Download Red giants aren`t just big, they`re turbulent

Going with the flow
Red giants aren’t just big, they’re turbulent
With hundreds of billions of stars in each of the universe’s hundreds of billions of galaxies,
you’d think astronomers had plenty to study. And in a way, they do. Using telescopes and
satellites they can measure the color, location, and changes in luminosity of 200 billion stars
within the Milky Way galaxy alone. The problem, however, is they can see only one of these –
the Sun – up close. Even then, they can’t look below its photosphere – the outer light-emitting
layer.
Since astronomers can neither zoom in on more distant stars nor peek under the cover of even the
nearest one, how do they learn what drives these stellar furnaces? If they are Paul Woodward
and David Porter, they create their own.
These astrophysicists, nearly as well known for setting computing records as for analyzing stellar
fluid dynamics, recently got up close to a red giant star. Along with other members of the
Laboratory for Computational Science and Engineering (LCSE) at the University of Minnesota,
they generated a 3D simulation of a red giant at NCSA with such detail that they could watch the
star pulsate. They also detected a convective pattern that encompassed nearly the entire star – a
region equivalent to the orbital radius of Jupiter around the Sun. This global convection pattern
flowed asymmetrically. One whole side of the star was generally hotter than the other. On this
side of the star, gas flowed outward from the center and around the surface to the cool side,
giving off heat to space during the journey. Once on the cool side, the gas sank back down,
forming a funnel of gas which was reheated upon passing by the hot, convectively stable stellar
core (see figure). If their further analyses confirm this global convective pattern, it may explain
differences in illumination within these very big and very bright pulsating stars – a finding that is
important to astronomers who rely on these “standard candles” for mapping distances in the
universe. It will also help scientists know what to expect from our own sun because eventually
it, too, will become a red giant.
Telltale signs of aging
Red giants are telltale signs of aging in stars. Like people, stars have lifecycles. They are born
from interstellar clouds of gas that collapse under the pull of gravity. The extreme temperatures
and pressures at the cores of these clouds fuse protons – hydrogen nuclei – into the nuclei of
helium, releasing energy (in the form of photons) that slowly works its way to the surface where
it escapes as the light we see. These nuclear reactions power the stars at the same time that they
halt the stars’ collapse by counterbalancing gravity. In this state of quasi-equilibrium, stars burn
hydrogen contentedly for millions to billions of years, depending on their masses. Large stars
burn hotter and more quickly than do smaller stars.
The Sun, an average star estimated to be at the midpoint in its life, is 5 billion years old. In
another 2 to 5 billion years, it will have exhausted its hydrogen fuel, beginning its dramatic
transformation into a red giant. With gravity no longer held at bay, the core will contract
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violently, shrinking from the equivalent volume of 300,000 Earths to the size of a single Earth.
At the same time, its envelope – the cooler, less dense layers of gas that surround its core – will
balloon to 100 times its original size.
Woodward and Porter’s interest in these dying stars is in their vigorous convective envelopes. In
younger stars, heat from nuclear fusion finds its way to the surface primarily through radiation
diffusion. Only during the cooler last third of its journey is this heat transported by the
convective motions of the stellar gas. In red giants, the entire envelope is convective, its layers
roiling like a pot of water boiling on a stove.
Modeling the convective movement of energy through this system is staggeringly complex.
Slight instabilities in one part of the flow spawn turbulent vortices elsewhere; or, as in
Woodward and Porter’s model, small surface eddies in the initial state ultimately lead to large
convective flows. Thus, a convective model must capture large-scale effects as well as fine
detail. In order to make the computation possible, the LSCE team simplified the red giant model
through some imaginative code work, a series of convenient physical approximations, and close
attention to the capabilities of NCSA’s distributed shared-memory Origin2000. Future
calculations will improve on this model, especially as the size and power of NCSA’s
supercomputers increase.
Pencilling in the details
The numerical approach adopted by the LSCE team models explicit hydrodynamics – following
all the sound and pressure waves that move through the system down to the smallest scale
represented on the mesh. “Because we do that, we have to restrict our timestep to be so small
that a sound wave cannot cross more than one cell at any timestep,” says Woodward. And
because convection velocities in red giants approach the speed of sound, timesteps small enough
to resolve sound in detail also capture convection.
An advantage of their explicit hydrodynamics approach is that their calculations are completely
local. In red giants, sound is the fastest signal in the system, beating out the net diffusion speed
of photons, which bounce randomly from one atom to another, scattering many times before they
can make much progress. Because their model follows the fast sound signals explicitly, they can
update the state of the fluid at one grid point without needing to know what is happening at other,
distant grid points. The effect is similar to being jostled in a crowd – the immediate impact is on
you, but the effect ripples outwards transmitted by a large series of local collisions. The local
nature of this team’s explicit hydrodynamics calculation allows many independent processors in
the Origin2000 to update different regions of the star in parallel.
Porter and Woodward also used a time-independent gravitational acceleration to localize
calculations. To simplify the physical model, they ignored effects of magnetic fields and pumped
heat steadily into the core without performing detailed computations of the nuclear reactions
there. Even with these simplifications the model required a mesh cube 512 grid cells on a side,
or 134 million computational cells. Five million billion (5x1015) floating point operations were
needed to advance this system by 7000 timesteps, and 1 terabyte of data was generated for
archiving in the process. This is the largest 3D simulation of a red giant to date.
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Exploiting this simplified and localized model for each timestep update, the LSCE team divided
the problem into “pencils” consisting of eight cells on a side and 512 cells long. “The grid pencil
is long and thin, just like the stencil of the PPM numerical technique,” says Woodward. “Grid
pencils can be updated independently of each other. Each update process needs some old data
from neighboring pencils, but no new data from them is required.” To update the grid, a given
processor simply retrieves into its cache memory a pencil from shared memory, updates the
pencil, returns it to global shared memory, then moves on to the next pencil in the queue. If a
particular chunk of grid took longer to update, the next processor in line simply moves onto the
next pencil, since access to shared memory does not tie it to any particular computation. After a
1D sweep of the grid is completed, the program begins the next 1D sweep. In effect this
algorithm transposes the entire data array each time the program executes a 1D sweep.
This ability to efficiently appropriate computing time where needed led to a breakthrough in
simulation – the LCSE modeled the red giant’s irregular, free-flowing surface on a regular 3D
Cartesian grid. That’s like squeezing a round peg into a rectangular hole. Cartesian grids are
necessary for dissecting the computational work into convenient and independent pieces that can
be spread across many processors. Curvilinear coordinates or irregular meshes, which can handle
more detailed flow, are far more complicated to implement. Self-scheduling the data processing
means that the very active surface can be treated more realistically, because the grid cells near
this surface can be updated more carefully, and more slowly, than the interior grid cells.
“We got the best of both worlds – irregular boundaries but a regular internal mesh,” says Porter.
“And these spherical systems are the first examples of what we can do with this. The surface is
actually free to move through the mesh. It can deform and change its topology. It can splash. It
allows for a wider range of fluid dynamical behavior.”
Concurs Woodward: “With the development of distributed shared-memory machines we saw
there was an opportunity to go beyond regular calculations and do irregular types, which opens
up a whole new class of applications.”
Simulation Stats [LINK]
Over 1 terabyte data
5 million billion (5 x 1015) floating point operations
7000 timesteps
134 million computational cells
100 GB of data streamed over vBNS from NCSA in Urbana to the LCSE in Minneapolis
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Here we see the model red giant star near the extrema of its pulsation. At the top, the relatively
diffuse envelope has contracted to about its minimum size, while at the bottom, the envelope is
shown at about its maximum size. These images show volume renderings of the temperature
perturbations relative to average values on each constant pressure surface. These temperature
averages were computed for a single state near the middle of the pulsation. Relatively warm
temperatures are red and yellow, while relatively cool temperatures are blue and aqua. The
volume renderings at the right are relatively transparent, allowing us to see right through the
envelope and to see the dense, stable stellar core within.
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Here the model
red giant star
is shown near
the middle of
its pulsation.
At the top, the
temperature
perturbations
are rendered
relatively
transparently,
so that we may
see right
through the
envelope to the
dense, stable,
and hot stellar
core within.
Note that in
this relatively
transparent
volume rendering, we have
the “limb
brightening”
effect familiar
to astronomers. This
effect causes
the warm
regions near
the surface of
the star to
seem more
prominent and
important than
they actually
are. Inside the
convective
envelope, the
largest
temperature excursions are in the cool gas, and therefore the relatively warm regions, which are
not really that warm, are pretty much transparent in this rendering. There is a large component
of a global convective mode encompassing the entire envelope. Relatively cool gas sinks from
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the surface at the upper right in the upper image, forming a rapidly moving funnel of gas which
strikes the stellar core. This cool gas is strongly heated as it flows around the core.
In the lower image we have moved inside the stellar envelope, viewing the funnel of cool gas
flowing around the core from much closer up but from precisely the same angle as in the upper
image. The turbulent nature of this flow past the core is evident, and heated gas can be seen
leaving the downstream side of the core. Animations of such images reveal that this large-scale
convection flow, in which one side of the stellar envelope is systematically cooler than the other,
persists throughout the pulsational period of the envelope. An analysis of this preliminary data
from the simulation, searching for quantitative correlations between the convective and pulsational motions, is underway.