Annu. Rev. Astron. Astrophys. 1978. 16: 103-39 Copyright © 1978 by Annual Reviews. All rights reserved

4.4. Density Wave Streaming

One of the major motivations for making extensive high-resolution radio-HI observations of velocity fields in spiral galaxies has been to search for the characteristic streaming motions of the gas caused by an underlying density wave in the stellar disk. The resolution requirements are severe for radio telescopes (Allen 1975a), and results are available for only a few nearby galaxies.

Much attention has of course been paid to M31, although its relatively high inclination makes the interpretation difficult. This is especially so along the minor axis where the radial component of the streaming is otherwise best observed. Guibert (1974) showed that the spiral pattern is at least consistent with the rotation curve and linear density-wave theory. The velocity field was studied in greater detail by Emerson (1976), who found peculiar motions of ~ 30 km/sec associated with the arms; on the major axis the motions are consistent with theory, but on the minor axis they appear to have the wrong sign. Another interpretation that is offered by Emerson for the motions near the major axis involves simply the self-gravitational effects of the HI gas in the arms. To complicate affairs, the WSRT observations (Shane 1978) have indicated that two arms around the near minor axis of M31 at 5 and 9 kpc from the center are apparently contracting and expanding with respectively 30 and 20 km/sec.

In M33 Warner et al. (1973) could find no evidence for density-wave systematic motions in the disk with amplitudes larger than 3 km/sec. On the other hand, Rogstad et al. (1974) do find some evidence for a weak density-wave streaming of about 4 km/sec with corotation at ~ 2.4 kpc.

A pattern of density-wave motions with velocities of ~ 20 km/sec was found in M101 by Rogstad (1971) from radio-HI observations with an angular resolution of 4'. Later measurements at a resolution of about 0'.5 (Allen 1975a) revealed that the HI is indeed concentrated in ridges on the optically visible arms, but there is little evidence for the interpretation in terms of streaming velocities as reported earlier. The different results serve to illustrate the serious effects of confusion of spiral arms in low-resolution observations, and confirm the need for a minimum resolution in terms of the arms spacing. Note that, owing to the low inclination of the galaxy, streaming motions of 15 km/sec in the plane are not yet excluded by the observations.

Segalovitz (1976) has constructed a nonlinear density-wave model for M51; however, after smoothing the model to the resolution of the radio-HI observations, the amplitude of the streaming motions becomes too small for a conclusive test. Tully (1974c) finds evidence for density-wave streaming in the H velocity map of M51 that is consistent with the linear theory.

The most convincing evidence for the existence of density-wave motions is to be found in the radio-HI map of the velocity field of M81. From measurements at 0'.5, Rots (1975) showed that there are indeed systematic motions in the spiral arms of M81 that are reasonably consistent with linear density-wave theory. An extensive and detailed analysis of the observations has been made by Visser (1975, 1978a, b): The spiral pattern of the underlying stellar density wave is computed with the linear theory, using the optical surface photometry by Schweizer (1976) to determine the wave amplitude; the flow pattern and density distribution of the HI is then calculated using nonlinear gas dynamics. The models are finally smoothed to the angular resolution of the observations for comparison (see Figure 5). From this it follows that the kinematical effects of the shock are visible when the resolution is about 1/6 of the arm spacing, while the systematic streaming motions can still be clearly detected with a resolution of 1/3 of the arm spacing. For beamwidths greater than about 2/3 of the arm spacing, density-wave effects are no longer discernable. A convincing picture emerges, with strict constraints on the parameters of the model. The results for M81 must be considered as strong evidence for the existence of density waves, and as supporting a description of these waves based on the WKBJ analysis of Lin & Shu (1964, 1966) and Roberts (1969). The question of the origin and maintenance of the density wave in M81 has not yet been investigated in the same detail; in this respect it is perhaps not entirely coincidental that the available observations of the area around M81 point to interactions with both M82 and NGC 3077 (Cottrell 1977, van der Hulst 1977).

Figure 5. Comparison of the observed velocity field in the HI of M81 with the predictions of a self-consistent density wave model (Visser 1978a, b). The underlying intensity distribution is the observed HI surface density distribution at a resolution of 25". The fulldrawn lines are observed contours of radial velocity after smoothing of the original data to a beam of 50" (indicated at lower-right). The dashed lines are the predicted velocities in the density-wave model also smoothed to the resolution of 50".

It is unfortunate that other galaxies that are similar to M81 in optical appearance are beyond the resolution capabilities of present day radio telescopes, at least as far as further detailed tests of the density-wave theory are concerned.

We mention finally one other case where systematic streaming velocities have been found. The optically observed velocity field in the central areas of the peculiar galaxy NGC 3310 shows strong noncircular motions associated with the spiral arms (van der kruit 1976a, Figure 6). If these velocities are ascribed to density waves, the amplitude of the streaming is 1/3 to 1/2 of the rotational speed. A number of other properties of this galaxy are at least qualitatively consistent with strong compression in the spiral arms: ridges of radio continuum emission, intense H emission, blue colors, and UV excess (van der Kruit & de Bruyn 1976). The inference from this and from the low M/L ratio is that the galaxy has experienced a recent (~ 10⁷ years ago) burst of star formation that may leave been caused by the excitation of an unusually strong density wave.

Figure 6. Severe effects of noncircular motions associated with the spiral structure are observed in NGC 3310 (van der Kruit 1976a). The velocity field shown here is constructed from measurements on emission lines in a large set of optical spectra. In spite of the large noncircular motions, Which are probably effects of unusually strong density-wave streamings, the basic rotation pattern is still visible . The orientation of NGC 3310 is that used for the schematic illustration in Figure 1.