stars: distancesstars:
fundamental parameters
L127, 1997 September 10
Trigonometric parallax observations made with the Hubble Space Telescope (HST) Fine Guidance Sensor (FGS) 3 of seven Hyades members in six fields of view have been analyzed along with their proper motions to determine the distance to the cluster. Knowledge of the convergent point and mean proper motion of the Hyades is critical to the derivation of the distance to the center of the cluster. Depending on the choice of the proper-motion system, the derived cluster center distance varies by 9%. Adopting a reference distance of 46.1 pc or m - M = 3.32, which is derived from the ground-based parallaxes in the General Catalogue of Trigonometric Stellar Parallaxes (1995 edition), the FK5/PPM proper-motion system yields a distance 4% larger, while the Hanson system yields a distance 2% smaller. The HST FGS parallaxes reported here yield either a 14% or 5% larger distance, depending on the choice of the proper-motion system. Orbital parallaxes (Torres et al.) yield an average distance 4% larger than the reference distance. The variation in the distance derived from the HST data illustrates the importance of the proper-motion system and the individual proper motions to the derivation of the distance to the Hyades center; therefore, a full utilization of the HST FGS parallaxes awaits the establishment of an accurate and consistent proper-motion system.
Subject headings: astrometrystars: distancesstars:
fundamental parameters
1 Present address: Purple Mountain Observatory, Chinese Academy of Sciences, 2 Beijing Xi lu, Nanjing, Jiangsu 210080, PROC.
2 Hubble Fellow.
3 Present address: Department of Physics, University of Rhode Island, Providence, RI 02912.
4 Present address: Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218.
5 Present address: Allied Signal Corporation, P.O. Box 91, Annapolis Junction, MD 20701.
The Hyades is the nearest rich star
cluster to the Sun, and it provides us with, among other things, a
benchmark for the determination of the distances to other star clusters
through the technique of main-sequence fitting. While the Pleiades is
sometimes used as a standard for this process because of its more
normal
metallicity,
its 3 times greater distance leads to a more uncertain zero point in the
derived distance scale. Through the determination of the absolute
magnitudes of nearby classical Cepheids in clusters with respect to the
Hyades
and
or
the Pleiades, the Population I extragalactic distance scale is derived.
Through the early 1960s the accepted distance to the Hyades was determined by deriving the convergent point from the cluster members' proper motions, as was done, for example, by van Bueren (1952). This distance was questioned by Hodge & Wallerstein (1966), who found it to be in conflict with a number of secondary distance estimators. Redeterminations of the convergent point by Hanson (1975) using absolute proper motions, Gunn et al. (1988) and Griffin et al. (1988) using radial velocities and the proper motions from Hanson (1975), and, most recently, Schwan (1990, 1991) using FK5 and PPM proper motions have led to a distance that is approximately 17% larger than the earlier accepted value of 40 pc. Using accurate masses for the double-lined eclipsing binary vB22 and an adopted mass-luminosity relation for field stars, McClure (1982), followed by Peterson & Solensky (1987, ">1988) who used the slope of the Hyades mass-luminosity relation, obtained a distance to the cluster center of 47 pc. Torres, Stefanik, & Latham (1997a, 1997b, 1997c) have derived orbital parallaxes from a combination of radial velocity and astrometric observations that lead to a distance to the cluster center of about 48 pc using the Schwan (1991) convergent point solution. The ground-based trigonometric parallaxes listed in the new edition of the Yale Parallax Catalogue (YPC; van Altena, Lee, & Hoffleit 1995) were recently analyzed by van Altena, Lee, & Hoffleit (1997), who found a distance of 46 pc. The YPC investigation included 100 stars and used a weighted mean of the parallaxes without use of the proper motions. This result should not be too much in error, because of the large number of stars and full spatial coverage of the cluster. A more detailed analysis of the YPC data is in preparation.
In 1968, van
Altena (1973) prepared a list of very probable Hyades members suitable
for parallax determination and distributed it to numerous observatories
involved in the determination of trigonometric parallaxes. Those stars were
selected to have high-accuracy proper motions indicative of membership in
the Hyades, to have UBV photometry that placed the stars close to
the main sequence or white dwarf ridge lines in the color-magnitude diagram
and selected against double stars,6 and to be in the magnitude range
914,
i.e., accurately observable with the parallax telescopes and detectors then
in use. Many of the high-weight parallaxes analyzed in the YPC study were
the result of intensive observational efforts on the stars in that list. In
addition, they formed the basis of our 1972 Phase B proposal to determine
the distance to the Hyades using what was then called the Large
Space Telescope and the 1977 Phase CD proposal for the Hubble
Space Telescope (HST). Because of the reallocation of overhead
in the observing procedures and ground control experienced by
all Guaranteed Time Observers, and especially by those using the Fine
Guidance Sensors (FGSs), the original list of 20 Hyades members was reduced
to seven main-sequence members in six fields, each observed 6 to 7
times (Nobs in Table 1)
instead of the originally planned 24 times. As a consequence, what was to
be a definitive determination of the Hyades distance is now only a
teaser.
Finally, by the time this Letter is in print, we will have the first
results from the HIPPARCOS Astrometric Satellite on their
determination of the distance to the Hyades.
The observations of the seven stars in six
fields (Table 1) were made over a period of three years
from 1993 October through 1996 September, each field being observed during
one orbit with FGS 3 at times of maximum parallax factor (average absolute
value = 0.97). Also listed in Table 1 for each field, is
the name of the Hyades member from van
Altena (1966,
1969) that is the principal target (627 is
in the same field as 622), additional cross-identifications, the number of
reference stars used, Nref, and the unit weight error of
the parallax and proper-motion solution in x and y corrected
for degrees of freedom. The observing procedures and corrections for
coordinate drift and optical field angle distortion (OFAD) were similar to
those outlined in Benedict et al.
(1994). Coordinate drift in FGS 3 during an orbit can amount to several
thousandths of an arcsecond (mas), and for that reason, the target star and
at times a second star were observed at the beginning of the orbit, halfway
through measurement of the six (on average) reference stars and again at
the end. Changes in the position of the target star
andor
the second star were interpreted as a drift in the coordinate system
and interpolated corrections were made to the positions of all measured
stars. The drift was modeled as being linear in time, although a quadratic
drift yielded similar results. The OFAD for FGS 3 was developed
by Jefferys et al. (1992), and the
OFAD appropriate to each observation date was computed by McArthur.
Local deviations of the actual focal plane from that predicted by the OFAD
exist at the milliarcsecond level, but these introduce noise into the
solutions and not systematic errors. A minor systematic deviation of the
OFAD from the focal plane was detected in the y-coordinate,
but since the observations were made at maximum parallax factor,
the y-solutions are used only for the proper-motion determination
and not for the parallax. Since the target stars were about 4 mag brighter
than the reference stars, we have searched for a possible systematic error
as a function of star brightness, the magnitude equation. No magnitude
equation has been found in either the OFAD or long-term stability tests,
which both have magnitude ranges similar to the Hyades observations, so we
do not believe that a magnitude equation exists in the Hyades data. Since
we have on average only six reference stars in each field
(Nref in Table 1), and they are all
rather faint
(14th16th
magnitude), we are unable to test conclusively for the existence of a
magnitude equation in the Hyades data.
The solutions for relative parallax and proper motion were made with the Yale parallax program developed by Auer & van Altena (1978) modified for use with HST FGS observations. Parallel solutions were made by McArthur with the completely different University of Texas Gaussfit program by McArthur, Jefferys, & McCartney (1994), and negligible differences in the derived relative parallaxes attributable to weighting and modeling schemes were obtained. The results presented here are from the Yale program.
Since the parallaxes and proper motions
determined with the HST FGS are relative to the means of those
quantities for the reference stars, it was necessary to determine the
respective corrections to absolute parallax and proper motion. The
corrections to absolute parallax were computed from a Galactic model used
to compute those corrections for the YPC as well as from spectrophotometric
parallaxes for the individual reference stars. The spectrophotometric
parallaxes used spectra obtained by Deliyannis and King with the Wisconsin,
Indiana, Yale, and the National Optical Astronomy Observatory (WIYN)
multiobject spectrograph
MOSHydra
spectrograph and CCD photometry obtained by I. Platais with the Cerro
Tololo Inter-American Observatory 0.9 m telescope. The data were reduced by
Lu, Lee, and Kozhurina-Platais and are being prepared for publication. The
two approaches yielded average corrections to absolute parallax of +1.3 to
+1.4 mas; we have used the individual corrections derived from
the spectrophotometric parallaxes. The corrections to absolute proper
motion were derived from a new galactic structure and kinematic model
developed by Méndez & van Altena
(1997) and measurements made for this purpose of the reference stars by
Hanson, Klemola, and Jones of the Lick Observatory Northern Proper Motion
(NPM) plates. The Lick NPM corrections in mas yr-1 for
the individual reference stars in right ascension and declination
were respectively +6.9 ± 2, -1.2 ± 2, while for 400
faint anonymous stars of the same magnitude range they obtained +4.2 ±
2, -3.0 ± 2. Méndez calculated from his galactic structure and
kinematic model +3.7 ± 0.4, -5.6 ± 0.4. We have adopted the Lick
NPM corrections for the individual reference stars, although the final
results are not significantly changed if we use the Méndez
corrections. The error estimates for the Lick NPM proper motions are
dominated by the zero-point error of the galaxy proper motions.
The convergent point for the cluster was
calculated by Schwan (1991) from 145 high-accuracy FK5
and PPM proper motions. Using a subset of 62 stars found to lie within 4 pc
of the cluster center, he found a convergent point for the
cluster (
= 97
68
±
042,
=
598
±
018), a
cluster center
( =
6559,
=
1627),
and a distance of 47.9 pc. Torres et al. (1997c)
calculated the mean proper motion at the cluster center from 53 of the 62
stars
as 
c
= 113.1 ± 0.7 mas yr-1. Gunn et
al. (1988) derived a slightly different convergent point
(
= 982
±
11,
=
61 ±
10) based
on the radial velocities determined by Griffin et
al. (1988) and the bulk proper motion of the Hyades derived from
the absolute proper motions of 59 stars from
Hanson (1975). Combined with their cluster center
( =
6615,
= 1665),
they obtained a distance to the cluster center of 45.4 ± 1.2 pc. We
can calculate the distance of the Hyades
center, Dc, for each star observed with
the HST FGS from
where the subscript c refers to the cluster center,
is
the absolute parallax derived here for each star,
is the
angular distance of the star from the convergent point on a great circle,
and is
the absolute proper motion determined here along that great circle. The
errors of the individual estimates of the cluster center distance
were derived from a propagation of the errors of the proper motions
and parallaxes, as the errors of
,
c,
and c
do not contribute significantly to the total error. Systematic errors in
c
and c
do, however, have a very important effect.
In Table 2 we list the equatorial coordinates for the equinox 1950 from Hanson (1975) for the first seven stars and from the PPM Catalog for the remainder. Also given are the magnitudes and colors, absolute parallaxes, proper motions and their standard errors, and the derived distance to the cluster center and its standard error. The latter two quantities are listed for both the Schwan (1991) and Gunn et al. (1988) cluster parameters. The first part of the table lists the seven stars measured in the HST FGS parallax program, while the second part lists the stars (vB24, vB57, and vB72) for which orbital parallaxes have been derived by Torres et al. (1997a, 1997b, 1997c), and the third part lists a trigonometric parallax and proper motion derived by Gatewood (1992) for vB24 that was inadvertently omitted from the YPC. The weighted mean distances of the cluster center are listed after each of the first two sections along with their formal errors.
The various Hyades distances are
summarized in Table 3 along with
their respective errors. Internal errors are defined as the formal
propagation of the parallax and proper-motion errors into the error of the
mean, while external errors are based on the dispersion of the
individually derived cluster center distances. As can be seen from a
comparison of the HST distances based on the
Schwan (1991) and Gunn et al.
(1988) solutions, the results depend critically on the proper-motion
system and the individual proper motions. According to equation (1), after scaling due to differing angular distances from
the convergent point, the distance of a star relative to the cluster center
is given by the ratio of the star's proper motion to that of the
cluster center. The cluster center distance is then derived from the
scaled proper-motion distance and the parallax of the star. The HST
parallaxes yield a cluster center distance (4.83 ± 2.0 pc) in
agreement with the orbital parallaxes and the YPC for
the Gunn et al. (1988) solution, since the HST
proper motions are small relative to the bulk proper motion of the Hyades
center as derived by Gunn et al. (1988) from
Hanson (1975), and the parallaxes are small. In
contrast, the smaller Schwan (1991) cluster center
proper motion places the HST stars closer to the center, and
therefore the small HST parallaxes move the center farther (5.25
± 2.7 pc) from the Sun. The orbital parallaxes are essentially
independent of the convergent point solution, since for consistency both
must use
the FK5PPM
proper motions and the cluster center proper motion derived from
Schwan (1991), as the three stars were either too
bright for accurate measurement in the study of Hanson
(1975) or were outside his field of view.
Based on the agreement of the HST parallaxes and proper motions presented here with the Orbital parallaxes and the YPC parallaxes, we are inclined to prefer the Gunn et al. (1988) solution and therefore adopt 48.3 ± 2.0 pc or m - M = 3.42 ± 0.09 for the Hyades distance as derived from our HST results.
It would be unwise to advocate any increase in the distance scale based on the HST FGS parallax results, but it should be noted that Feast & Catchpole (1997) recommend an increase of 10% ± 14% based on HIPPARCOS parallax observations of the classical Cepheids and Reid (1997) suggests an increase of 5% to 15% based on HIPPARCOS parallaxes of subdwarfs. Once the HIPPARCOS parallaxes of Hyades members are released and carefully analyzed, we should have a clearer picture of the state of the distance scale and can then discuss the astronomical consequences of any revision.
The fourth edition of the General Catalogue of Trigonometric Stellar Parallaxes in two volumes is available in printed form from the Yale Astronomy Department and in an abbreviated electronic form from the Astronomical Data Centers.
The authors of this Letter would like to acknowledge the assistance of the STScI and GSFC staff who assisted us in the preparation of many versions of the Observing Proposal forms and provided solutions for numerous obstacles that were encountered during the observations; we would not have been able to complete the observations without their invaluable help. In particular, we would like to acknowledge the collaboration of L. Nagel, D. Taylor, and P. Stanley. In addition, we would like to acknowledge the engineers and scientists at the Hughes Danbury Optical Systems who designed the FGS and supported us in the calibration and observations. In particular, we would like to mention L. Abramowicz-Reed, C. Ftaclas, and T. Facey. Finally, we would like to thank the referee of this Letter, D. Latham, for his helpful suggestions, which improved this Letter.
This research was supported in part by grants from NASA to the HST GTO Astrometry Science Team. The preparation of the YPC was supported in part by grants from the NSF. C. D. and J. R. K. also acknowledge support by NASA through grants HF-1042.01-93A and HF-1046.01-93A from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555.
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Baltic Astron., 6, 27 First citation in article | NASA ADS| vA a | Ha b | GH7 c | BD or Os d | Nobs | Nref |  1(x)
(mas) | 1(y)
(mas) |
| 310... | 312 | 196 | +17°715 | 7 | 6 | 1.6 | 4.0 |
| 383... | 378 | 212 | Os 373 | 7 | 6 | 2.1 | 3.4 |
| 472 e... | 420 | 228 | +13°685 | 6 | 4 | 1.2 | 3.3 |
| 548... | 472 | 241 | +15°634 | 7 | 5 | 1.2 | 2.6 |
| 622... | 505 | 249 |  | 7 | 7 | 2.2 | 2.6 |
| 627... | 509 | 250 | +17°744 | 7 | 7 | 2.2 | 2.6 |
| 645... | 517 | 253 | Os 749 | 6 | 5 | 1.7 | 3.6 |
| Name | Type | (1950) | (1950) | V
(mag) | B - V
(mag) |
(mas) |
(mas) |
(mas yr-1) |
(mas yr-1) |
(mas yr-1) |
(mas yr-1) | SCHWAN | GUNN | ||
| Dc
(pc) |
(pc) | Dc
(pc) |
(pc) | ||||||||||||
| vA310... | H | 4 21 22.9 | 17 53 21 | 9.99 | 1.05 | 15.4 | 0.9 | 105.0 | 0.9 | -14.1 | 0.8 | 59.0 | 3.5 | 54.3 | 3.2 |
| vA383... | H | 4 23 14.1 | 14 55 46 | 12.14 | 1.45 | 16.0 | 0.9 | 91.7 | 0.8 | -15.8 | 1.0 | 52.1 | 3.2 | 47.9 | 3.0 |
| vA472... | H | 4 25 15.1 | 13 45 29 | 9.03 | 0.84 | 16.6 | 1.6 | 78.9 | 1.3 | -16.7 | 1.5 | 44.5 | 4.6 | 40.8 | 4.3 |
| vA548... | H | 4 26 38.9 | 16 8 12 | 10.32 | 1.17 | 16.8 | 0.3 | 98.7 | 0.4 | -15.5 | 0.3 | 53.9 | 1.5 | 49.5 | 1.4 |
| vA622... | H | 4 28 35.2 | 17 36 46 | 11.85 | 1.44 | 21.6 | 1.1 | 99.6 | 1.0 | -26.1 | 1.3 | 43.4 | 2.4 | 39.9 | 2.2 |
| vA627... | H | 4 28 43.2 | 17 36 15 | 9.55 | 0.98 | 16.5 | 0.9 | 106.6 | 1.1 | -16.2 | 3.0 | 58.9 | 3.5 | 54.2 | 3.2 |
| vA645... | H | 4 29 1.2 | 15 23 38 | 11.05 | 1.28 | 15.7 | 1.2 | 102.5 | 1.4 | -14.0 | 1.4 | 60.8 | 4.8 | 55.9 | 4.4 |
| Weighted mean... | 52.5 | 1.0 | 48.3 | 0.9 | |||||||||||
| vB24... | O | 4 15 25.4 | 21 27 31 | 5.87 | 0.24 | 17.9 | 0.6 | 101.4 | 0.9 | -36.6 | 1.0 | 49.1 | 1.6 | | |
| vB57... | O | 4 22 45.8 | 15 45 42 | 7.05 | 0.49 | 21.4 | 0.7 | 105.0 | 3.1 | -25.3 | 3.5 | 44.8 | 1.9 | | |
| vB72... | O | 4 25 48.2 | 15 49 42 | 3.74 | 0.18 | 21.2 | 0.8 | 111.7 | 1.6 | -25.5 | 1.8 | 49.0 | 1.9 | | |
| Weighted mean... | 47.8 | 0.9 | | | |||||||||||
| vB24... | G | 4 15 25.4 | 21 27 31 | 5.87 | 0.24 | 19.4 | 1.1 | 96.8 | 0.7 | -36.0 | 0.4 | 43.5 | 2.5 | | |
Units of right ascension
() are hours,
minutes, and seconds, and units of declination
() are
degrees, arcminutes, and arcseconds.
-type
definitions are as follows: H is the HST trigonometric parallax from this
study; O is the orbital parallax from Torres et al.
1997a, 1997b,
1997c; and G is the ground-based parallax from
Gatewood 1992.| PARAMETER | AVERAGE AND INTERNAL ERROR | WEIGHTED MEAN AND EXTERNAL ERRORS | ||
| HST | Orbital | HST | Orbital | |
| Schwan... | 53.2 ± 1.0 | 47.6 ± 0.9 | 52.5 ± 2.7 | 47.8 ± 1.4 |
| Gunn... | 48.9 ± 0.9 | ... | 48.3 ± 2.0 | ... |