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Magnetohydrodynamic Puzzles in the
Protoplanetary Nebula
EUGENE H. LEVY
University of Arizona
ABSTRACT
Our knowledge of the basic physical processes that governed the
dynamical state and behavior of the protoplanetary accretion disk remains
incomplete. Many large-scale astrophysical systems are strongly magnetized
and exhibit phenomena that are shaped by the dynamical behaviors of
magnetic fields. Evidence and theoretical ideas point to the possibility that
the protoplanetary nebula also might have had a strong magnetic field. This
paper summarues some of the evidence, some of the ideas, some of the
implications, and some of the problems raised by the possible existence of
a nebular magnetic field. The aim of this paper is to provoke consideration
and speculation, rather than to try to present a balanced, complete analysis
of all of the possibilities or to imagine that firm answers are yet In hand.
INTRODUCTION
Magnetic fields are present and dynamically important in a wide variety
of astrophysical objects. There are at least three reasons why such magnetic
fields provoke interest: 1) The presence of a magnetic field invites questions
as to the conditions of its formation, either as a relict from some earlier
generation process, carried in and reshaped, or as a product of contempo-
raneous generation; 2) the Lorentz stresses associated with magnetic fields
are important to the structure and dynamical evolution of many systems;
and 3) magnetic fields can store, and quickly release, prodigious quantities
of energy in explosive flares. The possible presence of a magnetic field in
the protoplanetary nebula raises questions in all three of these areas.
70
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MAGNETIZATION OF METEORITES
71
Perhaps the most provocative, yet still puzzling and ambiguous, evi-
dence for strong magnetic fields in the protoplanetary nebula comes from
the remanent magnetization of primitive meteorites. Our ignorance of
the detailed history of the meteorites themselves, including the processes
of their accumulation, and ambiguities in the magnetic properties of the
meteorite material, causes difficulties in interpreting the significance of
meteorite magnetization. These latter ambiguities are especially confusing
to neat interpretations of the absolute intensities of the magnetic fields in
which the meteorites acquired their remanence. A further complication
arises because the meteorites exhibit a diversity of magnetizations, blocked
at different temperatures and in different directions on different scales. It
seems clear that a thorough understanding of meteorite magnetization, and
its unambiguous interpretation, has yet to be written (Wasilewski 1987~.
A variety of primitive meteorite materials carry remanent magnetiza-
tion (Suguira and Strangway 1988~. Of the wide variety of characteristics of
meteorite remanence that have been measured, two regularities in partic-
ular seem to be important. First, the intensities of the remanence-specific
magnetic moments seem typically to be larger for small components of
the meteorites (e.g., chondrules and inclusions) than for the aggregate
rocks. Second, the small, intensely magnetized components are frequently
disordered and oriented in random directions.
The inferred model magnetizing intensities for "whole rock" samples
tend to fall in the range of 0.1 1 Gauss (Nagata and Suguira 1977; Na-
gata 1979~. The connection of this "model" magnetizing intensity to a
real physical magnetic field depends to some extent on the way in which
the meteorite accumulated and subsequently evolved in the presence of a
magnetic field, as well as on the prior magnetic history of the individual
components. More provocatively, the inferred magnetizing fields for indi-
vidual small components of meteorites (for example, chondrules) range to
the order of 10 Gauss (Lanoix et al. 1978; Suguira et al. 1979, Suguira and
Strangway 1983~. Probably even these inferences, although based on mea-
surements of some of the physically simplest and least heterogeneous of
meteorite material, should be regarded as tentative, pending wider-ranging
and deeper studies of the processes involved in the acquisition of meteorite
remanence.
One interpretation of the measurements is that the meteorite parent
bodies were assembled out of small components that were already in-
tensely magnetized as individual, free objects before they were incorporated
into larger assemblages (Suguira and Strangway 1985~. This interpretation,
while simple and consistent with the measurements, is probably not unique.
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One might imagine, for example, that the randomization of the small com-
ponents occurred after magnetization, from an internally generated field on
a larger object, during the subsequent churning of a regolith. However, for
the present we will accept as a tentative inference that magnetizing fields
as high as 10 Gauss might have occurred in the protoplanetary nebula.
Inasmuch as the meteorites seem to have formed at several astronomical
units, of the order of three, from the Sun, this 10 Gauss magnetic field also
seems likely to have existed at that distance, although other possibilities
are not strictly ruled out.
THE POSSIBLE ORIGIN OF A NEBULAR MAGNETIC FIELD
Assuming the presence of such a nebular magnetic field, there are
several ways, in principle, that it could have arisen. One possibility is that
the field could have been generated in the Sun; another possibility is that
the field could have been a manifestation of the interstellar magnetic field
compressed by the collapse of the protosolar gas (Safronov and Ruzmaikina
1985~. Consider, however, the possibility that the nebular magnetic field
was rooted in the early Sun. This possibility is largely attractive in the
case that the nebula itself was too poor an electrical conductor to have
its own magnetohydrodynamic character. In that case, the solar magnetic
field must fall off at least as fast as r-3 in the electrically nonconducting
space outside of the Sun. (In fact, if there is some ionized gas outflow from
the Sun, even outside of the disk, the field might fall off somewhat less
rapidly with distance, but probably not so differently as to alter the general
conclusion here.) Then for a 10 Gauss magnetic field at 5 x 10~3 cm from
a 10~i cm radius Sun, the solar surface magnetic field would have had to
have been about 109 Gauss. Such a situation would have had a profound
influence on the Sun, especially with respect to the dynamical equilibrium
and stability of the system, since the energy associated with such a field
would have been comparable to the gravitational binding energy of the
Sun. Clearly, there are many other aspects of this that could be considered.
However, the purpose here is not to rule out completely the possibility of
an important nebular field arising from the Sun; rather it is to indicate that
such an assumption does not lead to an easy and obvious solution of the
problem of a nebular magnetic field.
Here we will presume a turbulent nebula in which the short mixing
times and low electrical conductivity, and the consequent rapid dissipation
of magnetic fields, quickly erase any memory of the nebular fluid's previous
magnetization. In this case, if the nebula is to carry-a large-scale magnetic
field, then it must be contemporaneously generated, most likely by some
sort of dynamo process (Parker 1979; Zel'dovich and Ruzmaikin 1987~.
The possible existence of conditions in the nebula that could have allowed
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73
the generation of such a magnetic field raises substantial physical questions.
However, in the spirit of the present discussion, we will assume whatever
is necessary and come back to the implications in the end.
The ability of a fluid flow to generate a magnetic field through hy-
dromagnetic dynamo action can, in simple cases, be parameterized by a
dimensionless number called the dynamo number, N. where
N= art
~2
(1)
I' is a measure of the helical part of the convection while ~ measures
the strength of the fluid shear, and ,7 is the magnetic diffusivity, c2/4,ra,
with electrical conductivity a; ~ is the scale length of the magnetic field.
Following a simple analysis for accretion disks (Levy 1978; Levy and Sonett
1978),
r
(2)
In a Keplerian disk, Q = (GM~/r3~/2, and to order of magnitude, I' ~ {Q.
where e is the large scale of the turbulence. Numerically then, ~ ~ 1.7 x
10~3r-3/2 see- ~ and, ~ ~ 1.1 x 10~3ir-3/2 cm see- i. Now, taking both the
scale of the largest eddies, 1, and the scale of the magnetic field, a, to be of
the order of the scale height of the disk gas, ~ 5 x 10~2 cm, we find that N
~ 1.3 x 1035 9-2, when r ~ 3 AU. Recent detailed numerical calculations
of magnetic field generation in Keplerian disks indicate (Stepinski and
Levy 1988) that magnetic field generation occurs at N ~ 102. Putting these
results together, we find that a regenerative dynamo can be expected to
be effective in such a disk if the electrical conductivity exceeds about 500
sect. We will return to this question in the end.
Now consider the strength that such a magnetic field might attain.
Inasmuch as the essential regenerative character of a dynamo fluid motion
is associated with the cyclonic or helical component of the motion, which
results from the action of the Coriolis force, then one estimate of the
possible maximum amplitude of a dynamo magnetic can be derived from
balancing the Coriolis force and the Lorentz stress:
VQ
4~t
-
(3)
Bp and B˘, represent the poloidal and toroidal parts of the magnetic field
respectively. Eking p ~ 10-9 gm cm~3 and V ~ 0.1 kilometers per
second, then with the other values as above, we find ~/2 ~ 1o
Gauss, as a measure of the maximum magnetic field strength that might
be produced in such a nebula. Other processes also can act to limit the
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strength of the magnetic field. For example, with the low ionization level
indicated above for the action of a nebular dynamo, the strength of the
magnetic field can be limited by the differential motion of the neutral and
ionized components of the gas: a phenomenon sometimes called ambipolar
diffusion. Consideration of this dynamical constraint (Levy 1978) yields a
limit on the magnetic field strength similar to the one just derived.
It is provocative that this estimate of the magnetic field strength
possible in a protoplanetary nebula dynamo agrees so closely with the
inferred intensity of the magnetizing fields to which primitive meteorites
were exposed. At this point, the general estimates are sufficiently crude,
and other questions sufficiently open, that this coincidence probably cannot
be considered more than provocative.
THE POSSIBILITY OF MAGNETIC FI^RES
One of the most intriguing puzzles posed by meteorites is the evidence
that some components were exposed to very large and very rapid transient
excursions away from thermodynamic equilibrium. Specifically, meteorite
chondrules are millimeter-scale marbles of rock, which apparently were
quickly melted by having their temperatures transiently raised to some
1700K and then quickly cooled. While there is some uncertainty about
the time scales involved, the evidence suggests time scales of minutes to
hours, though some workers have suggested even shorter melting events,
of the order of seconds. Although a number of possible scenarios have
been suggested for the chondrule-melting events, none seem to have been
established in a convincing way (King 1983; Grossman 1988; Levy 1988~.
Here we will focus on the possibility that chondrules melted as a result
of being exposed to energetic particles from magnetic nebular flares (Levy
and Araki 1988~.
In astrophysical systems, explosive restructuring of magnetic fields,
associated with instabilities that relax the ideal hydromagnetic constraints
and allow changes in field topology, seems to be among the most prevalent
of phenomena responsible for energetic transient events. Such events are
well studied in the Earth's magnetosphere (where they are involved in the
dissipative interaction between the solar wind and the geomagnetic field and
in geomagnetic activity) and in the solar corona (where they produce solar
flares and other transient manifestations). It is thought that many other
explosive outbursts in cosmical systems result from similar mechanisms.
1b summarize the analysis given in Levy and Araki (1988), following
the simple and basic analysis given by Petschek (1964), the energy emerging
from a flare event is estimated at
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75
F ~ B erg cm~2s~
87r~/~
(4)
Physically, this corresponds to an energy density equivalent to the energy
of the magnetic field flowing at the Alfven speed. Levy and Araki conclude
that, in order to deliver energy to nebular dust accumulations at a rate
sufficient to melt to the silicate rock the flares must occur in the disk's
tenuous corona, with local mass density in the range of 10-~8 gm cm~3,
and with a magnetic field intensity in the range of about 5 Gauss. Under
these conditions, they estimate that much of the flare energy is likely to
emerge in the form of 1 MeV particles, which are channeled down along the
magnetic field; in much the same way that geomagnetic-tail-flare particles
are channeled to the Earth's auroral ovals. Under these conditions, Levy
and Araki find that the value to which a particle's temperature can be
raised is given by
B3 ~114
T= ~ 167r5/2a~) ~
(5)
where To is the ambient temperature into which the particle radiates, and
which has no substantial influence on the result. From equation (5) it is
found that the above cited conditions in the flare site, pa 10-~8 gm cm~3
and B ~ 5-7 Gauss, yield flare energy outflows sufficient to melt chondrules;
substantially weaker magnetic fields or higher ambient mass densities yield
energy fluxes too low to account for chondrule melting. It is easy to see
that the time scale constraints for rapid chondrule formation are easily
met. At the equilibrium temperature given by equation (5), the rate of
energy inflow is balanced by radiative energy loss. Thus the heating time
scale is of the order of the radiative cooling time scale, second to minutes,
depending on the physical structure of the precursor dust accumulation,
and the temperature variation of the chondrule closely tracks the variation
of the energy inflow.
The conclusion from this exploration is that chondrules might plausibly
have been melted from magnetic flare energy in the protoplanetary nebula.
Apparently, the most reasonable conditions under which flares could have
accomplished this occur for flares in a low~ensity corona of the disk and
with magnetic fields having intensities of around 5 Gauss or somewhat
greater. It is provocative that these conditions are entirely consistent with
inferences about the possible character of nebular magnetic fields that were
summarized in the previous two sections.
If chondrules were made in this way, it is also necessary that the locale
of chondrule formation was at moderately high altitudes above the nebular
midplane: below the locale of the flares, but still high enough that the
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matter intervening between the flare site and the chondrule-formation site
was sufficiently tenuous to allow the passage of MeV protons. This implies
that the dust accumulations would have to have been melted at an altitude
of about one astronomical unit above the midplane. It is conceivable that
dust accumulations might have been melted into chondrules during their
inward travel from interstellar cloud to the nebula. It is perhaps more likely
that dust accumulations were lofted from the nebula to high altitudes by gas
motions. This latter possibility requires that the precursor dust assemblages
were very loose, fluffy, fairy-castle-like structures, somewhat like the dust
balls that accumulate under beds (Levy and Araki 1988~. However, this
is perhaps the most likely physical state of early dust assemblages in the
protoplanetary nebula.
Because the energetic particles associated with the flares described
here are likely to have had energies in the range of an MeV, it is pos-
sible that nuclear reactions might also be induced that could account for
some isotopic anomalies measured in meteorites. However, this possibility
requires further investigation.
EXTERNAL MANIFESTATIONS
It is especially instructive to estimate the gross energetics of the flares
described in the previous section. Again, following Levy and Araki (1988),
consider that the time scale of the flare is of the order of the heating time
of the chondrules, somewhere in the range of 102 to 104 seconds. Crudely,
the flare energy is derived from the collapse of a magnetic structure of
some spatial scale Lf in a time of. The rate of such collapse is expected
to occur at a fraction of the Alfven speed, say ~ 0.1 VA, SO that Lf ~ 0.1
VATf; the volume of involved magnetic field is then about (0.1 VATf)3.
Thus the total flare energy should be of the order of
ef ~ 10 364 B T3
(6)
Taking B ~ 5 Gauss and p ~ 10-~8 gm cm-3, then ef ranges from some 3
X 103° to 3 x 1036 ergs per flare, as the flare time scale ranges from 100
to 10,000 seconds. For a flare time scale of one hour, equation (6) gives an
energy of 1.3 x 1035 ergs. The total flare energy given by equation (6) is
an especially sensitive function of the magnetic field strength: a 10 Gauss
magnetic field would multiply all of the above energies by a factor of 32.
Now it is interesting to compare these results with the observations
of flaring T Tauri stars. Such stars show diverse flaring activities over a
range of time scales and intensities (Kuan 1976~. Worden e' al. (1981)
suggest that 10-minute flares on T Tauri stars release at least 1034 ergs
per event. This is in the range of flare energies given in the previous
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77
paragraph. Although there is considerable uncertainty in the numbers and
in the physical conditions, it is conceivable that at least some of the flares
observed on T Tauri stars are the same phenomenon that we have described
here as a possible energy source for chondrule melting.
In a possibly related development, Strelnitskij (1987) has interpreted
observed linear-polarization rotation angles, in an H2O maser around
a "young star," to require the presence of an approximately 10 Gauss
magnetic field at distances of 10 and more astronomical units from the
central star. It is not clear whether this surprising result has any connection
to the problems discussed here, but the observation is surely provocative
in terms of our understanding of the environments of young stars and
protostars.
DYNAMICAL EFFECTS OF THE MAGNETIC FIELD
A nebular magnetic field having the strength and distribution discussed
in this paper would have had substantial effects on the structure and
dynamical evolution of the system. The main effects would be of two kinds,
deriving from pressure of the magnetic field and the ability of the field to
transport angular momentum.
Consider that a 5 Gauss magnetic field exerts a pressure of just about
1 dyne/cm2. Compare this with the nebular gas pressure, which, for the
mass density p ~ 10-9 gm/cm2 and the gas temperature T ~ 300K, is
about 10 dynes/cm2. Thus the magnetic pressure is about 10% of the gas
pressure. Although a 10% change in the effective gas pressure seems like
a relatively small effect, within the context of the ideas discussed here,
the overall effect of the magnetic field will be, in fact, much larger. The
magnetic field constitutes a net expansive stress on the system, all of which
must be confined in equilibrium by the gravity acting on the gas. This
can be seen in a straightforward way from the magnetohydrodynamic virial
theorem. 1b the extent that the low-mass-density corona also is permeated
by a significant magnetic field, the expansive stress associated with the
coronal fields must also be confined by the disk mass. Thus, to make a
crude estimate, if the volume of coronal space filled with disk-generated
magnetic field is, say, five times larger than the volume of the disk itself,
suggested as a possibility in this discussion, then the effective expansive
stress communicated to the disk gas is some five times larger. In that case
the magnetic field becomes a major factor in the structure and dynamical
balance of the disk especially with respect to the vertical direction. Because
the magnetic field acts much like a bouyant, zero-mass gas, the dynamical
behavior of the gas and disk system would be expected to have similarities
to what we observe in the solar photosphere-corona magnetic coupling.
This is exactly the situation envisioned above in the speculative picture
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PIANETARY SCIENCES
of nebula-corona flares. In that case, the nebula would also be expected
to exhibit behaviors similar to those described by Parker (1966) for the
galactic disL
The magnetic contribution to angular momentum transport could have
similarly important effects with a magnetic field such as that considered
in this paper. Consider the torque transmitted across a cylindrical surface
aligned with disk ens and cutting the disk at a radius R:
T < BpB~ ~ 2 RENA)
(7)
where we have included the torque between z = ~tA Let hi; be the time scale
for angular momentum transport, then Hi; ~ LIT, where L is a characteristic
angular momentum of the system. Eking L ~ ~rR2~2A)pR2Q we find that
2,Tp~
~
(8)
Eking I/< BpB,~, ~ ~1-10 Gauss results in an evolutionary time scale
for angular momentum transport of 102-104 years. Thus, the presence
of such a nebular magnetic field would have a substantial impact on the
angular momentum transport and on the radial evolution of the system.
This angular momentum transport rate is large in comparison with the
time scales generally believed to characterize nebular evolution. In that
respect, it is worth noting effects that could alter the simplest relationships
between the 1-10 Gauss field strengths and the overall evolution time
scale. First, we note that MHD dynamo modes In a disk are spatially
localized (Stepinski and Levy 198%), so that such fast angular momentum
transport may extend over only limited portions of the nebula at any
one time. Second, detailed observations of the Sun show us that intense
magnetic fields may be confined to thin flux ropes, with the intervening field
strength being much weaker. Such a situation in the nebula, with a spatially
intermittent magnetic field, might admit the most intense magnetic fields
inferred from meteorite magnetization, while still producing an overall rate
of angular momentum transfer much lower than that estimated above.
Finally, angular momentum transport at the fast rate suggested in the
previous paragraph might be expected to produce sporadic, temporally
intermittent evolutionary behavior in the nebula over short time scales. One
might imagine that the 102 - 104 years magnetic timescale could represent
rapidly fluctuating local weather episodes during the slower, long-term,
large-scale evolution of the nebula.
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THE PROBLEM OF IONIZATION
79
Perhaps the most difficult barrier to understanding the possible pres-
ence of a substantial magnetic field in the protoplanetary nebula is the
question of electrical conductivity. Except near its very center, the neb-
ula was a relatively high-density, dusty gas at relatively low temperatures.
Under such conditions, the thermally induced ionization fraction and the
electrical conductivity are very low. Significant levels of electrical conductiv-
ity require some nonthermal ionization source to produce mobile electrons.
Consolmagno and Jokipii (1978) point out that ionization resulting from the
decay of short-lived radioisotopes might have raised the electron fraction to
the point at which the nebula gas was coupled to the magnetic field. Based
on their preliminary analysis, Consolmagno and Jokipii suggested that an
electron density of perhaps a few per cm3 would have been produced with
the then prevalent ideas about the abundance of 26A1 in the nebula. This is
sufficient to produce the behaviors described above. Thus, although more
complete calculations of nebular electrical conductivity are needed (and
are underway) in light of new information about the cosmic abundance
of 26~ (Mahoney et al. 10) and new information about the dominant
ion reactions, it is at least possible that the nebula was a sufficiently good
conductor of electricity to constitute a hydromagnetic system.
SUMMARY ANI) CONCLUSIONS
A coherent picture can be drawn of the possible magnetohydrodynamic
character of the protoplanetary nebula. This picture is based on a mixture
of evidence and speculation. From this picture emerges a reasonable expla-
nation of meteorite magnetization, a possible source of transient energetic
events to account for chondrule formation, a plausible picture of dynamo
magnetic field generation and field strength in the nebula, and a possible
connection to energetic outbursts observed in association with protostars.
This picture has potentially significant implications for our understanding of
the dynamical behavior and evolution of the protoplanetary nebula because
a magnetic field having the implied strength and character discussed here
would have exerted considerable stress on the system.
The primary unresolved question involves the electrical conductivity of
the nebular gas. In order for the described picture to be real, the nebular gas
must conduct electricity well enough to become a hydromagnetic fluid; this
requires a nonthermal source of ionization. However, other questions also
press at us. What is the real nature and genesis of meteorite magnetization?
Are the present, simplest interpretations correct, or is something eluding
us? Clearly important work remains to be done in this area. What were
the natures and histories of meteorite parent bodies? Could a magnetizing
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PLANETARY SCIENCES
field have been internally generated? We are seriously in need of in sim
investigation (with sample return) of comets and asteroids. What is the
nature of protoplanetary environments? Astronomical studies are needed
to ascertain the small-scale environments associated with star formation
and protoplanetary disks.
From a broader point of view, it is possible that many things begin to
fall into place if one presumes that the protoplanetary nebula did, in fact,
have the characteristics described here. The protosolar system then takes
on the aspect of a typical astrophysical system, which of course it was, with
dynamical behaviors thought to be common in many such systems. In this
case, it seems that a considerable conceptual gap separates the relatively
simple and well-behaved nebula that emerges from our planetary system-
based theoretical fantasies, and the energetic, violently active systems that
we associate with protostars in the astrophysical sly. Some considerable
work—theoretical, observational, and experimental remains in order to
close that gap.
ACKNOWLEDGEMENT
This work was supported in part by NASA Grant NSG-7419.
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Representative terms from entire chapter:
magnetic fields
