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Programas para la reinserción social de las personas privadas de su libertad en el

CAPÍTULO 2 EL MODELO INTEGRAL DE REINSERCIÓN SOCIAL EN MÉXICO

2.3. Programas para la reinserción social de las personas privadas de su libertad en el

A pure ‘disc-wind’ (not to be confused with the photo-evaporative disc winds mentioned above) model was developed by Blandford & Payne (1982), for appli- cation to extragalactic phenomena, who suggested that a poloidal magnetic field, originating from an accretion disc, acts as a launching mechanism for ionised material travelling near the surface of the disc (see Figure 1.3 for a diagram- matic representation). This material is accelerated centrifugally along the field lines and away from the disc, accurately adhering to the analogy of ‘beads on a wire’. As the accretion disc rotates, these field lines become more twisted (due to magnetic coupling) further from the disc and eventually jet collimation is in-

duced by ‘hoop stresses’ from the field’s increasing toroidal component. A later paper by Pudritz & Norman (1983) further developed this work in to the field of star formation providing an efficient way to remove angular momentum from accreting material and a general model accommodating for ranges in magnetic field geometry was presented by Pelletier & Pudritz (1992). Crucially that last work also predicted an accretion to jet mass loss ratio of 10 : 1. Simulations by Seifried et al. (2012) showed that massive protostellar jets were likely driven by this mechanism, with varying hoop stresses (enhanced by weaker magnetic fields, and suppressed by sub-Keplerian disc motions in the presence of strong fields) affecting the degree of collimation. This result predicted that collimation should relate to the evolutionary stage of the MYSO, with lower degrees of collimation for younger MYSOs. An observational result in support of this picture is the jet in W75N VLA 2 whereby collimation has been shown to increase over subsequent observations spread over 18 years (Carrasco-Gonz´alez et al. 2015), although the inferred velocity of the driven outflow was an order of magnitude higher than that predicted by the theoretical work.

On the other hand, Shu et al. (1994) proposed a model with a magnetic field originating from the central protostar, referred to as the ‘X-wind model’. This is so named because the launching radius for the jet in the disc is located at the X-shaped lines of equipotential (balancing points of gravitational and centrifugal forces) located near the truncated (by strong stellar magnetic fields), inner surface of the disc itself. With the inward flow of material in the accretion disc, mag- netic coupling bows the field lines inwards. Consequently, magneto-centrifugal processes accelerate the inflowing gas supersonically in a direction parallel to the poloidal field lines, resulting in an outflowing wind (see Figure 1.4). Twisted

Figure 1.3: Representation of the pure disc-wind model (reproduced from Pelletier & Pudritz 1992) showing forces acting on a particle coupled to the disc’s magnetic field lines (i.e. ‘bead on a wire’). Fg and Fc are the gravitational and centrifugal forces re-

spectively, with the perpendicular and parallel components of each force to the poloidal magnetic field’s direction shown with an extra ⊥ or k subscript. Important radii are r0,

the radius in the disc at which the line is embedded, rs, the slow magnetosonic radius

(the point at which centrifugal force dominates gravity and the particle accelerates away from the disc), rF, the fast magnetosonic radius (the point at which centrifugal

acceleration ceases and an increasing toroidal magnetic field collimates the flow) and rA, the Alfv´en radius.

Figure 1.4: Representation of the X-wind model (reproduced from Shu et al. 1994) showing jet streamlines and the X-point (Rx) where the material is launched from.

magnetic fields further away from the disc’s mid-plane focus the ionised material, resulting in a collimated, ionised jet. When applied to massive star formation, the X-wind model presents a problem since stellar magnetic fields are intrinsi- cally related to the convective nature of their protostars. For low-mass protostars, these convective models adhere well to reality with the onset of deuterium burn- ing (Stahler 1988). Simulations of the protostellar evolution of MYSOs, (e.g. Hosokawa & Omukai 2009) show them to evolve through radiative as well as convective stages, meaning the window for stellar magnetic fields is limited in time.

due to the small spatial scales on which differences are apparent. In terms of the launching radius from the disc itself, the pure disc-wind model suggests mate- rial launches from a range of radii from the disc (< 100 au), almost asymptoti- cally from the disc’s surface to its rotation axis (see figures within Zanni et al. 2007, for MHD simulations showing such). A X-wind model suggests that the launching radius is well defined, limited in range and not far from the inner truncation radius of the disc itself (≤ 10 au) where the X-shaped lines of cen- trifugal/gravitational equipotential are located. Morphologically the degree of collimation for the launched jet with disc-winds will be greater, while X-winds have a lower collimation (Pudritz et al. 2007) and wider opening angle. Obser- vations of collimated, parsec-scale jets (e.g. HH 80-81, IRAS 17527-2439, IRAS 13481-6124 from Marti et al. 1993; Varricatt 2011; Kraus et al. 2010, respectively) may therefore show that the X-wind model does not apply, however Shu et al. (2000) suggest that the highest density material at the centre of the jet encoun- ters the lowest density material in the surrounding envelope at the poles of the evacuated cavities, thus offering a mechanical form of collimation. Magnetically, disc-winds only require a magnetic field originating in the disc whose field lines are ≤ 60◦ from the disc’s surface (Blandford & Payne 1982), whereas X-winds

require protostellar magnetic fields, however polarimetric observations close to the forming massive star/disc are difficult. Primarily therefore, differentiating between the two models could be achieved by measurements of the launching radius whereby large radii would signify the dominance of the disc-wind model.

Due to current resolution limitations however, differentiating between these mechanisms on the scale of the launching radii (i.e. ≤ 10 au) is impossible for even the nearest massive star forming regions. Other differentiating characteristics

would be investigating ejection/accretion ratios, investigating the cross-sectional profile of the jets (which should be layered for disc winds) or (perhaps solely for the low mass case where there is a defined disc truncation radius) looking for the presence of dust in the flow. For studies at current resolutions, the former method is likely the most promising. However, it suffers from poor determination of both accretion (using NIR line proxies for accretion rates e.g. Cooper et al. 2013) and ejection mass loss rates, which can be overcome by large scale statistical surveys.