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SPACE 

TElESCOPE 

SOENCE NASA-CR-183252 

19880021195 

~----a..I INS I T I 'U..........-r""T f I E 

PRE PRINT SERIES 

No 203 

RADIO AND INFRARED PROPERTIES OF YOUNG STARS 

Nino Panagia 

(bASP-Cb-183252) RhDIC ANi I~FEAhED 

EfGf~~~i£S cr }C01G S11liS (~FaC€ ~elescope 

~c CSCL OJE !:ClEnce lnst.) LJ F 

---------_._-------

September 1987 

SPACE TELESCOPE SCIENCE INSTITUTE 

3700 San MJrt1l1 Dnve Baltimore, MD 21218 

GJ/93 

1188-3C579 

Uncl.aE 

01618t:4 

1111111111111 1111 11111 11111111111111111111111 

NF00251 

Operated b\ the k,~OClallol\:of l!nl\erS1l1e, for Re,earch 10 futronOm\, Inc, for the NallOnJI Aeron.lUllC:' dnd Space AdmlOlstrallon 
RADIO AND INFRARED PROPERTIES OF YOUNG STARS 

Nino Panagza* 

Space Telescope Science Institute 

Baltimore, MD, USA, 

and 

University of Catania, Italy 

Invited Lecture given at the NATO ASI 

"Galactic and Extragalactic Star Formation" 

June 21 - July 4, 1987 

Whistler, B.C., Canada 

* Affiliated to the AstrophysIcs DivisIOn, Space Sciences Department of ESA. 
ABSTRACT 

The observations and the theory of the radio and infrared emission from pre-mainsequence stars are reviewed and discussed. 

1. INTRODUCTION 

Observing young stars or, more appropriatedly, pre-main-sequence (PMS) stars, in 

the infrared and in the radio has the advantage over optical observations that the heavy 

extinction associated with a star forming region is only a minor problem, if at all, so that 

the whole region can be studied thoroughly. Therefore, it means being able: i) to search 

for stars and do statistical studies on the rate of star formation, ii) to determine their 

luminosity, hence, to study luminosity functions and initial mass functions down to low 

masses, iii) to study their spectra and, thus, to determine the prevailing conditions at and 

near the surface of a newly born star and its relations with the surrounding environment 

This thud point is the main interest of my review. In fact, I shall limit myself to considering 

the observations concerning the processes of outflows from, and accretion onto, PMS stars 

and the theory necessary to interpret them. Section 2 will discuss the radiative processes 

relevant in stellar outflows. The main observational results will be presented in Section 3. 

A discussion of the statistical properties of stellar winds from PMS stars will be given in 

section 4. 

2. EMISSION FROM EXTENDED OUTFLOWS: A THEORETICAL OVERVIEW 

In this section we shall review the problem of radiation transfer applied to the case of 

stellar outflows. Quite of number of authors have contributed to this field, both for the 

formation of the continuum (Panagia and Felli 1975, Wright and Barlow 1975, Glnon 1975, 

Marsh 1975, Chiuderi and Torricelli Ciamponi 1978, Felli and Panagia 1981, Schmid-Burgk 

1982, Castor and Simon 1983, Lamers and Waters 1984, Reynolds 1986, Felli and Panagia 

1987) and the lines (Krolik and Smith 1981, Simon et al. 1983, Rodriguez and CantO 1983, 

Felh et al. 1985a, Hamann and Simon 1986, Panagia et al. 1987). The most important 

points and results are outlined and discussed in the following subsections. 

2 1 Assumptions - Basic Transfer Problem 

In order to make the transfer problem easily tractable the following assumptions are 

usually made (e.g., Panagia and Felli 1975): . 

1. The wind is spherically symmetric with a steady mass loss, M. 

2. The wind is fully ionized. This condition, combined with the continuity equation 

gives the behaviour of the electron density ne with the distance, r, from the center of the 

star 

M 

ne = 41rr2v(r)J.le m H (1) 

where v(r) is the wind velocity, J.le is the mean atomic weight per electron 

2:, X,m, 

J.le = ". X Z LA , , 

2 

(2) 
~ = 1 

the observer 

s 

Fig. 1 - The geometry of the star+wind system. 

with X" m, and Z, being the abundance by number, the mass and the charge of the i-th 

ion, and m H is mass of a hydrogen atom. 

3. The wind velocity increases with radius hke a power law 

(3) 

where Vo and ro are the initial velocIty and radlUs, respectively, untIl It reaches Its terminal 

value Voo at a radlUs rl 

v = Voo (4) 

4. The wind is isothermal at the same temperature as the stellar photosphere, i e., 

Twind = T star (5) 

5. The wind material is in quasi-LTE conditions, in the sense that the Kirchoff law is 

valid 

iv = "'/lEv (6) 

where iv and "'v are the emissivity and the absorption coefficient, respectively. WIth these 

assumptions the radiative transfer equation along any line of sight can be written as 

d1 

ds = -",1 + J (7) 

where s is the current coordinate along the lme of sight (see FIgure 1 which Illustrates the 

geometry of the problem). Its solution is 

1 = 10 e-T + B(l - e- T ) (8) 

where 10 is the background intensity and T is the optical depth as integrated along the line 

of sight, i.e. 

(9) 

3 
With our assumptions it is possible to express the total optical along any line of sight 

(assuming the opacity to be proportional to n~) as 

T = To e-(3+2,) (10) 

where To represents the optical depth for impact parameter equal to unity, i.e., for the line 

of sight tangent to the stellar disk. 

The radiation that we receive from the system star+wind is the intensity integrated 

over all lines of sight parallel to line joining us to center of the star. It is immediately clear 

that for e < 1, i.e., for lines of sight which project on the stellar disk, 

10 =B 

I = Be- T + B(1 - e-T ) = B e<1 (11) 

In other words the presence of a wind in front of the star does not affect the radiation we 

receive from the stellar disk because the amount of radiation which is absorbed is perfectly 

compensated by the emission of the wind. 

For impact parameters greater than the stellar radius there is no background radiation 

so that we have simply 

(12) 

The total emission received from the star+wind system will then be given by 

Fv = ! 1vdO = 47r

1

d2 47r R 2

7r Bv [1 + 2 i

oo 

(1 - e- T

) ede] (13) 

Equation (12) can be rewritten as 

(14) 

where R is the photospheric radius and d is the distance; to represents the excess of radiation 

due to the presence of the wind and is given by 

(15) 

Equations (14) and (15) are the basic transfer equations which govern both for the continuum and the emission line problems. Analytical solutions to eq. (15) can be obtained for 

two cases, which eventually turn out to cover all relevant possibilities (Panagia and Felli 

1987): 

i. The quasi-optically case, which is valid for moderate optical depths (To ~ 3). In this 

case by expanding equation (15) to second order terms and after some manipulation one 

obtains 

aTo 

to - --:-- - 1 + bTo 

where the coefficients a and b are simple functions of the velocity slope "I: 

2 1 +2"1 

a = 1 + 2"1 b = 8 + 8"1 

4 

(16) 

(17) 
1 1 10 100 

tau 

Fig. 2 - The quantity (1 + €) as a function of the optical depth: curves for both the 

quasi-optically thin (dashed lines) and the optically thick (solid lines) cases are shown for 

some values of /. The points where the two approximations meet are marked as well as 

the lme of equal flux contributed by the wind as emitted by the star. 

Values of a and b for some values of / are given in Table 1. Since in general a ~ band 

b « 1 the radiation excess € increases essentially linearly with the optical depth and only 

for relatively high values of T (say> 1/2) the rise departs appreciably from linearity. 

ii. The optically thick case: here the optical depth is large (To> 3) and therefore one 

can write 

1 + € = 1 + 2 hoo 

{1- eXP[-To €-(S+21)]} €d€ ~ loo {1- exp[-To €-(S+21)n€d€ (18) 

This equation correspond to a gamma function, so that we obtain: 

1 + € = r (1 - 2 ) T 27~S = CTd 

2/ + 3 0 0 (19) 

Table 1 reports values of the coefficients C = r[1 - 2/(2/ + 3)] and d = 2/(2/ + 3) for 

some values of /. It is apparent that in this case the increase of the radiation excess with 

the optical depth is systematically slower than linear. 

5 
If we plot the quantity (1 + f) as computed with eq. (16) and (19), respectively, we see 

(Fig. 2) that the two curves join quite smoothly with each other for optical depths around 

2. Detailed numerical calculations show that where the two curves intersect each other the 

analytical formulae give the correct value of f to within better than 1.7%. Therefore, one 

can safely use eq. (16) for lower values of the optical depth and eq. (19) for higher values, 

thus covering the whole possible range with two simple formulae. Finally, it is worth noting 

that the excess radiation becomes equal to the original stellar emission for values of the 

optical depth of the order of unity: in particular 0.53, 2.09 and 4.82 for gamma values of 

0, 1 and 2, respectively (cf fig. 2). 

2.2. The continuum 

The main emission mechanism in the infrared and in the radio is the free-free (or 

bremsstrahlung) radiation (f-f). The free bound transitions (i.e. recombinations of free 

electrons to bound levels), which dominate the optical emission, are of modest importance 

in the near infrared (they provide 20% of the continuum at 2.2 J.£m) and become completely 

negligible at longer wavelengths. Therefore, for the sake of simplicity in the following 

discussIOn we shall consider only the f-f process. The f-f opacity per unit length, which we 

express as the product of the electron and ionic densities times a function k", is given by 

K:" = nen,k" = 3.69 X 108nen, [1 - e-~;] g/fT-1/ 2v 3 (20) 

At radio frequencies k" can be approximated quite accurately as (Mezger and Henderson, 

1967) 

k" = 8.44 X 10-28 [10 ~HZ] -2 1 [10~K] -135 (21) 

Although this formula is accurate only in the radio domain, for qualitative discussions 

it can also be used advantageously at infrared wavelengths as well. Inserting eq. (20) into 

(10) the optical depth at impact parameter equal to unity is evaluated to be 

. 2 

1". = 2J("V)n2 Rk ex ~v-2 1T-1 35 o I 0 " R3 2 Vo 

(22) 

with J(J) defined as 

J( ) = J1iT(J + ~) 1 2 r(J+2) (23) 

Values of J(J) for some values of 1 are given in Table 1. It is straightforward now to 

estimate the emitted flux by using equations (14), (16) and (19). In the quasi-optically thin 

case the flux is virtually proportional to To and therefore the main functional dependences 

of the excess flux are 

2 2 . 2 

F. 47rR B R B M R-1T- 135 - 21B WInd = -d2 7r "f ex -d2 "To ex -2 V" 

47r Vo 

(24) 

On the other hand, in the optically thick case the total flux is 

(25) 

6 
which, expanding the dependences of To upon the various parameters, becomes: 

(26) 

The first important point is the frequency dependence which correspond to a power law 

whose spectral index a (Fv ex: vQ) is given by 

4, + 1.8 

a = 2,+ 3 (27) 

i.e., always lower than the black body slope of 2 (see Table 1). This is because at lower 

frequency the opacity is higher (cf. eq. (21)) and, therefore, the radius at which the optical 

depth is of the order of unity becomes larger and the effective emitting surface increases. 

In other words, the emission correspond to that of a black body (as expected for a well 

behaved, optically thick, thermal source) whose size increases with wavelength, so that the 

overall decrease of flux with wavelength is slower than it is for a Planck curve. In fact, we 

can define an effective radius to be that of a black body at the wind temperature which 

emits the same flux as the wind. Therefore, from eq. (14) we obtain 

(28) 

Therefore, for large To the effective radius becomes a simple function of the frequency: 

(29) 

Such an effective radius can be considerably larger than the photospheric radius. For 

example, in the radio the size of the emitting radius can be several thousands of stellar radii 

for typical values of the mass loss. Therefore, since the accelerating force becomes weak 

at large radii, the velocity in the radio emitting region can be expected to be essentially 

constant. In the constant velocity case b = 0) one recovers the "classical" formulae of the 

radio emission from winds (Panagia and Felli 1975) 

F, -512 v ~ M Voo x 

o 6 0 1 [ . ]4/3 -4/3 

v - [10 GHZ] [lO<K] 10-6 ~ [100 km .-1] 

[ 

d ]-2 1 kpc m Jy (30) 

[ V] -0.7 [ T ] -0 45 Rv =6.23 X 10

14 

10 GHz 104 K 

[ 

. ]2/3 -2/3 

1O-~ 1# [100 ~: s-l] cm (31) 

v -0 7 T -0 45 [ M ]2/3 

(J =0.042 [10 GHZ] [104 K] 1O-6-¥f 

[ 

Voo ]-2/3 [ d ]-1 -- arcsec 

100 km s-1 1 kpc (32) 

7 
In this case a mass losing star is expected to be detected as having a characteristic vO 6 

radio spectrum and a source size of few hundrendths of an arcsec. We note that the theory 

is quite simple and the radio flux depends in a simple manner on if Therefore, radio 

measurements can provide reliable determinations of the mass loss rate provided that the 

terminal velocity can be estimated independently. Even so, to do it right one has to make 

sure that the radio spectrum is really that of a wind, i.e., that the spectral index is '" 0.6 

indeed. As discussed by Felli and Panagia (1981) this requires making radio measurements 

at three widely spaced frequencies. 

2.9. The emission lines 

The problem of lme radiation transfer is much more complicate because it involves 

bound levels which may not be in any simple equilibrium and because by its very nature 

the line opacity is a rapidly varying function of the frequency. However, the problem can 

be simplified by adding the following assumptions to those already listed in section 2.1: 

• The expansion velocity of the wind is much higher than the sound speed of the gas 

which is in the range 10-30 km s-1. This condition is generally well verified because the 

observed expansion velocities are not less than 100 km s-1 . 

• The line opacity is much larger than that of the continuum, so that the two transfer 

problems can be decoupled: this is certainly true in the IR but is not verified at radio 

wavelengths. 

With these assumptions the line radiative transfer is reduced to a local problem in that 

a photon can interact only with matter at the place of "perfect resonance" where due to 

systematic motions an atom is perfectly "tuned" for absorbing "that" photon. This is the 

so-called Sobolev approximation from the name of the russian astronomer who introduced 

it (Sobolev 1957). Following Castor (1970) the line optical depth can be expressed as 

1I"e2 !i1 - & 1 r(v t) - gf 91 9u R----=---

,I,. - me !1cl. 82 ( ) 

Vo c 1 +? 1-1 

(33) 

where Nl, Nu and gl, gu are the population and the statistical weight of the lower and 

upper levels of the transitions. The quantity p is the radial distance in the plane (8, e), 

i.e., p2 = 8 2 + e2 and like 8 and e is expressed in units of stellar radii. In the case of 

hydrogen lines, which is the case we will be dealing with, the population of the excited 

levels is proportional to the square of the ionized matter density and, therefore, the optical 

depth can be written as 

(34) 

where 

2 N, N. '2 1I"e ~ _!..!JA. M 

T - -gf gl gu R ex: -- o - me v v Ie R3 2 o 0 Vo 

(35) 

8 
-30 -2 5 -2 0 -1 5 -1 0 -0 4 0 4 1 0 1 5 2 0 25 30 

Fig. 3 - The projected surfaces of equal velocity (in units of the initial velocity) for 

the ~ase of v ex rl/2. The loci of constant optical depth are also shown (dashed lines) for 

T values of 10 (inner curve) and 1 (outer curve). 

represents the optical depth at e = 1 and at the center of the line, v = Vo. Note that 

all dependences on the frequency are "hidden" in the relationship between the projected 

velocity, hence the observed frequency, and the geometric coordinates 8 and p. As an 

illustration, let us consider the case of v ex r 1/ 2. Figure 3 shows the surfaces of constant 

projected velocity (as seen by an observer located at "infinite distance" on the right hand 

side of the figure) as well as some surfaces of constant optical depth. Note that at any 

value of p the optical depth (cf. equation 34) can vary only between To (for e = p and 

8 = 0) and Tol"! (for e = 0 and 8 = p) and, therefore, the surfaces of constant optical 

depth are almost spherical. 

As we have done for the continuum we can distinguish two extreme cases, i.e. optically 

thin and optically thick cases. However, since the transfer problem is rather more complicated than it is for the continuum, here we will limit ourselves to discuss the simplest 

concepts and to present the most straightforward results. 

In the optically thin case the total (i.e. integrated over the line profile) the line intensity 

is proportional to the volume emission measure of the wind (and, therefore, to the line 

optical depth) . 2 

Itot ex f ne n ,411"r2dr ex ~ (36) voR 

and the line width is proportional to the initial velocity through a constant which depends 

exclusively on the index "I. As long the terminal velocity is much higher than the initial 

velocity, the half-power-full-width (HPFW) of a line can be expressed as (Panagia et al. 

1987): 47+1 

HPFW = 28 7+1 (vo/e)vo (37) 

In the optically thick case there is no simple general solution. Two cases have been considered by Simon et al. (1983), i.e., "I = 0 and "( = 1, who solved the line radiative transfer 

problem numerically and expressed the results in formulae whose functional dependence 

9 
was derived from simplified theory and the coefficient was determined from a fit to the 

numerical results. Krolik and Smith (1981) have approached this problem in a general but 

very simplified manner which we follow here to illustrate the main characteristics of the 

emission lines formed in an optically thick wind. In such an approach, the size of emitting 

region is taken to be equal to the radius at which the optical depth becomes unity, i.e. 

1 

eef/ ~ p(r = 1,8 = 0) ~ r;h+1) (38) 

Thus, the intensity at the peak of the line will essentially be that of the black body with 

such a size, i.e. 

2 

Ipeak ~ 41rR21rB(vo)e;// ~ 41rR21rB(vo)r;h+1) (39) 

Similarly, the effective width of the line will correspond to the maximum velocity at which 

the optical depth is still equal to 1. This occurs at e = 0 (cf. eq. (34)) at a value of 

p = p(r = 1, e = 0), so that the frequency displacement at which the line is still strong 

will be 

A Vmaz Vo (ro) sC .. i!t-1) (40) ~v = --vo = - - Vo 

C C "f 

This formula essentially provides an estimate of the HPFW, whose functional dependence 

on the stellar and the wind parameters is 

(41) 

Hence, the total line intensity can approximately be estimated as 

Itot ~ Ipeak x HPFW = 41rR21rB(vo)r; ~ '7+1 Vo v; (42) 

It is interesting to note that this formula recovers the functional dependences derived by 

Simon et al. (1983) and extends their validity to any value of "f. However, due to the 

crudeness of the approach these formulae are accurate only to within a factor of two as 

compared with numerical results. More detailed calculations have been made recently 

by Panagia, Oliva and Felli (1987) both using refined analytical approximations and performing numerical calculations for a large variety of cases. Figures 4 and 5 present the 

results of the numerical calculations of the total intensity and the HPFW for emission lines 

formed in a wind where the optical depth is proportional to the square of the density, as 

appropriate for hydrogen lines. The analytical formulae they derive for the cases of high 

optical depths agree with the numerical results to better than 30% in general and better 

than 10% in most cases: 

Ipeak = 41rR21rB(vo)r (1 - 3("( ~ 1)) r;h~l) (43) 

I", = 4" R'" B (v,) 21"1 [r (1 - 3b: 1) ) r +l .:(7+;") "; v, (44) 

It also should be noted that at high optical depths, the higher the value of"f the wider the 

lines become both in the HPFW and the extension of wings: this is a natural consequence 

of the faster increase of the velocity with radius for higher values of "f. 

10 
" ')103 

>. 

5 

2 

.=. 

,: 

~102 

k 10 I: 

"" :?Ol 

iil 

0:: 0 " "5 1 05 

! 1 

0 2 ..> 

10 -I 5 

10 -I 1~ 1~ 1~ 1~ 1~ tau 

Fig. 4 - The total intensity of emission lines for several values of ,. 

10 -I 10' 102 103 10' 10" 10" tau 

Fig. 5 - The half-power-full-width of 

emission lines for several values of ,. 

2.4. Extension to more general cases 

In this section we will briefiy consider the effects of releasing some of the basic assumptions we have made in sections 2.1 and 2.3. 

2.4.1. Incomplete ionization 

We can identify two main possibilities: 

i) The wind is ionized bounded, i.e. the wind is fully ionized up to a certain radius and 

becomes mostly neutral beyond that: this the the analog to a Stromgren sphere for the 

case of an outfiow. This problem has been studied in detail by Felli and Panagia (1981) 

and Simon et al. (1983) who have shown that if such a situation occurs at all, the boundary 

is likely to be very close to the base of the fiow. As a consequence, the IR emission may not 

be strongly affected while the radio fiux can drastically be reduced by orders of magnitude. 

The maximum rate of mass loss for which a wind can be fully ionized by a star with a 

Lyman continuum photon fiux of NL is (Felli and Panagia, 1981) 

. -6 1/2 [ N L ] 1/2 [ Vo ] Me =5.75 X 10 (1 + 2,) 1049 s-1 100 km s-1 

[ 

R ] 1/2 [ T ] 0 4 M0 

10 R0 104K yr 

(45) 

Correspondingly the maximum radio fiux density which a wind ionized by such a star can 

emit is 

. 2/3 [ v ] 0 6 [ N L ] 2/3 [ R ] 2/3 

Fmax(wmd) =52.7(1 + 2,) 10 GHz 1049 s-1 10 R0 

[

Voo]-4/3 [_d ]-2 mJ 

Vo 1 kpc Y 

(46) 

It is clear then that a wind can never be a very strong source by emitting thermal radiation, 

I.e. its fiux density is unlikely to exceed a few tens of mJy. 

11 
ii) The gas is partially ionized everywhere throughout the wind. Natta et al. (1987) 

have shown that this situation may occur in the case of low luminosity protostars or young 

stars. In this case one can still apply the same kind of theory which has been outlined 

in the previous sections but now one should allow for the incomplete ionization in writing 

the dependence of the electron and ion density on the radius. In other words, one has 

to include the extra dependence on the ionization fraction in addition to those already 

present in the continuity equation. In the simplest case of a constant ionization fraction, 

all the equations discussed so far still hold with the only change that the mass loss rate 

should be replaced by the the product of the mass loss rate times the ionization fraction 

itself. The net effect is that in order to account for any given observed wind emission 

the required mass loss rate will be Ij(ionization fraction) times higher than in the case of 

complete ionization. 

fL/..e The outflow is not spherically symmetric: 

This case has been considered in quite some detail by Schmid-Burgk (1982) and 

Reynolds (1986). As for the slope of the continuum, the lack of spherical symmetry may 

affect it appreciably only if the fraction of solid angle filled by the flow varies systematically 

with the radius. For example, Reynolds has shown that in the case of collimated jets with 

cross section varying like w(r) = wo(rjro)'7 and a density within thejet ne(r) = no(rjro)-fJ 

the radio continuum spectral index is given by 

1+71 a(f3,71) = 2 - 2.1 2f3 - 71 (47) 

As for the absolute value of the flux it is found that, irrespective of the details of the source 

geometry, the formulae derived for a spherically symmetric wind are still valid, to within 

a factor of two, for more complex configurations as long as any ratio of the structural 

length scales in the source does not exceeds a value of about 10. In other words, only 

highly anisotropic structures can give results appreciably deviant from the predictions of 

the spherically symmetric models. Among these alarming cases one can consider a wind 

which consists solely of a number of narrow jets: in this case the radiating efficiency can 

be higher than in a spherical wind by as much as an order of magnitude and, therefore, 

the mass loss rate derived with spherical wind formulae may be strongly overestimated. 

For example, Reynolds (1986) has shown that a narrow conical jet with opening angle 00 

and seen with an inclination i can produce the same radio flux with a much smaller mass 

loss rate given by 

M(jet) = M(spherical wind) x 0.200~/4(sin i)-1/4 (48) 

e.4.S Time variability 

One of the basic assumptions is that the mass loss process is steady with time. On 

the other, variability is an observed fact and the more so in the case of young stellar 

objects. A discussion of the main effects has recently been presented by Felli et al. (1985b). 

Summarizing it briefly here, one can distinguish two cases: i) variation of the mass loss 

rate, and ii) variation of the ionization. In the former case one expects to d~tect short 

term variability in the optical and IR but not in the radio because even if the M variation 

is instantaneous the transit time of the front is 

ttran8it ~ Reff j v = 19.3 [:Oe!1] [ v 

o 100 km s ]

-1 

1 hours (49) 

12 
and, therefore, it is of the order of a few hours in the near IR but it can be of the order 

of weeks or months in the radio. Whether or not one sees any variation at all in the radio 

depends on the time scale of the intrinsic variation: if it occurs over a time much shorter 

than a few weeks, then the variations will completely be averaged out in the radio. In 

the case in which the ionization varies, the situation is different. Again assuming that the 

ionizing agent undergoes a sudden variation, the time scale of the phenomena is set by the 

recombination time which varies like a higher power of the radius: 

[ t __ 1 __ 7 4 M . ]-1 [ R elf ]2 rec - nef32 -. 10-6 M0 yr-1 10 R0 

[100 k: s-l] [i.~] [10: K r· B seconds 

(50) 

Therefore, one expects a much more prompt reaction in the optical and IR, which 

originate in the inner and denser layers, than in the radio. These points stress the importance of making simultaneous measurements at widely different frequencies in order to 

understand the nature and the origin of the variability. 

2.4.4 Accretion 

All throughout this theoretical section we have assumed that the emitting gas is flowing 

away from a young star. But the reverse situation, i.e. mass infall or accretion, may occur 

since we are dealing with just forming objects. And its occurrence is actually detected in 

some instances by the observation of inverse P eyg profiles of optical lines, i.e. lines with 

a red absorption and a blue emission, which are the unambiguous sign of gas falling onto 

the stellar surface. In these case, most of the theory remains valid apart for an obvious 

change in the velocity sign. In fact, one cannot distinguish the velocity sign, whether 

the mass flows in or out of a star, from observations in the continuum because its flux 

is solely determined by the density radial behaviour which is invariant with respect to a 

sign inversion as long as the modulus variation of the velocity stays the same. On the 

other hand, in the case of accretion one does not expect a lower velocity closer to the 

star because gravity will unavoidably accelerate the matter as it falls onto the star. As a 

consequence, the expected velocity slope is negative b < 0) whereas in the case of a wind 

both the theory and the observations suggest an outwardly acceleration, i.e. "( > o. Of 

special interest is the case of accretion in free fall conditions which entails v ex: rl/2. It is 

easy to verify that with the resulting density distribution n ex: r-3/ 2 the volume emission 

measure f nen,dV ex: n~r~ In(r/ro) (51) 

would diverge with increasing radius. Therefore, either the distance at which the inflow 

originates is suitably small or the gas will unavoidably be ionization bounded, i.e. neutral in 

the outer parts of the flow, for any accretion rate. For this reason the continuous spectrum 

will remain essentially flat even at those frequencies at which the flow is optically thick until 

the effective emitting radius will become comparable to the outer boundary. Felli et al. 

(1982) give an approximate expression for the radio emission. After some manipulation it 

can be written as 

(52) 

13 
where Maccr is the accretion rate, M is the stellar mass, rc is the radius at which the radial 

optical depth is equal to 3/4: 

[ 

'" ] -1 05 [ T ] -0 68 

rc = 3.66 X 10

14 

10 GHz 104 K 

[M' 1 [ M ] -1 [ ] 1 accr P-e -

10-7 M0 yr-l M0 1.2 cm 

(53) 

roo is the outer boundary, generally corresponding to the accretion radius 

rv (Ve8cape) 2 _ 2 65 1016 [ M ] [ Vturb ] roo - r 0 -. X M 1 cm 

Vturb 0 1 km s-

(54) 

Vturb being the turbulent velocity of the cloud where the accretion originates. The spectrum 

described by equation (51) is essentially flat, corresponding to spectral indexes between 

-0.1 to +0.1. This is possible because, although the central parts can be quite optically 

thick, still a considerable fraction of the flow remains optically thin. Equation (51) is valid 

as long as rc <: roo or, conversely, as long the frequency is higher than 

T -0 64 [if lO 95 M -1 43 

V - 169 _ accr -- c - [104] 10-7 M0 yr-l [M0 ] 

[

Vb ] 1 90 [II. ] -0 95 tur _r-_e MHz 

1 km s-l 1.2 

(55) 

At lower frequencies the spectrum will tend to the ordinary Rayleigh-Jeans tail of a black 

body, i.e. FII ex: ",2. It is clear then that the spectrum will remain essentially flat down to 

frequencies well below a gigahertz and then decline like ",2 at lower frequencies. Therefore, 

judging from the radio spectrum any accreting star could be mistaken for a compact HI! 

region, except that the widths of the emission lines would be drastically different, i.e. 

several hundreds of km s-l for an accretion flow as compared with the few tens of km s-l 

expected for an HI! region. 

2.5. Non-thermal emission 

The main non-thermal process which is relevant for young stars is synchrotron radiation. It is produced by electrons spiraling in a magnetic field and is regarded as a 

non-thermal process because it is an efficient process only with energetic electrons and 

these are abundant enough in non-thermal situations. This aspect makes much harder to 

uniquely define the parameters of a synchrotron emitting source or even to define the most 

probable situations, essentially because there are too many free parameters and too many 

unknowns. Therefore, here we will not discuss this emitting mechanism in detail but rather 

we shall limit ourselves to describing its main properties. More detailed summaries and 

discussions on the non-thermal emission processes in stars can be found in Dulk (1985), 

White (1985) and Andre (1987). The main characteristics of synchrotron radiation are i) 

a typical power law spectrum which, unlike to thermal spectra, increases with wavelength 

(until it starts becoming self-absorbed) ii) high polarization and iii) high brightness. This 

last property is due to the fact that very high energy particles are involved and, therefore, 

the limiting brightness temperature can be accordingly very high. Because of the same 

reason, a non-thermally emitting region can be much more compact than a thermal one. 

14 
Both the small size, which implies a short transit time, and the hlgh energy density, which 

implies a short energy loss time, concur in making the typical time scale of temporal variations of the non-thermal radio emission quite short. With the parameters appropriate for 

a star, such timescales range from hours to few days: this is orders of magmtude faster 

than it is possible in a thermal region. Therefore, short term variability can be taken as a 

fourth distinctive property of non-thermal emitting sources. 

3. RADIO AND INFRARED OBSERVATIONS OF YOUNG STARS 

9.1. The "well behaved" case 0/ S 106-IRS4 

One of the best studied young stars is S 106-IRS4. As its name suggests, it is a star 

associated with the HII region S 106 and has been discovered in the IR as a point like 

source (Sibille et al. 1975; Allen and Penston, 1975). In fact it cannot be seen in the 

optical because of about 21 magnitudes of visual extinction in front of it. The whole 

region has been the subject of a number of studies in the IR and in the radio (considering 

only papers relevant to the present discussion, see e.g.: Simon and Fischer 1982, Bally 

et al. 1983, Felli et al. 1984, 1985c and references therein). The radio observations show S 

106-IRS4 to be a point like source (Bally et al. 1983; cf Fig. 6) still unresolved at 22 GHz 

(diameter ~ 0.15", Felli et al. 1985c) and with a spectral index 0.7 ± 0.1 (cf Fig. 7). In the 

infrared, shortward of about lOjLm, it displays a clear excess relative to the stellar emission 

(Felli et al. 1984) and hydrogen emission lines (Bra, and Br"/; Simon and Fischer 1982, Felli 

et al. 1985c) whose HPFW is around 150 km s-1 and whose intensity ratios differ markedly 

from those of lines formed in HII regions. All of these aspects fit perfectly the pictupe 

of a star undergoing conspicuous mass loss. Combining all the available information Felll 

et al. (1984) deduced the following parameters for the star and the wind, for an assumed 

distance of 600 pc: 

Star 

Wind 

Effective Temperature, Tel I 

Radius, R 

Luminosity, L 

Lyman Continuum Photon Flux, N L 

Inferred Stellar Mass 

Matching Spectral Type 

Mass Loss Rate, M 

Velocity Index, "Y 

Initial Velocity, Vo 

Terminal Velocity, Voo 

28000K 

12 R0 

> 2 X 104 L 0 ("" 105 L 0 ) 

1.7 x 1048 photons s-1 

> 15M0 

09.5 V - BO III 

2.6 X 10-6 M0 yr-1 

0-0.25 

40-80 km s-1 

"" 300 km s-1 

Thus, S 106-IRS4 looks like the perfect "theorist's dream", i.e. the object whose 

observations fit all theoretical predictions. We shall see in the following sections that 

reality is not always so nice nor so simple. Even in this case the results are not "boring": 

w hat at first glance seems just a replica of an ordinary early type star, after a deeper exam 

reveals a number of peculiar properties: 

i) The ratio M / L is higher than 3 x 10-11 M0L"~/ yr-1: This is already an order of 

magnitude higher than it is measured in "normal" main sequence (~S) and supergiant stars 

(Tanzi et al. 1981) and is comparable to the values of WR stars ([M / L] = 4 X 10-11 M0L"~/ 

15 
.... 

0) 

o 

lO 

<Jl 

u 

w 

o 

30" 

::::::, 

) 

,3) G '-

'0 " BEAM 

15 11 ~ 

37°13' 0" I 

'1 

45" 

30 i?fo1 "," , ",,:';' ">:' c' ""~r '- . o..,~ ~'~ ,'~~) ,0:_ i 

; 1M.... c. • ' . • )..... , , ...... .. I 

15..i ;. ..; •.•• '. "0 ~·..'o 0 D I 

I') 

r'~~QD' ::",,," 

',,-, 

:,,,>~~o~\"'<J~''';~~11 ,.' ~ , 

o ~ ': __ " ': c;:> \J 0 0 

I 

~ .' .•.. U ' 

37'1" 0" ~ ~. '.:. -!? 0 •.. "" I 1 ~ ~ ".-: co"~ , ,,? ,.-,:-<:- ''', , --J 

365 34 5 

20 h 25 m 

RA(1950l 

32 5 

Fig. 6 - The VLA radio map of the S 106 region at 

15 GHz (Bally et al. 1983). 

20~ I 5106 IR /' I' 

15 1/ 

/ / 

~ I // .§ 10 ./ r:r. /10,7 

(f) '" ./ / Sv 

/ 

/ 

5 

/1 

5 

/ 

/ / 

15 

/I (GHz) 

22 

Fig. 7 - The radio spectrum of S 106-IRS4 (from Bally 

et al. 1983). 
yr-1 j Barlow et al. 198~). ii) The momentum carned by the wind exceeds that available 

in the radiation field: (Mvoo)/(L/c) ,...., 2. This is intermediate between ordinary OB stars, 

that have ratios lower than 0.5, and WR stars for which that ratio is higher than 10. iii) 

The terminal velocity, Voo = 300 km s-l, is much lower than that measured in MS and SG 

stars of comparable luminosity (voo ~ 1500 km s-l, see e.g. Panagia and Macchetto, 1982) 

These aspects suggest that S 106-IRS4 represents an especially "active", short-lived, premain-sequence phase of the evolution of a moderately massive star. We will see in sectIOn 

4 that most PMS stars seem to pass through such a phase before reaching the MS. Another 

interesting aspect is the marked absence of radio emission in a strip about 5" wide passing 

through the star in the SE-NW direction (cf Fig. 6). It can only be due to lack of ionizing 

photons in that direction because identical gaps are seen also in the IR, thus excluding the 

hypothesis of dust absorption occurring in a small disk/ring around the star. The most 

"natural" explanation is that of a genuine anisotropy of the stellar UV radiation, which 

is minimum on the equatorial plane and maximum toward the poles (Felli et al 1984). 

The orientation of this "void" region is perpendicular to the direction of the large scale, 

bipolar flow and is essentially coplanar with the disk-hke molecular region which projects 

in front of the star. Therefore, we see that one and the same geometric symmetry exists 

from a very small scale, i.e. the stellar radius,...., 1012 cm, up to a very large scale, i.e. the 

size of the molecular disk of about 3 X 1018 cm. The high degree of "organization" of very 

different scales suggests that all of these aspects are intimately connected with each other 

and have a common origin. 

9.2. General results of radio observations 

Essentially all possibilities considered theoretically in the previous sectIOns are observed 

III different objects. Andre (1987) in his review of the radio emission from young stars has 

defined four broad classes which are based on observed characteristics and can place the 

various objects into physically meaningful categories: 

1) Steady sources, unresolved, steep spectrum with posItive spectral index (a: > 0.5): 

thermal wind. Examples of this class are, in addition to the obvious S 106-IRS4, the BN 

object (Moran et al. 1983), Lk Ha: 101 (Brown et al. 1976) Lk Ha: 234 (Wilking et al 

1986), GL 490 (Campbell et al. 1986), CRL 961 (Snell and Bally 1986) and component 

#2 of Cep A (Hughes, 1985). All of these sources can be explained in terms of spherically 

symmetric, fully ionized winds with either constant or slightly increasing velocity. 

2) Steady source, resolved, flat spectrum: thermal jet or ultracompact HII region. 

Examples: GI29.58-0.04, NGC 2071, S 68-FIRSl, L1551-IRS5 (Snell and Bally 1986). 

The radio spectrum of this type of sources does not follow a simple power law, the spectral 

index being steeper at lower frequencies. An alternative to the HII region model is that 

such a spectrum is due to accretion. 

3) Steady source, unresolved, flat spectrum: thermal accretion flow or non-thermal 

emission? Typical examples are SI, VS 14 and WL 5 in the ~ Oph cloud (Andre et al. 

1987). The stable emission observed for these objects cannot be readily explained as due 

to flare activity but, on the other hand, being unresolved with the VLA their surface 

brightness seems to be too high for a ordinary thermal source. 

4) Variable source, unresolved: non-thermal stellar flares. Examples are: DoAr 21 

(= ROX 8), ROX 31 (Feigelson and Montmerle 1985)j V410 Tau, HP Tau/G2 and HP 

Tau/G3 (Cohen and Bieging 1986). The strong variability on short time scales identifies 

these sources as definitely non-thermal. Andre, Montmerle and Feigelson (1987) note that 

17 
their fluxes are comparable to those of post-main sequence RS CVn systems and suggest 

that they m.ay be associated with the m.ost lum.mous X-ray selected pre-m.ain-sequence 

stars. 

As remarked by Andre (1987) the objects in classes 1) and 2), i.e. those which do have 

stellar winds, show some definite evidence of large scale outflows, e.g. optical jets and/or 

association with HH objects for T Tau stars, bipolar flows for more powerful IR stars, so 

that they can easily fit with the same picture as drawn for S 106-IRS4 (cf. section 3.1). 

9.9. Radio Surveys 

If now we have an idea of what individual stars may do, still it isn't clear how many of 

them do that and for how long, i.e. we know about the phenomena that may occur but we 

cannot place them in the evolutionary history of a star. A step forward in that direction 

can be taken by making com.plete surveys in regions of star formation. In such a way, not 

only can one determine the properties of individual sources which were detected but also 

consider the "non-detections" to perform statistics which can tell us about the duration 

of the various phases in different classes of objects. Among the studies of this sort done in 

recent years I have selected three that are particularly relevant for our interests. 

1) Bleging, Cohen and Schwartz (1984) - They made VLA observations at 4 frequencies (1.5,4.9, 15 and 22.5 GHz) of all T Tau stars with logL/L0 > 0.2 associated with 

the Taurus-Auriga dark cloud (46 objects). Their results can be summarized as follows: 

• 12 stars out of the 46 (26%) were detected at one frequency at least. 

• For 8 of them the spectral index was determined: 

3 had a steep spectrum (a > 1) which could be interpreted as thermal emission; 

however, for one of them, V 410 Tau, the fast variability indicates a non-thermal 

origin of the emission. 

2 had a spectrum consistent with a stellar wind (a ,...., 0.6) 

2 had a flat spectrum but were unresolved: they could be explained as either nonthermal or accretion emission. 

1 had a negative spectral index (HP Tau/G2, a = -0.35) which speaks clearly of 

non-therm.al radiation. 

Therefore, in about half of the cases the emission is of thermal origin and, among these, 

in about half it originates from stellar winds. 

• The missed detection of 34 of the surveyed stars implies an upper limit to their mass 

loss rate of if,...., 2 x 1O-8M0 yr-l [v/200 km s-I]. 

• All of the 5 stars associated with HH objects do emit in the radio. 

2) Snell and Bally (1986) - They surveyed (complete VLA mapping at 1.4, 5 and 

15 GHz, to limiting fluxes of about 0.3 mJy at 5 GHz) 12 regions containing molecular 

outflows. The main results are: 

• Sources were detected in 8 out of the 12 surveyed regions. 

• A total of 43 sources were detected. However, based on a statistical argum.ent of source 

counts, it is concluded that about half of them are likely to be extragalactic. 

• 15 of the detected sources were identified with IR sources. In particular, all IR sources 

associated with the outflows having a bolometric luminosity higher than 100 L0 were 

detected (9 objects). In total, the IR sources detected in the radio amount to about 

2/3 of all genuine sources contained in these outflow regions. 

• For 7 sources the spectral index was determined: 

18 
3 had a spectral index and a size fully consistent with a stellar wind interpretation: 

CRL 961, Lk Ha 234 in addition to our friend S 106-IRS4. 

4 had a flat index: two (L1551 IRS5 and NGC 2071 IRS 1-3) are clearly extended 

and, therefore, are likely to be compact HII regions, whereas all possibilities, except 

a stellar wind hypothesis, remain possible for the other two. 

• For all sources, if the radio emission is formed by a steady, fully ionized wind, the 

implied mass loss parameters fail by more than an order of magnitude to explain the 

energetics of the associated molecular outflows. 

3) Andre, Montmerle and Feigelson (1987) - They made a VLA survey of the p Oph 

dark cloud, covering an area of 4 square degrees at 1.4 GHz (limiting fluxes 1-3 mJy) 

and observing the central part also at 5 GHz with a limiting flux of 1 mJy. Over the 

whole region, they detected 93 objects of which they judged that only 13 were truly stellar 

objects. Grouping the detected objects according to a variety of properties, they find: 

• 7, i.e. '" 60% of the sources, can be identified with near or far IR sources. However, 

among the three classes defined by Lada (1986; see section 3.4) only class III objects 

are detected: in particular, the detection rates are 0/5 for class I, 0/21 for class II and 

4/6 for class III. Three more IR sources detected in this survey could not be classified 

WIthin the Lada's scheme. 

• 10, i.e. 77% of the detected stellar sources, have a spectral index either flat or increasing 

with frequency. One of them, DoAr 21 is known to be non-thermal because of its 

variability. Most of the others are likely to be thermal sources. 

• 5 are associated with X-ray stellar sources. Since this cloud contains 47 such stars, 

only about 10% of the X-ray stars emit in the radio. 

• None of the 26 visible PMS (emission-line or T Tau) stars associat~d with the cloud 

was detected. This places an upper limit to their mass loss rate of M < 7 X 10-8 M0 

yr-1 [v/200 km s-1]. 

9.4. Infrared observations 

Infrared measurements are important for the study of young stars for two main reasons: 

first because the high extinction of star forming clouds, that prevents us from "penetrating" deeply into them at optical wavelengths, becomes less and less important at longer 

wavelengths. The second reason is that, especially for very young objects, the original 

circumstellar cocoon is still so thick that the bulk of the stellar energy is actually radiated 

in the infrared. In fact, most of the high luminosity PMS stars can only be detected in 

the IR, because their short evolutionary time makes it hard for the circumstellar material 

to dissipate before the star has reached the main sequence. A historically important example is the case of the Becklin and Neugebauer object (BN) which was discovered as an 

extremely cool obJect (T'" 700K) appearing in a map of the Orion Nebula at 2.2 J.tm and 

was immediately recognized as a possible protostar (Beck lin and Neugebauer, 1967). 

A systematic study of the energy distributions of young stellar objects has been done 

by Wilking and Lada (1983) and Lada and Wilking (1984) who made broad-band photometric observations of the embedded population in the core of the p Oph dark cloud. 

From an analysis of the derived energy distributions (.xFA vs .x) they identified three main 

morphological classes (see fig. 8): 

Class I - Sources with energy distributions broader than a black body and which are rising 

longward of 2 J.tm. 

19 
co 

o 

...J 

----- ~- ~ --- -I -- --- -

Protostor' 

,10 

T-Tourr Stor 

,----,--

Post T -Tau" Star 

I I 

Class I 

-- , , , , 

, , 

, 

'~Black Body , 

, 

, 

'" , ----~ 

'",Block Body , 

, 

, 

, 

\ 

\ 

\ 

Class m 

~Black Body 

10 2.0 100 1000 

Mp.m)-

Fig. 8 - Schematic representation of the classification of young stellar objects on the basis of 

their IR spectra (Lada and Wilking 1984). 

Class II - Sources with an energy distribution broader than a black body but which is flat 

or decreasing longward of 2 JLm. 

Class III - Sources whose energy distributions can be modeled with reddened black bodies 

and show no or little excess near infrared emission. 

Class I sources were all invisible and deeply embedded in the cloud whereas class II and 

III sources were associated mostly with visible stars. In particular, nearly all previously 

known class II objects were classified as T Tau stars. Moreover, the data available in the 

literature for a number of stars of low and moderate luminosity (L < 103 L0 ) fit equally well 

in this classification scheme. In particular, inspecting the Rydgren et al. (1984) catalog of 

the infrared spectra for 61 T Tau stars in the Taurus-Auriga complex one finds that among 

the 41 stars for which the wavelength coverage is complete enough to classify them, 34 falls 

in class II, 5 in class III and none in class 1. Lada (1986) suggests that such an empirical 

sequence may represent an evolutionary sequence in which class I objects are protostars, 

just formed and still deeply embedded in their original cloud. The circumstellar envelopes 

dissipate gradually with time, thus producing class II and III morphologies. The fact that 

many (but not all) class I objects and many (but not all) T Tau stars are associated with 

energetic outflows and/or stellar wind activity suggests that these processes represent the 

agents that dissipate the circumstellar envelopes and drive the evolution from class I to 

class III. From all of this it is clear that, due to the strong dust emission, in most cases 

(class I and class II objects) one cannot use IR continuum measurements to safely estimate 

the properties of the stellar wind. On the other hand, line emission is not affected by the 

20 
presence of dust, except for the obvious effect of extinctIOn. In addition, lines have the great 

advantage of carrying information about the velocity of the wmd; such an information is 

completely lost in the continuous radiation. Therefore, IR emission lines are very precious 

for specifying the detailed properties of the stellar winds. The most intense lines observed 

from PMS stars are generally hydrogen emission lines such as Bra (4.05 J..Lm), Bq (2.17 

J..Lm) or Ph (3.74 J..Lm). By using the theory outlined in section 2.3 one can determine both 

the mass loss rate and the characteristics of the velocity field in the wind. A number of 

searches have been carried out on PMS stars of all luminosities from"" 1L0 up to 106 L0 

(among the most recent studies we recall Thompson 1982, Simon et al. 1983, Thompson 

et al. 1983, Persson et al. 1984, Smith et al. 1987, Thompson 1987, Evans et al. 1987, 

Persson et al. 1987). The main result is that strong lines are indeed observed, with a 

strength much higher than predicted from the measured radio flux if the emitting region is 

assumed to be optically thin at all relevant wavelengths (the so-called HI! region theory). 

Such a result, surprising at first glance, is the obvious consequence of the wind properties, 

in particular the high optical depth. In fact, the wind is optically thick longward of few 

microns and the optical depth in the radio is several orders of magnitude higher than in the 

IR. Therefore, while both the IR and the radio fluxes are lower than in the optically thin 

case, the effect is much more conspicuous in the radio where the optical depth is higher. 

Hence, the ratio IRjradio in a wind can become considerably higher than it is in an HI! 

regIon. 

Another important result obtained from line measurements is the realization (e.g., 

Thompson 1982) that the ionization in the wind does requires a large number of ionizing 

photons, in many cases highly in excess to what the star can supply in the form of Lyman 

continuum photons (i.e., photons capable of ionizing the ground level of hydrogen, hv > 

13.6 eV). This problem will be discussed in some detail in the next section. 

4. STATISTICAL PROPERTIES OF STELLAR WINDS FROM YOUNG STARS 

Here, we discuss the available information on winds from PMS stars to try to understand their nature and their relation to the process of star formation. A more complete 

account of this analysis can be found in Panagia (1985). 

The data were collected from various sources in the literature, namely Cohen et al. 

(1982), Felli et al. (1982 and 1984), Persson et al. (1984), Simon et al. (1983), Thompson 

(1982), Thompson et al. (1983). The derived parameters, such as the mass loss and ionization rates, were directly taken from the original articles and may not be fully consistent 

with each other in that various authors sometimes have used different models to interpret 

their data. No attempt was made to 'homogeneize' the data and the possible discrepancies 

arising from the use of different models have been regarded as additional errors which sum 

up to the observational uncertainties. 

The quantities that we can consider to define the properties of PMS star winds are: 

1. The total radiative luminosity, Ltot , which includes the energy observed in the visual 

and, possibly, in the infrared plus the energy needed to ionize the wind (see point 3). 

2. The maximum expansion velocity, Vmax , as deduced from line profile observations. 

3. The wind ionization luminosity, L,on' i.e. the energy required to keep the wind gas 

steadily ionized. It is computed as the product of the number of ionizations occurring in 

21 
the wind (as deduced from IR/opticalline or IR/radio continuum observations) times the 

H ionization energy, 13.6 eV. 

4. The mass loss rate, M. It is deduced from either line measurements (mostly IR 

lines but sometimes optical, e.g. Ho:) or IR/radio continuum data. 

5. The momentumfiux defined as the product of the mass loss rate times the maximum 

wind velocity. The actual momentum carried away by the wind can be higher than this 

estimate, by a factor of'" 2, because part of the momentum is used to win the gravitational 

force (Abbott, 1980). 

6. The 'mechanical' luminosity, L bn, of the outfiowing wind defined as the product 

of the mass loss rate times 1/2v'lnaz. Note that the total kinetic energy carried by the 

wind away from the star may be higher because part of it has to be used to overcome the 

gravitational potential and part may have been transformed into heat. 

The total radiative luminosity will be used as the independent variable because it is the 

observational quantity which is essentially determined by the stellar mass and, therefore, 

best characterizes the properties of the star irrespective of the presence of the wind. Plots 

of the other quantities as a function of Ltot are displayed in Figures 9-13. 

The first interesting result is that in all cases the various quantities follow well defined 

trends as a function of Ltot . Clearly, there is some dispersion present in all plots but it 

is always much smaller than the total variation of the involved quantities and, therefore, 

there is no doubt that the apparent correlations are real. 

The second important aspect is that there is good continuity in the properties of the 

wmds of PMS stars over as much as six orders of magnitude in the luminosity from, 

say, about 1 L0 up to more than a million solar luminosities and correspondingly for 

stellar masses in the range from about 1 M0 up to almost 100 M 0 . Such a continuity of 

properties over a quite broad interval strongly suggests a great uniformity in the processes 

which induce and govern stellar winds in the PMS phase. 

Looking at individual plots, we see (Fig. 9) that the maximum expansion velocity is 

of few hundred km s-1 for all stars. Also, it is apparent that Vmaz is either lower or, at 

most, equal to the escape velocity from the stellar surface (veac = 2 GM/R): this is true 

whether we compute Veac using the stellar parameters of main sequence (MS) stars or if 

we adopt larger radii for any given luminosity as appropriate for PMS stars (hereafter we 

assume that a typical PMS star has an effective temperature a factor of 1.58, or 0.2 dex, 

lower than, and a luminosity equal to, that of a MS star of equal mass). Moreover, the 

observed velocities are much lower than those measured for the winds of MS stars, at least 

for those of high luminosity mass (e.g. Panagia and Macchetto, 1982). This suggests that 

the acceleration mechanism is different from that operating in MS stars. Furthermore, 

the fact that the terminal velocity is never higher than the escape velocity at the stellar 

surface suggests that the acceleration process is rather gradual and must operate up to 

relatively large distances from the stellar surface. 

Looking at Figure 10 we see that L~on is very well correlated with L tot over almost 6 

orders of magnitude with a modest dispersion of '" ±1/2 dex. The best-fitting power-law 

relationship is 

L L I2±O 2 ~on ex: tot 

Alternatively, the experimental correlation can be expressed as 

22 
35 

.. I --III 

S 3 

.!II: 

'-" 

2 

6 

4 

..J 

........... c 

.12 

QO 

o 

- o 

-2 

Flg 9 

• 

• 

o 

o 

•• 

• • • • • 

• 

2 4 

• 

log Ltot/Lo 

2 4 

6 

6 

..J 

'i: 

4 I- • . , 

• ••• 

~~' . . ~ 

J21- ., . ,It • •• 

tlO 

o 

- • - o - • , • .~ .. " ... • - 40n oc Ltot 12 

-2 I I 

o 2 4 

log Ltot/Lo 

Flg lOc # /' ~ ¢' /. .' I 

~/' ••• _$' o ::tl ~/ , •• ::to $;/ • , .§.I 

::-.~ -. -. §I ~~, .. '" 

,/ • .q/ 

• Sl 

O • / ~./, - ,. ' ... I. 

-2 I I 

o 2 4 

-

-

-

I 

6 

-

-

-

6 

Fig. 9 - The maximum wind velocity as a function of the total luminosity. The terminal 

velocities for MS star and for supergiant winds are displayed. Also shown are the escape 

velocities curves for MS and PMS stars. 

Fig. 10 - The ionization luminosity as a function of the total luminosity: a) The bestfitting power law is plotted; b) Lines of constant ratio L,on/ Ltot are shown; c) The curves 

of the ionizing radiation in the Lyman and the Balmer continua are compared with the 

data. 

to within a factor of three. In most cases, the ionizing flux is much higher than the stellar 

Lyman continuum flux but lower than the Balmer continuum flux expected on the basis 

of theoretical stellar atmosphere calculations (cf. Fig. lOc). Therefore, the wind could 

be ionized by Balmer continuum photons as suggested by Thompson (1982) and Simon 

et al. (1983). This problem has recently been addressed in detail by Natta et al. (1987, 

these proceedings). Alternatively, there may be a process which is capable to convert into 

ionization an energy corresponding to about 8% of the total observed stellar luminosity. 

Such an energy, however, cannot be provided at the expenses of the kinetic energy of 

the wind because this is generally smaller than 1% of the stellar luminosity (cf. Fig. 13). 

Among the number of possible processes the most plausible are: 

23 
I 

-4 _ FIg 11 

I I 

I I 

o 2 4 

I I 

2 r- FIg 13 

..J 

.......... c JO-

~ 

..9 

-2 h' 

o 

. , ..'. . . " • ,/0 L ldn oc LO?S 

". 

• 

I I 

2 4 

log Ltot/Lo 

I 

6 

I 

I 

6 

-

-

-

-

-

-

....-, 

-I 

(/) 

S-2 

~ 

-I 

s... 

>. 

-;1:4 

'-' 

o 2 4 6 

log Ltot/Lo 

Fig. 11 - The mass loss rate as a function of the 

total luminosity. The best-fitting power law is 

shown as a straight line. The areas occupied by 

early type MS, supergiant (SG) and Wolf-Rayet 

(WR) stars are also indicated . 

Fig. 12 - The momentum flux as a function of 

the total luminosity. The best-fitting power law 

is shown as a dashed line. Solid lines correspond 

to constant values of the ratio (Mv)/(L/c). 

The areas of MS, SG and WR stars are also 

indicated. 

Fig. 13 - The mechanical luminosity as a function of the total luminosity. The best-fitting 

power law is shown as a dashed line. 

i) The presence of a hot corona at the base of the wind: its temperature should not 

exceed few hundred thousand, and be higher than several tens of thousand, Kelvin degrees 

in order to be able to provide the necessary ionizing flux but escape detection both at UV 

wavelengths (e.g. IUE range 1150-3200 A) and in the X-ray domain. 

ii) Collisional ionization and excitation by thermal processes: this implies that the wind 

gas temperature be as high as 15000 K in order to make hydrogen 50% ionized. Clearly 

some heating agent must keep the gas at such a temperature: a possibility is dissipation 

of Alfven waves which have been proposed to explain the acceleration of the wind (Lago, 

1984). 

iii) Radiation produced by infall of matter onto the stellar surface: this accretion 

may represent the terminal phases of the very star formation process. In this case mass 

accretion and mass loss would coexist with each other: the former would prevail on and 

near the equatorial plane of the star and would originate from the molecular disk which 

gave birth to the star (Pudritz, 1985). The latter would dominate in the polar directions 

and, in addition to the ordinary wind manifestations, would also be responsible for the 

ionized component of the bipolar flows associated with PMS stars (e.g. see the discussion 

on S 106 by Felli et al. 1984). 

24 
As for the mass loss rate and the momentum flux (Figures 11 and 12) we see that again 

there is a good correlation of both quantities with Ltot , of the form 

M ex: L O 67±0 04 

tot 

Mv ex: LO 68±0 06 

tot 

The fact that the dependence of M and M v on Ltot is virtually the same is a direct 

consequence of the velocity being almost independent of the luminosity. Both the mass loss 

rate and the momentum flux are considerably higher that what one measures in "ordinary" 

stars, both MS or supergiant stars (e.g. Panagia and Macchetto, 1982; Felli and Panagia, 

1981) while they are comparable, after a suitable scaling, to the values observed in WR stars 

(e.g. Barlow et al. 1981). This indicates that stellar winds in the PMS phase are much more 

"active" than they will be in subsequent phases of the evolution. As a corollary, it appears 

that the mechanism which produces the mass loss is different from the one that operates in 

MS and supergiant stars but, because of the continuity of observed properties, it is hkely 

to be the same for all PMS stars. We also see that the momentum flux Mv is generally 

higher than the momentum carried by the radiation, Lie (cf. Fig. 12). Such high values of 

the momentum flux demand that the wind acceleration be due to either multiple scattering 

of the stellar radiation or to some non-radiative process (e.g., deposition of Alfven waves: 

Lago 1984). The former mechanism is able to account for the wind acceleration in early 

type stars (Panagia and Macchetto, 1982) but in order to work with comparable efficiency 

for PMS stars would require a high UV luminosity: this condition would also satisfy the 

ionization requirements but would imply a rather peculiar spectrum in that no trace of a 

strong UV continuum component has been observed in PMS stars with IUE (e.g., Gahm 

1980 and references therein). 

Finally, an inspection of Figure 13 reveals that the mechanical luminosity appears to 

correlate quite well with the radiative luminosity, i e. 

Lkln ex: L?~I6±0 11 

On the other hand, in all cases Lkm corresponds to a minor fraction of the total radiative 

luminosity 

Lkln ~ 0.01 Ltot 

and, therefore, it cannot play any major role in the interplay star/wind/environment. 

In summary we can conclude as follows: 

1. One and the same mechanism appears to be responsible for the mass loss in all 

PMS stars. The mechanism itself, however, is not identified. 

2. The wind ionization requires an agent external to the wind but the ordinary Lyman 

continuum radiation from the star is not enough for this purpose. Either Balmer continuum 

ionization or a more exotic processes is required to account for the wind ionization. 

3. The acceleration of the wind is likely not to be due to radiation and may be produced 

by direct deposition of energy into the wind. 

Finally it is worth considering the large scale properties of the winds of PMS stars 

and comparing them with the properties of the molecular bipolar flows which appear to 

be associated with PMS stars. Measurements of stellar winds probe regions of modest 

25 
size, say less than few 1014 cm, which corresponds to less than 0.1" at the distance of the 

closest T associations. On the other hand, one can currently observe ordered flows much 

farther away from the star but which undoubtedly originate from the star itself. This is, 

for example, the case of DG Tau B which displays an ionized, narrow jet (opening angle 

less than 5 degrees; Mundt and Fried, 1983) or S106-IRS4 (see section 3.1) These PMS 

stars and bipolar flows or jets appear to be associated with relatively massive molecular 

disks. They also appear to be aligned with the molecular flows which may extend over 

an even larger scale and seem to arise from the molecular disks moving approximately 

perpendicularly to the disk itself (Le., along the polar axis). Examples of these structures 

are S 106 (e.g., Felli or L 1551 (Lada, 1985 and references therein). In all cases, the 

momentum carried by the molecular flows is more than an order of magnitude higher 

than that carried by the ionized flow (Lada, 1985). Therefore, although it cannot be 

the stellar wind to push the molecular flow (because of the momentum problem) nor can 

the molecular flow directly produce the ionized flow and/or the stellar wind (because the 

former does not reach regions so close to the central star where the latter is observed to 

exist) a tight connection between the two phenomena must exist. It is quite possible that 

they both represent different manifestations of the same general phenomenon governing 

the formation of stars of any mass. 

26 
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