stars: evolutionstars: horizontal-branchstars: variables:
other
L58, 1997 November 1
New observations of variable stars in the globular cluster M3 reveal that the RR Lyrae variable V79 is a double-mode (RRd) variable with the first-overtone mode dominating. In all previous studies, V79 was found to be a fundamental-mode (RRab) pulsator with an irregular light curve. This is the first observed mode switch for an RR Lyrae variable, and it is direct observational evidence for blueward evolution of horizontal-branch stars in the Oosterhoff type I cluster M3. It also demonstrates that there is a connection between the Blazhko effect and pulsational mode mixing in RR Lyrae variables. These new observations also show that the strength of the overtone oscillations in the RRd star V68 in M3 may have increased in the last 70 yr, thus indicating blueward evolution for V68 as well.
A survey of previously published investigations of RRd stars in Oosterhoff type II systems indicates that there is marginal evidence for an increase in the strength of fundamental-mode oscillations in two stars: V30 in M15 and AQ Leo. If these increases are confirmed by future observations, it will indicate redward evolution for RRd stars in type II systems.
Subject headings: globular
clusters: individual (M3,
M15)stars: evolutionstars: horizontal-branchstars: variables:
other
1 Affiliated with the Department of Astronomy, University of Toronto, and Department of Physics and Astronomy, York University.
A standard method for investigating the evolution of horizontal-branch stars is to analyze the period changes of RR Lyrae variables in globular clusters. Period increases should indicate redward evolution, while decreases indicate blueward evolution, and the rates of change give information about the timescales. The models of Sweigert & Renzini (1979) and Lee, Demarque, & Zinn (1990) predict that the RR Lyrae variables in the Oosterhoff type I clusters cross the instability strip during their ZAHB phase and are therefore expected to have period decreases, which are followed later by increases, when the stars evolve away from the ZAHB. For the RR Lyrae variables in the more metal-poor Oosterhoff type II clusters, the models predict only increasing periods, because these stars cross the instability strip after their ZAHB phase. Since there are a few globular clusters that have been observed over an interval of 100 yr, it should be possible to use these observations to test the models. Unfortunately, the observational data do not give definitive results (cf. Smith 1995; Rathbun & Smith 1997). The evolutionary period changes seem to be masked by a period change noise of irregular character. Sweigert & Renzini (1979) have demonstrated that this noise could be caused by mixing events that alter the hydrostatic structure of the core and thus affect the star's pulsation period. Because of this, the observed rates of change are sometimes an order of magnitude too large and of the wrong sign, when compared with the rates predicted by evolutionary theory. However, if one assumes that, for a particular cluster, the mean rate of period change is a measure of the evolutionary change, then it may be possible to compare the observations with theory. Lee (1991) took this approach and found that the observed period changes of the RR Lyrae stars in five well-observed clusters could be attributed to evolutionary effects, provided the noise is random and of the order of 0.07 days per million years.
Another way to study the evolution of horizontal-branch (HB) stars is to examine the distribution of periods and modes of pulsation of RR Lyrae variables in globular clusters of the two Oosterhoff types. Some years ago, van Albada & Baker (1973) postulated that the difference in the period distributions for the Oosterhoff type I and II clusters is due in part to hysteresis in pulsation. According to their theory, the RRab variables in the type I clusters enter the instability strip as fundamental-mode pulsators (RRab stars) and evolve from red to blue, while the stars in type II clusters enter as overtone pulsators (RRc stars) and evolve from blue to red. Because of hysteresis, the transition period at which a star switches between the fundamental- and first-overtone modes will be different for the two cluster types, and consequently, the mean periods of both the RRc and RRab stars will be affected as well. The RR Lyrae variables in type II clusters should switch modes at longer periods, and as a result, their mean periods will be longer than those in the type I clusters. Also, the Oosterhoff type II clusters should have a higher proportion of RRc stars. These are the observed characteristics of the two Oosterhoff groups. If the van Albada & Baker scenario is correct, then the transition between the ab- and c-type RR Lyrae variables should occur near the blue edge for fundamental-mode pulsation in Oosterhoff type I clusters and near the red edge for the first overtone in Oosterhoff type II clusters. Using up-to-date convective pulsation models to locate the instability strip on the H-R diagram, Bono, Caputo, & Stellingwerf (1994) and Cox (1995) have presented evidence to indicate that this is, in fact, the case.
In the present investigation, we suggest another method for studying HB evolution: monitoring long-term changes in the pulsation characteristics of double-mode RR Lyrae (RRd) stars. If an RRd star is evolving blueward, then over a period of time, the amplitude of the first overtone should gain in strength relative to that of the fundamental, but if it evolves redward, the strength of fundamental-mode oscillations should increase. Our study is motivated by the recent discovery of Kaluzny et al. (1997, hereafter KHCR) that V79 in M3, previously classified as RRab, is now an RRd star with the first-overtone mode dominating. The KHCR finding was based on observations made in 1996.
The 1996 observations of M3 were obtained
on nine nights in the interval March
19April
2 by one of us (R. W. H.) with the 1 m Jacobus Kapteyn telescope at the
Observatorio del Roque de Los Muchachos, La Palma. The observations, which
include V photometry for 42 RR Lyrae variables on 176 frames, and
the reduction procedures have been discussed by KHCR.
One of the two previously known RRd variables, V68, was among the 42
stars, and so we have included it in our investigation. (V87, the other
RRd star, was not in our field of view.) A finding chart for the
variables in M3 was published by Bailey
(1913). We determined the primary periods for V68 and V79 with a
computer program that utilized Stellingwerf's
(1978) phase dispersion minimization (PDM) technique with a (5, 2) bin
structure. To search for the secondary period, we derived a mean light
curve by fitting a cubic
splineinterpolating
function to the bin means and then measured the residuals from this curve
and applied the PDM technique to the residuals. Next, we corrected the
magnitudes by subtracting the mean curve for the secondary period from the
raw magnitudes and then again applied the PDM technique to obtain a final
value for the primary period. Light curves for V68 and V79 are shown in
Figures 1
and 2. The top panel of each figure shows
the
raw
magnitudes plotted with the primary period, the first overtone. The curves
in the middle and bottom panels show, respectively, the corrected
magnitudes plotted with the first-overtone period and the residuals plotted
with the secondary (fundamental) period, both with the
interaction frequencies
(1
P
±1P
) removed.
Fig. 1 
Fig. 2
To assess the long-term behavior of these
stars, we compared our results with those of an earlier study of the
RRd stars in M3 by Nemec & Clement
(1989, hereafter NC). The
NC study was based mainly on data from a combination of
three sets of observations made in the interval
19201926
and published by Larink (1922),
Muller (1933), and
Greenstein (1935). NC
found that V68 was an RRd star with the fundamental mode dominant,
but they considered V79 to be an RRab star. The light curve of V79
(see Fig. 2 of NC) showed night-to-night scatter,
but a PDM period search of the residuals did not reveal any periodicity in
the range expected for first-overtone oscillations (see Fig. 3
of NC). They estimated that if there were any
first-overtone oscillations, they would have an amplitude less than 0.25
mag.
The pulsation characteristics of V68 and
V79 are summarized in Table 1. In the table,
we list their coordinates in arcseconds relative to the cluster center
according to Sawyer Hogg's (1973) catalog,
the first-overtone and fundamental
periods (P
and P),
their corresponding
amplitudes (A
and A)
and amplitude ratios derived from the 1996 observations, and the amplitude
ratios
for 19201926
based on NC's study. The data of Table
1 illustrate that for both stars, the first-overtone oscillations have
grown in strength since the 1920s, but for V79, the change is more
striking.
In order to find out what happened to V79
in the intervening years, we used the PDM technique to analyze other
published observations that were suitable for period searches. These
included observations obtained in the intervals
19381962
(Szeidl 1965)
and 19461948
(Belserene 1952). In the PDM technique, a
-statistic
that is a measure of the scatter on the light curve is evaluated for a
series of periods, and the period for which
is a
minimum is considered to be the best period.
In Figure 3 we show plots of
versus
period for the raw data over the range
0
34 to
050 for
the four epochs. The plot for the 1996 data in the bottom panel of the
figure indicates that the best period is
0358.
However, the plots for the first three epochs all show a clear minimum at a
period of approximately
04833, and
period searches of the residuals measured from their corresponding primary
light curves did not reveal any oscillations in the overtone mode even
though there were variations in the amplitude. Our analysis also indicates
that the fundamental period of V79 has decreased by a substantial amount in
the last 35 yr. The
04833
period derived from the previous studies is significantly longer than the
fundamental
period P=0480
that we determined for the 1996 observations and listed in
Table 1. If we plot the 1996 data with the longer
period, it introduces a phase shift that increases the scatter on the light
curve in the bottom panel of Figure 2. We therefore
conclude that two things have happened to V79 between 1962 and 1996.
First-overtone oscillations have either commenced or
increased significantly, and there has been an abrupt decrease in the
fundamental period. In his study of period changes of the RR Lyrae
variables in M3, Szeidl (1965) found that
the O-C diagram for V79 had a discontinuity between 1926 and
1938, and consequently, he was unable to detect any systematic period
change for the star. Rathbun & Smith (1997) cited
V79 as an example of a star that has
period changes
so erratic as to be impossible to even approximately describe with a single
number.
If the large, abrupt decrease we have detected
in P,
the fundamental period of V79, was caused by evolution on the horizontal
branch, then an O-C diagram is not a useful tool for
studying evolutionary period changes of RR Lyrae variables, at least not
for stars like V79 in M3.
Fig. 3
Since, prior to 1962, V79 was an
RRab star with an irregular light curve, a
Blazhko
variable, our investigation provides some insight into the actual cause of
the Blazhko effect in RR Lyrae variables. According to
Smith (1995, p. 109), most speculation has centered on
two possibilities: (1) that the effect is a
consequence
of some type of mixing of pulsational
modes
and (2) that the effect is
related
to magnetic cycles in the stars, perhaps coupled with
rotation.
Since we now know that at least one Blazhko variable, V79 in M3,
has exhibited mixed-mode pulsations, we consider the first possibility to
be more feasible.
It appears that regular monitoring of stars like V79 in M3 can provide important information about stellar evolution. If there are any available unpublished observations of this star between 1962 and 1996, it would be very informative to analyze them. It would be particularly interesting to know if there has been any change in luminosity or color, because this may put constraints on the boundaries of the different pulsational modes in the H-R diagram. We should also point out that there are other interesting stars in M3 that merit further investigation. For example, NC noted that the RRab star V28 was a promising RRd candidate. Unfortunately, it was not in the field of view for our present study. Perhaps V28 has also started to switch modes or will do so in the near future. It would be interesting to find out.
We have presented evidence that indicates
that two RRd stars in M3 are evolving blueward. Are the RRd
stars in Oosterhoff type II systems evolving redward? This question was
addressed by Purdue et al. (1995) in a
study of the long-term behavior of RRd stars in the Oosterhoff
type II cluster M15. They noted that the fundamental-mode oscillations
in V30 increased in strength relative to the first overtone between 1941
and 1991. In fact, their analysis suggests that the change happened
rather abruptly in the 1950s. A similar situation occurs for the
field RRd star, AQ Leo, which has periods and a period ratio
similar to those of RRd stars in Oosterhoff type II
systems. Jerzykiewicz, Schult, & Wenzel
(1982) compared the amplitude differences in a series of observations
made
in 19601961
and another in
19731974
and found that the first-overtone amplitude decreased by an
amount 0.012±0.011, while the fundamental-mode amplitude increased
by 0.017±0.011. They also found that an abrupt increase in the
first-overtone period occurred in the early 1970s. They stated that their
findings did not give direct evidence for mode switching but that it is a
possibility. The increase in strength of the fundamental-mode oscillations
and the period increase are events that are expected to occur if the star
is evolving redward.
Our investigation has shown that high-quality photometry of RR Lyrae stars, particularly RRd stars and stars that exhibit the Blazhko effect, can provide useful information about the evolution of horizontal-branch stars. We expect that future studies will confirm this.
This work has been supported by the
Natural Sciences and Engineering Research Council of Canada through
operating grants to C. M. C. and S. M. R. R. W. H. thanks the UK Particle
Physics and Astronomy Research Council for the award of a research grant.
J. K. was supported by Polish Komitet Baden Naukowych grant 2P03D011.12 and
by NSF grant AST 9528096 to
Bohdan Paczy
ski.
Full image (57kb) | Discussion in text
FIG.
1.Light
curves for V68 based on the 1996 observations. In the upper panel, the raw
magnitudes have been plotted with the dominant period, the first overtone.
In the middle panel, the corrected (prewhitened) magnitudes have been
plotted with the overtone period, and in the lower panel, the (prewhitened)
residuals have been plotted with the fundamental period. The different
symbols denote observations made on different nights. The
large night-to-night scatter of the points in the upper panel is typical
for a double-mode pulsator. The spread of the points on curves in the lower
panels is much less pronounced because after prewhitening, the scatter is
reduced.
Full image (53kb) | Discussion in text
FIG.
2.Light
curves for V79 based on the 1996 observations. The arrangement of the
curves is as in Fig. 1.
Full image (48kb) | Discussion in text
FIG.
3.The
transforms (plots of Stellingwerf's
-statistic vs.
period) for V79 for four different epochs. The period for which
is a
minimum is considered to be the best period. The diagram illustrates that
for observations prior to 1962, the best period was
approximately 048,
but in 1996 it was
036. This
indicates a mode switch from the fundamental to the first overtone.
| Star | x | y | P | P | A
(1996) | A
(1996) | AA
(1996) | AA
(1920 1926) |
| V68... | +21.9 | +174.8 | 0.356 | 0.479 | 0.389 | 0.348 | 1.12 ± 0.10 | 0.72 ± 0.20 |
| V79... | +43.4 | +349.4 | 0.358 | 0.480 | 0.337 | 0.195 | 1.73 ± 0.13 | <0.2 |