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Title: Need for context-aware computing in astrophysics
Author: Dilip G. Banhatti 302102 Affiliation: Madurai-Kamaraj University, India
Email: dilip.g.banhatti@gmail.com, banhatti@uni-muenster.de
For: 15th Annual IEEE International Conference on High Performance Computing - Main
Conference
Abstract: The example of disk galaxy rotation curves is given for inferring dark matter from
redundant computational procedure because proper care of astrophysical and computational
context was not taken. At least three attempts that take the context into account have not
found adequate voice because of haste in wrongly concluding existence of dark matter on the
part of even experts. This firmly entrenched view, prevalent for about 3/4ths of a century, has
now become difficult to correct. Context-awareness must be borne in mind at every step to
avoid such a situation. Perhaps other examples exist.
Keywords: dark matter; disk galaxy; rotation curve; context-awareness.
Topics: Algorithms; Applications.
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Manuscript
Astrophysical (and cosmological) context
Gravitating matter too faint to detect with state-of-art photon-detecting astronomical
instruments has evolved from being called missing mass in the 1930s [1] to missing light four
decades later to dark matter soon afterwards. The concept was originally invented to ensure
virial energy balance in clusters of galaxies. It was tested on smaller (galaxy groups' and
single-galaxy) scales and larger (observable universe) scales in a gravity-research-foundation
award-winning entry [2], and later acquired a memetic life of its own in many astrophysical
(and cosmological) contexts. It was soon joined by its sister concept dark energy.
Computation on individual galaxy scale
Galaxy formation scenarios and relevant observations indicate that interactions between
galaxy-sized matter agglomerations may be an essential feature of the formation of individual
galaxies. However, to a first approximation, individual galaxies (even if binaries or members
of larger groups) may be taken to be isolated stable dynamical systems. The large size of an
average individual galaxy warrants taking proper account of the different arrival times of
photons starting their journey (quasi-)simultaneously from its different parts. That we can
study whole galaxies as individual objects means that galaxian orbital and evolutionary
timescales are much longer than the differences in light-travel times between photons
originating from two sides of a galaxy. There is also the question of propagation of
gravitational interaction between different parts of a galaxy. Newton's laws of gravitation and
dynamics assume simultaneous inter-particle action, while general relativity properly applied
should incorporate the local and global space-time structure relative to the relevant matter-
energy tensor. As seen for Mercury's orbit in the inner solar system, general relativity theory
is needed to tally with observations (within errors), Newtonian dynamics and gravitation even
then being a very good approximation. It may, therefore, be applied, at least as a first
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approximation, on the galaxian scale. Applying Newtonian dynamics and gravitation has been
the practical recourse of choice for most astrophysicists studying disk galaxy dynamics or any
other topic in galaxian dynamics.
Three attempts to get disk galaxy dynamics right
(1) Fourier numerical method in cylindrical polar coordinates [3]
The disk plane is defined as z = 0 in a coordinate system with the radial coordinate
logarithmic to allow for central mass concentration. Effects of disk thickness and of any halo
must be taken into account by projection onto the base coordinate plane z = 0. Newtonian
gravitation (that is, force proportional to inverse-squared distance) is used between any two of
60000 particles, with a smoothing parameter added to the interparticle distance to avoid
infinity at coincidence of the two particles. Furthermore, leapfrog numerical scheme, also
called Verlet method in molecular dynamics, is used for fast but accurate convergence. The
actual operative calculations are carried out in the Fourier domain using fast Fourier transform
to switch between the physical and Fourier domains. This overall numerical scheme has been
used for various aspects of disk galaxies including spiral arms, tidal interactions and Seyfert
activity. The scheme is quite efficient and needs to be used to estimate galaxian physical
parameters from observed rotation curves without a priori assuming any dark matter in the
halo or (especially) the disk.
(2) Matrix inversion method in cylindrical polar coordinates [4]
The disk plane is designated z = 0 with 250000 particles distributed along 500 rings of radii
proportional to i2, where i is the ring number from centre outward, upto a finite outer radius
Rg of the galaxy disk. Each ring is assumed infinitely thin in the z-direction. Newton's force
equations are first written in finite element form, and then matrix-inverted to get the masses
mi of different rings, i = 0, 1, 2, ..., n; along with the constraint equation giving the sum over
mi to be the total mass Mg. The method is tested with known analytic solutions before
applying it to astronomical data for Milky Way Galaxy. This numerical scheme is also
eminently suitable for wider use.
(3) Mass distribution to rotation curve and vice versa (refs quoted by [5])
The forward problem of finding the rotation curve from the mass distribution of a thick disk
of a given profile as well as the reverse one of finding the mass distribution from a given
rotation curve is solved, judiciously using finite-element techniques on a cylindrical polar
coordinate grid. The number of axisymmetric rings used can be as few as 5, and needs to be
upto about 100 for good results. The numerical scheme is tested on known analytic results,
and then applied to a few disk galaxies for which astronomical data are readily available.
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Discussion
The first scheme was not really used for rotation curve ↔ mass distribution calculations, but
is very suitable for such a purpose. The second and third were explicitly designed for the
purpose, but the authors could not get a hearing from mainstream practitioners, who had in the
meantime amassed an enormous volume of publications based on redundant computational
procedure, as especially brought out by the author of the third scheme. In retrospect, it seems
that mainstream researchers in this area are not sufficiently context-aware to retract their
error. For a broader discussion of disk galaxy rotation curves vis-à-vis dark matter
distribution, see, for example, ref. [6].
References
[1] J. Oort 1932 Bull. Astron. Inst. Neth. 6 249-…: …; F. Zwicky 1933 Helvetia Physica Acta
6 110-8: …; S. Smith 1936 Astrophysical Journal 83 23-…: …; F. Zwicky 1937
Astrophysical Journal 86 217-46: On the masses of nebulae & of clusters of nebulae.
[2] D. N. Schramm & G. Steigman 1981 General Relativity & Gravitation 13(2) 101-7 A
neutrino dominated universe.
[3] G. Byrd et al 1986 Monthly Notices of the Royal Astronomical Society 220 619-31:
Dynamical friction on a satellite of a disc galaxy; R. H. Miller 1978 Astrophysical Journal
224 32-38: On the stability of disklike galaxies in massive halos; 1978 Astrophysical Journal
223 811-823: Numerical experiments on the stability of disklike galaxies; 1976 Journal of
Computational Physics 21 400-437: Validity of disk galaxy simulations; 1974 Astrophysical
Journal 190 539-542: Stability of a disk galaxy; 1971 Journal of Computational Physics 8(3)
464-: Partial iterative refinements; M. J. Valtonen et al 1990 Celestial Mechanics &
Dynamical Astronomy 48(2) 95-113: Dynamical friction on a satellite of a disk galaxy: the
circular orbit.
[4] D. Méra, M. Mizony & J. –B. Baillon 1996/7 preprint (submitted to Astronomy &
Astrophysics and Monthly Notices of Royal Astronomical Society): Disk surface density
profile of spiral galaxies and maximal disks.
[5] J. Q. Feng & C. F. Gallo {arXiv:0803.0556v1 [astro-ph] 4 Mar 2008} : Galactic rotation
described with thin-disk gravitational model + quoted refs, especially by Kenneth F.
Nicholson.
[6] Dilip G. Banhatti 2008 Current Science 94(8) 960+986-95 : Spiral galaxies & dark matter
+ Disk galaxy rotation curves & dark matter distribution (also astro-ph/0703430v7).
Acknowledgements
Gautam, Ranjani & Radha Banhatti’s comments improved the presentation.
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