MECHANICAL HEATING IN DISK-DRIVEN WINDS – THERMALSTRUCTURE & OBSERVATIONAL PREDICTIONS

DARREN O’BRIENCentro de Astrofísica da Universidade do Porto & Departamento de Matemática Aplicada da

Faculdade de Ciências do Porto

PAULO GARCIACentro de Astrofísica da Universidade do Porto & Faculdade de Engenheria da Universidade do

Porto

JONATHAN FERREIRALaboratoire d’Astrophysique de Grenoble

SYLVIE CABRITLaboratoire d’Astrophysique de Grenoble & Observatoire de Paris

LUC BINETTEInstituto de Astronomía, Ciudad Universitaria, Mexico

Abstract. Following the work of (Garcia et al., 2001a) (GFCB), we compute the thermal propertiesand ionization structure of magnetically-driven disk winds. The original model’s dominant heatingfunction along the jet, ambipolar diffusion, is augmented by a mechanical heating term supposed toarise from weak shocks, as used by (Shang et al., 2002). We add this mechanical heating function toa cold disk wind model and calculate its effect on the jet as a whole. The temperature and ionizationof the flow are calculated in the case of cold jet solutions consistent with the underlying accretiondisk (Ferreira, 1997). These solutions are compared to those of (GFCB) in order to quantitativelydetermine the effect of the mechanical heating on the flow. We then use the computed thermal andionization structures to calculate jet synthetic observations. We find that the addition of mechanicalheating leads to higher electron fractions, in turn leading to increased line fluxes and line ratiosapproaching observed values.

Keywords: ISM: Jets and Outflows – Stars: Pre-main sequence – MHD – Line: profiles – accretiondisks

1. Introduction

Collimated mass ejection in young T Tauri stars (TTS) is observationally found tobe correlated with the accretion process (Cohen et al., 1989; Cabrit et al., 1990;Hartigan et al., 1995). It is currently believed that magnetic forces are responsiblefor both the high ejection efficiency (Mjet /Macc ∼ 0.01−0.1) and the high degreeof collimation of these winds (Konigl and Pudritz, 2000; Shu et al., 1995).

In the regime of cold MHD, ejection is only possible from the disk by magneto-centrifugal launching on field lines sufficiently inclined from the disk axis, asno thermal energy is available to help matter cross the potential barrier. Of the

Astrophysics and Space Science 287: 129–134, 2003.© 2003 Kluwer Academic Publishers. Printed in the Netherlands.

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wide variety of models available in the literature, only two classes have producedsufficiently complete calculations of MHD solutions to allow comparisons withobservations.

– Disk winds from wide angle disk radii (Blandford and Payne, 1982; Konigland Pudritz, 2000; Ferreira, 1997).

– X-winds from a small extent in radii near the disk corrotation axis (Shu et al.,1995) and references therein.

Observationally, the information available from jets is in the form of emission lines,therefore in order to test models, synthetic observations must be generated. To dothis, we model the thermal evolution in the jet consistently with the jet dynam-ical approximation of cold MHD, i.e., the thermal pressure having no dynamicconsequences. This was attempted by (GFCB; Safier, 1993a) and (Shang et al.,2002).

The first two authors used ambipolar diffusion in the context of disk winds andfound it able to heat the gas to 104 K but with insuficient ionization fractions. Shangfound that ambipolar diffusion wasn’t able to heat the X-wind and invoked heatingvia weak shocks. This mechanical heating term is described by

�mech = αρv3/s (1)

where ρ, v & s are the density, velocity and distance along the flow respectivelyand α is a phenomenological constant of proportionality. One description of thisheat source is that consisting of many different post-shock turbulent elements,or eddies, resulting in a cascade of energy from the largest eddies down to thesmallest, where the energy is then dissipated into heat. By this process, mechanicalenergy is converted into thermal energy.

Here we describe the thermal effects of including �mech in disk winds, and showthat the extra heating is able to ionize the gas to observed values. It must be noted,however, that the heating arises from weak shocks, as we are adding a turbulentheating term while still using a laminar MHD solution (density and velocity fieldunchanged), so we made the assumption that the shocks are weak and the jumpconditions have negligible effect on the flow.

2. Thermal Structure

We studied the thermal effects of �mech on the Magnetised Accretion EjectionStructure (MAES) of (Ferreira, 1997), as in (GFCB). These solutions describe acold jet solution, i.e. a magnetically driven jet associated with weakly dissipativedisks thus without a hot corona (Ferreira and Pelletier, 1995). We concentrated ona model with ejection efficiency ξ = 0.010, a highly collimated solution.

We follow a fluid cell along a given flow streamline, characterized by ω0, thefield line footpoint radius in the disk midplane, and solve for its coupled temperat-ure and ionization evolution, including all relevant heating and cooling terms. We

MECHANICAL HEATING IN DISK-DRIVEN WINDS 131

Figure 1. Flow Characteristics along the inner flowline with ω0 = 0.007AU &Macc = 10−6M�yr−1. Shown are the evolution with α of T , fe , �mech, �rad , �drag, �adia ,�f ree & �phot . The α-values on the T and fe plots are 0.001 (solid), 0.015 (dashed), 0.030 (dotted)

& 0.060 (solid). At α = 0.015, T begins to rise above the plateau and approaches 105 at highervalues of α. χ = z/ω0, denotes the position along a streamline anchored at ω0.

include accretion rates Macc ranging between 10−8 and 10−5M�yr−1, covering theobserved range in accreting TTS (Hartigan et al., 1995).

The ionization state of the flow was solved using the Mappings Ic code of(Binette et al., 1985). This code considers an atomic gas composed of H, He, C, N,O, Ne, Fe, Mg, Si, S, Ca & Ar. As in (GFCB), Na was also added. The abundancesincluded depletion onto dust grains as described by (Draine and Lee, 1984) usingthe values of (Savage and Sembach, 1996).

We examined the parameter space from α = 0.001 − 0.100, and discovered thefollowing effects:

– The temperature at first only increased fractionally compared to that calcu-lated in (GFCB). However, this slight increase is enough to increase sig-nificantly the number of collisional ionizations. As α was increased further�mech began to dominate the heating and both T & fe began to reach valuessignificantly higher than those of (GFCB).

– The radiative cooling by collisions, �rad , which was present but not hugelysignificant in (GFCB), is increased dramatically in our results.This is due inpart to collisional ionization of H, and due to a large increase in the electrondensity as H becomes ionized (Spitzer, 1978). �rad then becomes the mostimportant cooling mechanism in the flow, as opposed to cooling via adia-batic expansion, �adia, which dominated in (GFCB). Allthough �rad values

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approach those of �drag, there is no ionization feedback between these twoterms and hence no temperature plateau (GFCB, Safier, 1993a) is produced.

– The ambipolar diffusion heating, �drag, is greatly reduced in our results. Thisterm arises from a drag force between ions and neutrals, thus it is heavilydependent on the neutral density. With the increased ionization beyond adistance of ∼10AU, �drag falls away.

– The increased ionization yields a wind model whose heating & cooling isdominated by �mech & �rad respectively. The main heating and cooling termsare plotted in Figure(1), along with T and fe.

– We analysed the results for all α-values used and found a saturation pointat α ∼ 0.015, where T begins to rise above the plateau. It is only when theflow approaches the recollimation point that it begins to cool down, as �rad

overcomes �mech.– Due to the increased T & fe respectively, photionization heating, �phot , and

free-free cooling, �f ree, are greater than those found in (GFCB). However,their magnitudes in comparison to the other heating & cooling terms are stillnegligible and so they have no great effect on the thermal structure of the flow.

3. Observational Predictions

The complete calculation of the thermal & ionization structure of the flow allowsus to make observational predictions. Here we limit our discussion to line ratios &line fluxes. Figure (2) shows comparisons of predicted integrated luminosities in[O I] 6300 as a function of Macc with observed T Tauri luminosities (Hartigan et al.,1995). Predictions made by (Garcia et al., 2001b) are also shown. These previousresults are compared with our predictions over a range of α values from 0.001to 0.100. It is evident from this diagram that the addition of mechanical heatingincreases this line flux above the results of (GFCB); however, it is at very highvalues (α > 0.050) that the predicted fluxes come closest to fitting the observeddata. The same can be said for the line ratio predictions ([N II]6584/[O I]6300 &[S II]6716/[S II]6731 vs [S II]6731/[O I]6300). However these high values of α

produce too high values for T & fe (Lavalley-Fouquet et al., 2000), and we notethat even at very high α we cannot fit the data due to the low density of the MHDsolution.

4. Conclusions

From the predictions discussed above, we conclude that the cold MAES flowsexamined can partially reproduce observed line ratios and fluxes when heated byturbulent dissipation. However the values of the phenomenological free parameterα that reproduced the observations also produce extremely high ionization fractions

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Figure 2. left Line fluxes of [O I]6300 with Macc from 10−8 to 10−5M�yr−1 using α valuesbetween 0.001 & 0.010. Also shown are the prediced fluxes heated predominantly by ambipolardiffusion with no mechanical heating term (Solution A of (GFCB), labelled α = 0). Fluxes wereintegrated out to 100 AU from the star. right Line ratios [N II]6584/[O I]6300 & [S II]6716/[SII]6731 vs [S II]6731/[O I]6300 for Macc = 10−6 at distances along the jet from -50 AU to 200 AU,after convolution by a 70 AU beam and summation perpendicular to the jet axis.

and temperatures. For these high values of α, the temperature plateau, a robustdisk wind property predicted by both (GFCB) and (Safier, 1993a), is lost. But forlower values of α (0.003–0.010) we were able to increase the electron densitiesby a factor of 10 without greatly increasing the temperature, thus solving one ofthe problems encountered in (GFCB). We will extend this work to include MAESmodels containing entropy injection at the disk surface (Casse and Ferreira, 2000)which naturally produce higher jet densities and lower terminal velocities. We be-lieve that these higher jet densities, when combined will help produce prediced lineratios and intensities without using surplus heating.

Acknowledgements

This work was supported by grant POCTI/1999/FIS/34549 approved by FCT andPOCTI, with funds from the European programme FEDER. D. O’Brien would liketo thank João Lima and Catherine Dougados for their helpful discussions duringthis work.

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