2 The origin of radio continuum emission from YSOs

In general, the radio continuum sources associated with YSOs are weak, and they are unresolved except with a subarcsecond resolution. It has been found that the shape of the SED at cm-wavelengths for YSOs is characteristic of thermal free-free emission. However, it is also known that this emission can not arise from a compact H II region which is ionized by stellar photons from the YSO. The required ionizing photon flux is that of an early B type star (Torrelles et al. 1985), which is orders of magnitude greater than the expected flux from the associated YSOs. Thus, there must be other mechanisms involved which contribute to the inferred ionization, unless YSOs produce much more Lyman continuum radiation than expected.

The different mechanisms can be distinguished by the shape of the radio spectrum, if observations over a large enough wavelength range are available. In the following we discuss some of them briefly. For a review of ionized winds from young stellar objects see André (1987) and Panagia (1991).

2.1 Thermal emission from accretion

The accretion models are of special interest in this case, because there is evidence of mass infall towards the IRAS source, based on millimeter molecular line observations (Lehtinen 1997).

In Bertout's (1983) model of accretion onto a protostellar core the radio-emitting region is photoionized by soft X-ray and EUV radiation from an accretion shock around a protostellar core. In this model the spectrum has roughly a $S_{\nu} \propto \nu^{0.6}$ shape.

Felli et al. (1982) have modelled thermal emission from an extended, ionized circumstellar envelope which is in a state of accretion. This model produces a non-power-law flat spectrum, $S_{\nu} \propto \nu^{-0.1}-\nu^{0.1}$ (Felli et al. 1982; Panagia 1991; André 1987). The predicted flux density is (Panagia 1988)

$$S_{\nu}\mbox{(acc)} \approx 8.18~ \left( \frac {\nu} {\mbox{10~GHz}} \right) ^{-0.1} \left( \frac {T} {10^{4}~\mbox{K}} \right) ^{-0.35}$$

$$\times \left( \frac {M} {{M}_{\odot}} \right) ^{-1} \left( \frac ... ...c}} \right) ^{-2} \ln \left( \frac {r_{\infty}} {r_{\rm c}} \right)~ \mbox{mJy}$$ (1)

where $\dot{M}_{\rm {accr}}$ is the mass accretion rate, M and dare the stellar mass and distance, T is temperature, $r_{\rm c}$ is the radius at which the optical depth equals 3/4, and $r_{\infty}$ is the outer boundary (generally the accretion radius). This equation is valid when $r_{\infty} \gg r_{\rm c}$.

2.2 Thermal ionized stellar wind

Ionized stellar wind models have been presented which are either spherically symmetric (Panagia & Felli 1975; Wright & Barlow 1975; Felli et al. 1982; Panagia 1991) or nonsymmetric (Schmid-Burgk 1982; Reynolds 1986). In the case of ionized stellar wind in general, the frequency dependence has a large range from $S_{\nu} \propto \nu^{-0.1}$ to $S_{\nu} \propto \nu^{2}$ (Reynolds 1986 and references therein). In the case of a spherical, fully ionized, isothermal and constant-velocity flow, which is considered as the "standard'' spherical wind, the 3 to 6 cm spectral index is 0.6 for large opacity. Significant deviations from the spectral index or flux predicted by the "standard'' spherical wind occur only if the solid angle filled by the flow varies systematically with radius or the wind is highly anisotropic (Schmid-Burgk 1982; Reynolds 1986).

2.3 Thermal shock emission

Shock-induced ionized model was first proposed by Torrelles et al. (1985). The required ionizing photons are produced when a powerful, high velocity neutral stellar wind is shocked by dense matter surrounding the YSO. The now collimated wind produces a molecular outflow. The shock-ionization model predicts a $S_{\nu} \propto \nu^{-0.1}$ dependence for radio continuum emission (Curiel et al. 1987, 1989) The predicted flux density in the optically thin case is (Curiel et al. 1989)

$$S_{\nu}\mbox{(shock)} \approx 3.98\times 10^{-2} \left( \frac {\nu} {\mbox{5~GHz}} \right) ^{-0.1} \left( \frac {T} {10^{4}~\mbox{K}} \right) ^{0.45}$$

$$\times \left( \frac {\dot{M}} {10^{-7}~{M}_{\odot}~\mbox{yr}^{-1}... ...0~\mbox{km~s}^{-1}} \right) ^{0.68} \left( \frac {d} {\mbox{kpc}} \right) ^{-2}$$

$$\times \left( \frac {\Omega} {4~\pi} \right)~ \mbox{mJy}$$ (2)

where $\dot{M}$ is the mass loss rate, $v_{\infty}$ is the terminal velocity of the wind, and $\frac{\Omega}{4~\pi}$ is the solid angle subtended by the surrounding matter as seen from the star.

2.4 Thermal dust emission

Yet another possible source of emission is thermal emission from dust grains, which has a positive spectral index. If we assume a $\nu^{4}$frequency dependence for emission between 1.3 mm and 3 cm, typical for optically thin dust emission, the 223 mJy flux at 1.3 mm (Henning et al. 1993) can be used to predict a flux density of 0.4 $\mu$Jy at 3 cm for the IRAS 13036-7644.

2.5 Non-thermal emission

A source that has a non-thermal spectrum ( $\alpha <-0.1$) would probably be a nonstellar background object. However, not every source with $\alpha <-0.1$ is necessarily a nonstellar object; Abbot et al. (1984) have detected non-thermal emission from two O stars. For YSOs the relevant non-thermal emission process is synchrotron radiation.