BR CVn (SAO 44590, HD 116475) is a poorly observed 6th magnitude star of spectral type M4111 (B—V=1.55). It is located about 1^o almost due west of the Whirlpool nebula M51 at RA 13h 23m 05.5s, Dec +47° 00’ 06" (2000.0).¹ It appeared as star 69 on the now obsolete BAA chart (1984 April 12) for TU, Y and V CVn. In the past, the star was used as a convenient comparison for V CVn at maximum,² and light curves of V were adversely affected by BR. Not surprisingly it was visual observers of V who first raised doubts as to the constancy of BR. Reports by Tristram Brelstaff, Richard Fleet, Róbért Fidrich, Patrick Maloney and John Toone were recorded as far back as the early 1980s, and by 1986 most visual observers had stopped using BR as a comparison. The confidence of some visual observers in reporting variability was hampered by the redness of BR. Three BAA visual observers used an alternative comparison of similar colour and magnitude to star 69, located about half a degree to the northwest, and reported a range of variability in close agreement with subsequent photometry. The same comparison has been used in the present study.

Observations were made by West at his observatory at Ryde on the Isle of Wight. Despite its low altitude (37 metres), the site is near a hilltop and is protected from valley mists. Photometry was performed using an Optec SSP3 photometer equipped with the manufacturer’s V-filter and attached to a 20cm aperture Newtonian telescope. Data in the form of the four-figure SSP3 output were logged manually into a notebook and later transferred into a spreadsheet for reduction.

Although photoelectric photometry can appear complex and difficult, the actual operation of the Optec SSP3 is simplicity itself, and gave the author a user-friendly entry into the field. He would therefore recommend this model and would encourage other amateur astronomers to attempt PEP.

A total of 136 observations were made by West using the setup described. A further 19 observations were made by László Kiss, a Hungarian observer at Szeged Observatory, using a 40cm Cassegrain telescope and Optec SSP5A photoelectric photometer with the V-filter supplied. Coincident observations showed a good match between the two data sets. The accuracy is discussed in a later paragraph. The spectral response of the Optec filter was matched closely to the Johnson V-standard, thereby minimizing transformation corrections (see Reduction section). Each star count comprised three 10-second integrations followed by a background sky count.

Differential photometry was carried out using HD 116172 (V=7.0, B—V=1.1, K0III) as comparison (Co) and HD 116957 (V=5.88, B—V=0.97, K0III) as a check (Ch). The observing sequence has been modified during the course of the programme to improve accuracy and error estimation. Initially, to confirm variability, the following sequence was used:

Co, V, Co, V, Ch, Co

with further doublets of (V, Co) being added if sky transparency was judged to vary excessively, based on experience gained from reducing earlier data. Varying sky transparency, essentially noise in the raw counts, translates into increased errors. This experience aided judgement at the telescope. An adopted rule of thumb as to maintain signal to noise ratio above 100 (see discussion of accuracy). After confirmation of variability the following minimum sequence was adopted:

Co, V, Co, V, Co, Ch, Co, V, Co.

Again further doublets were added when necessary. This ensured that variable and check star counts were always bracketed by a comparison. Each star count was followed by a sky count which was subtracted at reduction.

The atmosphere causes extinction of the light reaching a detector. In PEP, allowance must be made for the fact that comparison and variable may be of different colours (B—V) and observed at different altitudes. Thus two extinction factors must in general be determined. One is for so-called ‘primary extinction’ (dependent mainly on altitude and sky transparency) and the other for ‘secondary extinction’ (colour dependence causing reddening at low altitudes). Also, any photometric system (telescope, photometer, filter) is likely to differ from the original Johnson system. For each filter, it is necessary to determine a correction factor or transformation coefficient so that observations made using different systems can be compared and combined. Methods for determining the above are given by Adams.⁶

The differential magnitudes (in the sense V—Co =∆V and Ch—Co = ∆V_k) were calculated in a spreadsheet and reduced to instrumental magnitude using:

∆V =2.5 log (N_comp /N_var).

The constancy of the selected comparison star was verified by calculating its differential magnitude relative to the check star using:

∆V_k =2.5 log (N_comp /N_check).

where N_comp, and N_check are the mean of three 10-second integrations, respectively of comparison, variable and check with sky subtracted.

k ́_v = 0.25 to 0.40

k ́ ́́́́́́́́́́́_v = 0.00

All of these values are close to accepted and published values for the SSP3 photometer system at sea level sites. The primary coefficient ḱ́́́́́́́́́_v is dependent upon sky transparency and the range shown above reflects values obtained under best and worst (photometric) sky conditions. Very similar values were obtained for the system used by Kiss, supporting the correspondence between the combined observations. These were:

k’_v =0.20 to 0.40

k" _v = 0.00

Experience has shown that the dominant source of error is sky transparency and its fluctuations with time.

Each of West’s observations yielded at least 3 measures of and one of ∆V_k. The standard deviation of the three measures ∆V_v was found and also the deviation ∆V_k from the mean of all previous ∆V_k measures. The larger of these two figures was adopted as the uncertainty. Most observations fell within a 0.01 magnitude error bar and nearly all within 0.02 mag. Any over 0.05 mag were discarded. Excessive fluctuations in star counts indicated changing sky transparency due to invisible cloud. This would be particularly evident in the five bracketing comparison star counts which ideally should provide a constant baseline. In the event of these fluctuations the sequence was increased, and during reduction the signal to noise ratio S_n obtained via:

S_n = S/N

Photoelectric photometry can achieve millimag (0.001 mag) accuracy when allowance is made for transformations, and primary and secondary extinction, but this does necessitate more thorough and time consuming observing sequences and reductions. It was decided by the authors that in order to cover a programme of some 18 stars, including BR CVn, an internal accuracy of 0.02 mag was a reasonable compromise.

Further confidence was gained in this estimate of error bars by comparison with other PEP observers of BR and other variables. These were always within 0.03 mag and nearly all within 0.02 mag.

The original data comprised 155 observations, spanning a period of 1264 days (a little under three and a half years) from 1994 May to 1997 October. These are shown plotted against time in Figure 1.

On the four occasions that two observations were made on the same night, both were removed and replaced with the average of the pair, in order to avoid giving an unjustified extra weight to these nights’ results. This was the only adjustment that was made to the data before beginning the frequency analysis. The (now 151) estimates had an average spacing of about 8.4 days, a mean value of 6.76 magnitude and a standard deviation of 0.15 magnitude.

The Discrete Fourier Transform was performed on the data to yield an amplitude spectrum, employing a method similar to that used by Howarth for the analysis of T Cas observations.⁷ The range of frequencies was 0.00025 to 0.06 cycles per day at an increment of 0.00025 cycles per day (cpd). The separation between frequencies was fine enough to ensure that no periodicity could be overlooked by falling between adjacent frequencies. The largest frequency corresponded to a period of 16.67 days, roughly twice the average time between observations. This. was felt to be a suitable compromise between avoidance of aliases and not missing any real frequencies at the high end. Inspection of the spectrum (Figure 2) shows two dominant peaks, at 0. 001405 and 0.01409 cpd, having respective half peak-to-peak amplitudes of 0.144 and 0.130 mag. The corresponding periods were 711.8 (±15.0) days and 70.9 (±0.16) days. The shorter period shows pronounced variation in magnitude, being less (about 0.1 mag peak-to-peak) at JD2449900 and much greater (over 0.5 mag peak-to-peak) at JD2450500. Both of the periods can be identified by eye from Figure 1. Nevertheless, it was decided to check for aliasing, and a spectrum of the window function was constructed (Figure 3). The relatively even distribution of observations produced a clean window function. The small peak at 0.00256 cpd (391 day period) probably reflected a seasonal variation in the density of observations, but could not explain either period in terms of the other. For completeness, the effect was tried of removing each period in turn (‘prewhitening’), and transforming the result. As expected, in neither case was the other period significantly affected.

Using the technique of photoelectric photometry over the longer term, it has been possible to record the lightcurves of stars typically in the magnitude range V = 5 to 7. Taking comparison stars of established constancy, the technique has given reliable and apparently accurate data over many years. We suggest that it is particularly applicable to red stars, which give considerable scatter when observed by eye, and for objects which have more than one periodicity in the tenths of magnitude amplitude range. The technique is recommended to other amateurs with the facility for PEP.

The observations of BR CVn yield two periodicities: of about 710 days and 71 days, the latter showing variations in amplitude of 0.1 to 0.5 mag peak-to-peak. It is not yet possible to comment on the permanence of each period until more data are obtained, or until a more thorough analysis of Hipparcos and visual data is undertaken, though the shorter period seems to have been established for many complete cycles.

In carrying out the present programme of PEP observations it is a pleasure to acknowledge the invaluable assistance given by the following: John Greaves, in drawing our attention to the Hipparcos data and for his help with the analysis; John Isles for comparative observations of TX Psc; Chris Lloyd for checking comparisons and much helpful advice on photometry; Roger Pickard and John Saxton for comparative observations of X Per; and the visual observers previously named.

Address (KW): 5 Edward Street, Ryde, Isle of Wight P033 2SH. [kwest@ryde.prestel.co.uk]

BR CVn is observed as part of a programme of long term PEP monitoring of some 18 northern declination stars, most of which are on the BAA binocular programme. At the time of writing, the main programme and number of observations comprise the following:

In addition Five Cepheid variables have been observed to obtain folded minima. Eight eclipsing binaries have been observed to obtain minima. Numerous other variables and suspects have been observed from time to time. Futher details can be obtained from West.