The Phenomenology of Jets in Astrophysics
Objective of the study
- In this paper we focus our attention on the measure of the spreading of the laboratory jets and the comparison with the results obtained by numerical simulations.
- We also discuss the appearance of sinuous structures observed in some laboratory jets and the extent to which these features may develop as the response to non-axial perturbations in numerical simulations.
Among the astrophysical phenomena that involve high velocity matter flows, jets are the most widespread in the universe. They are found in the most diverse environments and show a wide range of sizes and powers. At one end, we have jets from Active Galactic Nuclei (AGNs) that are the largest in size, up to a few megaparsecs in length, and the most powerful ones (kinetic power up to ∼1047 48− ergs s−1 , (Godfrey and Shabala 2013, see also HD simulations by Zanni et al 2003 and Hodges-Kluck and Reynolds 2011). At the other end, we have jets from Young Stellar Objects (YSOs) that are located inside the Giant Molecular Clouds present in our galaxy, and in other ones as well. YSO jets are up to some parsecs long and attain kinetic powers up to ∼1033 ergs s−1 (Reipurth and Bally 2001 for a review and recent observations by Hartigan et al 2011). While AGN jets have relativistic velocities, YSO jets speeds are the typical escape velocity from stars of a few solar masses, and amount to a few hundreds kilometers per second, corresponding to Mach numbers in the range 10–40. A striking characteristic of jets is their high degree of collimation, in particular YSO jets have opening angles that vary between 0.5 to 5° (Mundt et al 1991, Ray et al 1996).
In recent years, we have seen many laboratory experiments that try to reproduce some aspects of the jet phenomenology, with particular concern towards YSO jets. These aspects are mainly related to the jet origin, propagation, and emission (Bellan et al 2005, 2009, Falize et al 2011, Gregory et al 2008, González et al 2009, Hartigan et al 2009, Lebedev et al 2005, Suzuki-Vidal 2010, Rus et al 2002).
With the goal to address the propagation of YSO jets and their interaction with the ambient medium, Tordella et al (2011) (Paper I) and Belan et al (2013) (Paper II) studied in the laboratory and by numerical means hypersonic hydrodynamic (HD) flows. In Paper I the authors considered as main jet parameters the Mach number M and the jet-to-ambient density ratio η and studied, both experimentally and numerically, representative cases of high and small values of density ratio. In Paper II they analyzed several cases with Mach number and density ratios consistent with those derived from the observations of YSO jets.
JETS IN ASTROPHYSICS
We have gradually become aware that jets are ubiquitous phenomena in astrophysics. It is in fact tempting to connect a broad range of phenomena that manifest extended linear structures with jets produced by processes in accretion disks.
The bi-polar flows in star-forming regions appear to represent one low-energy extreme. The precessing jet in SS433 (see, e.g., Brinkmann & Siebert, 1999) and the galactic microquasars (see, e.g., Mirabel et al. 1992 for a discussion of 1E1740.7−2942; and Cui 1999, and these proceedings for a discussion of GRS 1915+105) seem to occupy the other limit for galactic sources. Of course, active galaxies and quasars, in this view, can be considered the high-energy extreme of their galactic “cousins.”
Apparently, the galactic center also has some evidence for jet-like structures in the infrared. This bears out some aspects of the early work by Beall (1979) and Dennis et al. (1982), which showed that the galactic center had hard X-ray emission of a nature kindred to that of AGN.
While we do not generally focus on this when we talk about jets in active galaxies, Seyfert galaxies have linear radio structures which, while extended to 10’s and 100’s of parsecs, remain confined to their cores. On the other hand, it is well known that elliptical can have jets extending up to 10’s and 100’s of kiloparsecs. The “standard” model of AGN supposes that all active galaxies are driven by accretion disks of material spiraling onto black holes.
BL Lacs sources are thought to be different only in regard to their orientation with respect to the observer.
Even things as remarkable as γ-ray bursts have not been spared the application of a jet model. For example, Woosley, Zhang, and Heger (2002) suggest that a jet generated during collapse of massive star interacts with the overburden of material in the envelope to produce the intense γ-ray flare seen in γ-ray bursts. In this case, the energetics would be less problematic (provided that the GRBs are at cosmological distances) since any emission observed would be beamed toward the observer.
EXPERIMENTAL AND NUMERICAL SETUPS
The laboratory experiment makes use of facilities designed and built specifically for studying free hypersonic jets. The main features of these facilities, described in detail in the works by Belan et al (2008, 2010, 2011, 2013), will be exposed in this section. The jets studied in the present work are generated by means of de Laval nozzles; they travel along the longitudinal axis of a cylindrical vacuum vessel, as shown in figure 1.
A large set of jets has been studied in this experiment: the Mach numbers range from 7 to 21, and the density ratios η from 0.5 to more than 100. Some of these have also been compared with the corresponding numerical simulations.
Figure 2 represents the set of configurations considered in the present experimental campaign, labelled by the two main parameters M and η. The nozzles and the pair of gases (jetambient) used for each test are also reported. The dashed line on the left side marks the boundary of a region where the low Reynolds number effects are so important that the experiments cannot give reliable results, since the physics is in that case dominated by the molecular diffusion, in such a way that the jets can also be destroyed on a short scale by the mixing with the ambient and the associated kinetic energy dissipation. The dotted line on the right side marks the boundary of a region where both Mach number and density ratio are so large that the behaviour of the jets tend to resemble the motion of a rigid column.
We have examined two basic aspects of the propagation of hypersonic jets: spreading and stability. Observations (see e.g., the review by Reipurth and Bally 2001) point out that jets from YSOs have an observational Mach number ranging from 10 to 40, a jet-to-ambient density ratio in between 1 and 10 and a Reynolds number exceeding 1010. Although in this laboratory experiment the length scales are very different from astrophysical systems, two critical dimensionless parameters, such as the Mach number and the density ratio, have similar values. And the parameters that are larger in astrophysical systems, such as the Reynolds number, are sufficiently large for the experiment to capture the asymptotic behaviour. Moreover, it should be noted that, as long as radiation transport and relativistic and magneto-hydrodynamic effects can be ignored in the astrophysical situation of interest, the scaling between the experimental system and the corresponding astrophysical systems will primarily depend on the internal Mach number of the jet and on the density ratio, that can be reproduced by the present setup. On the other hand, in this experiment the radiative effects cannot be considered because of the limitations of the present setup, which is a low energy density facility.
Our results indicate that the spreading decreases with the jet Mach number and becomes smaller for heavier jets. The resulting jet opening angle remains well within the variability range observed in jets from YSOs.
Starting from non-axially symmetric oscillations, observed in Paper II for high Mach number jets, we have carried out 3D numerical simulations for testing the onset and the nonlinear evolution of potentially disruptive asymmetric modes. We have imposed two different values of the initial perturbation amplitude and transverse velocity and found that the jet was undergoing non-axial oscillations but maintained its integrity for the length of the domain.
Finally, in order to test the consequences of the main limitation of the diagnostics technique, that is the possibility of observing a limited fraction of the jet, we have performed a test case by treating the simulated data with the same juxtaposition technique used for the laboratory data. By comparison with the original figure, we have verified that this technique leads to a reasonable representation of the actual jet propagation details.
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