On the Photometric Variability of Very Sharp-lined Cool mCP Stars

We investigate the photometric variability of very sharp-lined cool mCP stars from a list published in 1970 by Dr. George W. Preston who suggested that some belonged to the long-period tail of the period distribution. In this study, we discuss our Strömgren uvby observations obtained with the Four College Automated Photometric Telescope (FCAPT) at the Fairborn Observatory for 22 of the stars in Preston’s list. We improved the periods of 11 stars. Further, we discuss results from the literature concerning the light, magnetic, and spectrum variability of these stars. Eleven of the stars are found to have periods longer than 20 days, and all but one of these stars display variations in the u and v filters that cannot be explained by the simple oblique rotator theory. We discuss some possible causes of this behavior.


Introduction
Forty-five years ago, almost all of the known photometric, spectrum, and magnetic periods of the magnetic chemically peculiar (mCP) stars were less than a month, but a few exceptions had longer periods (Preston 1970a). These were Sr-Cr-Eu or cool mCP stars. Stars in the long-period tail of the period distribution can provide information about the rigid rotator model of mCP stars, especially possible deceleration mechanisms and the differences over observed hemispheres derived at random phases in the derived elemental abundances, magnetic field strengths, and photometric observations. Are they the same as those found from faster rotating stars? To provide a framework within which to answer these questions, Preston (1970b) surveyed the rotational velocities of mCP stars brighter than m pg = 9 from which he extracted a list of 25 cool, very sharp-lined mCP stars with v sin i<10 km s −1 for the study of this problem. He also noted some efforts to find photometric variability with UBV photometry of his stars. Winzer (1974), as part of his extensive UBV survey of mCP stars, observed seven of the stars in Preston's list (HD 2453, HD 9996, HD 22374, HD 110066, HD 176232, HD 201601, and HD 204411). Of these stars, he suggested a possible period of 17.492 days for HD 201601 and a possible very small variability for HD 176232. Adelman (1973aAdelman ( , 1973b derived the elemental abundances of 21 included stars, assuming that they were constant stars. He used one high-dispersion spectrogram for each star.
Their stellar variability means that he sampled the abundances of his stars at random phases.
As part of our work using uvby differential photometric data obtained with the Four College APT (FCAPT) at Fairborn Observatory, mainly at Washington Camp, AZ, we obtained observations of 22 of our PhD thesis advisor's stars and found or confirmed photometric variations in all but five. Our study updates the efforts of Wolff to find their periods (see, e.g., Wolff & Morrison 1973). However, until now we have only published only a few results. This paper publishes analyses of all of these data. We also reference other particularly relevant studies in the literature of these stars. Table 1 contains information for the observed stars from Hoffleit (1982), Hoffleit et al. (1983), and the SIMBAD database. Included are the number of data points (new, in the case of stars with previously published data), the time interval over which the star was observed, and the observer. The FCAPT method of observations is outlined in several previous papers (e.g., Adelman 2006). The FCAPT operated from 1990 through 2014. Table 1 does not include the stars for which periods could not be determined (see Section 3).

Observations
The mean wavelengths and halfwidths of the Strömgren (1963) intermediate bandwidth filters are summarized in Table 2, which also includes the values of the 10-color photometric system (Schöneich et al. 1976) that is discussed in Section 4.16. In this paper, we are using the Strömgren bandpasses to study light variations using differential photometry. The b-y, m 1 and c 1 indices, which are used to derive the stellar properties of normal main sequence stars, are not useful in the case of the cool mCP stars due to the distorted energy distributions of these stars. In the discussions of several stars, we also refer to the β index, which measures the strength of the Hβ line using wide and narrow interference filters centered on this line (e.g., see Musielok & Madej 1988).
The spectrophotometry of mCP stars with bandwidths typically of 25 Å often exhibit broad, continuum features centered near λ4200, λ5200, and λ6300. The published spectrophotometry that detected these features was not continuous, so their profiles are only approximately known. The widths of the λ4200 and λ5200 features are about 100 Å and 900 Å, respectively, with typical depths of a few percent and 10%, respectively (Adelman 1980;Pyper & Adelman 1985). The v and y filters include the λ4200 and λ5200 features, respectively (Adelman 1979). The strengths of the features are not necessarily correlated with one another, 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.  The FCAPT is an automated telescope without an on-site observer. Thus, the users of its data have to be especially careful about which data to keep. Data from groups which were not completely observed were not analyzed. In a group, if 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). Still light curve inspections showed some obvious outliers. Then we compared the difference between the value of an apparent outlier and the value of the fit at a given phase to the standard deviation of the fit. If a point is more than three standard deviations from the fit in any filter, then all of the values in its group are removed from the data sets of all filters.

Period Determination
For stars with no previously published periods or whose previously published periods are ambiguous, we searched for periods using the Scargle periodogram program (Scargle 1982;Horne & Baliunas 1986). For stars that had good published data sets, we determined the periods that best matched these data and the FCAPT data. Table 3 summarizes the ephemerides for the stars whose periods have been determined, including those already published; the stars for which we could not determine a periodic variation are also listed. The v sin i values are from Preston (1970b) except where otherwise noted. We do not include three stars on Preston's list that were not observed with the FCAPT (HD 24712, HD 89069, and HD 187474). In most cases, the FCAPT photometry best defines the light curves, so we have chosen the values of HJD0 based on our uvby data. Also, in most cases, the FCAPT data has been used to improve the estimated precision of the periods. To estimate precision, we used the practical method of comparing the two good data sets most widely separated in time and determined how much the period had to be changed to see a definite shift in phase. The photometric data are in Tables A1-A11, which are included as supplementary data to this paper. The photometric data for the stars for which we could not determine a period are not included in the supplementary tables, but are available from either author. Table 4 lists the uvby standard deviations for these stars.

Analysis of Observations
In the following subsections, we discuss our FCAPT observations of 16 of this paper's stars that have not been reported in the literature (Section 4). When they extend previously published observations, we combine both sets of data. In Section 5, we briefly discuss our results for six other stars where we have published all our FCAPT observations. In  Wolff (1975) published only c 1 values for observations of HD 2453. By comparison with Cameron's (1966) data, Wolf proposed a period of 525 days. Optical region fluxes (Adelman 1981b) contain a moderately strong λ4200 feature and a strong λ5200 feature.  found that HD 2453 had spectral lines resolved into magnetically split components. Glagolevskij (2004) constructed a model of the magnetic field as a dipole shifted by r = 0.09R from the center where R is the stellar radius.

HD 2453 = GR And
We compared our c 1 values with those of Wolff and found the best fit was a period of 518.2 days ( Table 3 and supplemental  TableA1). As is seen in Figure 1, b and y vary in phase, u is out of phase with them, in that its maximum is at a phase of 0.8 rather than 0.0, and v varies out of phase with b and y. The light curves of v and b are double-valued, implying a complicated distribution of elements over the photosphere. The behavior of v is similar to what is seen in HD 9996, HD 196502, and HD 221568. The longitudinal magnetic field (H e ) measured by Wolff varies in phase with v ( Figure 1). Previous UBV photometry (Winzer 1974;Catalano & Vaccari 1985;Catalano & Leone 1990) had phase coverage that was too sparse for comparison with our data. The FCAPT data do not vary in the period of 546.87 days suggested by Catalano & Leone. The variation of v might be due to variations in the λ4200 feature, but it would have to vary by a large amount. There is no indication from the spectrophotometry by Adelman of variation in the blue Paschen continuum or a large variation of the λ4200 feature. We found no published data on the variations of the Balmer lines or other spectrum variations in this star. North et al. (1998) found that HD 8441 is the primary component of a triple star system. Its binary period is 106.537 days and the orbital period of the third component is more than 5000 days. Its photometric period of 69.5 days (Wolff & Morrison 1973) from Strömgren photometry was refined to 69.43 days by Rakosch & Fieldler (1978) using UBV photometry. Babcock (1958) published longitudinal magnetic field measurements for HD 8441 that do not vary in the period determined here. Auriere et al. (2007) observed longitudinal magnetic field values ranging from −20 to +157 G that vary in the period of Wolff & Morrison, and proposed a model with an offset dipole. Optical region spectrophotometry (Adelman 1981b) shows a relatively shallow λ5200 feature and a moderate λ4200 feature which may reach a minimum near light maximum.

HD 8441=HN And
Using the FCAPT u observations ( Table 1 and supplemental  Table A2) compared with the u values of Wolff & Morrison, we found that a period of 69.51 days best fits both sets of data (Table 3, Figure 2). The period of Rakosch & Fiedler was based on their incomplete phase coverage in U and is too short. The light variations are unusual in that the u filter shows a large amplitude (0.08 mag) while the v, b, and y filters all have amplitudes less than 0.02 mag. If flux redistribution from the ultraviolet is the cause of the variations of v, b, and y, there must be an additional cause of the greater variation in u, possibly variable line blanketing, although this is not indicated in the spectrophotometry of Adelman. No spectrum variations have been published for this star. Preston & Wolff (1970) first suggested that HD 9996 varies in a period of 22 to 24 years based on changes in its spectrum, magnetic field, and light. They also found it to be a single-lined spectroscopic binary with a period of 273.2 days. Metlova et al. (2014) summarized the previous observations of the longitudinal magnetic field for this star, which varies from −1670 to +650 G. They determined a period of 7940±22 days based on the comparison of the previously published data with their own. These magnetic field measurements apparently indicate a rather complicated field distribution where the maximum roughly coincides with the y/V maximum and reverses   Figure 3). It is unclear whether the large scatter around magnetic minimum indicates differences between measurement systems or changes in the magnetic variations from cycle to cycle.  found that HD 9996 had spectral lines resolved into magnetically split components. Although their phase coverage is limited, it appears that the magnetic modulus á ñ ( ) H has a maximum of about 5000 G and coincides with the minimum of the longitudinal field.

HD 9996 = HR 465 = GY And
We were able to obtain FCAPT Strömgren photometry of HD 9996 for 22 years ( Table 1 and supplemental Table A3). When the FCAPT y data are compared with the y data obtained by Pyper at Kitt Peak National Observatory (KPNO) in 1981-83 (Table 5), the best fit is for a period of 7850± 100 days (Table 3). This period is in agreement (within the errors of measurement) with the period of Metlova et al.
The values of y (0.14 mag) and v (0.15 mag) have the largest amplitudes and vary out of phase; u (0.05 mag) and b (0.06 mag) are double-valued with one maximum at v maximum and the other at y maximum. The average values/year for the FCAPT Strömgren data (Table 6) are plotted in Figure 3 along with the KPNO Strömgren data. For the y/V plot, previously published Johnson V data sets (referenced in the figure caption) are also included. No attempt was made to correct for the small systematic differences in the various data sets, which are probably due to different filter systems, comparison stars and instruments. The larger scatter in the Abt & Golson (1962) data is because they did not use differential photometry. The Eu and Cr estimated line  Table 3. Open circles represent the FCAPT Strömgren photometry. In the c 1 and H e plots, the filled diamonds are the values of Wolff (1975). Note the different scale for the c 1 plot.  Table 3. Open circles are the same as in Figure 1. In the u plot, the filled squares are the values of Wolff & Morrison (1973). strengths of Preston & Wolff (1970) and Rice (1988) are also shown; the maximum Eu line strength coincides with the y/V maximum, while the Cr line strengths vary in anti-phase with Eu with a smaller amplitude. The u and b light curves may be influenced by variable line blanketing. As is the case for HD 2453, the variation of v is difficult to explain but may be due to large variations in the λ4200 feature or variable line blanketing. It is unlikely to be due to variations in Hδ (see Section 4.16). There is no available information on line blanketing or spectrophotometry for HD 9996.

HD 12288 = V540 Cas
Wolff & Morrison (1973) observed HD 12288 using Strömgren photometry and found a period of 34.9 days. Later  Preston & Wolff (1970). The FCAPT error bars are about the size of the symbols. In the y/V plot, filled stars, pluses, and filled triangles are the V values of Abt & Golson (1962), Stepien (1968) and Winzer (1974), respectively. In the H e plot, open triangles, open diamonds and filled diamonds are the average values of Babcock (1958), Scholz (1978Scholz ( , 1983 and Bychkov et al. 2012, respectively. The Eu and Cr plots represent estimated line strengths; the filled inverted triangles are the values of Rice (1988). Note. Phase is calculated from the ephemeris in Table 3.  found a period of 24.79±0.12 days from the mean magnetic field modulus. Glagolevskij (2013) characterized its magnetic field as a central dipole. Four optical flux distributions (Adelman 1981a) show strong λ5200 and λ4200 features. In comparison of the FCAPT data (Table 1 and supplemental  Table A4) with the Wolff & Morrison data, the best match is for a period of 34.99 days (Table 3, Figure 4). The scatter is large and the amplitudes are small, with u having the largest amplitude at 0.03 mag. Figure 4 shows that v and b are in phase, but u reaches a maximum at a phase of 0.02 and y shows no variation. The magnetic data of Mathys et al. also vary in this period with the magnetic modulus reaching a maximum at approximately u minimum. The two photometric data sets do not match when the shorter period of Mathys et al. is used. No longitudinal magnetic field measurements or spectrum variations have been published for this star. 4.5. HD 22374 = 9 Tau = V486 Tau Babcock (1958) measured a small magnetic field of +140 G for HD 22374 based on one spectrogram. No other magnetic or spectrum variations have been reported in the literature. Belmonte et al. (1988) reported short timescale light variations, suggesting that it is a possible roAp star, but Martinez & Kurtz (1994) find no evidence of short-term photometric variations. Winzer (1974) measured HD 22374 in UBV and determined a period of 10.61 days, which also fit the uvby data of Wolff (1975).
This star is a rather small amplitude variable, with the smallest amplitude, 0.015 mag. in u; v and y vary by 0.020 mag., and b by 0.025 mag. We were able to refine the period with FCAPT uvby data ( Table 1 and supplemental Table A5). The Scargle algorithm for the FCAPT b data yields a most likely period of 10.646 days, and on comparison with the Wolff data, the best fit is to a period of 10.6478 days (Table 3, Figure 5). The data sets of Winzer and Wolff are too sparse and have too much scatter to compare shapes of the light curves with the FCAPT data, although the uvby data of Wolff may show a broader maximum and sharper minimum than do the FCAPT data ( Figure 5).
The u variations are slightly out of phase with v, b, and y, showing a minimum at phase 0.01. The optical spectrophotometry of Adelman (1981a) shows a moderate strength λ5200 feature and a modest λ4200 feature but the phase coverage is too sparse to be able to determine whether any variations occur. 4.6. HD 110066 = HR 4816 = AX Cvn Wolff (1975) suggested about 10 years, and Stepien (1998) suggested 13.5 or 27 years for the period of HD 110066. Winzer (1974) found no variations based on a year or less of observations. Ten spectrophotometric scans (Adelman 1981b) show a moderate λ4200 feature and a strong λ5200 feature. Babcock (1958) published five measurements over 2 years of the longitudinal magnetic field with values between −55 and +300 G; this is typical scatter for Babcock's measurements (see Babcock's data plotted in Figure 9) and is consistent with a weak constant field.  noted that HD 110066 had spectral lines resolved into magnetically split components; four observations over a period of about 500 days show no variations.
The FCAPT observations were obtained every year over a 12-year span ( Table 4). The Scargle algorithm yielded null results and plots of uvby versus HJD show no variations greater than 0.01 mag over this time range. 4.7. HD 115708 = HH Com Wade et al. (1996b) discovered that the longitudinal component of the magnetic field of the mCP star HD 115708 varies with a period of 5.0762±0.0004 days, which is consistent with that of Leroy (1995), and also takes into account observations of Babcock (1958). Wade also derived a displaced dipole model based on the magnetic variations. Adelman (1999) was able to improve the period to  Table 3. The symbols are the same as in Figure 2.  Table 3. The symbols are the same as in Figure 1.
The amplitudes of variation are 0.02 mag, 0.03 mag, 0.01 mag, and 0.015 mag. in u, v, b, and y, respectively ( Figure 6). The light curves for u and v are in phase, but out of phase with b and y. The magnetic extrema occur at approximately phases 0.4 and 0.0, close to those for light variability in u and v. This indicates a very complex surface abundance distribution.
As Adelman subsequently obtained an additional 40 good sets of uvby photometry for 2004-05 and 103 sets of uv photometry for 2009-10 and 2011-12 (Table 1 and supplemental Table A6), we decided to study all of the Strömgren photometry of this star to see if the period can be further improved and to check on its constancy. All of the FCAPT data are plotted in Figure 6, along with Wolff's data for u and v and the magnetic measurements of Wade. We improved the period to 5.07633 (Table 3), but due to the scatter in the u and v plots, the error estimate could not be improved over that of Adelman. The b and y values have smaller amplitudes and have minima at the u and v secondary minima but their maxima fall at phase 0.1. This again emphasizes the complex nature of the surface distributions of element abundances. The longitudinal magnetic field varies in phase with u and v in a single wave between −1860 and +1160 G.
It should be mentioned that there is a discrepancy in the published v sin i values for HD 115708. Preston's (1970b) original list had a value of v sin i = 8 km s −1 for this star, but his 1971 paper lists a value of 13 km s −1 . The model of Wade et al. predicts v sin i to be 14 km s −1 which better agrees with Preston's 1971 value. 4.8. HD 137909 = HR 5747 = b CrB HD 137909, one of the brightest mCP stars, has a large variable longitudinal magnetic field (Babcock 1958). Preston & Sturch (1967) found a period of 18.487 days from the magnetic data which also fit that of Borra & Landstreet (1980) and Vogt et al. (1980). Brodskaya (1970) and Adelman et al. (1992) obtained UBV observations and found that the light variation agreed with this period. Kurtz (1989) found a rotational period of 14.4868 days based on the magnetic data of Mathys (1994) and . Pyper & Adelman (1985) obtained uvby and optical region spectrophotometry and found that v and b varied with small amplitudes but that there was no evidence for the variability of the λ5200 feature. The spectrophotometry shows that the blue continuum shortward of about 4700 Å is depressed. This depression shows up in about 20% of the stars with spectrophotometric measurements. Preston (1969) and  found that HD 137909 had spectral lines resolved into magnetically split components. The magnetic modulus has an amplitude of 800 G and varies in a single wave with the same period as the longitudinal field. Bagnulo et al. (1999) produced a model to explain the variations of the longitudinal magnetic field and the magnetic modulus. They proposed a period of 18.4877 days. Glagolevskij (2013) also found its magnetic field could be characterized as a shifted dipole. Radial velocity measurements by Hatzes & Mkritichian (2004) show that it is a low-amplitude  Table 3. The uvby symbols are the same as in Figure 1. The H e values are those of Wade et al. (1996b). rapidly oscillating (roAp) star, although Martinez & Kurtz (1994) found no evidence of photometric short-term variations.
The FCAPT data for HD 137909 (Table 1 and supplemental  Table A7) shows in phase variations for u, v, b, and y with amplitudes of 0.01, 0.04, 0.015, and 0.01 mags., respectively (Figure 7). The measurements of the longitudinal magnetic field show a maximum at light maximum and at a minimum at light minimum (references given in Figure 7). The magnetic data of Borra & Landstreet are not plotted, but vary in phase with the other data. In comparison with the b data of Pyper & Adelman, we found that the best fit was for the Bagnuolo et al. period of 18.4877 days ( Table 3). This period also fits all of the previous data mentioned above and in Figure 7. One other star listed in Preston's 1970b paper, HD 81009 (Adelman 2006; Section 5.3), has FCAPT light curves similar to those of HD 137909. 4.9. HD 137949 = 33 Lib = GZ Lib Wolff (1975)'s magnetic field measurements of HD 137949 suggested a period of 23.26 days, while van den Heuvel (1971) and Kurtz (1982) suggested 18.4 days and 7.194 days, respectively, from their magnetic measurements. The energy distribution (Adelman 1981a) indicates that the blue region of the Paschen continuum is depressed, as is also the case for HD 137909.  found that HD 137949 had spectral lines resolved into magnetically split components and suggested it is rotating very slowly. HD 137949 is a roAp star (e.g., Sachkov et al. 2011).
The FCAPT data over a time interval of 14 years (Table 4) show no apparent variations greater than 0.01 mag when HJD is plotted versus magnitude. They also do not vary in the shorter periods previously published. The Scargle periodograms also show a null result for the FCAPT data. Kurtz suggested that i may be less than 10°. If this were the case, any variations would be expected to be very small and probably not detectable with the precision of the FCAPT measurements. 4.10. HD 176232 = HR 7167 = 10 Aql = V1286 Aql Although Stepien (1968), Preston (1970b), Guerrero & Mantegazza (1973), and Winzer (1974) had suggested periods of 6 to 9 days for HD 176232, Wolff & Morrison (1973) found that it was constant. Previously Babcock (1958) published five magnetic field measurements with values between +440 and −315 G; they do not vary in any of the suggested periods and suggest a weak and possibly constant field. Adelman (1981c) obtained 10 optical region spectrophotometric scans that showed at best it was slightly variable. The λ5200 feature is if present quite weak and there is no clear λ4200 feature. HD 176232 is a roAp star (e.g., Nesvacil et al. 2013).  Table 3. The open circles are the same as in Figure 1. In the b plot, the filled circles represent the b values of Pyper & Adelman (1985). In the H e plot, the filled triangles, open squares, crosses, and inverted open triangles represent the values of Wolff & Bonsack (1972), Mathys (1994), , and Vogt et al. (1980), respectively.
The FCAPT data over a time interval of 12 years (Table 4) show no apparent variations greater than 0.01 mag when HJD is plotted versus magnitude. They confirm the findings of Wolff & Morrison in that they do not vary in the shorter periods previously published. We also found no period for the FCAPT data from the Scargle periodograms.

HD 191742
Babcock (1958) measured three magnetic field values from −175 to −913 G for HD 191742. As for HD 176232 and HD 110066, this is consistent with a weak constant field. Wolff & Morrison (1973) considered it to be a non-variable star. Adelman (1981c) found it has definite λ4200 and λ5200 broad, continuum features. The Scargle periodograms show null results for the FCAPT data for 11 years (Table 4). Likewise, the HJD versus mag. plots do not show variations greater than 0.01 mag. in any of the uvbyfilters. Thus, we agree that this star is constant within the precision of our measurements. 4.12. HD 196502 = 73 Dra = AF Dra HD 196502 has long been recognized as a spectrum and magnetic variable (Morgan 1933;Durham 1943;Babcock 1958). Stepien's (1968) UBV photometry established the period as 20.2754 days. Preston (1967) measured the longitudinal magnetic field and spectrum variations, Bonsack & Markowitz (1967) also measured spectrum variations that agree with those of Preston and Wolff & Bonsack (1972) did further magnetic measurements; all vary in the period found by Stepien. Stepien  Table 3. The open circles are the same as in Figure 1. In the y/V plot, the filled triangles represent the V values of Stepien (1968), normalized to agree with the FCAPT y values. In the H e plot, filled squares and open diamonds are the values of Preston (1967) and Wolff & Bonsack (1972), respectively. In the Cr/Fe and Eu/Ti plots, open squares, crosses, filled circles, and open triangles are the estimated line strengths of Preston (1967) for Cr, Fe, Eu and Ti, respectively.
(1989) produced a model for HD 196502 showing that i = 90°, i.e., the star is seen equator-on.
The FCAPT data (Table 1 and supplemental Table A8) show that the variations are double-valued with u having the greatest amplitude of variation at 0.06 mag, while v, b, and y have amplitudes of 0.025, 0.02, and 0.02 mag., respectively. The light curves are complicated in that u, b, and y are in phase and v is out of phase with them ( Figure 8). We compared the FCAPT y with the V of Stepien and found that both agree with Stepien's period within the errors of measurement (Table 3).
Stepien's V values appear to have a slightly larger amplitude than the FCAPT y , but both data sets are too sparse to provide strong evidence for this. The longitudinal magnetic field data of Preston and Wolff & Bonsack display a maximum at u maximum and a minimum at y/V maximum (Figure 8). Preston's measurements of the spectrum variations show that Mg, Cr, and Fe are at a maximum at u maximum and Ti, Mn, and Eu have maxima at y/V maximum (Fe, Cr, Ti and Eu are plotted in Figure 8). The y/V variation thus may be attributed to flux redistribution from the ultraviolet, probably due to variations of the REE. That the primary maximum in u falls at the secondary maximum in y/V may be due to the Cr and Fe variations, but they are of much smaller amplitude than those of Eu. The variations of v remain unexplained. The β index measured by Musielok & Madej (1988) varies with a small amplitude in phase with v, so the variation of Hδ cannot account for the v variation. 4.13. HD 201601 = HR 8097 = g Equ = 5 Equ Babcock (1958) observed the magnetic field of HD 201601 between 1946 and 1956, and found it varied from +185 to +880 G. Bonsack & Pilachowski (1974) suggested a period of order 70 years based on magnetic observations. Mathys (1991) compared his measurements of the longitudinal magnetic field with previously published values and found a decline from +400 to −1000 G over about 7000 days and suggested that it may have a period of about 100 years. Later,  found that it had spectral lines resolved into magnetically split components. Optical region spectrophotometry (Adelman 1981b) shows that HD 201601 has a very flat Paschen continuum energy distribution compared with other mCP stars. Its λ5200 feature is very weak. Huber et al. (2008) discuss the MOST photometry of this roAp star. Strömgren photometry is contained in Manfroid et al. (1995).
The Scargle algorithm yielded no period over the 14 years of FCAPT observations (Table 1 and supplemental Table A9). Because there are y or V values overlapping the time span of the magnetic data from several authors (listed in the Figure 9 caption), we plotted yearly averages of the y/V magnitudes and magnetic values versus HJD (Figure 9). The FCAPT data extend beyond the most recent magnetic measurements and show a slight upward trend in brightness. The FCAPT v and b magnitudes are not plotted but show a similar increase in brightness over the same period. Although speculative, there does appear to be a slight decrease in brightness from JD2439000 to 24345000, which is about the magnetic low point. Thus, the photometric data show weak support for a possible 95 to 100-year period for HD 201601. 4.14. HD 204411 = HR 8216 Preston (1970b) suggested that HD 204411 might possibly be a long-period variable due to differences in the description of its spectrum and its UBV colors. Spectrophotometric scans (Adelman 1981c) show a weak λ5200 feature. Adelman (2003) discussed FCAPT photometry of this star from 1990 to 2002. There were slight changes in its b and y values that were suggestive of long-term variability. Auriere et al. (2007) discovered a weak longitudinal magnetic field (approximate range 0 G to −100 G) that varies with a period of 4.8456 days; they did not publish a precision for this period. They derived a model with i = 7°and β = 5°to explain the magnetic measurements.
In this paper, an additional decade of photometry is presented. The most recent FCAPT data (Table 4) when  Deul & van Genderen (1983), and the y values of Manfroid et al. (1995) and FCAPT (this paper), respectively. In the H e plot, the filled stars, filled triangles, pluses, filled squares, and filled inverted triangles are the values of Babcock (1958), Bonsack & Pilachowski (1974), Stepien (1979), Borra & Landstreet (1980). and Mathys (1991), respectively. combined with the previous FCAPT data show no periodic variability when analyzed with the Scargle algorithm or when plotted versus HJD. The small changes seen by Adelman (2003) seem to occur after the system was changed and can probably be ascribed to instrumental effects. The period of Auriere et al. is not detected in the FCAPT data either in the entire body of data or when analyzed by year. This is not surprising if their model is correct, as the star would be seen almost pole-on and the magnetic and rotational axes are almost the same. It is therefore reasonable to expect any variations to be below the level of detection for the FCAPT photometry. Babcock (1958) discovered that the Sr II lines were variable in the cool mCP star HD 216533. Later, Wolff & Morrison (1973) found uvbyvariability with a period of 17.20 days. Floquet (1979) noted that there was no synchronism between the orbital motion with a period of 16.03 days and the rotation of the star. Floquet also derived a model based on spectrum variations and the photometry of Wolff & Morrison. In this model, all of the variable elements appear to be concentrated in a large spot near the negative magnetic pole; however, this is based on only three measurements of the magnetic field by Babcock (1958). Optical spectrophotometry (Adelman 1981a) shows a modest λ4200 feature and a strong λ5200 feature. There are not enough observations to determine if these features are variable.

HD 216533 = MX Cep
The three years of FCAPT observations (Table 1 and  supplemental Table A10), in comparison with the u, b, and y photometry of Wolff & Morrison, enabled us to improve the period to 17.2280 days (Table 3, Figure 10). The FCAPT u, b, and y magnitudes vary in phase with amplitudes of 0.05, 0.03 and 0.015 mags, respectively. The v magnitude only varies by 0.01 mag. and is probably in phase with the other filters. Floquet's (1979) measurements of variable lines show that Sr, Mg and Ti are at maximum strength at light maximum, which agrees with the oblique rotator explanation for the light variations in u, b, and y. Floquet (1977) also measured the variations of Hγ, Hδ and Hε in HD 216533. All vary in phase with maximum strength at a phase of about 0.8. This variation may account for the small amplitude of v, since that filter includes Hδ. Musielok & Madej (1988) noted that Osawa's star HD 221568 had the largest variations of the Balmer line equivalent widths among the then investigated mCP stars. Kodaira (1967) carried out an extensive study of the spectrum and found variations of a number of elements, principal among them being the REE, Si, Fe and Cr. Schöneich & Zelwanova (1985) performed 10-color photometry whose variability agreed with the 159.0 day period of Nakagiri & Yamashita (1979) from UBV photometry. We found no published magnetic field measurements.

HD 221568 = V436 Cas
The FCAPT uvby light curves ( Table 1, TableA11) confirm the results of Schoeneich & Zelwanowa. By comparison with their data, we were able to improve the period to 159.10 days  Table 3. The open circles and filled squares are the same as in Figure 2. The á ñ W W plot represents the normalized Sr/Mg/Ti equivalent widths from Floquet (1977). ( Table 3). The effective wavelengths and bandwidths for the 10-color system (Schöneich et al. 1976) used by Schöneich & Zelwanowa are summarized in Table 2. As can be seen in Figure 11, the U, X, Y, and V light curves vary with u, v, b, and y, except that Y may be fainter than b at phase 0.0. The Strömgren light curves are very similar to those of HD 9996 in that they are double-valued, implying a complicated distribution of elements over the surface of the star, and vis out of phase with u, b, and y ( Figure 11). For HD 221568, the amplitudes are 0.05, 0.17, 0.04, and 0.12 mag. for u, v, b, and y, respectively. Kodaira's measurements show that Eu II, Si II, and Fe I vary in phase with all the Strömgren and 10-color filters except for v, P, and X, while Cr I varies weakly in antiphase to them (Figure 11). It is difficult to account for the out of phase v light curve, which is also displayed by the X and P magnitudes (Figure 11). Possible causes for this behavior could be variable line blanketing in this region of the spectrum or variable hydrogen line strengths, as v includes Hδ, X includes both Hδ and Hε, and P includes H7 through the Balmer limit. However, when we look at the variations of the β index measured by Musielok & Madej (Figure 11), we see that Hβ is strongest at v maximum. This is also the case for Hγ which was measured by Kodaira (1967). We thus consider it reasonable to assume that all the Balmer lines vary with Hβ and Hγ, which means that the hydrogen line variations would have the effect of decreasing the amplitude of variation of v, X, and P. The longer wavelength S, MR and DR filters show the same variation as do y and V and thus all may reflect flux redistribution from the ultraviolet, possibly due to Si, Fe and the REE. The u, b, U, Y, and Z filters may be also affected by line blanketing but we lack information about line blanketing for HD 221568. Any variations in the broad, continuum λ4200  Table 3. The open circles are the same as in Figure 1. The filled triangles are the values of Schöneich & Zelwanova (1985) for U, P, X, Y, and V. The filled circles represent the measurements of Musielok & Madej (1988). The filled squares, open squares, crosses, and filled inverted triangles are the normalized equivalent widths á ñ ( ) W W from Kodaira (1967) for Eu II, Si II, Fe I and Cr I, respectively. feature would affect the v and X magnitudes but not P. There is no spectrophotometry for this star, so we have no information about this feature.

FCAPT Analyses of Stars with Previously
Published Observations 5.1. HD 5797 = V551 Cas Walther (1949) suggested that HD 5797 may be a Sr variable. Optical spectrophotometry (Adelman 1981a) shows that HD 5797 has a very strong λ5200 feature and a strong λ4200 feature. The three complete scans of λ3300-7100 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 bright pole, but weakly in phase near the other pole. Semenko et al. (2011) obtained seven measurements of the longitudinal magnetic field. Wolff (1975) obtained 22 sets of differential Strömgren photometry of HD 5797 with HD 5380 as the comparison star; the best period was 69.0 days. Recently, Dukes & Adelman (in preparation) analyzed 343 groups of FCAPT Strömgren photometry of this star. Using the Period04 period-finding program (Lenz & Breger 2005), they determined the period was 68.0457 days ( Table 3).
The variation in the v filter is unusual, as it has the smallest amplitude and is double-valued. This may be due to variations of the strong λ4200 feature, the Hδ line, variable line blanketing, or a combination of the three. There is no information available on line blanketing or Balmer line strengths. Adelman's spectrophotometry indicates that the λ4200 feature may vary by 0.015 mag., but it would have to vary by more than 0.04 mag. to account for the observed variations in v. The u, b, and y variations are in phase with a decreasing amplitude with wavelength from 0.05 mag. to 0.03 mag. This star will be discussed in further detail by Dukes & Adelman (in preparation).

HD 18078
Adelman (1981b) noted that differences among three spectral energy distributions of HD 18078 supported variability. Its λ5200 broad, continuum feature is strong while its λ4200 feature has moderate strength.  found that it had spectral lines resolved into magnetically split components. Mathys et al. (2016) combined measurements of the magnetic field modulus from 1990 to 1997 with determinations of the mean longitudinal magnetic field 1999-2007 to find a rotational period of 1358 days ( Table 3). The magnetic field to first order is a collinear multipole field whose axis is offset from the center of the star. This result is consistent with FCAPT uvby photometry observed between 1995 and 2004, although there are gaps in the phase coverage. This is the only long-period star observed with the FCAPT in which u, v, b, and y all vary in phase. The plot can be seen in Mathys et al. 2016. 5.3. HD 81009 = HR 3724 = KU Hya = ADS 7334 Optical spectrophotometry (Adelman 1981a) exhibits a λ5200 feature of a least moderate strength with λ4200 features that are quite different from one another. Recently, Adelman (2006) presented new observations of HD 81009 which agreed with the earlier period he found (Adelman 1997) of 33.984 days. However, when we re-examined all the FCAPT v data and compared them with the v values of Wolff (1975), we found that a slightly longer period of 33.987 days better fits all the data ( Table 3). Because the v light curve minimum is the best defined for this star, we changed the value of HJD 0 to reflect this. The light curves are interesting in that u, v and b are all in phase but the v light curve shows an amplitude of 0.06 mag. (Figure 12), which is much greater than those for u (0.015 mag.) and b (0.02 mag.); y is constant. This behavior is similar to that of HD 137909 (Section 4.8) and HD 188041 (Section 5.5). Possible causes of this behavior might be variable line blanketing in this region of the spectrum or variations of the λ4200 broad continuum feature, but they would have to be greater than 0.04 mag. to account for the variation. Adelman's (1981a) measurements of this latter feature show a large scatter but there are only three measurements and they are of limited phase coverage. There is no information available on line blanketing.

HD 126515 = FF Vir
Adelman & Sutton (2007) considered FCAPT Strömgren photometry of HD 126515 used by North & Adelman (1995) and FCAPT photometry obtained after the publication of that paper. They found that all the FCAPT photometry fit the period of 129.99 days found by North & Adelman. Mathys et al. (1997), on the other hand, suggested a period of 129.95±0.02 days from the mean magnetic field modulus compared with Preston's (1970a) data. The 129.99-day period is a bit too long, as there is a shift between the data sets of Mathys et al. and Preston when plotted with this period. The 129.95-day period is more likely to be correct due to its being based on precise data values in the Mathys et al. and Preston data ranges, which are about 38 years apart (Table 3, Figure 13). The error of measurement in the period quoted by Adelman & Sutton is 0.04, so it is the same within that error as the 129.95-days period; in fact, we see no phase shift in the FCAPT data between the 1990-91 and 2004-05 observing seasons when plotted with this period. The light curves for v, b, and y are close to being in phase, but differ considerably from those for u, which reaches a maximum at a phase of about 0.80 ( Figure 13). We have changed the HJD 0 in Table 3 to correspond to the v and y minima, which are sharp and welldefined. Preston (1970a) proposed a model where the star is seen near to equator-on, while Glagolevskij (2013) indicates that HD 126515 exhibits a transverse shifted dipole. The longitudinal magnetic field variations ( Figure 13) have an unusual shape with a sharp minimum and maximum. The maximum coincides with the maximum brightness in u, but not v, b, and y. It is also unusual that the minima of these last three filters do not coincide with an extremum of the magnetic field. The light variations in v, b, and y is what would be expected in the oblique rotator model, as the spectrum variations of Ti, Eu, Si, and Cr measured by Preston all vary in phase with them (Eu and Si are plotted in Figure 13). It is unclear what is the explanation for the u light curve, although variable line blanketing may be a factor. 5.5. HD 188041 = HR 7575 = V1291 Aql Adelman (2007) found that his FCAPT measurements of HD 188041 agreed with the period of 223.826 days found by Mikulášek et al. (2003). We adjusted the value of HJD 0 to a more precise value for v minimum ( Table 3). The Strömgren photometry of Jones & Wolff (1973) shows that the v amplitude (0.09 mag.) is much greater than that of y (0.01 mag.) and is out of phase with it; the b data are consistent with no variation. They also found that u (0.02 mag.) varies in phase with v. The FCAPT data show that v is out of phase with ywith the same amplitudes as measured by Jones & Wolff, and that b and u do not vary ( Figure 14). The small variation in u measured by Jones & Wolff could also be the case for the FCAPT data, but it is masked by the larger scatter. Glagolevskij (2013) reported that the magnetic field of HD 188041 is best described as a shifted magnetic dipole. The longitudinal magnetic field measured by Babcock (1954) and Wolff (1969) reaches a maximum at v minimum and b and y maximum. Babcock noted that the line strengths of Sr, Eu, and Gd vary in phase with the magnetic field; he estimated the line strength of Gd II (Figure 14). These variations may account for the y variation, but not that of v. The β index (Musielok & Madej 1988) varies in phase with v and so cannot explain the v light curve. The small variations or lack of variation of u, b, and y are also puzzling, given the moderate variations of Gd. 5.6. HD 192678 = V1372 Cyg Adelman (2006), using FCAPT measurements from 1995 to 2005, determined a period of 6.4193 days for HD 192678 ( Table 3). The v, y, and Hipparcos (ESA 1997) light curves are constant, while the amplitudes for u and b, which are plotted in Adelman (2006), are about 0.014 and 0.011 mag., respectively.
The optical energy distribution of HD 192678 (Adelman 1981c) shows strong λ4200 and λ5200 features. Comparison of the three scans are consistent with the low level of variability found by the photometry. Wade et al. (1996a) proposed a magnetic field consisting of an oblique rotating dipole with modified field line inclinations. Their model shows that the star is seen close to pole-on (i = 15°), which may account for the small amplitude of photometric variation. Leroy (1995) and Glagolevskij (2000) also proposed HD 192678 had a magnetic field with a central dipole.  found that HD 192678 had spectral lines resolved into magnetically split components.  Table 3. The uvby symbols are the same as in Figure 1. The H e values are those of Wade et al. (2000).

Discussion and Conclusions
One of the main goals of our FCAPT photometric project was to improve the periods of a large number of mCP stars in order to clarify the way their various parameters interact. In this respect, we were able to accomplish this for the majority of the stars on our program list. One of our goals was to see whether the photometric behavior of these stars can be explained by the oblique rotator theory, which supposes that the light variations are due to aspect effects as the star rotates due to a patchy distribution of elements in the photosphere resulting in flux redistribution from variable line blanketing in the ultraviolet. Variable line blocking in the visible region of the spectrum may also be a factor. The Rare Earth elements, Si, Fe, and Cr have been suggested to be the primary causes of these variations. If this is the case, all of the mCP stars that display light variations must have non-uniform photospheric patches of some elements. Such variations have been detected in only a few stars, but this may be due to the difficulty of measurement because of the large number of lines in the spectra of these stars. For the 22 stars discussed here, we have FCAPT uvby data for 10 long-period variables that we define (after Mathys 2008) as having periods greater than 30 days, with a subset of four stars with periods longer than 500 days. Clearly, this latter group is not a complete population, as there are more long-period variables discovered by  from their magnetic variations. For the stars having periods shorter than 20 days, we have FCAPT data for 25 more cool stars, which will be addressed in further publications, so we will only mention a few commonalities among the seven sharp-lined stars with periods less than 30 days. We can only mention trends due to the small number of stars and the fact that many of them do not have published data for longitudinal magnetic fields or spectrum variations. Adelman & Woodrow (2007) Table 3. The open circles are the same as in Figure 1; the filled circles are the values of Preston (1970a published a summary of the amplitudes of the FCAPT stars observed by Adelman, including those discussed in this paper (see Table 1). We intend to expand this study in a future summary paper. Of the stars in this paper, we were unable to detect any periodic variation in 6 stars, but our y data provide some supporting evidence that γ Equ has a period of about 95 years. Another of these stars, HD 204411, apparently has a short period, but photometric variations are not detectable because it is seen very near to pole-on. HD 137949 (33 Lib) may also fall in this category, but its rotational period remains unknown. For the other three stars, there is not enough information available to determine whether they are slow rotators, are seen pole-on or are not variable.
For the stars with determined periods, the three stars with periods greater than 500 days broadly resemble all the shorter period mCP stars with Strömgren photometry; this is true as well for magnetic fields and spectrum variations. For example, HD 9996 (7850 days) and HD 221568 (159 days) have very similar light curves and HD 196502 (20 days) also shows some similarities. Thus, it seems that the variations are consistent with rotation in all these cases, probably even that of γ Equ (HD 201601), which may have a rotation period of about 95 years.
To date, no period changes have been detected in any mCP stars with periods longer than two days. Period changes have been discovered in a few hot, short-period mCP stars such as CU Vir (Pyper et al. 1998(Pyper et al. , 2013 and 56 Ari (Adelman et al. 2001) and several others have been reported (see Mikulášek 2016). We have unpublished FCAPT photometry for several of these stars and will discuss this phenomenon in detail in future publications. To test for period changes, one requirement is to have several years of observations with good phase coverage. Our observing program was designed to produce good-quality light curves to improve the periods of the stars, so this criterion is met by the FCAPT observations for most of the stars discussed here whose periods have been determined. The exceptions were the three stars with periods longer than 500 days and HD 8441 for which we had only one year with complete phase coverage. For the remaining stars, we determined periods that matched all the FCAPT data. Another important criterion to detect period changes is to have available at least two good sets of data with complete phase coverage, separated by a large time span, which is also the case for these stars. As a check on the constancy of the periods of the 12 stars in this paper meeting the above criteria, we compared yearly plots with large enough FCAPT data sets using our bestdetermined periods. We found no evidence for any period changes in our data or in comparison with previously published Figure 14. Photometric, magnetic and spectrum variations of HD 188041 according to the ephemeris in Table 3. The open circles are the same as in Figure 1. The filled Hexagons represent the uvby values of Jones & Wolff (1973). The filled triangles are the values of Babcock (1954) and the open squares are those of Wolff (1969). The Gd plot shows Babcockʼs estimated line strengths. data for this group of stars, as is seen in the figures. This provides further support for the idea (e.g., Borra et al. 1985) that magnetic braking is the primary cause of the slow rotation periods of the cool mCP stars and that most, if not all, of this process must occur in the pre-main sequence stages of these stars, since their longer periods would require a much more efficient braking mechanism than could occur during the main sequence stage (e.g., see Glagolevskij 2003).
As we have noted above, four of the stars discussed in this paper are confirmed roAp stars. The well-studied roAp star HD 24712 is also included in Preston's 1970 list, but was not observed with the FCAPT. Besides their short-term pulsations, these stars are cool (most are later than A5) and the pulsations appear to be associated with the stars' surface magnetic fields (Martinez & Kurtz 1994). Because we are concerned with rotational periods here, this raises the question as to whether there is any relation between the roAp oscillations and the rotations of these stars. Of the stars we studied, the rotation periods of 33 Lib (HD 137949) and 10 Aql (HD 176232) are unknown; while γ Equ (HD 201601) probably has a very long rotational period (95 years?) and β CrB (HD 137909) rotates with a period of 18.5 days. Kurtz et al. (2006) published a list of 36 known roAp stars, including the stars mentioned above. From the references in that paper and in Renson & Manfroid (2009), we found published rotational periods for 12 more of them in addition to γ Equ and β CrB, plus 2 roAp stars discovered from data from the Kepler satellite (Kurtz et al. 2011;Smalley et al. 2015). So in all, there are two roAp stars with periods greater than 30 days (both uncertain) and 14 stars with periods less than 30 days (three uncertain). This does not appear to be significantly different from the distribution of periods of the cool mCP stars in general. A re-examination of this situation will have to await the determination of rotation periods for the remaining currently known roAp stars and the discovery of more roAp stars. Additionally, there does not appear to be any correlation between the period of the shortterm oscillations and the rotational periods of these stars.
Of the 10 stars that have periodic variations and published longitudinal magnetic field variations, we found that all display extrema of the light variations at or near one or both of the extrema of the magnetic field. In many cases, this conforms to the oblique rotator theory, as the element overabundances (especially of the rare earth elements) that cause the light variations have been found to occur at the zones of maximum field strength that are at the magnetic poles. However, this is not true of all filters in every case.
For the five stars that have published measurements of spectrum variations, the case is not so clear-cut. HD 216533 shows uvby maxima at the maximum strength of Sr, Mn and Ti, which all vary in phase. These are the only elements detected to vary, but it is not clear that they can provide the ultraviolet opacity required to account for the uvby light variations. Prvák et al. (2016) computed light curves for the Si star j Dra from a model of surface element distributions. The calculated light curves agree fairly well with the measured light curves, which are all in phase. This agrees with the predictions of the oblique rotator model and this paper provides an objective confirmation of this prediction. The authors attribute the light variations to ultraviolet absorption by Si and Fe, but in HD 216533, neither of these elements is seen to vary. For HD 9996, HD 196502, and HD 221568, Eu and Cr vary out of phase and in HD 221568 Si and Fe also vary in phase with Eu. This may account for the double-valued variations of u, b, and y, as all have peaks at both Eu and Cr maxima. However, in HD 9996 and HD 221568, v varies strongly in anti-phase to Eu and this is also true for HD 196502 although the latter variations are of smaller amplitude. For HD 188041, Gd, Eu, and Sr vary in phase and these variations are also in phase with the very small amplitude variation of y but in this star v also varies strongly in anti-phase with these elements. For HD 126515 Ti, Si, Cr, and Eu, all vary in phase and are also in phase with v, b, and y, while the u filter is out of phase with them.
In general, of the stars discussed here with periods greater than 20 days, all but HD 18078 show anomalous behavior of the v and/or the u filter observations which are difficult to explain according to the oblique rotator theory, which predicts that all four filters should vary in phase. The u anomalies include variations in anti-phase to v, b, and y, maxima and minima that are shifted with respect to v, b, and y and in HD 8441 a variation that is in phase but whose amplitude is much greater than those of v, b, and y. It may be possible to explain these behaviors in terms of variable line blanketing in the region covered by the u filter in combination with flux redistribution from further in the ultraviolet.
The v light curve anomalies are harder to explain. The v filter contains the Hδ line, as well as the λ4200 broad, continuum feature. If either or both of these are variable, they could affect the v light curve, as can variable line blanketing in this spectral region. We cannot say much about the variations of the λ4200 feature because the published spectrophotometric scans have only sparse phase coverage, but the data that are available do not indicate strong variations of this feature. For HD 216533, the measured variations of Hδ are in the correct sense to explain the smaller amplitude of v in this star. There are six stars where v varies out of phase with y. Three of them have published variations of the β index. In all three of these stars, the β index is greatest at v maximum, which should cause v to vary in phase with u, b, and y, but with a smaller amplitude (if we assume that Hβ and Hδ vary in phase). This would appear to rule out the variations of Hδ as the cause of the anti-phase variations of v in these three stars and possibly the other three stars in this group as well.
We hope to have a clearer picture on the nature of the uvby variations after we discuss the rest of the stars observed by the FCAPT (in preparation). Even for the subset of stars discussed here, it is clear that further spectrophotometry and information on variable line blocking would be very useful in attempting to address the relationship of the Strömgren light curves to overall models of the stars.