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Astron. Astrophys. 351, 506-518 (1999)

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5. Discussion

Kinematical studies of the system of young stars in the solar neighbourhood over the last decades have revealed some clear features associated to the Gould Belt, which have been reinforced by the accurate picture of the stellar kinematics in the solar neighbourhood provided by Hipparcos (Lindblad et al. 1997, Palous 1998, Torra et al. 1999). These features can be summarized as follows:

  • The A constant has a value smaller than that corresponding to pure galactic differential rotation.

  • The B constant is negative, and its absolute value is at least similar, and probably somewhat larger, than that corresponding to pure galactic differential rotation.

  • The K constant, which should be null for pure galactic differential rotation, is clearly positive. The same seems to be true for the C constant.

To these features, one can add the ones related to the vertical motion that have been described in Sect. 2 of this paper:

  • There is a small gradient of [FORMULA] km s-1 kpc- 1 in the vertical component of the velocity.

  • The stars of the Gould Belt oscillate around the galactic plane around an axis that is misaligned by [FORMULA] with respect to the nodal line marking the intersection between the Gould Belt and the galactic plane.

These are the features, together with the observed orientation of the Gould Belt and its persistence over a time span of [FORMULA] years or more, that any kinematic model should aim at accounting for. Is any of the scenarios described in Sect. 4 favoured by these observed features?

Expansion models in which the stars of the Gould Belt formed in a small volume successfully account for the observed behaviour of the A, C, and K constants. Nevertheless, they seem to be excluded by the large negative value of B, as noted by Lindblad 1980and Palou 1998. Models that assume that the stars formed in a narrow strip and expand initially along a preferential direction also account for the values of A, C, and K, although they do so only after an early evolution characterized by large positive values of A and K, and a large negative value of C. However, the previous objection concerning B applies in this case too, as a permanent null value of B is also predicted in this scenario.

The main objection to those expansion models, namely their inability to reproduce a value of B significantly different from zero, weakens if the Gould Belt started its expansion from a plane that had already a considerable extent. In this case, the observed features in A, C, and K are still successfully reproduced, but now with a clearly negative value of B, in better agreement with the observations. As far as the Oort constants and the orientation of the Gould Belt are concerned, the predictions of both the model of radial expansion and the model of expansion along a line are essentially the same. However, none of the expansion models is able to account for the main feature discussed in this paper concerning the vertical motion of stars, namely the large offset between the axis of vertical oscillation and the nodal line. Moreover, radial expansion models require a large initial tilt of the plane of the Belt, as can be seen in Figs. 4 and 5, and it is difficult to imagine a formation mechanism that could account for such a large value.

The rotation model is the only one among the models studied here that predicts the offset between the axis of vertical oscillation and the nodal line. Most interestingly, the choice of an initial rigid body rotation with [FORMULA] km s-1 kpc- 1, and of the initial orientation parameters of the Gould Belt, is able to produce a remarkably good fit, at least qualitatively, to all the features observed in the Gould Belt, including its present orientation, the peculiarities of the Oort constants, and the characteristics of its vertical motion, if the age of the Gould Belt is [FORMULA] years. The agreement can be appreciated by comparing the measured values of the different parameters with those predicted by the model at that age, given in Table 1. In such comparison, we have adopted the values of Table 4 of Torra 1999 for their sample of stars at a distance of less than 600 pc from the Sun and an age below [FORMULA] years. As to the results of Lindblad et al. 1997, the values listed correspond to their sample of 144 stars within the rectangular area limited by [FORMULA], [FORMULA]. The differences between both sets of results may provide an idea of the subsisting uncertainties in the derived value of the Oort constants.


Table 1. Comparison between observed characteristics of the Gould Belt and those predicted by the best fitting rotation model.

The dating of the Belt based on its kinematical behaviour at present is strongly constrained by the mild gradient observed in the vertical component of the velocity: a difference of only [FORMULA] years would result in [FORMULA] km s- 1 kpc-1, a value that would start conflicting with the observations. The accurate dating based on the small value of G is a common feature for all the models, but unfortunately different models place the age at which G is sufficiently small at different times. Therefore, it is not possible to use the observed value of G for a model-independent dating of the Gould Belt. Nevertheless, the fact that the pattern based on the evolution of a disk initially in rotation is by far the one providing the best fit to the data leads one to strongly favour [FORMULA] years as the true age of the Gould Belt. Remarkably, as can be seen from Fig. 8, the direction of the axis of vertical oscillation changes rapidly with time when the Belt is near its greatest tilt with respect to the galactic plane. For this reason, even the large uncertainty in the value of [FORMULA] is a more stringent constraint on the present age of the Belt, as a difference of only [FORMULA] years brings the predicted value of [FORMULA] outside the range allowed by the observations. An age of [FORMULA] years is in good agreement with the one adopted by Palou 1998, although the Keplerian rotation pattern proposed in that paper is different from the solid body rotation studied here. It should be noted that the non-linear dependence between positions and velocities implied by the Keplerian rotation pattern makes the formulism developed in Sect. 3 not applicable to that case, which is why such a pattern has not been considered in the present study. Moreover, an initially Keplerian rotation lacks the property of keeping the stars distributed on a plane as time passes.

The initial rotation of the Gould Belt system has important implications concerning possible hypotheses for its origin. The failure of pure expansion models in explaining basic features of the present day kinematical behaviour of the Belt rules out models invoking a very energetic event, or a chain of them, in a small volume as the cause for the velocities of the stars. This does not mean that such explosive events have not taken place at all: on the opposite, they must have been relatively frequent as the oldest most massive members of the Gould Belt have exploded as supernovae, or as the stellar winds from its O and B stars have injected large amounts of energy in their surroundings. Many features in the interstellar medium of the Gould Belt, such as the Local Bubble (Cox & Reynolds 1987, the Lindblad Ring of HI (Lindblad et al. 1973), or the shells around the Scorpius-Centaurus-Lupus association (de Geus 1992) testify to the importance of the past and present interaction of the Gould Belt stars with the interstellar medium. However, the mechanism that gave origin to these stars in the first place has most probably to be searched elsewhere.

A simplified, straightforward interpretation of the kinematical history of the Gould Belt may be to assume the existence of a giant, rotating molecular cloud that started to form stars about [FORMULA] years ago, becoming unbound in the process, probably because of the loss of the gas that was not employed in the formation of stars. Although such a scenario seems in principle plausible, it would require an initial tilt of the molecular cloud of [FORMULA] with respect to the direction perpendicular to the galactic plane, whereas actual giant molecular clouds are seen to have their rotation axes well aligned with that direction (Blitz 1993).

An alternative model for the origin of the Gould Belt was proposed by Comerón & Torra 1992, 1994 based on the consequences of the impact of a high velocity cloud from the galactic halo on the galactic disk. The model was proposed mainly to account for the initial tilt of the Belt, which appeared as a natural consequence of an impact along a direction not perpendicular to the galactic disk. The rotation pattern of the resulting layer of dense shocked gas, where star formation would then proceed, could not be considered in the two-dimensional hydrodynamical simulations presented in those works. However, it is conceivable that some rotation of the resulting structure may well result as a consequence of the collision, due to the transfer of the angular momentum of the impinging cloud to the shocked layer. A detailed examination of this aspect of the collision is beyond the scope of this paper, and should be studied by means of fully three-dimensional hydrodynamical simulations, which should ultimately decide whether the observed kinematical patterns are compatible or not with this hypothesis.

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© European Southern Observatory (ESO) 1999

Online publication: November 3, 1999