Annu. Rev. Astron. Astrophys. 2001. 39: 137-174
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When Margaret and Geoffrey Burbidge (1960) initiated their observational program to determine the kinematics and hence masses of spiral galaxies, they were reproducing the technique employed by Pease (1918), but with improvements. Telescopes were larger, spectrographs were faster, photographic plates were sensitive in the red. The strong emission lines of Halpha and [NII] could be more easily detected and measured than the weak broad H and K absorption lines. Since the 1980s, larger telescopes and improved detectors have existed for optical, radio, and mm observations. The combination of high spatial and high spectral resolution digital detectors and speedy computers has permitted a sophistication in the velocity analyses (Section 3) that will surely continue.

2.1. Halpha and Optical Measurements

Optical astronomers have available several observing techniques for determining rotation curves and velocity fields for both the ionized gas and stars. Traditional long slit spectra are still valuable for deducing the rotation curve of a galaxy from emission lines (Rubin et al. 1980, 1982, 1985; Mathewson et al. 1992, 1996; Amram et al. 1992, 1994; Corradi et al. 1991; Courteau 1997; Vega Baltran 1999), but methods which return the entire velocity field, such as Fabry-Perot spectrographs (Vaughan 1989) or integral (fiber-optic) field instruments (Krabbe et al. 1997) offer more velocity information at the price of more complex and time-consuming reductions. Although Halpha, [NII], and [SII] emission lines have traditionally been employed, the Seyfert galaxy NGC 1068 has become the first galaxy whose velocity field has been studied from the IR [Si VI] line (Tecza et al. 2000). Distant planetary nebula (Section 2.5) and satellite galaxies are valuable test particles for determining the mass distribution at large distances from galaxy nuclei. For a limited number of nearby galaxies, rotation curves can be produced from velocities of individual HII regions in galactic disks (Rubin & Ford, 1970, 1983; Zaritsky et al. 1989, 1990, 1994).

2.2. HI line

The HI line is a powerful tool to obtain kinematics of spiral galaxies, in part because its radial extent is often greater, sometimes 3 or 4 times greater, than that of the visible disk. Bosma's thesis (1981a, b; van der Kruit & Allen 1978) played a fundamental role in establishing the flatness of spiral rotation curves. Instrumental improvements in the last 20 years have increased the spatial resolution of the beam, so that problems arising from low resolution are important only near the nucleus or in special cases (Section 4). While comparison of the inner velocity rise for NGC 3198 showed good agreement between the 21-cm and the optical velocities (van Albada et al. 1985; Hunter et al. 1986), the agreement was poor for Virgo spirals observed at low HI resolution (Guhathakurta et al. 1988; Rubin et al. 1989). For low surface brightness galaxies, there is still discussion over whether the slow velocity rise is an attribute of the galaxy or due the instrumentation and reduction procedures (Swatters 1999, 2001; de Blok et al 2001; Section 7.5).

2.3. CO Line

The rotational transition lines of carbon monoxide (CO) in the millimeter wave range [e.g., 115.27 GHz for 12CO(J = 1 - 0) line, 230.5 GHz for J = 2 - 1] are valuable in studying rotation kinematics of the inner disk and central regions of spiral galaxies, for extinction in the central dusty disks is negligible at CO wavelengths (Sofue 1996, 1997). Edge-on and high-inclination galaxies are particularly useful for rotation curve analysis in order to minimize the uncertainty arising from inclination corrections, for which extinction-free measurements are crucial, especially for central rotation curves.

Because the central few kpc of the disk are dominated by molecular gas (Young & Scoville 1992; Young et al. 1995; Kenny & Young 1988; Garcia-Burillo et al. 1993; Nakai et al. 1994; Nishiyama & Nakai 1998; Sakamoto 1999), the molecular fraction, the ratio of the molecular-gas mass density to that of total of molecular and HI masses, usually exceeds 90% (Sofue et al. 1995; Honma et al. 1995). CO lines are emitted from molecular clouds associated with star formation regions emitting the Halpha line. Hence, CO is a good alternative to Halpha and also to HI in the inner disk, while HI is often weak or absent in the central regions. The Halpha, CO, and HI rotation curves agree well with each other in the intermediate region disks of spiral galaxies (Sofue 1996; Sofue et al. 1999a, b). Small displacements between Halpha and CO rotation curves can arise in the inner regions from the extinction of the optical lines and the contamination of the continuum star light from central bulges.

Decades ago, single dish observations in the mm wave range had angular resolutions limited from several to tens of arc seconds due to the aperture diffraction limit. Recently, however, interferometric observations have achieved sub- or one-arcsec resolution (Sargent and Welch 1993; Scoville et al. 1993; Schinnerer et al. 2000; Sofue et al. 2000), comparable to, or sometimes higher than, the current optical measurements (Fig. 1). Another advantage of CO spectroscopy is its high velocity resolution of one to several km s-1.

Figure 1

Figure 1. Position-velocity diagram along the major axis of the edge-on galaxy NGC 3079 in the CO (J = 1 - 0) line emission at a resolution of 1".5 observed with the 7-element interferometer consisted of the 6-element mm-wave Array and the 45-m telescope at Nobeyama (Sofue et al. 2000). The lower panel shows a composite rotation curve produced by combining the CO result and HI data (Irwin and Seaquist 1991) for the outer regions.

2.4. Maser Lines

Radial velocity observations of maser lines, such as SiO, OH and H2O lines, from circum-stellar shells and gas clouds allow us to measure the kinematics of stellar components in the disk and bulge of our Galaxy (Lindqvist et al. 1992a, b; Izumiura 1995, 1999; Deguchi et al. 2000). VLBI astrometry of SiO maser stars' proper motion and parallax as well as radial velocities will reveal more unambiguous rotation of the Galaxy in the future. VLBI measurements of water masers from nuclei of galaxies reveal circumnuclear rotation on scales of 0.1 pc around massive central black holes, as was successfully observed for NGC 4258 (Miyoshi et al. 1995; see Section 4.4).

2.5. Planetary Nebulae, Fabry-Perot, and Integral Field Spectrometers

Planetary nebulae (PN) are valuable tracers of the velocity fields of early type and complex galaxies, at large nuclear distances where the optical light is faint or absent (Jacoby et al. 1990; Arnaboldi 1998; Gerssen 2000), and for galaxies in clusters (Cen A, Hui et al. 1995; Fornax A, Arnaboldi et al. 1998). The simultaneous analysis of absorption line velocities for inner regions and hundreds of PN in the outer regions can constrain the viewing geometry as no single tracer can, and thus reveal valuable details of the kinematics and the mass distribution (Rix et al. 1997; Arnaboldi et al. 1998).

Fabry-Perot spectrometers are routinely used to derive the Halpha velocity fields of spirals of special interest (Vaughan 1989; Vogel et al. 1993; Regan and Vogel 1994; Weiner & Williams 1996). Like Integral Field Spectrometry (Krabbe et al. 1997), these techniques will acquire more adherents as the instrument use and the reduction techniques become routine.

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