1. PyRISM: The Pythonic Red Interstellar Machine
Sam Berney, Dan Stinebring, Tim Dolch
Oberlin College
GW, Pulsars, and the ISM
Gravitational Waves, a prediction of Einstein's Theory of General
Relativity, are described as waves in the curvature of spacetime,
caused by the merging of two celestial bodies such as two
supermassive black holes. Gravitational waves occur throughout
the decay of the orbit of the binary system, particularly in the
late stages. Gravitational waves are the mechanism by which
gravitational energy leaves the binary system, and thus by
conservation of energy the cause of accelerated orbital decay and
merger of the two celestial objects. Just such a decaying orbit in
a binary pulsar system was detected by Hulse and Taylor in
1974. They were awarded the 1993 Nobel Prize for their prior
discovery of this binary pulsar system, the existence of which
constitutes an indirect detection of gravitational waves.
Acknowledgements
I’d like to thank Dan Stinebring, Timothy Dolch, Ryan Shannon,
NANOGrav, and the IPTA; and the National Science Foundation
which funds the Oberlin College pulsar lab.
Accompanying Shannon 2010 is a simulation of various ISM delays.
The Big Red InterStellar Machine (BRISM) models the well-
understood Dispersion Measure (DM) delay, geometric and
barycentric delays, and Refractive Interstellar Scintillation (RISS).
RISS is the delay of interest.
BRISM has 2500 lines. Its structure is characteristically C-like, and
it is difficult to understand for nonspecialists. As undergraduate
researchers are frequent users of BRISM, the purpose of this project
has been to create a more accessible version. PyRISM, or Pythonic
Red InterStellar Machine, attempts to reproduce BRISM's
functionality in python. With BRISM as reference and Shannon’s
dissertation as guide, PyRISM has been built from the ground up.
PyRISM is intended to package many of the utilities already
developed for python into interactive functions which are easy to
understand for pulsar physicists. It is also designed for continuous
development. PyRISM is completely self documenting and cites each
equation when used.
Figure 3: At left, 10 runs of PyRISM. At right, 100 runs of BRISM.
Image credit: Sam Berney, Tim Dolch.
A pulsar is a rapidly rotating neutron star that emits two
electromagnetic 'lighthouse' beams. Frequently, pulsars are
aligned so that one such beam is incident with the Earth, and
observed as a quick, intense, repeating burst. Because of their
extreme density and quick period of rotation, pulsars can be used
as highly stable clocks. Pulsars rotate up to 700 times a second,
such pulsars being called Millisecond pulsars.
Two astronomers, Hellings and Downs, predicted that
gravitational waves would alter the effective distance a light ray
would travel to reach the earth in a very particular way (Figure
2). The observation of this correlation between pulsar position
and delays would constitute a direct observation of gravitational
waves. The International Pulsar Timing Array (IPTA) aims to
detect gravitational waves by monitoring correlation of delays in
the timing of millisecond pulsars.
However, gravitational waves are not the only delay in the
arrival time of a pulse. Such delays include geometric
considerations, such as the movement of the solar system
through the Milky Way, and material effects, such as the
pervasive plasma known as the Interstellar Medium (ISM) which
introduces refractive and diffractive effects to the
electromagnetic waves. The delays of a gravitational wave are
tiny compared to some of these delays, which must be corrected
for before gravitational waves become apparent.
Figure 1: Artist’s
impression of GW emitted
from a white dwarf
merger.
Image credit: NASA/Dana
Berry, Sky Works Digital
Figure 2: Pulsar astronomer’s illustration of changes in
pulsar path length due to distortions in spacetime
caused by a GW. Image credit: David J. Champion
BRISM and PyRISM
Delays
Because the refractive effects of the ISM are frequency dependent,
in order to eliminate delays from an observation, data in multiple
radio frequencies are required. Currently, pulsar astronomers
observe at two frequencies and fit for Dispersion Measure (DM).
Astronomers would need to observe at four frequencies to correct for
RISS. A primary use for PyRISM is to see how effective current
techniques are for eliminating ISM delays from an observation.
RISS
RISS is modelled as light waves refracted through a thin screen.
This screen focuses and defocuses the rays causing variations in a
pulsar’s apparent intensity and timing. The refractive properties of
the thin screen are modelled by a pixelated map of E&M phase
offsets in the transverse plane, called a phase screen. These phase
offsets produce a delay on any pulsar ray reaching that pixel. Thus a
map of delays as a function of transverse space could theoretically be
produced. However in practice, a pulsar has a very small angular
resolution on the sky. To model the observed phenomena, we produce
an intensity-weighted sum of the delay over the transverse plane,
where the intensity is processed to represent the image as it appears
in the sky. This produces a single value representing the RISS delay
associated with a an observation. Figure 3 contains a plot of the sum
of this RISS delay and the DM delay as it evolves over a long period.
The two delays are visually separable in Figure 3. The DM delay
is proportional to and can be seen as large scale variation,
whereas RISS is proportional to and can be seen as small scale
variation. ( is the radio observing frequency. These relations guide
the number of frequencies needed to correct the delay.)
Citations
Shannon 2010, Cordes et al 1986, Cordes and Shannon 2010,
Gwinn et al 1998, Kaspi et al 1994, Shannon and Cordes 2011,
Verbiest et al 2009
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