction") if the comparison star is carefully matched in spectral distribution. Milone & Robb (1983) discuss the practical use of the system and demonstrate its effectiveness.

2.1.3 Photoelectric Observations

Photoelectric data may be obtained in the form of direct current, voltage, or pulse counts, but pulse counting became the data acquisition method of choice for photoelectric photometry. Recording digital observations is now almost always done by computers. Two types of data are sought: Standard star data and program star data. "Standard stars" are those which help to define the photometric system being used and their observation will provide the standardization needed for the program star data. The brightness of the "program star" must be determined in the passbands of the standard system and its observations need to be transformed to that standard system. The process of standardization, which we discuss in detail below, is important because observations corrected only for terrestrial atmospheric extinction are written in a kind of private code, effectively, and are subject to misinterpretation or miscomprehension until decoded. If the program star is variable, the observations must be gathered in intervals which permit good time resolution. Usually such observations are made in conjunction with constant-light "comparison" and "check" stars. The comparison star is observed before and after the variable star and should be sampled at frequent intervals. It provides the first-order extinction correction, and if it is relatively well matched in color to the variable star, the brightness difference between them should be independent of the color effects of extinction, again, to first order.

Multiple comparison stars are especially valuable when the variable star amplitude is very low, as in many 8 Scuti variables, a class of short-period pulsating stars. In any case, observation of a second comparison star is a good idea. The comparison stars must be observed frequently and over a relatively long range of time; consequently, if one of them turns out to be variable, the other comparison star (the check star) will save the day. The variable star observer measures a time-dependent flux,3 the display of which against time or phase (the repeated foldings of the time into the period of variation) is known as the light curve. The reduction and standardization of photometric observations will be discussed in Sect. 2.1.5.

In EB light curves, the photometric phase is the decimal fraction of the cycle of variation, with zero phase often set at mid-primary minimum. This is the photometric usage; spectroscopists may use the instant of passage through a node of the orbit (one of the two points marking the intersection of the orbit with the plane of the sky) as zero phase. In eclipsing variable star work, orbital phase may be computed as

where <s denotes a constant offset which often will simply be zero, frac{x} denotes the decimal part of x, the time of mid-observation, t is best expressed in the continuously increasing Julian Date or Julian Day Number and decimal fraction thereof; 8t is the heliocentric correction, the correction for the difference between light travel time of the starlight to the Earth and that to the Sun; t is the Heliocentric Julian Date; E0 is the epoch or instant of an adopted time of minimum; and P is the orbital period. Typical precision in P is ~ 0.d0001, or better. Both E0 and P are determined from a series of times of minimum light, and the precision increases with the range in time over which the observations are obtained (assuming that the period and epoch are constant and there are no very large gaps in the record). Each individual time of minimum requires a careful set of observations and several methods are available for the determinations [see, e.g., Ghedini (1982)]. The heliocentric correction depends on the relative locations on the sky of the star and the Sun (and therefore the solar date and the coordinates of the star). It may be computed4 or interpolated in the tables of Landolt & Blondeau (1972). If there are poorly determined or no eclipses, radial velocities may provide the best ephemeris. For eccentric orbit binaries, the phasing is more complicated as discussed in Sect. 3.1.2.2.

3 Usually the magnitude differences, Amk = m* — mk, relative to a comparison star, are measured, but in light curve analysis we prefer normalized flux. Therefore the conversion Ik = 10—10A(Amk—40) is applied to all measurements k where is chosen such that the maximum normalized flux is about unity.

4 See Henden & Kaitchuck (1982) or Duerbeck & Hoffmann (1994) for computational formulas and examples.

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