RADIO-CONTINUUM EMISSION FROM STELLAR FLOWS IN LOW MASS STARS
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1 RADIO-CONTINUUM EMISSION FROM STELLAR FLOWS IN LOW MASS STARS R.F. González Instituto Astronômico e Geofísico (IAGUSP), Universidade de São Paulo, Cidade Universitária, Rua do Matão, 1226, São Paulo, SP 558-9, Brazil rgonzalez@astro.iag.usp.br J. Cantó Instituto de Astronomía (UNAM), Ap.Postal 7-264, CP: 451, México D.F., México Abstract Young stars of low masses frequently show continuum emission in radio frequencies. The observed flux densities and spectral indices indicate that, in most cases, this emission is of thermal origin and is produced in the powerful stellar flows emanating from the stars. We present a model in which the emission is produced by internal shocks in the flow. These shocks are the result of periodic variations of the flow velocity at injection. It is shown that the free-free radio emission predicted by the model is in good agreement with those observed in young stars of low and intermediate masses. Introduction Radio-continuum emission is frequently observed coincident with young stars of low masses (Evans et al. 1987, Natta 1989, Curiel et al. 1993). Both the observed flux densities and spectral indexes suggest a thermal (free-free) origin for this emission. However, it has been recognized that there are serious difficulties in producing the ionization in these flows (see for instance Rodríguez & Cantó 1983). Photoionization of hydrogen from its ground level can be ruled out due to the lack of the required UV photons rate with enough energy to ionize these powerful winds. Rodríguez & Cantó (1983) and Torrelles et al. (1985) pointed out that the necessary ionization rate could be obtained by thermalizing a 1
2 2 r m2 r m1 To the observer Figure 1. surfaces. Schematic diagram of a stellar wind with a set of outgoing working small fraction of the kinetic energy of the flow. Such a thermalization could be produced by shocks in the supersonic flow. Supersonic flows are always subject to the development of shock waves given the right conditions and mechanical support. Raga et al. (199) show that supersonic variabilities in the ejection velocity in a supersonic flow result in the formation of two-shock wave structures (called working surfaces) which travel down the flow. These working surfaces emit continuum radiation that may be detected in radio. We estimate the emission in radio-frequencies of the working surfaces generated in a stellar wind subject to variations in its injection velocity. For this, we have used the formalism of Cantó et al. (2) to obtain the kinematical properties of the working surfaces given the variations of the injected flow, and then use the results of Ghavamian & Hartigan (1998) to estimate the emission of each working surface. The dynamical model Initially, we consider an isotropic stellar wind with mass loss rate ṁ and terminal velocity v subject to periodic variations in the latter quantity. In particular, we will assume variations such that the terminal
3 Radio-Continuum Emission from Stellar Flows in low-mass Stars Figure 2. Predicted radiocontinuum fluxes at 2 cm (solid line), 6 cm (dotted line) and 2 cm (dashed line) from a stellar wind with a periodic variation in the ejection velocity. The wind parameters are given in the text. Figure 3. Spectral indices α 2 6 (dotted line), and α 6 2 (solid line) obtained from the fluxes presented in Fig. 2. velocity suddenly increases by a factor a(> 1) during a finite interval of time, and then instantaneously returning back to its original value. The changes repeat periodically with a period τ. It can be shown (see González & Cantó 22) that each working surface forms instantaneously (as the fast flow begins to be ejected) at the base of the wind moving initially with constant velocity. This initial stage ends when the low velocity downstream material is completely engulfed by the working surface (at r m1 ); after this time, the outer shock disappears and the working surface starts to be accelerated until the fast upstream flow is also completely engulfed (at r m2 ) (see Fig. 1). Ghavamian & Hartigan (1998) have performed detailed calculations of the free-free emission expected to emanate from planar interstellar shock waves. Their results are shown in the form of brightness temperature, which we convert into effective optical depth obtaining that, τ ν = β ( n )( cm 3 v s 1km s 1 ) γ ( ).55 ( ) Tex ν , (1) K 5GHz where T ex is an average excitation temperature, n is the preshock density, v s is the shock velocity and ν is the frequency.
4 4 The constants β and γ take different values according to the shock velocity: for 2 km s 1 v s 58 km s 1, we find that β = 3.61 x 1 7 and γ = 5.78; for higher velocities (58 km s 1 v s 1 km s 1 ), we obtain β = 1.7 x 1 7 and γ = According to our simplified model for the emission of shocks, the flux emitted by the configuration shown in Figure 1 can be estimated by simply adding the optical depths of the working surfaces intersected by each line of sight to obtain the total optical depth along this line of sight, and then we use it to estimate the intensity emerging from this direction. The flux is finally obtained by integrating this intensity over the solid angle. The sizes of the radio-continuum sources associated with T Tauri stars in the Taurus cloud are in the 75 to 15AU interval (Natta 1989). Also, the central source of the radio jet in Serpens shows a physical size of 6AU (Curiel et al. 1993). If one identifies those dimensions with the radius (r m1 ), it is possible to estimate the variation period of the ejection velocity (see González 22). An example is shown in Figures 2 and 3. We have chosen representative values for T Tauri stars in the Taurus cloud: a steady mass loss rate ṁ= 1 6 M yr 1, with an initial ejection velocity v = 35km s 1 which suddenly increases by 3%. Assuming these velocity parameters, a variation period τ=.1672yr is predicted. The source is located at a distance D = 15pc from the observer. Bipolar Outflow Consider a bipolar outflow ejected with conically symmetry from a central star. The opening angle of the cones is θ a and the angle between the outflow axis and the plane of the sky is θ i (see Fig. 4). The mass loss rate ṁ is assumed to be constant and the injection velocity v e (τ) (being τ the injection time) of the form, v e (τ) = v w v c sin(ωτ), (2) where v w, v c and ω are constants. Using the formalism of Cantó et al. (2), it can be shown that each working surface moves with variable velocity and it is not formed at the base of the flow.
5 Radio-Continuum Emission from Stellar Flows in low-mass Stars 5 z z Bipolar outflow axis θ i θ a x To the observer θ i x Working Surface Figure 4. Schematic diagram showing a bipolar ejection with conically symmetry from a central star. The opening angle of the cones is θ a and the inclination angle of the outflow axis [z ] with the plane of the sky [y z] is θ i. The axes y, y are perpendicular to the figure. The flux emitted by the configuration shown in Figure 4 can be estimated again by simply adding the optical depths of the working surfaces intersected by each line of sight to obtain the intensity emerging from each direction; then the flux is computed integrating this intensity over the solid angle (see González 22). Figure 5 shows the predicted radio-continuum fluxes at λ = 2, 6 y 2 cm from a bipolar outflow with a sinusoidal ejection velocity. We have assumed v w = 36km s 1, v c = 6 km s 1, ω = 25.13yr 1, ṁ = 1 6 M yr 1 and a distance to the source D = 15pc to the observer. The opening angle of the cones is θ a = 3 o with an inclination angle θ i = 45 o. In Figure 6, we show the spectral indices obtained from the fluxes presented in Figure 5. The emission shows (at every wavelengths) a similar behaviour to that obtained in the case of an isotropic stellar wind, however, the emission from a bipolar outflow is weaker. In our example, the first working surface is formed at a time t c =.34yr and at a distance r c = 16.77AU from the central star. Also we have found in our example that the stellar outflow is optically thin since the formation of the first working surface.
6 Figure 5. Predicted radiocontinuum fluxes at λ = 2, 6 y 2 cm for a bipolar outflow with a sinusoidal ejection velocity. Figure 6. Spectral indices between 2-6 cm (dotted line) and between 6-2 cm (solid line) obtained from the radio-continuum fluxes presented in Fig. 5. Conclusions Our model predicts fluxes and spectral indices in good agreement with those associated with recently formed low mass stars. The flux and the spectrum from an isotropic stellar wind with periodic jump variations in the ejection velocity is initially optically thick (α = 2.). Afterwards, the spectral index decreases adopting a varying value intermediate between optically thick (α = 2.) and optically thin (α =.1). In the case of a bipolar outflow with a sinusoidal velocity at injection, the spectrum is optically thin since the formation of the first working surface. Variability periods of some months are predited by the model assuming physical sizes of 5-1 AU for the emitting regions. References Cantó, J., Raga, A.C., & D Alessio, P. 2, MNRAS, 313, 656 Curiel, S., Rodríguez, L.F., Morán, J.M., & Cantó, J. 1993, ApJ, 415, 191 Evans, N.J.,II, Levreault, R.M., Beckwith, S., & Skrutskie, M. 1987, ApJ, 32, 364 Ghavamian, P., & Hartigan, P. 1998, ApJ, 51, 687 González, R.F., 22, Ph.D. Thesis, U.N.A.M. (México) Gonzalez, R.F., & Cantó, J. 22, ApJ, 58, 459
7 Radio-Continuum Emission from Stellar Flows in low-mass Stars 7 Natta, A. 1989, ESO Workshop on: Low Mass Star Formation and Pre-Main Sequence Objects, Edited by Bo Reipurth (ESO), 365 Raga, A.C., Cantó, J., Binette, L., & Calvet, N. 199, ApJ, 364, 61 Rodríguez, L.F., & Cantó, J. 1983, Rev. Mexicana Astron. Astrof., 8, 163
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