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It is the opinion of this Panel that, except for very
small applications (in which the cost of even a small
minicomputer is not justified) or very large applications
(in which the jobs are so long that the speed difference
between a large vector machine and a minicomputer with
array processor is important), the minicomputer, with an
array processor if needed, is the most cost-effective way
to perform the vast majority of scientific computations.
Of course, this Panel is not the first to recognize
the advantages of minicomputers. Their proliferation has
already started. A large number of astronomers have now
had experience with minicomputers, and they are finding
wide acceptance in the astronomical community. One cau-
tionary remark is necessary, however. Today there is
little experience in the astronomical community with the
minicomputer-array processor combination. Although no
major problems are anticipated, additional experience
should be obtained before it can be definitely stated
that this is a viable mode of operation.
IV. THEORETICAL COMPUTING
The Panel has been aided in its investigations of theo-
retical computing needs by a joint meeting with the Panel
on Theoretical and Laboratory Astrophysics (see Chapter
4), the participation of a representative from that Panel,
and by a Workshop on Computational Astrophysics held at
the NASA/Ames Research Center on the two days preceding
the third meeting of the present Panel (which was also
held at NASA/Ames). The material that follows is drawn,
in part, from all three sources.
Many important insights and breakthroughs in modern
astronomy have been obtained through large-scale compu-
tation. Astronomical phenomena typically combine complex
interplays of several physical processes with strongly
nonlinear effects. Hostile or unattainable environments
preclude laboratory studies. Large-scale computation
provides the only hope for sorting out and understanding
such interacting processes. Conversely, astronomical
situations sometimes represent a setting in which certain
kinds of physical processes manifest themselves without
hopeless entanglement with other effects. The astronomical
context often provides the best setting in which to study
the physics of these processes; it is, in effect, our
laboratory.
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The complexities of astronomical phenomena together
with greatly improved observational data conspire to
broaden the scope of problems that demand attention and
to sharpen the detail sought in interpreting observations
Qualitatively new kinds of data (from Space Telescope,
high-efficiency imaging detectors, and the Very Large
Array and satellite data from previously unattainable
wavelength regions, for example), as well as significantly
improved accuracy and greatly increased data rates on more
traditional observations, yield a flood of new data and
introduce new kinds of problems that demand interpretation
or solution. All of this makes access to more computa-
tional capability imperative if theorists are to keep
abreast of observational data, let alone investigate new
problems. Lacking sufficient capability, interpretations
offered to explain observational data from the Space
Telescope, the Very Large Array, and other sources will
necessarily be based on guesses or other shortcuts; only
with adequate facilities will we be able to take the full
range of physical effects into account and develop theo-
.
retical interpretations whose quality matches the quality
of the observations.
The last decade has witnessed a tremendous growth in
the use of computers in constructing and testing theo-
retical models of astrophysical systems. Computers were
used in the 1960's mainly to construct one-dimensional
models, for which the demands on computation time are
modest by today's standards. In that decade, the greatest
advances were made in the field of stellar evolution.
Computer experiments played a key role in connecting our
understanding of nuclear physics in stellar cores to the
observational data, which necessarily refer to only a
thin layer at the stellar surface. Computer simulations
have been our only means of testing theories of phenomena
in stellar interiors, such as the events leading to a
supernova explosion. During the 1970's, increased com-
puter speed and sophisticated computer programs have
permitted much more detailed analysis of supernova
models. Such computer calculations have made a major
contribution to our understanding of nucleosynthesis.
Computers have played a major role in the study of
radiative transfer and the calculation of emission spec-
tra. Computational techniques have been used to study
radiative transfer in stellar atmospheres, the spectra of
protostars, and the appearance of dense interstellar
clouds in molecular lines. These computer models have
played an essential role in relating the observational
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data to physical models of stellar pulsation (e.g.,
Cepheid variables), stellar mass loss, star formation,
and gravitational collapse of dense clouds. The compu-
tation of emission spectra in situations where the radia-
tive transfer is not coupled to a hydrodynamical calcula-
tion is less demanding of computer capability, but here
the computer is no less essential. Such computations
have helped us to understand the physical conditions in a
wide variety of astrophysical objects--x-ray sources,
quasars, planetary nebulae, and coronas.
Beginning in 1969, computer simulations were applied
to models of star formation and over the last decade have
increased dramatically in sophistication. Two-dimensional
hydrodynamical calculations have been used to study the
early stages of star formation. mese calculations have
focused on the initial compression and the onset of col-
lapse and also on the effects of cloud rotation and mag-
netic fields on the subsequent evolution of the collapsing
clouds. Only one-dimensional calculations have been per-
formed for the later stages of protostellar core forma-
tion, but these have become very detailed. Apart from
simple arguments based on the virial theorem and similar-
ity solutions of limited applicability, computer modeling
has provided our only solid means of interpreting the
wealth of observational data obtained in this field over
the last decade.
Computer calculations have played an important role in
the investigation of the structure and dynamics of gal-
axies. In the 1960's, many N-body calculations were
carried out with small numbers of stars interacting
through gravitational forces. These calculations yielded
excellent models of star clusters, but it was only at the
end of the decade, with the development of the particle-
following numerical methods, that galactic systems could
be simulated with models capable of producing the compli-
cated structures characteristic of real disk galaxies.
These stellar dynamical models have been refined during
the 1970's and extended to treat three-dimensional sys-
tems. In addition, gas-dynamical simulations have
greatly aided the interpretation of the 21-cm radio
observations of galaxies.
A new application of computational methods in astronomy
has been the simulation of general relativistic systems.
This work is now in its infancy; not even simple flows
are fully understood. Because of the immense difficulty
in obtaining analytic solutions, this is a field in which
numerical computations are likely to have a tremendous
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impact. The computations of even very simple situations
require an enormous amount of computer time, and we may
expect more interesting problems to be attacked only as
computers become more powerful and more easily available
in the future.
Impressive as this list of accomplishments may appear,
progress in all these areas has been severely limited by
the availability of computational facilities. Many of
the projects that have been undertaken only very recently
could have been done a decade ago had there been suffi-
cient access to the computers existing at that time. The
limitation has rarely been the availability of willing
manpower or sufficiently powerful computational tech-
niques. The slow progress over the decade in galaxy
modeling is the case in point. The early spiral galaxy
models have barely been surpassed, although much more
realistic simulations are possible. When so much can be
learned from this experimental approach, it is mystifying
that the computational facilities necessary for vigorous
pursuit of this research program have not been provided.
A significant fraction of the spiral-galaxy simulations
during the last decade was performed in England, where
computational resources were made available through the
controlled fusion program. Three-dimensional simulations
of galaxies, like the work on disk galaxies, has pro-
gressed at a rate determined by availability of computer
time rather than the availability of manpower or compu-
tational techniques.
Another example of unnecessarily slow growth in the
computer simulation of astrophysical systems is in the
area of hydrodynamics. Hydrodynamic computer codes
capable of modeling a variety of astrophysical systems in
two dimensions have been available for at least a decade.
Nevertheless, hydrodynamic computations performed on
reasonably fine grids are a rarity even today. Computa-
tions that involve the much more complicated and time-
consuming algorithms for multifluid or implicit hydrody-
namics or that also involve radiative transfer are even
rarer. In fact, a major portion of this kind or work is
now performed in Germany, where easy access to a powerful
vector machine has been arranged through the Max Planck
Institute in Munich (a third of the machine time is
available for astrophysical calculations). Many impor-
tant problems, such as the calculation of the nonlinear
development of Parker's instability in two dimensions,
have gone without solution because the computer facili--
ties are unavailable. Such calculations could easily
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have been performed a decade ago; the computers, codes,
and experts were there, and only the computation budgets
were lacking.
The availability of facilities for theoretical computa-
tions has been inadequate in recent years and must be
improved if the astronomy program in the United States is
to have the proper interplay and balance between theory
and observation.
Computation capability is made available through three
main sources. For small problems, university computer
centers are adequate and are cost-effective when the com-
puter capability required does not justify the purchase
of a dedicated minicomputer-array processor system. These
minicomputer-based systems are the second main source of
computational capability for theoretical computations and
are probably powerful enough to meet the needs of the
large majority (perhaps 90 percent) of theoretical compu-
tations. Finally, there are problems requiring access to
the largest and fastest machines available. These prob-
lems have traditionally been attacked through cooperative
arrangements between astronomers and large laboratories
such as the Lawrence Livermore Laboratory, NASA/Ames,
NASA/Langley, Los Alamos National Laboratory, and the
National Center for Atmospheric Research.
At present, the first and third methods of performing
theoretical calculations are dominant, with minicomputer-
array processor systems just beginning to play a role.
The Panel believes that these three methods will continue
to be important in the 1980's, but their relative impor-
tance will show a dramatic shift. Because of its cost
effectiveness, the minicomputer-array processor config-
uration should be performing most of the theoretical
astronomical computations by the end of the 1980's. This
will occur mostly at the expense of computations performed
at university computer centers, which, toward the end of
the decade, will be used primarily to support astronomical
computations at universities where only small amounts of
computation are performed. In addition, some of the
problems that are now studied with the biggest machines
are amenable to solution with minicomputer-array processor
systems.
However, there will remain problems--black-hole
dynamics, star formation, radio sources and jets, super-
novae, galactic chemical evolution, magnetic fields and
plasmas, and solar phenomena, for example--that are at
the cutting edge of theoretical research and merit atten-
tion beyond the fraction of astronomical computing they
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represent. Approximations must be made to fit these
problems into the largest and fastest machines available
today; our confidence in the results is weakened because
of these compromises. Larger and faster machines expected
in the coming decade may allow improved treatment of these
problems and, very probably, attacks on additional prob-
lems that cannot be fit into machines available today.
The Panel makes the following recommendations concern-
ing theoretical astronomical computations in the 1980's:
1. The primary recommendation is that the funding
agencies [the National Science Foundation (NSF) and the
National Aeronautics and Space Administration (NASA)]
make available funds to purchase approximately 10 mini-
computer-array processor systems for the purpose of
theoretical calculations in astronomy. m e "canonical"
system and its associated costs are described in Appendix
A. These funds should be supplied at a steady level of
funding in real dollars. This will allow the purchase of
1.7 systems per year for 6 years (a typical useful life
for a computer system before it becomes obsolete), after
which the oldest systems would be replaced. The funds
made available for this purpose should be primarily new
funds if theoretical astronomy is to have the increased
support that it requires. In addition, funding, perhaps
on a cost-sharing basis, is needed to support the main-
tenance, operations, and software expenses for ten such
systems after a steady state is reached. These computers
need not be distinct from those used to perform image
processing and analysis (see the next section), but an
equivalent of 10 such systems should be dedicated to
theoretical computations.
m e exact number of such systems required is difficult
to quantify. The number 10 represents the Panel's best
guess at the number that is required and feasible; how-
ever, the proposed steady-state funding plan is flexible.
If it turns out that twelve systems are required, they can
be purchased with the same level of funding, provided they
are replaced at just over 7-year intervals rather than
6-year intervals.
2. m e funding that supports computing at university
computer centers should be maintained in those cases where
the level of astronomical computation at a given univer-
sity does not warrant a switch to a dedicated system.
However, the funding agencies should be alert to those
cases where one or two medium-scale users (about $30,000/
year) and/or several small users (about $10,000/year) are
Representative terms from entire chapter:
radiative transfer
