Astronomy & Astrophysics manuscript no. 2nd˙submission November 16, 2004 (DOI: will be inserted by hand later) On the long-term evolution of jet-driven molecular outflows R. Keegan and T.P. Downes School of Mathematical Sciences, Dublin City University, Ireland Received date ;accepted date Abstract. We use numerical simulations to examine the mass-velocity, m(v), and intensity-velocity, I (v), relations in jet-driven molecular outflows up to an age of 2300 yrs. We find that the m(v) relation is a power-law, m(v) ∝ v −γ , the exponent of which increases with time up to γ ≈ 1.6 at t ≈ 1500 yrs. It then becomes roughly constant. This indicates that γ does not evolve throughout the lifetime of a molecular outflow, at least in the context of the jet-driven model. We also investigate the effect of long-period episodicity of the jet on the m(v) and I (v) relations. We find that, contrary to previous expectations, these relations are not significantly changed with the introduction of such variability into the jet. Finally, we present a novel, and relatively simple, parallelisation method for the code used in these simulations. This gives an increase of roughly a factor of 4 in speed over standard methods, and allows the simulations presented here to be run fairly easily, even with modest computational resources. Key words. hydrodynamics – shock waves – ISM:jets and outflows – ISM:molecules 1. Introduction Various authors have noted that the intensity-velocity relation- ship observed in low-J CO lines in molecular outflows tends to follow a broken power-law I CO (v) ∝ v -γ with γ ≈ 1.5 – 2 up to line-of-sight velocities v break ≈ 10 – 30 km s -1 and γ ≈ 3– 7 at higher velocities (e.g. Rodr´ ıguez et al. 1982; Stahler 1994; Bachiller & Tafalla 1999; Richer et al. 2000). More recently, similar behaviour has been observed in observations of the H 2 S(1) 1–0 line in various outflows (Salas & Cr´ uz-Gonz´ alez 2002). The exponents in this latter intensity-velocity relation, I H 2 (v) tend to be smaller than those in the I CO (v) relations for the same outflows. These authors also suggested that v break may be lower for I H 2 (v) than for I CO (v) but it is difficult to be cer- tain of this due to the relatively low spectral resolution of their observations (∼ 25 km s -1 ). The I CO (v) relation has been reproduced in numerical sim- ulations of jet-drivenoutflows where the molecular outflow is identifi ed as the molecular material which has been swept up by the bowshock created by the jet advancing into the ambient medium (e.g. Smith, Suttner & Yorke 1997; Downes & Ray 1999; Downes & Cabrit 2003). In addition, Downes & Cabrit (2003) reproduced qualitatively similar I H 2 (v) relations to those observed by Salas & Cr´ uz-Gonz´ alez (2002). Rosen & Smith (2004) have also reported on I H 2 (v) profi les calculated from their simulations. These latter relations appear to be somewhat different to those observed, particularly at low velocities. It is likely that at least some of the difference can be attributed to Send offprint requests to: T.P. Downes, turlough.downes@dcu.ie Correspondence to: School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9, Ireland problems with the resolution of these latter simulations and this will be the subject of a forthcoming paper. All these numerical simulations show a systematic increase with time of γ at low velocities. This behaviour of γ appears to be supported by the observations (e.g. Richer et al. 2000 and references therein; Salas & Cr´ uz-Gonz´ alez 2002). To date, sim- ulations have only addressed the early-time behaviour of these outflows, with simulation ages being typically in the range of 400 – 1000 yrs. This leaves open the question of whether the temporal behaviour of γ seen in simulations is something which only occurs in young jet-driven flows or, indeed, whether it is a transient effect arising from initial conditions in the sim- ulations. Downes & Ray (1999) found no evidence that variability in the jet velocity affects the value of γ, even for large varia- tions (up to 60%) of the jet velocity. However, the variations were of short period (only up to 50 yrs) and these authors sug- gested that large variations over much longer periods may have a signifi cant impact on γ. They were unable to examine this possibility due to computational constraints restricting the age to which they could simulate jets, and hence the time-scales associated with the variability of the jet. Moreover, Arc´ e& Goodman (2001) used an analytic treatment of the problem of episodic outflows to suggest that episodicity could, in fact, in- crease the value of γ. In this paper we present the results of two long-duration simulations of jet-driven molecular outflows up to ages of 2300 yrs, one of which is for an episodic jet with a periodicity of 800 yrs. We examine the temporal behaviour of γ for both the mass- and intensity-velocity relations in each case and study whether episodicity can affect γ. The overall aim is to assess the long