A&A 367, 148-158 (2001)
DOI: 10.1051/0004-6361:20000349
W. Pych1 - J. Kaluzny1 - W. Krzeminski1,2 - A. Schwarzenberg-Czerny1,3 - I. B. Thompson2
1 - Copernicus Astronomical Center, ul. Bartycka 18, 00-716 Warszawa,
Poland
2 -
Carnegie Institution of Washington, 813 Santa Barbara Street, Pasadena,
CA 91101, USA
3 -
Astronomical Observatory of Adam Mickiewicz University, ul.
Sloneczna 36, 60-286 Poznan, Poland
Received 28 June 2000 / Accepted 27 November 2000
Abstract
We present CCD photometry of SX Phe variables in the field of the
globular cluster M 55. We have discovered 27 variables, three of which
are probable members of the Sagittarius dwarf galaxy. All of the SX Phe
stars in M 55 lie in the blue straggler region of the cluster
color-magnitude diagram. Using period ratio information we have
identified the radial pulsation modes for one of the observed
variables. Inspection of the period-luminosity distribution permits
the probable identifications of the pulsation modes for most of the
rest of the stars in the sample. We have determined the slope of the
period-luminosity relation for SX Phe stars in M 55 pulsating in the
fundamental mode. Using this relation and the HIPPARCOS data for SX Phe
itself, we have estimated the apparent distance modulus to M 55 to be
mag.
Key words: globular clusters: individual: M 55 - (stars): blue stragglers:
stars: variables:
Sct - stars: oscillations - stars: population II
The Clusters AgeS Experiment (CASE) is a long term project with a main goal of determining accurate ages and distances of globular clusters by using observations of detached eclipsing binaries (Paczynski 1997). As a byproduct we obtain time series photometry of other variable stars located in the surveyed clusters.
M 55 (NGC 6809) is a metal-poor globular cluster in the Galactic halo
(
).
Because of its proximity and small reddening (
;
Harris 1996) it was selected as one of the targets in
our survey for eclipsing binaries in globular clusters.
Olech et al. (1999) presented our investigation of RR Lyrae
variables in this cluster. In this contribution we present
the results for the short period pulsating variables.
The relatively large number of SX Phe variables in M 55
allows us to make a basic statistical analysis of their properties and a
new determination of the slope of the period-luminosity relation.
In the interval from 1997 May 8/9 to 1997 August 16/17 we carried out
CCD photometry on the 1.0-m Swope telescope at Las Campanas
Observatory. The telescope was equipped with the SITe3
CCD
camera with an effective field of view
arcmin (
pixels were used), at a scale of 0.435 arcsec/pixel. The cluster was
monitored on 13 nights for a total of 36.4 hours. The light curves
typically have about 750 data points in Johnson V and about 60 data
points in Johnson B. Exposure times were 150 s to 300 s for the
V filter and from 200 s to 360 s for the B filter, depending on the
atmospheric transparency and seeing conditions. On photometric nights
several fields of standard stars (Landolt 1992) were observed to obtain
transformation coefficients to the photometric standard system. We
used procedures from the IRAF noao.imred.ccdproc package for
de-biasing and flat-fielding the raw data. Instrumental photometry was
obtained using DoPHOT (Schechter et al. 1993).
We identified 27 SX Phe variables in the field of M 55. Following the nomenclature of Olech et al. (1999) the stars are designated as NGC 6809 LCO V16 through NGC 6809 LCO V42. Here-after we use the designations V16 - V42 respectively. Finding charts for these variables are presented in Figs. 1-3.
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Figure 1: Finding charts for SX Phe variables in M 55. Part I - variables V16 - V24. Each chart is 1 arcmin on a side, with north to the top and east to the left |
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Figure 2: Finding charts for SX Phe variables in M 55. Part II - variables V25 - V33. Each chart is 1 arcmin on a side, with north to the top and east to the left |
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Figure 3: Finding charts for SX Phe variables in M 55. Part III - variables V34 - V42. Each chart is 1 arcmin on a side, with north to the top and east to the left |
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Figure 4: The color-magnitude diagram of the globular cluster M 55. Filled circles denote single-mode SX Phe variables, open circles denote double-mode SX Phe variables, filled triangles denote SX Phe variables from the Sagittarius dwarf galaxy |
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The positions of these objects in the color-magnitude diagram are shown in Fig. 4. All of the SX Phe stars belonging to M 55 lie on the blue straggler sequence. Three of the observed SX Phe type stars: V28, V29, V30, are 3.5-4 mag fainter than the rest of our sample stars. This difference in magnitude places these 3 stars in the Sagittarius dwarf galaxy (Ibata et al. 1994; Fahlman et al. 1996). The 24 remaining SX Phe variables constitute approximately 50 percent of all the blue straggler stars present in our data.
Preliminary period estimates were obtained using the CLEAN algorithm
(Roberts et al. 1987).
We used a method developed by
Schwarzenberg-Czerny (1997) to improve the
period determination and to fit a Fourier series to the V-band light curves
in the form:
Standard deviation of the residuals is 0.014 mag, consistent with
that expected for the size of the telescope and stellar magnitude.
Thus observational errors of an average value of 1/4 all observations
should be as small as
mag. However,
the averages calculated by selecting 1/4 of points around minimum and
maximum phases should differ by more than the (half)amplitude of the
oscillation, consistent with well over
significance level
of detection even for the secondary oscillation. The AoV statistics
used by us tends to yield higher significance levels than the above
simple estimate.
star | RA (J2000.0) | Dec (J2000) | P | <V> | <B> | <B>-<V> | AV |
hh:mm:sec | deg:':'' | [days] | |||||
V16 | 19:40:09.20 | -30:56:42.04 | 0.0534204(8) | 16.94 | 17.32 | 0.38 | 0.016 |
V17 | 19:40:11.33 | -30:59:25.06 | 0.0412615(3) | 17.18 | 17.43 | 0.25 | 0.049 |
V18 | 19:40:06.87 | -30:56:32.12 | 0.0465555(4) | 16.98 | 17.32 | 0.34 | 0.029 |
V19 | 19:39:57.67 | -30:57:01.31 | 0.0382367(2) | 17.27 | 17.64 | 0.37 | 0.033 |
V20 | 19:39:54.95 | -30:58:21.25 | 0.0332118(2) | 17.04 | 17.34 | 0.30 | 0.102 |
V21 | 19:39:58.27 | -30:59:06.05 | 0.1355924(2) | 15.76 | 16.19 | 0.43 | 0.036 |
V22 | 19:40:07.80 | -31:00:12.60 | 0.0456394(1) | 16.81 | 17.17 | 0.36 | 0.337 |
V23 | 19:39:51.82 | -30:55:52.83 | 0.0413989(3) | 17.22 | 17.58 | 0.36 | 0.050 |
V24 | 19:39:45.49 | -30:56:02.68 | 0.0418206(5) | 17.06 | 17.40 | 0.34 | 0.026 |
V25 | 19:39:51.55 | -30:56:21.27 | 0.0985309(1) | 15.88 | 16.23 | 0.35 | 0.899 |
V26 | 19:39:47.06 | -30:57:33.98 | 0.0820096(2) | 16.11 | 16.51 | 0.40 | 0.173 |
V27 | 19:39:54.05 | -30:58:07.46 | 0.0410265(5) | 17.09 | 17.45 | 0.36 | 0.029 |
V28* | 19:40:15.04 | -31:05:15.03 | 0.0537630(6) | 20.61 | 20.92 | 0.31 | 0.260 |
V29* | 19:39:42.58 | -30:55:58.34 | 0.0343115(2) | 20.71 | 20.92 | 0.21 | 0.295 |
V30* | 19:39:41.02 | -30:50:25.23 | 0.0563464(5) | 20.35 | 20.68 | 0.33 | 0.258 |
* Probable member of the Sagittarius dwarf galaxy.
The basic parameters derived for the single-mode oscillators are listed
in Table 1, including the variable number, equatorial
coordinates (J2000.0), derived periods, mean V-band magnitudes, mean
B-band magnitudes, mean colors (<B>-<V>), and full amplitudes of
the oscillations in V. Table 2 presents values of A1,
R21, ,
R31,
measured for the
single-mode variables. By analogy to Cepheids, we can look for the
signature of the resonance between the radial pulsation modes in a
-period plot (Fig. 5).
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Figure 5:
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Figure 6 presents the light curves of the single-mode SX Phe variables observed in the field of M 55.
We constructed a synthetic light curve for each of the variables using
the measured Fourier parameters for that variable. After subtracting
this light curve from the observed data points, we
searched for a new period with a new fit of a Fourier series. If the
full amplitude of the resulting light curve was larger than an
arbitrarily chosen value of 0.01 mag, then the object was classified
as a double mode variable. Two modes of pulsation were detected in the
light curves of 12 of our variables. The parameters for these
double-mode SX Phe variables are listed in Table 3, including
the variable number, equatorial coordinates (J2000.0), periods of
pulsations for both modes, mean V-band magnitudes, mean B-band
magnitudes, mean colors, and full amplitudes in V for the longer
period. Table 4 presents the values of A1A, R21A,
,
A1B measured for the double-mode variables. We use
the designations A and B for the longer and shorter periods,
respectively.
Figure 7 presents the light curves of the double-mode variables phased with the periods of each mode after prewhitening with the other mode.
Amplitudes generally yield no definitive clues for the identification of modes, except that large amplitudes are more likely to occur in radial pulsations. Our identification of pulsation modes relies on the period ratios and on the distribution of stars in the period-luminosity (P-L) plot.
We observe amplitudes ranging from 0.016 mag to 0.899 mag. The
amplitude of V25 (AV=0.899 mag) is one of the largest known among
all SX Phe type variables. It is not likely that such an amplitude
arises in non-radial oscillations. For most of the double-mode
variables the amplitude of the longer period oscillations is larger
than that for the shorter one. An exception is V38 which has a larger
amplitude for the shorter period. For this reason it is very likely
that in the double mode stars the oscillations with larger periods and
amplitudes are radial (Gilliland et al. 1998).
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Figure 6: V-band light curves for single-mode SX Phe variables observed in the field of M 55 |
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star | A1 | R21 |
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R31 |
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V16 | 0.0079 ![]() |
- | - | - | - |
V17 | 0.0246 ![]() |
- | - | - | - |
V18 | 0.0144 ![]() |
- | - | - | - |
V19 | 0.0166 ![]() |
- | - | - | - |
V20 | 0.0500 ![]() |
0.126 ![]() |
2.33 ![]() |
- | - |
V21 | 0.0178 ![]() |
0.125 ![]() |
2.55 ![]() |
- | - |
V22 | 0.1609 ![]() |
0.250 ![]() |
2.06 ![]() |
- | - |
V23 | 0.0252 ![]() |
- | - | - | - |
V24 | 0.0130 ![]() |
- | - | - | - |
V25 | 0.3454 ![]() |
0.480 ![]() |
2.19 ![]() |
0.240 ![]() |
4.50 ![]() |
V26 | 0.0839 ![]() |
0.221 ![]() |
2.16 ![]() |
0.034 ![]() |
4.66 ![]() |
V27 | 0.0143 ![]() |
- | - | - | - |
V28 | 0.1276 ![]() |
0.190 ![]() |
2.01 ![]() |
- | - |
V29 | 0.1477 ![]() |
- | - | - | - |
V30 | 0.1191 ![]() |
0.321 ![]() |
2.13 ![]() |
0.132 ![]() |
4.59 ![]() |
In Fig. 8 we present a color-amplitude relation for the stars in our sample. Note that the larger amplitudes are exhibited by stars close to the center of the instability strip. The amplitudes of the double mode stars tend to be smaller than the amplitudes of the single mode stars, but a few single mode stars display very small amplitudes as well. Both effects, if real, are consistent with theoretical expectations. However, the large scatter in Fig. 8 makes any detailed discussion of amplitude effects premature.
star | RA (J2000.0) | Dec (J2000.) | PA | PB | <V> | <B> | <B>-<V> | AV(PA) |
hh:mm:sec | deg:':'' | [days] | [days] | |||||
V31 | 19:40:00.99 | -30:57:56.53 | 0.0388471(2) | 0.0382042(5) | 17.23 | 17.60 | 0.37 | 0.041 |
V32 | 19:39:58.14 | -30:58:32.66 | 0.0414874(2) | 0.0405483(5) | 16.92 | 17.28 | 0.36 | 0.097 |
V33 | 19:39:54.56 | -30:59:57.88 | 0.0593067(3) | 0.0573473(4) | 16.40 | 16.74 | 0.34 | 0.054 |
V34 | 19:40:01.02 | -31:00:37.93 | 0.0370203(3) | 0.0360939(6) | 17.23 | 17.54 | 0.31 | 0.029 |
V35 | 19:39:50.37 | -30:55:12.41 | 0.0486858(2) | 0.0452695(7) | 16.57 | 16.91 | 0.34 | 0.070 |
V36 | 19:39:48.56 | -30:56:45.04 | 0.0393958(2) | 0.0373768(4) | 16.74 | 17.05 | 0.31 | 0.067 |
V37 | 19:39:49.87 | -30:57:42.53 | 0.0437976(3) | 0.0428239(7) | 16.96 | 17.26 | 0.30 | 0.051 |
V38 | 19:39:58.86 | -30:58:14.78 | 0.0391971(5) | 0.0381747(3) | 16.69 | 17.04 | 0.35 | 0.044* |
V39 | 19:40:11.99 | -31:02:04.48 | 0.0358151(3) | 0.0341535(5) | 17.21 | 17.52 | 0.31 | 0.034 |
V40 | 19:40:01.90 | -30:55:38.20 | 0.0369762(4) | 0.0346515(7) | 17.20 | 17.56 | 0.35 | 0.028 |
V41 | 19:40:02.95 | -30:58:28.34 | 0.0451669(2) | 0.0364552(3) | 16.53 | 16.83 | 0.30 | 0.106 |
V42 | 19:39:58.61 | -30:57:23.93 | 0.0366655(3) | 0.0356382(5) | 17.16 | 17.52 | 0.36 | 0.053 |
* Amplitude of PB pulsations (see text).
star | A1A | R21A |
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A1B |
V31 | 0.0204 ![]() |
0.074 ![]() |
1.19 ![]() |
0.0093 ![]() |
V32 | 0.0478 ![]() |
0.143 ![]() |
2.20 ![]() |
0.0194 ![]() |
V33 | 0.0271 ![]() |
- | - | 0.0181 ![]() |
V34 | 0.0144 ![]() |
- | - | 0.0060 ![]() |
V35 | 0.0349 ![]() |
- | - | 0.0099 ![]() |
V36 | 0.0333 ![]() |
- | - | 0.0119 ![]() |
V37 | 0.0254 ![]() |
- | - | 0.0106 ![]() |
V38 | 0.0122 ![]() |
- | - | 0.0218 ![]() |
V39 | 0.0170 ![]() |
- | - | 0.0080 ![]() |
V40 | 0.0141 ![]() |
- | - | 0.0068 ![]() |
V41 | 0.0532 ![]() |
- | - | 0.0243 ![]() |
V42 | 0.0263 ![]() |
- | - | 0.0171 ![]() |
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Figure 7: V-band light curves for double-mode SX Phe variables observed in the field of M 55. The upper panels show light curves phased with longer period after subtraction of variability with the shorter period approximated by the Fourier series. The lower panels show light curves phased with shorter period after subtraction of variability with the longer period approximated by the Fourier series |
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The periods of the SX Phe variables in M 55 span the range 0.033 to
0.136 days. We use PA for the longer periods and PB for the
shorter periods of the double mode variables. Figure 9 presents
PB/PA plotted against PA for the double-mode
variables. The PB/PA ratio does not depend on the period of the
pulsations. The weighted mean of PB/PA for V31, V32, V33, V34,
V37, V38, and V42 is
.
The period ratios of V35, V36,
V39 and V40 exhibit a larger scatter lying in the range
0.92 - 0.96.
Since there are no radial modes spaced so closely in frequency, at
least one of the modes in our double-mode SX Phe variables is
non-radial in origin. However we are unable to say with
assurance which of the two modes is radial, if any, using only period
information.
V41 is an exceptional case in that its period ratio is extreme
compared to other double mode SX Phe stars in M 55 (Fig. 9).
This period ratio helps us to identify its pulsation modes with some
confidence. The observed value of
is close to the
first and second overtone ratio for SX Phe stars (0.801, see
Petersen & Høg 1998 for a discussion). For this reason we identify PAand PB with the first and second radial overtones, respectively. In
Fig. 10 we plot the period-luminosity relation for the principal
periods of all of the stars in our sample. Except for V41 all of the
secondary periods of the double-mode stars lay close to their primary
periods and are not plotted to avoid confusion. For V41 the secondary
period PB lies off of the general P-L relation, toward lower
periods. It is
consistent with our identification of PB with the second overtone.
This is true for all slopes of P-L relations discussed in
the literature, ranging from -3.3 to -3.7
(McNamara 1995; McNamara 1997).
However, we caution that these results are extremely sensitive against
selection of the observational data. The latter paper claims 5-fold decrease
of scatter of MV without explainable improvement in the quality of the
observations.
In Fig. 10 the stars V20, V35, V36, V38 and V41 are marked with filled symbols. These stars form a distinct branch away from the main group of SX Phe stars, shifted towards lower periods. Following our identification of V41 as a first overtone pulsator we extend this identification onto the whole group.
Previous investigations have not revealed such a clear separation of the radial modes of SX Phe stars in globular clusters. These investigations have had to rely on small samples from different clusters, and so relative distance errors and spatially variable reddening both introduce significant scatter in the period-luminosity diagram (McNamara 1995; Kaluzny & Krzeminski 1993).
The dotted line in Fig. 10 represents a linear least squares
fit to the first overtone P-L relation:
We classify all remaining stars in Fig. 10 (plotted with open
symbols) as SX Phe stars pulsating in the fundamental mode. The
continuous line in Fig. 10 represents a linear least squares fit to
this P-L relation:
Our fundamental mode P-L relation is less steep than the overtone
relation. However the relatively large error of the slope derived for
the first overtone P-L relation, does not reject the hypothesis of
equal slopes. This is in agreement with the discussion by Nemec et al. (1994).
This P-L relation for the fundamental mode stars exhibits a fair amount
of scatter. The cause of this might be misidentification among close
radial and non-radial modes. The average period ratio of 0.97 in
bimodal stars is consistent with a scatter of 0.03 in
due to
mode misidentification. In addition, some scatter is to be expected
from the finite width of the instability strip.
McNamara (1995) derived a P-L relation with a slope a=-3.3 from a
compilation of cluster SX Phe stars. This compilation relies on a smaller
and less homogeneous data set than that presented here, and hence a realistic
estimate of the error of this latter value is expected to be large
compared to our error of 0.17. Thus the McNamara (1995) value for the
slope is marginally consistent with our value. A comparison of these
results indicates the degree of the external errors involved in P-L
relations for SX Phe stars.
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Figure 8: The color-amplitude relation for SX Phe stars in M 55. Squares denote single mode pulsators, triangles denote double mode pulsators |
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Figure 9: Period ratio (PB/PA) versus PA relation for double mode SX Phe variables in M 55. The open symbols represent the stars with the period ratios 0.9<PB/PA<1.0 - at least one of the modes must be non-radial. The filled circle denotes V41 with the period ratio equal to 0.807 - characteristic for pulsations in the first and the second radial overtones |
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Figure 10: The period-luminosity dependence for SX Phe stars in M 55. The squares denote single-mode variables, the triangles denote points corresponding to longer periods of double-mode variables, the circle denotes the point corresponding to the second overtone period of V41. The solid line represents linear least squares fit to the points marked with open symbols (fundamental mode pulsators). The dashed line represents linear least squares fit to the points marked with filled symbols (first overtone pulsators). The horizontal line represents the period shifts of V41: between the first and the second overtones, and to the fundamental mode |
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Figure 11: The period-color dependence for SX Phe stars in M 55. The squares denote single-mode variables, the triangles denote points corresponding to longer periods of double-mode variables. The solid line represents linear least squares fit drawn through the plotted points |
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Our P-L slope of a=-2.9 is inconsistent with the
value a=-3.7 obtained by Petersen & Høg (1998) from the parallaxes of
Scuti stars observed by HIPPARCOS. This is not surprising given
the observed scatter in the P-L relation for the HIPPARCOS stars.
In addition, these calibrations do not take into account the fact that
SX Phe itself is the star in the sample with the shortest period
and the lowest metallicity at [Fe/H] = -1.37 (Hintz et al. 1998).
The other 5
Scuti stars from the HIPPARCOS sample have high
metallicities ([Fe/H]
). Nemec et al. (1994) demonstrated
that SX Phe stars follow a period-luminosity-metallicity relation
with a coefficient of 0.32 for the [Fe/H] term, and so the slope of the
P-L relation from the HIPPARCOS stars will be over-estimated.
Our P-L slope is also inconsistent with the value of -3.7 obtained
by McNamara (1997) for the highly inhomogeneous sample 26 HADS, for which
P-L dependence was found indirectly, via many intermediate steps.
On the other hand the HIPPARCOS parallax of SX Phe is
crucial for a determination of the zero point of the P-L relation for our
M 55 stars. The metallicity of SX Phe is similar to
M 55 ([Fe/H] =-1.54, Rutledge et al. 1997).
The parallax of SX Phe ( miliarcsec)
is well determined with a relative error
.
The absolute magnitude of the SX Phe, derived using the HIPPARCOS
parallax, is
mag (Petersen & Høg 1998).
Oudmajier et al. (1998) determined that when the relative error of the
parallax is smaller than about 0.15, the Lutz-Kelker correction
(Lutz & Kelker 1973) accurately describes the probable shift in the
derived absolute magnitude. In the case of SX Phe, the Lutz-Kelker
correction is equal to -0.02 mag, so the corrected absolute
magnitude is 2.86 mag. This value, when combined with Eq. (5)
for the fundamental mode period of SX Phe of
P0=0.0550 days (Petersen & Høg 1998), yields our final P-L
relation:
Scuti and SX Phe stars close to the red border of the
instability strip have periods significantly longer than the periods of
stars at the center of the strip (Pamiatnykh 2000).
The period-color (
)
dependence for
Scuti stars
from the Galactic Bulge was described by McNamara et al. (2000).
A linear least squares fit to our data, presented in Fig. 11
yields the following relation:
SX Phe type variables seem to be good distance indicators. Although
their luminosities are too low for investigations in distant galaxies,
they are bright enough to be observed in nearby galaxies.
The largest number of SX Phe variables in one globular cluster
was found in Cen (Kaluzny et al. 1996; Kaluzny et al. 1997a),
but due to its varying
metallicity this cluster is not suitable for distance calibration.
In M 55 we discovered
the richest population of SX Phe among the rest of globular clusters.
M 55 is thought to be chemically homogeneous (Richter et al. 1999).
This enabled a separation of the fundamental and first overtone stars and
an estimate of the errors caused by
misidentification of nearby radial non-radial frequencies. In this way
we obtained a reliable slope of the P-L relation for the
fundamental mode stars. Combined with the HIPPARCOS parallax for SX Phe
itself, we obtain an improved P-L relation (Eq. (6)).
Despite being based on just one star, our zero point should be reliable
as HIPPARCOS parallax of SX Phe has an error of 6 percent and
metallicities of SX Phe and of M 55 are as close as -1.37 and -1.54.
Using our revised P-L relation for SX Phe stars we measure the apparent
distance to M 55 to be
mag.
Acknowledgements
We would like to thank Alosha Pamiatnykh and Wojciech Dziembowski for their enlightening comments. JK and WK were supported by the KBN grant 2P03D.003.17. WP was supported by the KBN grant 2P03D.010.15. JK was supported also by NSF grant AST 9819787 to B. Paczynski. IBT and WK were supported by NSF grant AST-9819786. ASC was supported by the KBN grant No. 2P03D 018 18.