Studies of FCAPT uvby Photometry with Period04: The mCP Stars HD 5797, HD 36792, HD 27309, HD 47913, HD 74521, HD 120198, HD 171263, and HD 215441

We present differential Strömgren uvby Four College Automated Photometric Telescope (FCAPT) observations of eight magnetic chemically peculiar stars: HD 5797, HD 26792, HD 27309, HD 49713, HD 74521, HD 120198, HD 171263, and HD 215441. Our data sets are larger than those of most mCP stars in the literature. These are the first FCAPT observations of HD 5797, HD 26792, HD 49713, and HD 171263. Those for the other four stars substantially extend published FCAPT data sets. The FCAPT has observed some stars for a longer time range and with greater accuracy than other optical region telescopes. We determine very accurate periods and u, v, b, and y amplitudes, as well as if there are any long-term periods. Further, we compare our results with those of magnetic field measurements, when they exist, to help interpret the light curves. For each star, we used the Period04 computer program to analyze the uvby light curves. This program provides errors for the derived quantities. Our derived periods of 68.0457 ± 0.0200 days for HD 5797, 3.80205 ± 0.00015 days for HD 26792, 1.5688908 ± 0.0000046 days for HD 27309, 2.135361 ± 0.000031 days for HD 49713, 7.05053 ± 0.00024 for days HD 74521, 1.3857690 ± 0.0000058 days for HD 120198, 3.99744 ± 0.00015 days for HD 171263, and 9.487792 ± 0.000049 days for HD 215441 are refinements of the last determinations in the literature. We also found a low-frequency term for HD 49713 in all four filters.


Introduction
The chemically peculiar stars of the upper main sequence are identified by the spectral absorption lines of certain elements that are anomalously strong (or weak) for their spectral type. According to Preston (1972), the various subtypes based on spectral classification can be grouped into four types, one of which is the magnetic Ap stars or the magnetic chemically peculiar (mCP) stars. (The spectral types of the variables in Table 1 show some of their subtypes.) This group contains all of the early-type (late O-early F) mainsequence stars in whose spectra magnetic fields have been determined, as well as those stars with similar spectra. The magnetic fields and light curves vary periodically with a range from about one-half day to decades (see, e.g., Preston (1970), Adelman & Woodrow (2007)). Their magnetic variations are frequently accompanied by synchronous light and spectrum variations (Preston 1971). Leckrone (1974) found using OAO2 observations that the optical region variability of the mCP star HD 215441 was produced by a time variable redistribution of flux from the ultraviolet to visible spectral region due to the rotation of the photosphere with its nonuniformly distributed anomalous abundances, which are usually greater than solar except for helium, which tends to be underabundant. The region near the bandpass λ2980 varies in phase with the visible. Near the bandpass λ2460 the star is essentially photometrically constant, and shortward of λ2460 the star varies 180°out of phase with the visible. Molnar (1973aMolnar ( , 1973b previously found similar behaviors for the mCP variable stars α 2 CVn and ò UMa, and this appears to occur in all mCP stars. Later, Adelman (1983) studied the optical region spectrophotometry and showed that the effective temperature of HD 215441 was constant. The location of the constant region appears to depend on the stellar effective temperature. In the cooler mCP stars, it can be longward of λ4000. The variability seen in visible intermediate band and broadband filter photometry can be modified by the broad λ4200 and λ5200 features (see below). These features vary in strength and in phase among the mCP stars. The variability depends on the observed hemisphere of the photosphere.
The mCP stars have non-aligned rotation and magnetic axes with emergent energy distributions, abundances, and magnetic field strengths being functions of photospheric position. Hence, when such a star rotates, a distant observer can see photometric, spectrum, and/or magnetic variability. Hydrodynamical processes, including radiative diffusion and gravitational settling, act in the radiative envelopes that have strong magnetic fields and produce anomalous photospheric abundances, particularly in regions where the field is nearly vertical. The values depend on the local magnetic field strength and the evolution of the field and the elemental abundances, at least since when the stars were on the zero-age main sequence (Michaud & Proffitt 1993). The photometric variability is explained in terms of the abundance spots, see, e.g., Shulyak et al. (2010), and its study is usually the primary technique to determine the rotation period since photometric observations require less time and can be made with smaller telescopes than magnetic or high-dispersion spectral observations. A knowledge of the stellar magnetic configuration should help interpret the photometric variability. Most mCP stars have dipolar magnetic fields. What one observes depends on these factors and on the angle of inclination of the rotation axis to the sky; the angle between the magnetic axis and the rotation axis; the configuration of the magnetic field; the limb darkening; and for spectra the stellar rotational velocity. Limb darkening is greater towards shorter wavelengths.
Studies by Adelman and his coauthors using uvby differential photometric data from the Four College Automated Photoelectric Telescope (FCAPT) now at Fairborn Observatory, Washington Camp, AZ, have found or improved the periods and light curves of 68 mCP stars (see Adelman & Woodrow (2007) for references to individual studies). These investigations relate observations taken at different times and have detected variable light curves see, e.g., Adelman (2006). Adelman & Woodrow (2007) used this ensemble of photometric variable stars to conclude by extension that all mCP stars are intrinsic photometric variables. Further, Aurière et al. (2007) found that all their firmly classified mCP stars showed detectable magnetic surface fields and that there was a magnetic threshold for such stars. Thus, all mCP stars are both photometric and magnetic variables and by implication spectrum variables due to the Zeeman effect. Hence, detecting one of the three types of variability for a star with a mCP spectral type means that it also varies in the other two ways that may or may not be easy to detect. Table 1 presents photometric information for the eight stars of this paper from Hoffleit (1982), Hoffleit et al. (1983), and the SIMBAD database. Paunzen & Maitzen (1998) used the extensive Hipparcos Variability Annex (ESA 1997) to search for peculiar A stars included in catalog of mCP stars of Renson (1991): HD 26792, HD 49713, and HD 171263 are three such stars. The spectral types of the mCP stars with just new FCAPT photometry are from Renson & Manfroid (2009). Our photometry was obtained with the FCAPT. It measures the dark count and then in each filter sky-ch-c-v-c-v-c-v-c-ch-sky for each group of variable (v), check (ch), and comparison (c) stars where sky is a reading of the sky. Corrections were not made for any neutral density filter differences among the stars of each group. We chose the comparison and check stars from presumably nonvariable stars according to Hipparcos photometry (ESA 1997) or some previous photometric study that are near the variables on the sky with similar V magnitudes and B-V colors if possible. Strömgren (1963) intermediate bandwidth filters have mean wavelengths of λ3500 for u, λ4110 for v, λ4670 for b, and λ5470 for y with halfwidths of 300 Å, 190 Å, 180 Å, and 230 Å, respectively. The spectrophotometry of mCP stars with bandwidths typically of 25 Åoften exhibit broad, continuum features centered near λ4200, λ5200, and λ6300. Thus the v and y values are affected by such features (Adelman 1979). Their strengths are not necessarily correlated, which complicates the interpretation of the results (Pyper & Adelman 1986). Khan & Shulyak (2007) explain the λ5200 depression in terms of Si, Cr, and Fe overabundances. Table 2 contains a sample of the FCAPT photometry of analyzed stars in this paper. A complete version is included in the electronic version of this paper. For some stars, it contains some data taken with different filters as noted in the discussions in Section 3. Due to the summer monsoon season in southern Arizona, no observations are normally possible between early July and late September. The first observing season for the FCAPT was fall 1990 through spring 1991.

Photometry
Without an observer at the site monitoring the weather, quality control depends on a several part process of closely inspecting the data. We excluded data from groups which were not completely observed as they were probably affected by clouds and/or by telescope and instrumental problems. If in the group observations, any of the standard deviations of the comparison-check star values exceeded 2% of the average values, we excluded all the observations of a group so affected, following Strassmeier & Hall (1988).
Even after carefully removing points judged bad on the basis of the comparison minus check values, the inspection of the light curves revealed some obvious outliers. The difference between the value of an apparent outlier and the value of the fit at a given phase is compared with the standard deviation of the fit. Any points with a value more than three standard deviations from the fit in any filter are removed from the data sets of all filters.

Analyses
From the available software packages designed for period analysis, including some we have written, we adopted Period04 by Lenz & Breger (2005) as our standard tool. Period04 was designed for sophisticated nonuniformly spaced time string analyses and it includes tools to both extract the individual frequencies from multiperiodic time series and perform multifrequency fitting. We found a preliminary rotation period from the Period04 periodogram for each filter and then used the accompanying non-linear least square tool to refine this period. We then repeated the periodogram analysis on the residuals from the fit to determine other periods. In this way, we found the higher harmonics for those stars with non-sinusoidal light curves and the low-frequency terms described below. Table 3 contains the fitting parameters for our eight stars, while Table 4 shows the derived ephemerides along with the published results. We used for JD0 the same values as the older ephemerides whose sources are indicated. The error bars were found from functions in Period04. After comparing results from analyses of the normalized versus unnormalized data, we based our analysis on the unnormalized data. We found possible lowfrequency terms in three of the eight stars. These are a puzzle, but could be due to seasonal changes in instrumentation, sky conditions, etc. Indeed, we first assumed that this was the case here. We initially inspected a plot of all the data versus time looking for any seasonal variation that might be due to instrumental effects. We then normalized the data so that the seasonal mean of the variable minus comparison data was zero. Even after this adjustment, program analysis reveals the presence of possible low-frequency terms in three data strings. The low-frequency terms in HD 5797 and HD 26792 did not pass the test based on the signal-to-noise ratio (S/N). On the other hand, the strength of those in HD 49713 leads us to believe that this term is present in the variation of the star. The possibility that the low-frequency found in HD 47913 is real is bolstered by the suggestion of Shore & Adelman (1976) that the rotation axis of the mCP star 56 Ari precesses about the magnetic axis. Then, due to the nonuniform surface brightness, one might expect to see variability due to a precessional period in the photometry, the magnetic field, and/or spectra. Adelman et al. (2001) presented and analyzed observations whose results are consistent with this theory. They found a secondary period of 5 years. Further, Pyper & Adelman (2005) showed Strömgren FCAPT photometry of some mCP stars that showed differences in shape for different observing seasons.   We also plotted the longitudinal magnetic field values of HD 5797, HD 27309, HD 74521, HD 120198, and HD 215441 with the photometry as there are sufficient values to cover the periods.

HD 5797
HD 5797 (V551 Cas, BD+59 163, HIP 4717) is a very sharp-lined mCP star. Carrier et al. (2002) gave the upper limit as v sin i3km s −1 . Walther (1949)discovered it was a    spectrum variable. Wolff (1975) obtained 22 sets of differential Strömgren photometry using HD 5380 as the comparison star. A period of 69.0 days best fit the data, but three other periods could not be eliminated. Based on the variation of the correlation depth for just 12 spectroscopic observations, Carrier et al. (2002) found a period of 68.02±0.10 days. Adelman (1973) and Semenko et al. (2011)performed abundance analyses of this metal-rich spectrum variable. The latter authors obtained seven measurements of the longitudinal magnetic field. When they plotted their phases according to the ephemeris of Wolff (1975), they found that this data followed a sinusoidal curve. The extrema of which were near +1000 Gauss and −150 Gauss, suggesting that one pole definitely crosses the observed disk. New photometry for HD 5797 was obtained by the FCAPT in years 1995-96 (17 values Table 2, but due to the differences in neutral density filters it was not included in the final analysis.
The periodogram for data in all four filters of HD 5797 is given in Figure 1. The phase diagram is given in Figure 2. The amplitude of variation is greatest in u. The v variation is unique in having both the smallest amplitude and an apparent period one-half the periods determined from the other filters. The amplitude of the second harmonic is therefore greater than the  amplitude of the first harmonic. However, the amplitude of the first harmonic is still significant.
Optical spectrophotometry of HD 5797 (Adelman 1981) shows that it is a cool mCP star with a very strong λ5200 feature and a strong λ4200 feature. The three complete scans covering λ3300-7100 Å show variability over this wavelength interval. Both features show scan-to-scan differences in their profiles. The λ4200 broad, continuum feature which lies in the v bandpass, may be varying opposite that of the rest of the optical region near the brighter pole, but weakly in phase near the other pole. Cowley & Cowley (1965) found that HD 26792 (DH Cam, BD+56 899, HIP 20004) was a Sr subtype mCP star. While no magnetic field detections have been reported in the literature, its photometric variability was found by Hipparcos photometry (see Paunzen & Maitzen (1998)). As a result of the spectroscopic classification and the photometric variability, HD 26792 is considered to be a mCP star. The  Figure 3. In Figure 4, the weak maximum in the light curve is at phase 0.5, while the much stronger one is at phase 0. The u amplitude is several times greater than the other filters. Further, the ratio of amplitudes of the first harmonic to second harmonic is smallest in u and greatest in v (u=1.64, v=2.93, b=2.32, y=2.77).

HD 26792
The u light curve can also be viewed as having a complicated minimum with two sub-minima. There are suggestions of this behavior especially in the b light curve, but the smaller  amplitude makes it difficult to confirm. We again see a diminution of the amplitude of the v light curve, presumably due to the presence of a λ4200 broad, continuum feature that Adelman (1979) found was present in about 90% of the mCP stars.

HD 27309
Winzer (1974) discovered with UBV photometry that the mCP star HD 27309 (56 Tau, V724 Tau, HR 1341, HIP 20186) was a large-amplitude photometric variable. Musielok et al. (1980) refined it to 1.5691 days. Adelman (1975Adelman ( , 1977 examined Wolff's (1967) optical region spectrophotometry and detected the presence of a λ5200 broad continuum feature that he later (Adelman 1982) found to be variable. North & Adelman (1995) used both Geneva and Strömgren photometry to improve the ephemerides of this variability. They found no evidence for any secular change in the light curve. They found a period of 1.5688840±0.0000047 days. The amplitudes are 0.055 mag. for u, 0.018 mag. for v, 0.028 mag. for b, and 0.027 mag. for y. Previous UBV observations were also made by Nikolov (1974) and Musielok et al. (1980). The Geneva values were made in 1971-73, 1979-80, 1984, and 1987 Table 2.
The u periodogram ( Figure 5) shows that a significant second harmonic exists in the rotational modulation. This is evident in the non-sinusoidal nature of the phase curves ( Figure 6). The other periodograms show a similar behavior. The phase curves show that the primary maximum has a blocky shape, perhaps due to two spots rather than a more sinusoidal shape as suggested by North & Adelman (1995).

HD 49713
Walther (1949) first classified HD 49713 (V740 Mon, BD-01 1395, HIP 32745) as a peculiar A star. Kazarovets et al. (1999) found it was a variable mCP star. Two magnetic observations of +2200 and −2880 Gauss indicate that it has a strong reversing magnetic field (Kudryavtsev et al. 2006). If the magnetic field is dipolar, then both poles are observed. Niemczura et al. (2009) Figure 7 shows strong power up to the third harmonic, making this the most asymmetric of the eight stars being studied. The light curves of this star shown in Figure 8 demonstrate this asymmetry. The optical region is variable in synchronism. The rising branch covers about 60% of the light curve between approximately phases 0.45 and 0.05. The maximum and the minimum occur at slightly different phases for each light curve. This photometric asymmetry is not that expected for a dipolar magnetic field whose axis goes throughout the stellar center. When the periodograms of other filters are similar to one shown, they are not plotted. Besides an offset magnetic dipole, HD 49713 might have a higher order magnetic field such as, for example, a quadrupole.  . This star has the lowest amplitude variation of any of the eight stars in the current paper. The magnetic field data is from Bohlender et al. (1993) and from Mathys (1994).

HD 74521
Previous photometric measurements of HD 74521 (HR 3465, 49 Cancri, BI Cancri, HIP 42917) include those of Stepien (1968), Winzer (1974), Rakosch & Fielder (1978), Lanz & Mathys (1991), and Catalano & Leone (1993). Adelman (1998)  Historically, the small amplitudes made it difficult to find the period. Adelman & Pyper (1979) obtained 13 optical spectrophotometric observations and found that the λ4200 and λ5200 broad, continuum features may be variable. Shorlin et al. (2002) find v sin i=10 s −1 . One needs to prewhiten for the fundamental period to see clearly the second harmonic in the periodogram (Figure 9). Individual light curves are asymmetric with the rise to maximum light taking longer than the fall to minimum. They have low amplitudes (Figure 10).   Wade et al. (1998). The magnetic field is varies approximately in phase with the light variation. Leone (2007) made two measurements of the effective magnetic field of HD 74521 which were 1030±30 and 794±28 G. Hubrig et al. (2007) measured a mean longitudinal magnetic field of 813 G. But their model parameters depend on a period 10% too long. More recent magnetic field values are those of Bohlender et al. (1993) and Mathys (1994). Catalano et al. (1998) discovered that HD 74521 was variable in the infrared, but they failed to tabularize their data and their period was incorrect. Wraight et al. (2012) found a period of 6.9071 days using STERO satellite photometry. Celestia 2000 (ESA 1998) yields a period of 7.0517 data from Hipparcos photometric data. Since the u, v, b, and y light curves do not have exactly the same shapes, they are best not combined with the Hipparcos photometry as did Leone (2007) to give a period of 7.0486 days. Table 3 lists our derived period as 7.0505 days. The asymmetric light curves indicate that the magnetic field could be an offset dipole and/or we are seeing at least two spots. Rice & Wehlau (1994) found that HD 120198 (HR 5187, HIP 67231, CR UMa, 84 UMa) exhibits modest spectrum variability. They refined the rotational period of Burke & Barr (1981) based on UBV photometry to be 1.380682 days. Their Doppler imaging study of the Cr and Fe abundance distributions resulted in complex maps which are similar to one another. Wade et al. (1998) used their longitudinal magnetic field measurements and FCAPT uvby values to find a period of 1.38576±0.00080 days which was inconsistent with previously published values. Analysis of the magnetic measurements indicated a weak dominantly dipolar magnetic field with the following parame-tersi=59°, β=48°, and B d =1620 G. Further they found that HD 120198 was close to the Zero Age Main Sequence in the Hertzsprung-Russell Diagram. The u, v, b, and y light curves have amplitudes less than 0.02 mag. Those of b and y appear to be in phase with that for v having a smaller amplitude and a light minimum with a larger range in phase. The u light curve is more complex with the part near light minimum similar to those of b and y, but its light maximum occurs at a different phase than those of the other three light curves. Shorlin et al. (2002) find its apparent rotational velocity is 45 km s −1 .

HD 120198
We analyzed 453 uvby values of HD 120198. The 70 for year 6 (1995-1996) and 44 for year 7 (1996-1997) were also studied by Wade et al. (1998) Wade et al. (1998). We used the zero Figure 13. Periodogram of HD 171263 There is little aliasing allowing the weak 2f term to stand out without pre-whitening.  Table 4). Strong aliases make identifying the fundamental frequency in the periodogram difficult ( Figure 11).
We show in Figure 12 the longitudinal magnetic field measurements of Wade et al. (1998) whose negative minimum is close to the minimum of the uvby light curves. But the magnetic curve shape differs somewhat from those of these photometric light curves, possibly as the magnetic field and photometric measurements are sampling photospheric quantities, which are distributed over the observed photosphere in somewhat different manners. Slettebak & Nassau (1959) classified HD 171263 (QU Ser, BD+05 3786, HIP 90990) as a peculiar A star, but no detections of its magnetic field have been reported in the literature; it is considered to be a magnetic star for the same reasons as HD 26792.

HD 171263
The  (Figure 13) shows little aliasing allowing the weak 2f term to stand out without prewhitening. The results for b, v, and y are similar. The light curves for this star are similar to those of HD 215441, but not so sinusoidal (Figure 14). That is, there is the hint of a second maximum which appears more as a flattening of the minimum in the u filter while the amplitude is smallest in the v filter. The periodograms of the four filters are similar which reflects that the light curves are in phase. A problem in analyzing the photometry is that the period is close to 4 days. Each observing season only covers part of the light curves as the observed phase changes slowly at a given time of the night. Babcock (1960) discovered that the peculiar A star HD 215441 (GL Lac, HIP 112247, BD+54 2846) had a 34 kG variable magnetic field. Jarzebowski (1960) found its large photometric variability and its period of 9.49 days. Other sources of significant photometry are Cameron (1966), Stepien (1968), Blanco et al. (1973), Schoeneich et al. (1976, Musielok & Madej (1988), Zverko & Panov (1983), and North & Adelman (1995). The last pair of authors used Geneva photometry taken    with 42 values. Despite the large amplitude, these authors found only one harmonic was sufficient to fit the observations. The amplitudes are 0.094 mag. for u, 0.067 mag. for v, 0.073 mag. for b, and 0.059 mag. for y. The light curves are in-phase and can be described as sinusoids with only the first harmonic being present. Both Babcock (1960) and Preston (1979) observed only subtle spectrum variability. Adelman (1983) made 14 spectrophotometric observations of HD 215441 and found variability (see also Adelman & Pyper 1993). The energy distribution shows a large λ5200 broad, continuum feature which is still prominent after correction for E(B-V)=0.21 of interstellar reddening. Leone et al. (1996) discuss its radio spectrum.

HD 215441
The u periodogram is shown in Figure 15. Unlike HD171263 (Figure 13), the second harmonic is not apparent without prewhitening. As seen in Figure 16, magnetic minimum for HD 215441 agrees with light minimum, but light maximum and magnetic maximum are offset. This observation lead Glagolevskij (2009) to derive the magnetic configuration of HD 215441 in terms of the offset-dipole model, a result confirming the Doppler-Zeeman map of Khokhlova et al. (1997) and found i=67.5°and β=10°. Borra & Landstreet (1978) obtained magnetic field measurements of HD 215441 with an Hβ Zeeman analyzer. They discuss the measurements of Babcock (1960) and Preston (1969) made with photographic plates.
We used 293 uvby values for HD 215441. They include 33 from year 1991-92 and 41 from year 1992-93 used by North & Adelman (1995) North & Adelman (1995). For u and y the light curves are sinusoidal, while for v and b very small contributions are made by the second harmonic. The light curves are for practical purposes in phase. The North & Adelman (1995) ephemeris is marked B min , which is really the numerical minimum that is the light maximum. We used the zero epoch of North & Adelman (1995) for our ephemeris given in Table 4.

Discussion
As expected, the analyses of these eight mCP stars lead to more accurate periods that can be used to better phase photometric, spectroscopic, and magnetic field data over a longer date range. This is also important in studying the magnetic field configurations and Doppler imaging studies. Similar studies taken a decade or more in the future might reveal somewhat different light curves. The relatively large number of high-quality photometric observations of these stars resulted in well-defined amplitudes for both the first and higher harmonics. For five of the stars, the absence of a long period indicates that their light curves are extremely stable. For HD 5797 and HD 26792, the observed long period might be instrumental. The strength of the observed long period of HD 49713 seen in all four filters indicates its origin is likely to be stellar. To confirm these conclusions, additional photometry is desired. Photometry of additional stars with similar observing windows should be examined to see if the low-frequency variation is similar. If the origin is photometric errors, we would expect data from other stars with similar amounts of data to also show these effects. In this case, we need to understand why the amplitudes vary between data sets for different stars. However, if the long periods are intrinsic to the stars themselves, then further study should show different amplitudes and periods for each star. For seven stars, the analyses revealed statistically constant periods as usually are found for mCP stars. However, this conclusion is statistically stronger than those of the usual photometric studies of such stars, but for HD 49713, we found a statistically real long period of 1.56 years. The best documented case for a similar mCP star is 56 Ari. Adelman et al. (2001) found a long period of more 5 years. It supports the model of Shore & Adelman (1976) that the rotation axis is precessing about the magnetic axis. The low discovery rate for this effect could be due to the quality and range of the data studied or could reflect that a detectable effect will be found only in a small percentage of mCP stars.
Our attempts to phase our photometry with the currently available magnetic field data did not yield consistent results for those stars with both magnetic and photometric data. The Pyper & Adelman (2017) study of sharp-lined cool mCP stars confirms this result. Radiative diffusion theory indicates that the magnetic field poles should coincide with light extrema. New observations of the magnetic field around the rotational period should be useful in interpreting the light curves and the location of the magnetic poles. Further, for those stars exhibiting some rotation, a Doppler Imaging Analysis could be performed with high-dispersion spectra. This would indicate the distribution of elemental abundances over the stellar surface. The spots are regions where the abundances are usually greater than solar in which case the atmospheric structure has been modified by enhanced line blanketing and flux distribution from the ultraviolet to the optical region. When a new spectrophotometer, such as ASTRA ) becomes operational, instead of four data points of order 500 measurements covering the optical spectra will become available. This data should be a major aid in interpreting the variability of mCP stars.
To try to understand the nature of these stars we have drawn on the work of Mikulasek et al. (2007). The variation of effective amplitude with wavelength is related to the nature of the spots on the surface of the star as well as the paths of the spots across the observed hemisphere. In an effort to express quantitatively and compare the variation in amplitude with wavelength for these mCP stars we calculated an effective amplitude for each filter for each star. We added in quadrature the amplitudes of the various harmonics for each filter. This is similar to, but less sophisticated than, the effective amplitude defined by Mikulasek et al. (2007). The results are shown in Figure 17. We see that all except HD 49713 are similar in appearance with the minimum effective amplitude occurring in the v filter. On the other hand, HD 49713 has essentially the same effective amplitude for the three shortest wavelength filters with the y filter being somewhat lower. Figure 18 shows the same data with each amplitude being Figure 19. Ratios of the effective amplitudes for higher order harmonics to that for the first harmonic. Again, arranged in order of increasing central wavelength. The legend is the same as that for Figure 17. HD 5797 and HD 74521 deviate from the pattern of the other six stars that have their largest amplitude for the u filter. Figure 18. Effective amplitudes (as described above) normalized to the amplitude in the u filter. The legend is the same as that for Figure 17. normalized to the u amplitude for that star. Here, HD 74521 stands out with the b amplitude being significantly higher than the others. HD 215441 shows the smallest variation of amplitude with filter after HD 49713.
We also investigated the relative effective amplitudes of the higher harmonics compared with the first harmonic. These are shown in Figure 19. Deviations from sinusoidality are indicative of the distribution of the spots on the surface of the star. From this, we find HD 5797 and HD 74521 showing quite different behavior than the other stars; for these stars, we noted that the v variability could be due to that of the λ4200 feature. For the other six stars, the 2f frequency has a S/N4 which is the accepted value for being statistically significant except for y in HD 49713 and in HD 215441 and for v and y in HD 74521 and in HD 120198.
Comparison with the light curve examples given by Mikulasek et al. (2008) lets us classify these stars into one of their four types. Thus, HD 5797, HD 26792, and HD 120198 belong to group 1, which is described as "a double-wave light curve with two unequally prominent bright spots centered at phases 0 and 0.5." HD 27309, HD 47913, HD 74521, HD 171263 and HD 215441 belong to group 2 described as "a single wave light curve."