We have obtained photometric observations of the peculiar RR Lyrae star V442 Her during six observing seasons spanning an elapsed time of nearly nine years. The period has undergone two large, abrupt changes in the past five years. Although light curve modulation is not unusual among RR Lyrae stars, the modulation of the light curve of V442 Her is unique for its large amplitude, long period, extreme alterations in light curve shape and large period changes.
We have undertaken a survey of 107 bailey type ab RR Lyrae stars to determine the frequency and characteristics of multiperiodic behavior among such objects. Multiperiodicity will be identified by observing the stars near the phase of maximum light and identifying those in which the magnitude of maximum does not repeat well from one cycle to another. As of now, observations have been finished for about two-thirds of the survey sample. Rather than await the conclusion of the survey, results for interesting individual stars from the sample will be published as they are completed. This is the first in a series of such papers.
Although V442 Her is classed as a Bailey type ab RR Lyrae star in the General Catalogue of Variable Stars (Kholopov 1985), a light curve obtained by Schmidt (1991; see also Schmidt and Reiswig 1993) exhibited an amplitude of only a few tenths of a magnitude, much too small for such a star. Furthermore, the shape of the light curve did not resemble either a Bailey type ab or type c RR Lyrae. Subsequently, Lee (1997) included V442 Her in his survey of light curve modulation among RR Lyrae stars. His observations during 1995 produced a light curve similar in shape and amplitude to that from the earlier observations. In both 1991 and 1995 there was evidence of significant changes in the variation over times of two or three months. We have monitored this star since that time and now have observations in six seasons spanning nearly nine years. This paper presents all of those observations and demonstrates the extreme behavior of this star compared with other RR Lyrae stars.
Photometry in the V and R bands was obtained with the CCD photometry system on the Behlen Observatory 0.76-meter telescope. The methods used in obtaining and analyzing the data were the same as described earlier (Schmidt 1991 and references therein). In the case of the present observations, there were three comparison stars of which two were used for most of the observations. They are listed in Table 1 where the first column identifies the star and the second gives its number in the HST Guide Star Catalogue (in the format rrrrnnnn where rrrr is the small region of the GSC and nnnn is the star number in that region). Columns three through eight contain the mean magnitudes and colors of the stars and their standard errors (in milimagnitudes). Column nine indicates the number of nights which were used in forming the mean magnitudes and colors. For stars C1 and C2, these numbers refer to photometric nights with adequate standard stars for all-sky photometry. Star C3 was not observed on such nights and its magnitudes and color in Table 1 are based on differential measurements relative to C1.
Comparison Stars
| Star | GSC Number | V (mag) | s.e. (mmg) | R (mag) | s.e. (mmg) | V-R (mag) | s.e. | n |
| C 1 | 31112054 | 14.101 | 8 | 13.595 | 9 | 0.508 | 9 | 9 |
| C 2 | 31111434 | 12.677 | 6 | 12.602 | 9 | 0.076 | 6 | 11 |
| C 3 | 31110957 | 15.108 | 3 | 14.735 | 5 | 0.374 | 4 | 44* |
* There were no photometric nights on which C3 was observed. The mean magnitudes and color are based on differential measurements relative to C1.
Table 2 summarizes the data we have obtained. Column one lists the year of the observations, while column two gives the range of Modified Heliocentric Julian Date (MHJD = HJD - 2,440,000) over which the data were obtained. The third and fourth columns list the number of nights on which observations were obtained and the number of individual light curve points obtained. The individual observations of the variable have been placed in the IAU Archives of Unpublished Variable Star Observations as file number 340E. See Breger (1990) for a description of the archives and how to access data in them.
Log of Observations
| Year
|
Range of
MHJD |
Number of Nights | Number of
Observations |
| 1991 | 8102--8192 | 11 | 26 |
| 1995 | 9871--10002 | 10 | 362 |
| 1996 | 10233--10357 | 20 | 294 |
| 1997 | 10655--10796 | 15 | 171 |
| 1998 | 10845--11138 | 24 | 276 |
| 1999 | 11251--11299 | 2 | 22 |
Within each season we have divided the data into between two and five subsets. The subsets were selected to span an interval short enough to encompass little change in the light curve while still containing an adequate number of data with adequate phase coverage to define the light curve. The subsets are listed in Table 3 where the first column gives the year of the observations and the second column displays the range of MHJD included in each subset. Column 3 indicates the plot symbol for that subset in Figure 2. The number of nights on which observations were made and the number of observations are listed in columns four and five. Note that these numbers do not always total to the corresponding values in Table 3 since some points did not meet the criteria for inclusion in any subset. When possible, we have determined an epoch of maximum light (column six of Table 3 ) and its estimated uncertainty (column seven), the amplitude (column eight) and the intensity mean magnitude (column nine) for each subset. When either maximum or minimum light was not present in our light curve, we have reported the difference between the brightest and faintest observation as a lower limit for the amplitude.
Summary of the Subsets of the Photometry
| Year | Interval of MHJD | Sym* | # of nights | # of obs. | MHJD of maximum | ± | V | <V> |
| 1991 | 8102.8--8112.8 | a | 4 | 7 | 8110.64 | 0.01 | >0.15 | 12.78 |
| 8149.6--8192.6 | b | 7 | 19 | -- | -- | 0.27 | 12.82 | |
| 1995 | 9871.7--9885.9 | a | 3 | 53 | 9885.68 | 0.01 | 0.44 | 12.82: |
| 9958.6--9986.7 | b | 6 | 277 | 9974.73 | 0.03 | >0.19 | 12.84: | |
| 10002.6--10002.7 | c | 1 | 32 | -- | -- | >0.19 | -- | |
| 1996 | 10233.7--10238.9 | a | 2 | 14 | 10238.73 | 0.03 | >1.00 | 12.86: |
| 10260.6--10267.9 | b | 4 | 99 | 10265.72 | 0.01 | 1.24 | 12.83 | |
| 10279.6--10304.7 | c | 6 | 42 | 10288.72 | 0.01 | >1.33 | 12.82 | |
| 10320.6--10332.8 | d | 2 | 28 | -- | -- | >0.82 | -- | |
| 10340.6--10357.7 | e | 6 | 111 | 10353.71 | 0.01 | 1.39 | 12.82 | |
| 1997 | 10655.6--10656.9 | a | 2 | 32 | 10655.71 | 0.01 | 0.87 | 12.81 |
| 10702.6--10709.7 | b | 3 | 43 | 10705.64 | 0.01 | >0.53 | -- | |
| 10717.6--10723.7 | c | 3 | 39 | 10723.74 | 0.03 | 0.54 | 12.83 | |
| 10726.5--10740.7 | d | 4 | 42 | 10731.71 | 0.01 | 0.49 | 12.88 | |
| 1998 | 10893.8--10921.9 | a | 8 | 50 | 10894.81 | 0.01 | 0.73 | 12.82 |
| 10950.6--10985.9 | b | 4 | 96 | 10950.91 | 0.01 | 0.98 | 12.80 | |
| 11013.6--11019.9 | c | 2 | 18 | 11013.67 | 0.01 | 1.04 | 12.75 | |
| 11034.6--11047.8 | d | 4 | 72 | 11047.70 | 0.01 | 0.99 | 12.80 | |
| 11068.7--11096.7 | e | 4 | 38 | 11075.53 | 0.04 | >0.81 | 12.80: | |
| 1999 | 11251.8--11299.9 | a | 2 | 22 | 11299.86 | 0.02 | 0.80 | 12.78 |
*Symbols in Figure 2: a, circles; b, triangles with vertex up; c, triangles with vertex down; d, diamonds; e, crosses.
An examination of the data showed that a single period could not be found which was valid over the entire interval of our observations. We have plotted the O-C diagram in Figure 1 using maxima listed in Table 3 . The predicted dates of maximum were determined with a period of 0.44194 days and an epoch of MHJD = 10705.64 which were derived form the data from 1997 and 1998 (MHJD = 10655—11097). The maximum from 1991 was omitted from the plot because the gap of four years until the next maximum precluded a meaningful cycle count.
Some RR Lyrae stars have been observed to exhibit steadily increasing or decreasing periods over number of years while in others the period is constant most of the time with sudden changes. In Figure 1 we show fits to the observed phase shifts using both assumptions (and omitting one point as discussed below). The parabola (dashed line ) is a fit for a steady decrease in period while the series of three straight lines (solid line) represents the case with sudden period increases. The solid lines clearly represent the better fit to the data. Thus, we will adopt the assumption that the period of V442 Her is stable over intervals of one or two years with sudden period changes.
The point farthest to the left in Figure 1 appears to be anomalous. To accommodate it we would have to adopt a period of 0.407 days or less prior to MHJD = 9958. On the other hand, the data from MHJD = 9958 - 10003 (the second and third subsets of data from 1995) require a period of about 0.442 days, consistent with observations from 1996, MHJD = 10233 - 10358. A period change of 0.035 days or more during a single observing season is implausibly large. For this reason and because of the light curve peculiarities discussed below, we have neglected the left-hand most point in determining the period of V442 Her. The adopted period which is implied by the fitted line before MHJD 10560 in Figure 1 is 0.44223 ± 0.00003 days.
Unfortunately, failure of the CCD photometry system terminated the observations during the 1999 season and we were only able to obtain a single epoch of maximum light. Figure 1 shows that this epoch is inconsistent with the 1997/1998 period. However, there are unresolved ambiguities. The point and line plotted in Figure 1 for 1999 correspond to a period of 0.4416 days (i.e. a decrease of 0.0003 days) on the assumption that a sudden change occurred at the end of the 1998 season. A larger change and hence shorter period would be obtained if the change had occurred later. On the other hand, if we decreased the cycle count between 1998 and 1999 by one, the derived period would increase to 0.4424 (an increase of 0.0005) which is equally plausible. Without further data, we can not resolve these ambiguities and adopt the shorter period. This has no effect on the discussion below.
Period changes apparently occurred near MHJD 10560 (between the 1996 and 1997 observing seasons) and after 11060 (at or after the end of the 1998 observing season). The adopted periods and epochs listed in Table 4 for the various observing seasons. All of these periods were based on the above discussion except that for 1991. That period was determined from a power spectrum analysis of all the data for that year.
In Figure 2 all of our photometry for V442 Her is plotted against phase calculated with the appropriate periods and epochs from Table 4. Data from each season is presented as a separate panel. Points from the various subsets defined in Table 3 are denoted by different symbols as indicated in the third column of the table.
Adopted Ephemerides for V422 Her
| Year | Period | ± | MHJD of maximum |
| 1991 | 0.4414 | 0.00005 | 8110.64 |
| 1995,1996 | 0.44223 | 0.00003 | 10288.72 |
| 1997,1998 | 0.44194 | 0.00005 | 10705.64 |
| 1999 | 0.4416* | ------ | 11299.86 |
If period changes in RR Lyrae stars were produced by stellar evolution, they would generally be very small, much less than a day per million years (Sweigert & Renzini 1979 and Lee 1991) and might be expected to produce a smooth, continuous increase or decrease in the period. Although many RR Lyrae stars exhibit continuous changes at rates consistent with evolution, there are numerous stars which exhibit larger rates. Some exhibit long intervals of constant period with sudden increases or decreases while others show random changes which are difficult to catagorize (see Tsesevich 1972 for a discussion of field stars, Smith 1995 and references therein for stars in clusters and Sweigert and Renzini 1979 for a theoretical discussion). In many cases, limited temporal coverage and uncertainties in times of maximum obscure the behavior.
As noted above, during the past five seasons V442 Her has undergone two abrupt period changes of DP @ 3 × 10-4 days separated by 1.3 years. In a large majority stars where abrupt period changes have been observed, they are one or more orders of magnitude smaller than this (e.g. Tsesevich 1972, Table 4 lists 42 field stars with abrupt period changes ranging from 0.015 × 10-4 days to 0.76 × 10-4 days; Storm et al. 1991 list period changes for ten stars in M5 which range up to 0.32 × 10-4 days; Smith and Sandage 1981 list period changes for 30 stars in M15 which range up to DP = 0.34 × 10-4 days ; Clement et al.1993 list period changes for 23 stars in M68 which range up to DP = 0.31 × 10-4 days; Stagg and Wehlau 1980 found that V25 in NGC6934 had a period increase of DP @ 1.6 × 10-4 days). Note that most of these stars exhibit only a single period jump in many decades of monitoring. In those with more than one change, the changes are normally separated by at least 20 years.
Stars which may be similar to V442 Her in regard to their period changes are V 104 in w Cen (Belserene 1964), SZ Hya (Tsesevich 1972, Figure 4) and DI Lyr (Tsesevich 1977). w Cen-V104 may have exhibited period decreases of DP @ 4 × 10-4 days and DP @ 3 × 10-4 days separated by about 13 years. However, this is uncertain in as much as the temporal coverage would permit a parabolic fit to the O-C diagram which is nearly as good as several line segments. In the case of SZ Hya, there may have been two period decreases of DP @ 1 × 10-4 days separated by about ten years or, as Tsesevich suggests, the period may have decreased steadily by 2 × 10-4 days over ten years. DI Lyr experienced a period increase of DP @ 4 × 10-4 days followed by a decrease to the original period four years later.
As indicated above, any discussion of period changes in RR Lyrae stars is confused by the difficulty of interpreting some of the (O-C) diagrams. However, it is clear that the size of the period changes in V442 Her and the relatively short interval between them are extreme compared with most other RR Lyrae stars and may even be the most extreme case known.
As can be seen from Figure 2 and from Table 3, the amplitude of V442 Her undergoes large changes from one year to another and significant changes over times of weeks or months. The measured amplitudes and lower limits are plotted against MHJD in Figure 3 (again omitted data from 1991). The two maxima near MHJD 10350 and 11000 and the minima at 10000 and 10700 suggest a time scale of about 700 days. On the other hand, if the small amplitude in 1991 represents another minimum, it would require a somewhat longer modulation period, about 900 days. We conclude that the amplitude of V442 Her varies irregularly over a time scale somewhat less than a thousand days.
An inspection of Figure 2 shows that the appearance of the light curve changes completely as the amplitude varies. For example, during 1996 (Figure 2c) when the amplitude was large, the light curve was typical of a Bailey type ab RR Lyrae star. The changing amplitude over the four months spanned by the observations is typical of stars exhibiting the Blazhko effect. Similarly, in 1998 (Figure 2e) the star also exhibited a light curve that would be classed as type ab. However, even though the amplitude was similar in 1996 and 1998 and both times are during an interval of increasing amplitude, there are significant differences in the appearance of the light curve. In 1996 there was a flat minimum lasting about a third of the cycle followed by a rapid rise to maximum in less than five percent of the cycle. On the other hand, in 1998 the minimum was rounded and the rise to maximum occupied about twenty percent of the cycle.
During 1991 (Figure 2a) and 1995 (Figure 2b), times of small amplitude, the light curves did not resemble an RR Lyrae star at all. Although the variations repeat well from cycle to cycle over a short interval, over a period of weeks there are significant changes. A peculiarity of the 1995 data is the apparent maximum at phase 0.61 and the sequence of points sloping downward to a magnitude of 12.95 at phase 1.0 (solid circles in Figure 2b). This feature is the source of the anomalous maximum in Figure 1 which was discussed above. These points were taken on three nights in a two week interval at the start of the 1995 season with a large majority on a single night (MHJD = 9885.67 - 9885.87). Given the fact that the data from the latter part of 1995 are consistent with the period indicated by the 1996 observations, we speculate that the maximum may, in fact, correspond to the small bump around phase 0.6 in the data from the latter part of the observing season. That would then suggest that a relatively large bump was present at the start of the 1995 observing season and decreased over several months. At the same time, the maximum appears to have increased although it is poorly defined due to the gap near phase 0.
Finally, we note that during 1997 (Figure 2d) the star was at an intermediate, decreasing amplitude. While the earliest data in that season exhibit a type ab light curve similar to that observed in 1998, by the end of the season the top of the light curve appears to be truncated. This produces a humped light curve reminiscent of those shown for type II Cepheids by Diethelm (1983, his type BL). This behavior is unknown among RR Lyrae stars and appears to represent a stage in the transition between typical RR Lyrae behavior and the peculiar small amplitude behavior.
In our 1996 light curve (Figure 2c) the latest data (MHJD = 10340 - 10358, crosses) leads the data from 70 to 80 days earlier (MHJD = 10260 - 10268, triangles with vertex up) during rising light by about 0.02 cycles. Similar phase shifts are apparent in the 1998 data (Figure 2e). Phase changes relative to a long term mean period are relatively common in Blazhko stars (Lee 1997). For example, in RR Lyrae itself, the phase of maximum drifts by about 0.05 cycles over the Blazhko cycle (see the light curves shown by Walraven 1949).
The last column of Table 3 lists the intensity mean magnitude of V442 Her during the various intervals of the observations. The reliability of these numbers is strongly influenced by the phase coverage and some are marked as uncertain for that reason. A close examination of all of the data shows that nearly all of the values of <V> given in the table are consistent with the hypothesis that as V442 Her experiences its large light curve modulations the mean magnitude remains constant. As would be expected, the <V> - <R> colors are even more constant so we conclude that the modulation does not generally affect the mean luminosity of the star. The only exceptions are the mean magnitudes for MHJD 10717.6 - 10723.7 and 10726.5 - 10740.7. In (Figure 2d) it can be seen that the maxima in both those intervals, denoted by triangles with vertex down and diamonds respectively, do not reach the level of the previous well-defined maximum (circles) while the brightness around minimum is similar, particularly in the 10726.5 - 10740.7 interval. This indicates that we observed a genuine diminution in the luminosity of the star by about 5% at the end of the observing season. Thus, the mechanism which produced the apparent chopping off of the peak of the light curve redistributed a significant amount of energy and there should be a subsequent increase in the luminosity to maintain long term equilibrium. Unfortunately, the next data was 150 days later and the star had apparently returned to its equilibrium luminosity by then. Link to (Figure 2f)
The Blazhko effect in RR Lyrae stars can produce changes in amplitude, phase drift and changes in the shape of the light curve (see, for example, a description of the effect by Smith 1995 and an example of light curves in Walraven 1949). All these are present in V442 Her. However, while the phase drift we have found is similar in size to many stars exhibiting the Blazhko effect, the large amplitude modulation, the long period of the modulation and the radical changes in the form of the light curve are extreme compared to other known stars. Stars which have been studied in detail show amplitudes which typically vary by up to a half a magnitude over the Blazhko cycle (see, for example, Lee 1997 and Walraven 1949). An extreme example is WY Dra (Chis et al. 1975) where the amplitude ranges over nearly a magnitude. However, it is never less than about 1.2 magnitudes. In contrast, the amplitude of V442 Her has varied from 0.27 to 1.39 magnitudes, a range of 1.12 magnitudes, during our observations. Additionally, modulation occurs over a time scale of the order of 700 days or more while the longest known Blazhko cycle is about 530 days in RS Boo (Oosterhoff 1946; Kanyo 1980; Firmanyuk 1988; note that a small modulation of the pulsation may also occur on a 48 day time scale). Finally we note that the light curve form for V442 Her ranges from that of a typical Bailey type ab star at large amplitude to one which bears no resemblance to an RR Lyrae light curve during times of low amplitude. Again, this is not true of other RR Lyrae. For example, Teays (1993) used Fourier decomposition to show that as RR Lyrae goes through its Blazhko cycle, the light curve shape always matches other stars of similar period. We conclude that if the behavior of V442 Her is due to the Blazhko effect, it is perhaps the most extreme example of this behavior known.
As demonstrated above, V442 Her exhibits behavior unlike that known in any other RR Lyrae star; it is an interesting object for further study. In particular, it may offer insights into the Blazhko effect and should be observed further. Broad band photometry must be continued to clarify the long term behavior and to show whether there is a stable modulation period present. Spectroscopy or narrow band photometry would be useful to determine where V442 Her falls in the metallicity range of RR Lyrae stars. Finally, as observational tests are devised for various explanations of the Blazhko effect, V442 Her should clearly be included due to its extreme behavior.
The instrumentation used for the observations described in this paper was funded by the NationalScience Foundation (Grant No. AST-8504072) and some of the observations were conducted with support from NSF Grant No. AST-8815806. Support for publication expenses was provided by the American Astronomical Society through its small grants program.
Belserene, E.P. 1964, AJ 69, 475.
Breger, M. 1990, IBVS No. 3422.
Chis, D., Chis, D. & Mihoc, I. 1975, IBVS No. 960..
Clement, C.M., Fernace, S. & Simon, N.R. 1993, ApJ 412, 483.
Diethelm, R. 1983, A&A 124, 108.
Fermanyuk, B.N. 1988, IBVS No. 3259.
Kanyo, S. 1980, IBVS No. 1832.
Kholopov, P.N. 1985, General Catalogue of Variable Stars, 4th Ed. (Moscow: Nauka).
Lee, K.M. 1997, Ph.D. Thesis, University of Nebraska.
Lee, Y.-W. 1991, ApJ 367, 524.
Oosterhoff, P.Th. 1946, BAN 10, 101.
Schmidt, E.G., 1991, AJ, 102, 1766.
Schmidt, E.G. & Reiswig, D.E., 1993, AJ, 106, 2429.
Smith, H.A. 1995, RR Lyrae Stars (Cambridge: Cambridge University Press).
Smith, H.A. & Sandage, A. 1981, AJ 86, 1870.
Stagg, C., Wehlau, A. 1980, AJ 85, 1182.
Storm, J., Carney, B.W. & Beck, J.A. 1991, PASP 103, 1264.
Sweigert, A.V. & Renzini, A. 1979, A&A 71, 66.
Teays, T.J. 1993, in New Perspectives on Stellar Pulsation and Pulsating Variable Stars, eds. J.M. Nemec and J.M. Matthews (Cambridge: Cambridge University Press), p 410.
Tsesevich, V. 1972, in Vistas in Astronomy, Vol 13, (Pergamon Press; Oxford) Ed. A. Beer, p. 241.
Tsesevich, V. 1977, IBVS No. 1370.
Walraven, Th. 1949, BAN 11, 17.
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