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Astron. Astrophys. 318, 416-428 (1997)

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1. Introduction

It is now well established that the rotation curves of spiral galaxies, including the Milky Way, are not decreasing at large radii, but generally remain nearly flat even beyond the end of the optical disc, revealing the presence of dark matter.

The rotation curve of the Milky Way itself has proved hard to determine, especially for [FORMULA], because of our unfavorable position in the middle of its disc. As the tangent-point method using HI gas cannot be applied towards the outer disc, one needs a population of tracers - preferably bright - whose radial velocity and distance can be determined independently. Recent determinations using planetary nebulae, clusters or HII regions include Schneider & Terzian (1983), Hron (1987), Fich et al. (1989). For a different approach using HI, see Merrifield (1992).

These studies outline a rotation curve with a dip beyond the solar radius, then flat or rising at large radii. The most widely cited method consists of measuring the radial velocity of the gas in HII regions and their distance by ZAMS fitting to the exciting stars (see review in Fich & Tremaine 1991). This seems to indicate a rotation curve that rises to 250 km s-1 from R=10 kpc outwards (for [FORMULA] kpc and [FORMULA] km s-1 assumed). But the data are sparse and scattered beyond R=12kpc and these values are not unambiguously defined. Moreover the distance determination for HII regions is a very delicate procedure (Turbide & Moffat 1993).

Hence the idea of extending a precise determination of the rotation curve to the outer disc using classical cepheids is a reasonable alternative. Their intrinsic brightness, reliability as distance indicators and young age make classical cepheids ideal tracers for studying the rotation curve of the Milky Way (Joy 1939, Stibbs 1956). Recent studies using cepheids define the rotation curve in the range R=6-11 kpc (Caldwell & Coulson 1987, Pont et al. 1994). Beyond this range, the objects become fainter (Fig. 1), and before this study very few had been measured in radial velocity.

[FIGURE] Fig. 1. General characteristics of the sample: distribution of periods (top), magnitudes (middle) and galactic coordinates (bottom)

This paper presents the results of a programme aimed at extending the determination of the rotation curve out to [FORMULA] using cepheids. Our strategy has been to choose cepheids beyond [FORMULA] kpc along the two directions [FORMULA] and [FORMULA]. To this was added a control sample in the anticentre direction ([FORMULA]) in order to detect a possible non-axisymmetric component in the velocity field - towards the anticentre, the line of sight is perpendicular to the rotation velocity, and only non-axisymmetric motions affect the radial velocity. The gradual recognition of the fact that the Galaxy probably contains a bar or triaxial spheroid (Blitz & Spergel 1991, Weinberg 1992, Dwek et al. 1995), as well as the asymmetries observed in HI kinematics, have recently led to some non-axisymmetric models for the Galaxy (Blitz & Spergel 1991, Kuijken 1994, Kuijken & Tremaine 1994). These models make testable predictions about the velocity field of the outer disc.

The target stars have been selected as the classical cepheids (DCEP) and cepheids of unknown type (CEP) in the GCVS (Kholopov 1985) which were estimated, based on photometric data found in the stellar database SIMBAD, to be situated beyond R=11 kpc by a crude distance estimate.

The resulting list contains 48 objects, of V magnitudes between 9 and 15, periods between 2 and 26 days, 11 in the north ([FORMULA]), 11 towards the anticentre ([FORMULA]) and 26 in the south ([FORMULA]). This uneven distribution reflects the fact that the absorption is much lower in the third galactic quadrant. We have measured these objects in radial velocity, and in photometry when the data available were not sufficient to obtain reliable distances.

The distributions of visual magnitudes, periods and galactic coordinates for the sample are displayed in Fig. 1.

Sect. 2 of this article presents the radial velocity and photometric data. Distances are computed in Sect. 3, using period-luminosity relations corrected for metallicity effects. Sect. 4 presents the resulting rotation curve, and examines the non-axisymmetric component of the velocity field. In Sect. 5, the results are compared with other observational studies and confronted to some models, and the effects of modifying some assumptions are examined.

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© European Southern Observatory (ESO) 1997

Online publication: July 8, 1998