Figure
1 – An example of a detection from the
Investigators
Richard
M. Crutcher, professor,
Nicholas
Hakobian, graduate student,
Thomas
Troland, professor,
Project Background
Understanding star
formation is a fundamental astrophysical problem. For thirty years what has
sometimes been called the standard model has been that magnetic fields control
the formation and evolution of the molecular clouds from which stars form,
including the formation of cores and their gravitational collapse to form
protostars (Shu et al. 1999; Mouschovias & Ciolek 1999). However, in recent
years doubts about the validity of this model have been raised by those who
argue that turbulence controls the formation of clouds and cores, with cores
either dissipating back into the general interstellar medium or collapsing and
forming stars if they are self-gravitating when formed (MacLow & Klessen
2004). In spite of decades of intense research, there is still not consensus on
the role that magnetic fields play in the star formation process.
The most direct approach
to testing star formation theory is to measure magnetic field strengths in
molecular clouds in order to see whether they are weak or strong. The crucial
parameter is the ratio of the mass to the magnetic flux. This ratio plays an
equivalent role in molecular cloud dynamics to that of gravity and thermal
pressure in stellar structure and evolution. For stars, their self-gravity that
would make stars collapse is balanced by thermal pressure generated by
thermonuclear fusion in stellar cores. For molecular clouds, self-gravity is
balanced by magnetic pressure (in the strong magnetic field model) or
turbulence (in the weak field model). If the mass-to-flux ratio is observed to
be too large, gravity overwhelms magnetic pressure and clouds would collapse
rapidly. There is a critical value of the mass-to-flux ratio at which molecular
clouds would be in equilibrium. Subsequent evolution would occur slowly, by a
process called ambipolar diffusion. Neutrals are not affected directly by
magnetic pressure, but are free to collapse through the ions and the magnetic
field. That collapse is significantly slowed by collisions between the neutrals
and ions, leading to a slow, near-equilibrium collapse. On the other hand, if
magnetic pressure is weak, turbulence can provide support against gravitational
collapse. However, turbulence will shock and dissipate on time scales
comparable to the gravitational free-fall time scale. Only if the turbulence is
continually re-generated will molecular clouds be in a near equilibrium state.
Observing Magnetic Fields in
Star Formation Regions
The Zeeman
effect provides the only known method to measure directly magnetic field
strengths in dense gas. However, only atoms and molecules with an unpaired
outer electron will have a strong Zeeman effect. Except for the very strong H2O
masers, all interstellar Zeeman detections has involved the few species with unpaired
electrons: H I, OH, and CN. For the usual case of Zeeman splitting much smaller
than the line width, only the line-of-sight component BLOS can be
determined. The Stokes V spectra reveal the direction and magnitude of BLOS.
Previous Zeeman work
Most previous
Zeeman detections in molecular clouds (e.g., Crutcher 1999) have been toward
clouds associated with H II regions. Dark clouds offer the possibility of
measuring the role of magnetic fields at an earlier stage of the star formation
process, especially for the low-mass star formation case where the standard
model may best apply. Troland & Crutcher (2007) used the
Figure
1 – An example of a detection from the
Figure
2 - Plot of BLOS against the H2
column density (N21 = 10-21 N). The solid line is the
weighted mean value of the mass-to-flux ratio with
respect to critical and before geometrical corrections. The dotted line shows a
critical mass-to-flux ratio.
The result from
figure 2 is that the measured mass-to-flux ratio = 4.8 with respect to critical. However, all of the BLOS
results are lower limits to the total magnetic field strength. The
statistical correction for this is a factor of 1/2. In addition, if strong
magnetic fields result in a disk morphology for cloud cores, then the
statistical correction becomes 1/3, which includes in addition the fact that NLOS
rather than N along the magnetic field direction is observed. Hence, the result
from the Troland & Crutcher dark-cloud study is a mass-to-flux ratio = 1.6 with
respect to critical, similar to the result (1.7) found in the earlier study
(Crutcher 1999).
These Zeeman observations had the potential to eliminate one of
the two models for the star formation process. If the mass-to-flux ratio had been found to
be unambiguously highly supercritical, the ambipolar diffusion driven model
would have been eliminated. If the mass-to-flux ratio had been found to be unambiguously
subcritical, the turbulence driven model would have been eliminated. The statistical result is that the mass-to-flux ratio in molecular clouds is observed to be approximately
critical, which is consistent with the possible predictions of both models.
The definitive GBT test
The
definitive test of the importance of magnetic fields in the star formation
process is measurement of the difference in the mass-to-flux ratio between the envelope and the
core of a cloud. The magnetic support/ambipolar diffusion model makes a
specific prediction that can be tested. It requires that the mass-to-flux ratio be subcritical in the envelopes
of clouds with cores. The turbulence model predicts the opposite
behavior of the differential mass-to-flux ratio between envelope and core.
The
definitive observational test to distinguish the two major theories is
therefore to make a relative measurement of the mass-to-flux ratio between the envelopes and cores of molecular clouds,
using the same Zeeman species. This will eliminate or at least greatly reduce
the uncertainties inherent in absolute measurements of the mass-to-flux ratio. First, we seek only a change in the mass-to-flux ratio from envelope to core, not the absolute values
themselves. This avoids all of the geometrical correction problems in going
from BLOS to Btotal and from Nobs to NB
(the column density along B). We do not need to know the angle between
the line of sight and B, because we will be making a differential
measurement. Further, no geometrical correction for the measured column
densities will be necessary. Also, by observing BLOS in the core and
envelope using the same tracer, such as OH, the ratio OH/H, needed to convert
measured OH column density to total (H2) column density in order to
find the absolute value of the mass-to-flux ratio, is
irrelevant.
What
is needed now is to measure NOH/BLOS in the envelopes
of these cores to test the prediction that ambipolar diffusion increases the
mass but not (at least very much) the field in cloud cores. Zeeman observations
in molecular envelopes have generally not been attempted before, since line
strengths are weaker and Zeeman detections are difficult to obtain. The
telescope that is ideal for this project is the GBT. The GBT is being used to
make a four-point Zeeman map around the core with the GBT, dividing the
observing time equally between the four positions and combining the spectra to
obtain a mean Stokes I and V for the envelope region. The off-core positions
are 6 arcminutes north, south, east, and west of the core position. Therefore,
we will have BLOS and NOH separately for the core and envelope material. GBT
Stokes I spectra and V spectra would be observed. The ratios [NOH/BLOS]core
and [NOH/BLOS]envelope will then be available
for the clouds. The strong field/ambipolar diffusion theory for core
formation requires that the mass-to-flux ratio between core and envelope = [NOH/BLOS]core/[NOH/BLOS]envelope
be greater than 1 (that is, that the mass-to-flux ratio increases from envelope to core), so these observations could result
in the ambipolar diffusion model being proved wrong. It could also result in
the driven turbulence, ideal MHD simulations being proved wrong, if we find
that [NOH/BLOS]core/[NOH/BLOS]envelope
is less than 1. It is of course essentially impossible to prove a theory is
correct, but our proposed observations will provide a definitive observational
test of star formation theory. Such a result would have a profound effect on
further theoretical work on star formation, and would be a major advance in
understanding the star formation process.
Currently
(5 Dec 2007) we have approximately 40 hours to total integration time on the
envelopes of two cores, L1448 and B217-2. Data reduction is underway, and
further observations on other cores will take place starting later in December.
We will post results here as soon as they are available.
References
Crutcher, R. M. 1999, ApJ,
520, 706
MacLow M.-M.
& Klessen R. S. 2004, Rev. Mod. Phys., 76, 125
Mouschovias, T. Ch. &
Ciolek, G. E. 1999, in The Origin of Stars and Planetary Systems, ed. C.
J. Lada & N. D. Kylafis (Kluwer: Dordrecht), p. 305
Shu, F.,
Allen, A., Shang, H., Ostriker, E. C., & Li, Z.-Y.
1999, in The
Origin of Stars and Planetary Systems, ed. Charles J. Lada & Nikolaos
D. Kylafis, (Kluwer:
Troland, T. H. &
Crutcher, R. M. 2006, to be submitted to ApJ