PHOTOIONIZATION AND MAGNETIZED WINDS:
HII REGIONS AND PLANETARY NEBULAE
FRANCO AND GUILLERMO GARC
JOSE
A-SEGURA
Instituto de Astronom
a-UNAM, Mexico
1.
Introduction
Photoionized nebulae are generated by hot stars located at the two ends
of the stellar mass spectra (and near the extremes of their evolutionary
tracks): H ii regions are excited by recently formed massive stars, and
Planetary Nebulae (PNe) are generated by low mass stars evolving toward
the white-dwarf phase (see Osterbrock 1989). They display a variety of
fascinating shapes, with irregular forms delineated by dusty laments and
bright rims, and with a complex network of velocity elds, ionization fronts,
shock waves, and instabilities. At large scales, integrated over time and
space, these objects can have a strong impact in the evolution of gaseous
galaxies. For instance, massive stars inject large amounts of radiative energy
which photoionizes and disrupts the parental clouds, setting the eciency
of star formation at galactic scales (e.g. Cox 1983; Franco et al. 1994; Shore
& Ferrini 1994; Diaz-Miller et al. 1998). In contrast, evolved low mass stars
do not have such a disrupting eect but they provide a generous gas mass
return rate. Thus, PNe ejecta can maintain the gaseous component at the
late stages of galaxy evolution, and are responsible for the enrichment of
several heavy elements.
H ii regions form a class of relatively well studied objects but there are
no clear denitions of the dierent types. They are sometimes classied
as ultracompact, compact, and extended HII regions (e.g. Habing & Israel
1979). Ultracompact H ii regions (UCHIIs) have small sizes, of about 0:1
pc, and are located in the inner, high-pressure, parts of the parental molecular cloud (e.g. Kurtz et al. 1994; Xie et al. 1996). Compact H ii regions
(HIIs) have larger sizes, 0:1 0 0:3 pc, and are carving their way out of the
parental clouds. Extended H ii regions, on the other hand, have sizes of
up to several parsecs and they represent the mature state of these objects.
86
FRANCO AND GUILLERMO GARC
JOSE
A-SEGURA
Thus, one can sketch a simple evolutionary link with the size growing in
time and, after Stromgren (1939) and Kahn (1954) set the physical basis to their modeling, the details of the expansion has been studied with
a variety of dierent analytical and numerical tools, and under dierent
cloud conditions, over the last four decades (see Yorke 1986; Franco et al.
1989,1990; Garcia-Segura & Franco 1996). In the case of PNe, there are
a variety of dierent morphological classes. They have been cataloged as
bipolar, elliptical, point-symmetric, irregular, spherical, and quadrupolar
(see Manchado et al. 1996). They are formed by the mass ejected at the
nal stages of low-mass star evolution, and the shapes are created by at
least two interacting winds. Dust shells around AGB stars, the progenitors
of PNe, do not show signs of asphericity and, during the transition from the
AGB to the post-AGB phase, one or more physical processes responsible
for the shape of these objects must be initiated. The origin of aspherical
nebulae remains as one of the fundamental problems of PNe formation
and evolution, and stellar rotation and magnetized winds can produce the
observed morphologies.
2.
H ii Regions
Star clusters are formed inside molecular cloud complexes, which are composed of a collection of high-density condensations interconnected by a more
diuse intercloud medium. The internal density distributions in clouds are
proportional to r0w , with an average value of w 2 (e.g. Arquilla &
Goldsmith 1985; Gregorio Hetem et al. 1988), and there are also disk-like
fragments (e.g. Torrelles et al. 1983; McCaughrean & O'Dell 1996). The
high-density condensations, or cloud cores, have peak densities of about
107 cm03 and peak temperatures above 102 K (e.g. Bergin et al. 1996;
Hofner et al. 1996). These observed values already indicate that the gas
thermal pressures are large inside the cloud cores. In addition, the existence of large non-thermal \turbulent" velocities, of several km s01 , and
strong magnetic elds, ranging from tens of G to tens of mG (see Myers &
Goodman 1988 and references therein), imply that the total pressures are
obviously higher and the cores of massive molecular clouds are highly pressurized regions. The resulting maximum core pressures (generated by their
own self-gravity) could reach values in excess of 5 2 1006 dyn cm02 (see
Garcia-Segura & Franco 1996). Thus, H ii region expansion in high-density
cores will be aected by their large total pressures. Numerical and analytical models of H ii region evolution under these conditions (i.e., n(r) / r0w
and disk-like density distributions, and large total pressures) provide many
details of the ows (Franco et al. 1989, hereafter FTB89; Franco et al. 1990,
hereafter FTB90; Garca-Segura & Franco 1996, hereafter GF).
PHOTOIONIZATION AND MAGNETIZED WINDS
87
For constant stellar UV uxes and uniform ambient densities, the expansion of H ii regions has well dened evolutionary phases (see Spitzer
1978 and Osterbrock 1989). During the formation phase, the radiation eld
creates an ionization front that, in a recombination time, reaches the initial
2
3
Stromgren radius (Stromgren 1939) RS = 3 F? =4 n20 B 1=3 , where n0 is
the ambient density, F? is the total number of ionizing UV photons per unit
time, B = 2:6 2 10013 cm3 s01 is the hydrogen recombination coecient
to all levels above the ground level. For a dusty cloud, the initial radius is
smaller and is given by RS;dust ' RS e0 =3 (FTB90), where is the optical
depth due to dust absorption. This simple formula agrees with the results
of radiative transfer calculations, and indicates that the initial Stromgren
radius is probably smaller than is usually considered (Daz-Miller et al.
1998; hereafter DFS). In addition, the radiation pressure on dust grains is
transferred to the ionized gas and, at late times, a central hole can be created in dusty H ii regions (Mathews 1967). After the formation time, due to
the pressure dierence with the surrounding medium, the recently formed
H ii regions expand and drive a strong shock wave ahead of the ionization
front. The expansion continues until the photoionized gas reaches pressure
equilibrium with the ambient interstellar medium (GF). If the ionization
front encounters a strong negative density gradient and overruns it, then
the expansion will enter into its \champagne" phase (Tenorio-Tagle 1982;
FTB90).
2.1 High Ambient Pressures and the UCH ii Class
The photoionized region reaches its equilibrium temperature, Ti 104 ,
K in a relatively short time-scale, and expands (in a nearly isothermal
fashion) into the neutral medium whose pressure is P0 . Assuming that the
ion density ni is equal to the electron density ne (i.e., for a pure hydrogen
nebula), the thermal pressure of the ionized region is Pi = 2ni kTi , where k
is Boltzmann's constant. The advance of the ionization front is controlled by
recombinations in the photoionized gas and, for a region of radius RHII , the
03=2 . The corresponding
average ion density is < ni >= [3 F? =(4 B )]1=2 RHII
0
1
03=2 . For a constant density
internal pressure is Pi = 3 k2 Ti2 F? = B 1=2 RHII
medium and Pi P0 , the HII radius grows as RHII / t4=7 , and the internal
pressure decreases as Pi / t06=7 . The expansion continues until Pi ! P0 ,
and the internal pressure tends to a constant value. These limits show
that, for a constant density medium, evolves as a function of the pressure
dierence from 4/7 to zero. When pressure equilibrium is reached, the ion
01 cm03 ,
density is simply given by ni;eq = (P0 =2kTi ) ' 3:6 2 104 P7 THII
;4
where P7 = P0 =1007 dyn cm02 , and THII;4 = Ti =104 K. The stagnation
radius of the H ii region, then, corresponds to a Stromgren radius at this
1=3
2=3
02=3 pc , where F =
equilibrium density RS;eq 2:9 2 1002 F48
THII
48
;4 P7
88
FRANCO AND GUILLERMO GARC
JOSE
A-SEGURA
0.06
0.04
R(pc)
Shock
Sonic Point
0.02
Ionization Front
0
0
Figure 1.
UCH
with P7 = 1.
ii
1
2
4
t (10 yr)
3
4
5
region evolution, for a star with F48 = 1, in a high-pressure medium
F? =1048 s01 .
The interstellar pressure at the solar circle is about PISM 10012 dyn
0
cm 2 , and the equilibrium values for single massive stars (with F48 1) are
ni;eq 0:4 cm03 and RS;eq 30 pc (the corresponding sizes for \naked" OB
associations can reach a few times 102 pc). The time scales at which these
equilibrium values are reached, however, are very long, teq > 107 yr, and
most massive stars move out of the main sequence earlier. For high-pressure
cores with P7 1 and rc 0:1 pc (see GF; Xie et al. 1996), the resulting
UCH ii could be stable and long lived. The equilibrium stage is reached in
time scales of the order of teq 104 yr, and the corresponding values are
very similar to the observationally derived sizes and electron densities in
ultracompact H ii regions, UCH ii (see Kurtz et al. 1994).
2.2 Density Gradients
If the star is located near the core boundary, or moves towards the
edge, the ionization and shock fronts can move out of the core and the gas
accelerates out of the high-density core. The relative position of the exciting
star, then, denes whether the UCH ii reaches pressure equilibrium or not.
For static or slowly moving stars, which are born near the center of the
core, the ultracompact stage can be long lasting. Otherwise, when the stars
are born at a distance smaller than RS;eq from the boundary, the ionized
ow is accelerated outwards and the UCH ii stage is a transient one (a
possible example of this type of transient UCH ii region is G29.96, which
is probably younger than 105 yr and has a champagne ow: see Lumsden
& Hoare 1996 and Watson & Hanson 1997).
The evolution in decreasing density stratications displays a rich variety
of hydrodynamical phenomena with internal shocks, receding ionization
fronts, rapid evaporation of cloud cores, and the creation of new clumps in
the expanding shocked shell (FTB89; FTB90; Rodriguez-Gaspar et al. 1995;
89
PHOTOIONIZATION AND MAGNETIZED WINDS
GF; Franco et al. 1998). For spherical clouds with density distributions
consisting of a central core (with radius rc and constant density n0 ) and an
envelope with a power-law density stratication, nH2 (r) = n0 (r=rc )0w , the
H ii region growth is approximated by (FTB90)
R(t) ' Rw
"
7 0 2w
12
1+
4
9 0 4w
1=2
ci t
Rw
#4=(702w)
:
(1)
The expansion phase has a critical exponent, wcrit = 3=2, which is independent of the initial conditions and is not aected by dust absorption. For
w < 3=2, the interface between the ionization front and the leading shock
accumulates neutral gas. For w = wcrit , the ionization front and the shock
front move together without a neutral interface. For w > 3=2, the ionization front overtakes the shock front and proceeds to ionize the whole cloud.
Once the whole ionized cloud is set into motion, the expanded core feels
the strongest outwards acceleration, and there is a wave driven by the fast
growing core. Thus, fast ows can be generated in steep density gradients.
For instance, ow velocities between 20 and 30 km s01 are generated in
w 2 distributions, and the speeds can increase to more than 100 km s01
for w > 3. This implies that UCH ii can be formed in high-pressure cores
with Rs < rc , but a rapid evaporation of the core occurs when Rs > rc
(Rodriguez-Gaspar et al. 1995).
For a gaseous disk, with a density distribution along the z -axis equal
to n(z ) = n0 G(z=H ) [where n0 is the density at midplane, H is the
2
2
scale height, and G(z=H ) is the disk stratication; say, e0z=H , e0z =H ,
or sech2 (z=H )], the density fall-o is steeper than r03=2 . Thus, ionization
front can become unbounded (during the expansion, however, the ionization front can recede; see FTB89). The initial shape of the ionized region
is dened by photoionization equilibrium, but initial size of the H ii region
as a function of the azimuthal angle .
2.3 Fragmentation of the Shocked Shell
The shock generated by the expanding H ii region collects and accelerates the ambient gas and, after radiative losses become important, a cold
and dense shell forms. The ionization front is located at the inner boundary
of the shell, and their evolution is subject to instabilities. In particular, the
ionization front exacerbates the growth of the thin shell instability and the
models performed by GF, which assume ionization equilibrium to dene
the location of the ionization front, show that these instabilities generate a
rapid fragmentation of the shell. The shapes of the resulting fragments are
similar to those observed in cometary globules and elephant trunks, and the
ow instabilities appear under a wide variety of conditions. Figure 2 shows
the instability for an H ii region evolving in a disk-like cloud. The model
90
FRANCO AND GUILLERMO GARC
JOSE
A-SEGURA
-22.0
-21.5
-21.0 -20.5 -20.0
log density (g/cm3)
-19.5
2.0
Z (pc)
1.5
a
d
b
e
c
f
1.0
0.5
2.0
Z (pc)
1.5
1.0
0.5
2.0
Z (pc)
1.5
1.0
0.5
0.0
0.5
1.0
R (pc)
1.5
2.0
0.5
1.0
R (pc)
1.5
2.0
Expanding H ii region evolving in a disk-like molecular cloud. Panels a-c;
stable shell of an adiabatic shock. Panels d-f; shell fragmentation in a radiative shock.
Figure 2.
illustrates the continuous formation of clumps by the shocked shell. The
presence of a strong stellar wind also generates clumpy structures and the
composite structures formed around massive stars with strong winds and
expanding H ii regions display a complex behavior (see Franco et al. 1998).
The wind-driven shell forms large density clumps and the UV photon eld
creates long photoionized ngers in the directions that are free of clumps.
Also, the radiation eld with energies just below the Lyman limit creates a
photodissociated region (PDR) between the H ii region and the rest of the
molecular cloud (e.g. Bertoldi & Draine 1996). This shell of HI gas, with
its photodissociating front, adds new complications to the dynamical evolution (Roger & Dewdney 1992; DFS). In addition, hot stars produce large
composite H ii regions with PDRs, but intermediate mass stars produce
only PDRs (DFS found that the the minimum stellar temperature required
to create a sizable PDR is about 1:3 2 104 K).
3.
Planetary Nebulae: Toroidal Fields and Collimation
It is commonly accepted that the formation of PNe involves the action of at
least two interacting stellar winds (Kwok, Purton & Fitzgerald 1978; Balick
PHOTOIONIZATION AND MAGNETIZED WINDS
91
1987; Kwok 1994; Aller 1993). It has been shown by Langer (1997,1998)
and Garca-Segura et al. (1998) that luminous blue variables (LBVs) and
asymptotic giant branch (AGBs) stars can reach critical rotation. GarcaSegura et al. (1998) have shown that the result is a slow, massive, equatorially conned outow. The striking similarity of the shapes of some PNe
and LBV nebulae (i.e., compare the \Hourglass Nebula", MyCn18, with
the \Homunculus Nebula" surrounding Carinae) indicates that the same
physical processes may be responsible for their morphologies. If this is the
case, the main cause of bipolarity could be due to stellar rotation. Asymmetries of the precursor AGB wind are not the only factor responsible for the
shaping of PNe. Using the thin shell approximation, Begelman & Li (1992)
obtained self-similar solutions of aspherical nebulae produced by a fast rotating neutron star with a magnetized fast wind. Their procedure did not
include wind asymmetries, and the aspherical shapes were due solely to the
tension of the toroidal magnetic eld. This was later applied by Chevalier &
Luo (1994) to the case of PNe winds and found similar steady-state aspherical results. More recently, with the aid of 2-dimensional MHD simulations
in cylindrical coordinates, Roz_ yczka & Franco (1996) found that the timedependent evolution has a very complex behavior and jet-like features and
collimated outows can be created (see Figure 3). The 3-D computations
performed by Garca-Segura (1997) corroborate 2-D results, with the main
dierence that the collimated gas can be probably subject to kink instabilities. Thus, the formation of jets and ansae are conrmed in 3-D, axis-free,
calculations. Now Garca-Segura et al. (1998) is performing 2-D, spherical
calculations, including the eects rotation and magnetic elds that seem to
be responsible for the wide variety of observed nebular morphologies. The
magnetic eld in an outowing wind from a rotating star has a toroidal
component that decreases with distance as r01 . The precise form of the oequator distribution of this toroidal component is unimportant, provided
that the eld is suciently strong to cause a deformation in the shocked
wind region (Roz_ yczka & Franco 1996). The radial eld component decreases as r02 , and can be neglected, so the used eld conguration obeys
r 1 B = 0.
The main eects of the magnetic eld is the elongation of the nebula
in the polar direction, and the creation of jets. The generation of a jetlike outow has been described by Roz_ yczka & Franco (1996). First, the
outer part of the magnetized shocked wind region becomes magnetically
rather than thermally dominated (the magnetic energy density gets larger
than the thermal energy density). Second, the tension of the toroidal eld
slows down the expansion in the directions perpendicular to the symmetry
axis, while the expansion in the direction parallel to the axis proceeds
unimpeded. Third, a ow from the equatorial parts of the shocked wind
92
FRANCO AND GUILLERMO GARC
JOSE
A-SEGURA
Interacting winds: magnetic fast wind interacting with a slow AGB wind. Both
winds are spherically symmetric and the fast post-AGB wind has a toroidal magnetic
eld.
Figure 3.
region toward the symmetry axis is initiated, leading to the formation of
stagnation regions at the axis and to the formation of jets. The gas arriving
at the polar regions of the nebula forms relatively dense blobs which can be
identied with the ansae observed in PNe (such as the ones in NGC 7009;
see Lopez et al. 1993). Perhaps the most important issue that has to be
stressed here, is that magnetic collimation becomes very ecient (even for a
spherically symmetric outow) after the ow has been processed by a shock.
Also, the collimation is operative up to very large distances, even when
the resulting jets develop kink instabilities. Note that external anisotropic
density distributions are not required but, if they occur, they can produce
even more elongated structures. When stellar rotation is included in the
AGB wind, a high-density region with a compressed B -eld is generated
near the equatorial plane (see Ignace, Cassinelli & Bjorkman 1998). In this
case, all the eects described above occur faster and have a stronger impact
in the evolution of the resulting nebula: the magnetic eect is enhanced, and
a higher degree of collimation is achieved. Thus, a combination of rotation
and a magnetic eld can naturally account for some of the most interesting
features in PNe. This however does not preclude that other eects (such as
external density anisotropies) can take place at the same time, resulting in
even richer morphological structures.
PHOTOIONIZATION AND MAGNETIZED WINDS
4.
93
Summary
Molecular clouds are composed of a collection high-density clumps, with
densities reaching 107 cm03 . These dense clumps, or cloud cores, are supported by non-thermal motions and seem to be the actual sites of star
formation. The initial shape and early evolution of the H ii regions, then,
are controled by the core density distributions. Depending on these distributions, and the corresponding stellar UV eld, the photoionized regions
can either reach pressure equilibrium inside the high-pressure cores (with
sizes and densities similar to those observed in UCH ii regions), or create
blister-type H ii regions with champagne ows. Disk-like cores can generate photoionized regions with a bipolar shape, and the ows are accelerated
along the steeper density gradients. In all cases, the density inhomogeneities
engulfed within the ionization fronts are smoothed out in short timescales,
but new clumps are continuously created by the fragmentation of the dense
shells generated by the shock fronts. Instabilities in the ionization/shock
front drive the fragmentation of the shell, and the resulting nger-like structures can explain the existence of elephant trunks and cometary-like globules in most H ii regions. Finally, when one includes the external dissociation front, a double shock structure with a complex behavior is formed.
The dissociation front destroys additional molecular gas and, eectively,
diminishes the productivity of star formation.
In the case of PNe, the ambient density structure is strongly modied
by winds from the progenitor star. Stellar wind asymmetries and magnetic
elds from rotating stars, along with the ionizing ux from the star, can
create the wide range of observed PNe morphologies and magnetically collimated outows (jets). This magnetic collimation is also operative in young
stellar objects and can be responsible for the generation of protostellar jets.
Perhaps the most important issue here is that magnetic collimation, and jet
formation, becomes very ecient after the ow has been passed through a
shock. All these features warrant further research, and future studies should
shed more light on magnetic collimation in shocked regions.
We are grateful to our good friends Rossy Diaz-Miller, Tim Freyer,
Beto Lopez, Norbert Langer, Mordecai-Mark Mac Low, Michal Rozyczka,
and Steve Shore who have collaborated with us in dierent aspects of the
work reported here. We also thank Frank Bertoldi for suggestions on PDRs.
This work was partially supported by DGAPA-UNAM, CONACyT grants
400354-5-4843E and 400354-5-0639PE, and by a R&D CRAY Research
grant. Part of the computations were performed at the Supercomputer Center of UNAM.
94
FRANCO AND GUILLERMO GARC
JOSE
A-SEGURA
References
Aller, L. H. 1993, in Planetary Nebulae, ed. R. Weinberger & A. Acker (Dordrecht:
Kluwer), 1
Arquilla, R. & Goldsmith, P. F. 1985, ApJ, 297, 436
Balick, B. 1987, AJ, 94, 671
Begelman, M. & Li, Z. Y. 1992, ApJ, 397, 197
Bergin, E., Snell, R. & Goldsmith, P. 1996, ApJ, 460, 343
Bertoldi, F. & Draine, B. T. 1996, ApJ, 458, 222
Bodenheimer, P., Tenorio-Tagle, G. & Yorke, H. W. 1979, ApJ, 233, 85
Chevalier, R. A., & Luo, D. 1994, ApJ, 421, 225
Cox, D. P. 1983, ApJ, 265, L61
Daz-Miller, R. I., Franco, J. & Shore, S. N. 1998, ApJ, in press (DFS)
Franco, J., Daz-Miller, R. I., Freyer, T. & Garca-Segura, G. 1998, in Astrophysics from
Antarctica, ASP Conf Series, in press
Franco, J., Shore, S. N. & Tenorio-Tagle, G. 1994, ApJ, 436, 795
Franco, J., Tenorio-Tagle, G. & Bodenheimer, P. 1989, RMexAA, 18, 65 (FTB89)
Franco, J., Tenorio-Tagle, G. & Bodenheimer, P. 1990, ApJ, 349, 126 (FTB90)
Garca-Segura, G. & Franco, J. 1996, ApJ, 469, 171 (GF)
Garca-Segura, G. 1997, ApJ, 489, L189
Garca-Segura, G., Langer, N., Roz_ yczka, M., Mac Low, M.-M., & Franco, J. 1998,
RevMexAA, ConfSer, 7, 50
Gregorio Hetem, J., Sanzovo, G. & Lepine, J. 1988, AAS, 76, 347
Habing, H. J. & Israel, F. P. 1979, ARAA, 17, 345
Hofner, P. Kurtz, S., Churchewell, E., Wamsley, M. & Cesaroni, R. 1996, ApJ, 460, 359
Ignace, R. Cassinelli, J. & Bjorkman, J. 1998, ApJ, in press
Kahn, F. D. 1954, BAN, 12, 187
Kurtz, S., Churchwell, E. & Wood, D. O. S. 1994, ApJs, 91, 659
Kwok, S. 1994, PASP, 106, 344
Kwok, S., Purton, C. R., & Fitzgerald, P. M. 1978, ApJ, 219, L125
Langer, N. 1997, in LBVs: Massive Stars in Transition, ASP ConfSer, 120, 83
Langer, N. 1998, A&A 329, 551
Lopez, J. A., Roth, M. & Tapia, M. 1993, A&A, 267, 194
Lumsden, S. L. & Hoare, M. G. 1996, ApJ, 464, 272
Manchado, A., Guerrero, M., Stanghellini, L., & Serra-R icart, M. 1996, The IAC Morphological Catalog of Northern Galactic PNe, IAC, Spain
Mathews, W. G. 1967, ApJ, 147, 965
McCaughrean, M. J. & O'Dell, C. R. 1996, AJ, 111, 1977
Myers, P. C. & Goodman, A. A. 1988, ApJ, 326, L27
Osterbrock, D. E. 1989, Astrophysics of Gaseous Nebulae and Active Galactic Nuclei,
Mill Valley: University Science Books
Rodrguez-Gaspar, J. A., Tenorio-Tagle, G. & Franco, J. 1995, ApJ, 451, 210
Roger, R. S. & Dewdney, P. E. 1992, ApJ, 385, 536
Roz_ yczka, M. & Franco, J. 1996, ApJL, 469, L127
Shore, S. N. & Ferrini, F. 1994, Fund.CosmicPhys, 16, 1
Spitzer, L. 1978, Physical Processes in the Interstellar Medium, New York: Wiley
Stromgren, B. 1939, ApJ, 89, 526
Tenorio-Tagle, G. 1982, in Regions of Recent Star Formation, eds. R. S. Roger & P. E.
Dewdney, Dordrecht: Reidel, 1
Torrelles, J. M. et al. 1983, ApJ, 274, 214
Watson, A. M. & Hanson, M. M. 1997, ApJ, 490, L165
Xie, T., Mundy, L. G., Vogel, S. N. & Hofner, P. 1996, ApJ, 473, L131
Yorke, H. W. 1986, ARAA, 24, 46