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 05508-090, Brazil
rgonzalez@astro.iag.usp.br
J. Cantó
Instituto de Astronomı́a (UNAM), Ap.Postal 70-264, CP: 04510, 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
rm2
rm1
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. (1990)
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. (2000) 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 v0 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
2
2
1.5
1.5
1
1
0.5
0.5
0
0
0
0.5
1
1.5
2
Figure 2.
Predicted radiocontinuum fluxes at 2 cm (solid line),
6 cm (dotted line) and 20 cm (dashed
line) from a stellar wind with a periodic variation in the ejection velocity.
The wind parameters are given in the
text.
0
0.5
1
1.5
2
Figure 3.
Spectral indices α2−6
(dotted line), and α6−20 (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 2002) 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 rm1 ); 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 rm2 ) (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,
µ
τ̄ν = β
n0
cm−3
¶µ
vs
100km s−1
¶γ µ
Tex
104 K
¶−0.55 µ
ν
5GHz
¶−2.1
,
(1)
where Tex is an average excitation temperature, n0 is the preshock density, vs is the shock velocity and ν is the frequency.
4
The constants β and γ take different values according to the shock
velocity: for 20 km s−1 ≤ vs ≤ 58 km s−1 , we find that β = 3.61 x 10−7
and γ = 5.78; for higher velocities (58 km s−1 ≤ vs ≤ 100 km s−1 ), we
obtain β = 1.07 x 10−7 and γ = 3.55.
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 150AU interval (Natta 1989). Also,
the central source of the radio jet in Serpens shows a physical size of
' 60AU (Curiel et al. 1993). If one identifies those dimensions with
the radius (rm1 ), it is possible to estimate the variation period of the
ejection velocity (see González 2002).
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= 10−6 M¯ yr−1 , with an initial ejection velocity v0 = 350km s−1
which suddenly increases by 30%. Assuming these velocity parameters,
a variation period τ = 0.1672yr is predicted. The source is located at a
distance D = 150pc from the observer.
Bipolar Outflow
Consider a bipolar outflow ejected with conically symmetry from a
central star. The opening angle of the cones is θa and the angle between
the outflow axis and the plane of the sky is θi (see Fig. 4). The mass
loss rate ṁ is assumed to be constant and the injection velocity ve (τ )
(being τ the injection time) of the form,
ve (τ ) = vw − vc sin(ωτ ),
(2)
where vw , vc and ω are constants.
Using the formalism of Cantó et al. (2000), it can be shown that each
working surface moves with variable velocity and it is not formed at the
base of the flow.
Radio-Continuum Emission from Stellar Flows in low-mass Stars
z
z’
5
Bipolar outflow
axis
θi
θa
x
To the observer
θi
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 θa and the inclination angle
of the outflow axis [z 0 ] with the plane of the sky [y − z] is θi . The axes y, y 0 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 2002).
Figure 5 shows the predicted radio-continuum fluxes at λ = 2, 6 y
20 cm from a bipolar outflow with a sinusoidal ejection velocity. We
have assumed vw = 360km s−1 , vc = 60 km s−1 , ω = 25.13yr−1 , ṁ =
10−6 M¯ yr−1 and a distance to the source D = 150pc to the observer.
The opening angle of the cones is θa = 30o with an inclination angle
θi = 45o . 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 tc = 0.34yr and at a distance rc = 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
0.3
0.2
0.2
0.1
0
0
0.5
1
1.5
0.1
0.3
0.2
0.1
0
0
0.5
1
1.5
0
0.5
1
1.5
0
0.3
0.2
0.1
0
-0.1
Figure 5.
Predicted radiocontinuum fluxes at λ = 2, 6 y 20 cm
for a bipolar outflow with a sinusoidal
ejection velocity.
0
0.5
1
Figure 6.
Spectral indices between
2-6 cm (dotted line) and between 620 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 = 2.0). Afterwards, the
spectral index decreases adopting a varying value intermediate between
optically thick (α = 2.0) and optically thin (α = −0.1). 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 50-100 AU for the emitting regions.
References
Cantó, J., Raga, A.C., & D’Alessio, P. 2000, 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, 320, 364
Ghavamian, P., & Hartigan, P. 1998, ApJ, 501, 687
González, R.F., 2002, Ph.D. Thesis, U.N.A.M. (México)
Gonzalez, R.F., & Cantó, J. 2002, ApJ, 580, 459
1.5
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. 1990, ApJ, 364, 601
Rodríguez, L.F., & Cantó, J. 1983, Rev. Mexicana Astron. Astrof., 8, 163