Sky and Telescope - August 2016 - 19

you need a computer that is eight times as fast (at least),"
explains Heggie. Even though computers have been
getting faster for decades - processor performance has
grown about 50% per year since the mid-1980s, until a
slowdown in the 2000s to about 20% per year - this
cubic relationship has meant the size of simulations has
grown much more slowly.
Before parallel computing and advanced acceleration
hardware, scientists would be doing well if they could
model the evolution of more than a handful of stars.
"What you could do on a desktop PC at that time was
maybe 100 particles if you were lucky," recalls Simon
Portegies Zwart (Leiden University, The Netherlands).
And even supercomputers of the time could only handle
about 1,000 stars. Yet that wasn't good enough: astronomers needed million-body (and more) simulations, for
two main reasons. First, the majority of GCs start their
lives with at least this number of stars. Second, the
results of smaller simulations cannot be scaled up to
model larger clusters - the scaling inevitably leads to
unphysical behavior. Just as trying to smooth out wallpaper bubbles with your hand leads to more pesky bubbles
appearing elsewhere, ﬁ xing one problem when scaling
up smaller simulations always leads to another.
But the computers just weren't up to the simulating
task. Indeed, at the start of the 1990s, solving the GC
million-body problem was regarded as a pipe dream.
But then came GRAPE (Gravity Pipe) - a computer
speciﬁcally designed to simulate the evolution of a GC
and a quantum leap in computing, being the ﬁrst in the
world to perform a trillion operations in a single second.
"With GRAPE 4, we could go up to 10,000 particles,"
Portegies Zwart explains. "This jump was absolutely
amazing." GRAPE drove an almost exponential increase

in the number of bodies that could be simulated: from
10,000 in 1996 to 100,000 in 2003, 200,000 in 2012, and,
most recently, 485,000 in 2014 by Heggie.

Bugs in the System
Heggie's 485,000-body simulation was run on "the kind
of PC that you would put under your oﬃce desk, though
on the big side" and took around 2½ years to complete.
With so much time invested in one simulation, it was
important that there were no bugs. However, after just
one year he noticed something was wrong. "The simulation had one unfortunate feature: there was a line in the
code which meant that black holes would have a much
larger diameter than they should have," he recalls. "This,
in turn, meant that they collided and coalesced much
more often than they should."
This type of problem is common to GC simulations.
"If you get a result [you don't expect] there are two things
you can do: you can distrust the answer, but then you have
to reevaluate the code you have been writing; or you have
to take it seriously and publish it," oﬀers Portegies Zwart.
"And that's a bit scary sometimes because there are bugs
in every code - the question is, how serious are they?"
By its nature, designing astrophysical models (of
stars, clusters, or whole galaxies) involves extreme simpliﬁcations and assumptions of very intricate processes.
As Corinne Charbonnel (University of Geneva, Switzerland) elucidates, this can add another level of uncertainty
and frustration to the mix. "Sometimes we need months
of computations before we can validate or disclaim each
assumption, and sometimes one single new observation
invalidates most of the previous work."
The longest of the four initial simulations Wang has
done so far took about a year to complete, and so the

A MILLION STARS THROUGH TIME The Dragon team ran four cluster simulations
and created mock observations of their models so that they could compare the simulated
clusters with observed ones. Shown here is the end result of one simulation (left). The
simulation began with 1,050,000 stars and followed their evolution over 12 billion years.
Step by step, the simulation calculated each star's gravitational eﬀect on the others,
even as it tracked the stars' aging and deaths. Above, the series of six snapshots show
diﬀerent populations of objects within the cluster after 12 billion years: from left, AGB
stars, white dwarfs, binary stars, black holes, red giants, and main-sequence stars (those
fusing hydrogen in their cores, as the Sun does). Over time, these populations appeared
and grew. The black holes notably settled to the center as the cluster aged. How concentrated the cluster became depended primarily on how top-heavy the initial stellar population was in terms of mass. Watch two clusters evolve at http://is.gd/dragonsims.
DRAGON SIMULATION PROJECT

Sk yandTelescope.com August 2016

http://www.is.gd/dragonsims http://www.SkyandTelescope.com

Sky and Telescope - August 2016

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