Timing Analysis...Taking the Pulse of the Universe
"Taking the Pulse of the Universe" means getting very accurate
measurements of how objects change in time. Take a moment to think about
things that change in time. Everyone has
experienced day and night. As the Earth rotates, or spins on its axis,
the side of the sphere that is illuminated by the Sun changes. The
length of the day is just the rotation period of the Earth.
Rotation is a property of many objects in astronomy that we can
measure by accurate timing measurements.
We also are aware that the seasons change in a repeatable way. In the
summer, the days are longer and temperatures higher in the Northern
hemisphere. This is because
as the Earth revolves around the Sun, the sunlight received on our
hemisphere changes due to the tilt of the Earth's axis. In summer we
receive more sunlight here, and in winter less. The seasons repeat after
one year, which is the Earth's orbital period about the
Sun. Orbital period is another property that we can measure in many
astronomical objects by accurate timing measurements.
Many of the properties we measure in exotic astronomical objects have
analogs in the Solar System that we are all very familiar with.
This is because the laws of physics that determine the motion of
objects are the same everywhere.
History of Timing in Astronomy
At first glance, you may think that timing in astronomy is a relatively
new field, aided by ever-improving modern technology. For example, the
Rossi X-ray Timing Explorer (RXTE) is a relatively new X-ray satellite. It was
launched in 1995 and performs precise timing measurements of cosmic
X-rays, a region of the electromagnetic
spectrum that astronomers have only had access to for the last few
In fact, timing celestial events has been very important in the history
of human culture! Let us look at a few examples.
The First Calendars
Early farming societies were at the mercy of the seasons. In
order for a group of people to sustain a successful farming culture,
they needed to come up with accurate ways of predicting when spring
would occur (to know when to plant) and when the first frost
could be expected (to know when to harvest). Early
civilizations recognized repeating patterns that the Sun and stars made
in the sky. They soon realized that the seasons repeated in the same
cycles as much of what they saw in the skies. Patterns that stars
make, called constellations, rise slightly earlier each
night for part of the year; they come back to the same place in the sky after a full year has
passed. The highest position of the Sun in the sky also goes through a
repeating pattern, reaching its highest
point on the first day of summer and its lowest point on the first day
of winter. Early civilizations built elaborate constructs, such as
Stonehenge in England, to precisely determine when the Sun's position had
reached these points in its path on the sky. By
understanding and predicting the seasons in this way, they were able to
succeed at farming. This is an early example of the importance of
timing in astronomy.
Early astronomers came up with ingenious ways of finding out
information about the Earth, Moon, and Sun from careful observations
using accurate eclipse times. During a lunar eclipse, the Moon passes
into the Earth's shadow for a while, blocking reflected
sunlight which normally causes the Moon to shine brightly. Early
astronomers realized that they could find out the relative sizes of the
Earth and the Moon by timing how long the Moon stayed in the Earth's
shadow during a lunar eclipse. Modern astronomers use a similar
method today to estimate the diameters of stars in
binary (double) star systems.
The Danish astronomer Tycho Brahe was very careful about making
accurate position and timing measurements of objects in the sky,
particularly the planets. He designed an elaborate observatory for this
purpose, and during many years of observations he collected a great
wealth of position and timing data on the planets. Years
after his death, other astronomers (such as Kepler and Newton) used
these precise data to develop empirical laws describing the motions of
the planets, and theories of the physics of motion. Had Brahe
not collected such an impressive array of
information, who knows how long it would have taken for these basic laws
of physics to be understood?
Measuring the Speed of Light
Timing the motions of the satellites of Jupiter led astronomers to one
of the first ways to measure the speed of light. Astronomers noticed
that when Jupiter and Earth were close to each other on their orbits
about the Sun, Jupiter's satellites would pass in front of the planet a
few minutes ahead of the predicted time. When
the two planets were far separated on their orbits, the transits
occurred slightly later than expected. The difference arose from the
fact that the information travels at the speed
of light, and the distance from Jupiter to Earth is not constant, but
varies by a few light minutes depending on where in their orbits the two
planets are. Realizing this, astronomers calculated a reasonably
accurate value for the speed of light by timing the transits of
Jupiter's moons at different points along its orbit.
When astronomers look at the Sun with special filters, they see
that it is not just a uniformly bright ball of hot gas but is
with dark spots of various sizes and shapes, called sunspots. The
number of sunspots, and their location on the Sun's
surface, changes in a regular way, repeating itself roughly every 11
years. Early Chinese astronomers took note of the sunspot number as
early as 28 B.C. Astronomers have learned much information about
the magnetic field of the Sun and its interaction with Earth
through accurate observations of the sunspot
number and how this correlates with magnetic disturbances on Earth.
Astronomers use the same basic principles of timing regular changes in various characteristics of cosmic objects to gain information
about objects outside the Solar System, as well.
An X-ray binary system is a pair of stars in orbit about
one another, where one of the stars is a compact object
dwarf, neutron star, or black
hole) and the other is a normal star. Material from
the normal star accretes onto the surface of the compact
companion, heats, and emits X-rays that we detect on Earth.
X-ray binaries typically exhibit a wide range of variability,
particular in the X-ray region of the electromagnetic spectrum.
One type of variation is periodic. When two stars orbit
each other, there are three "clocks" in the system, which each give
rise to a regular period. These clocks, which are also present in
the Sun-Earth system, are 1) the ROTATION of the compact object,
2) the ORBITAL MOTION of the stars about their common center of mass
and 3) the PRECESSION of an accretion disk, a thin disk of material
from the normal star orbiting about the compact companion. This disk
is often tilted and twisted, and can shadow the X-ray source
Pulsars, Doppler Shifts, and Neutron Star Masses
When a pulsar is in a binary system, its motion about the
center of mass of the system can be measured from the Doppler shift shift
of its pulse period. During the part of the orbit when the pulsar is moving toward observers on
the Earth, the period appears to be shorter, and when it is moving away
the period appears longer. In some X-ray binary systems, the motion of
the normal star can also be measured by the Doppler shift in the
spectral lines in the optical. Using this information from both stars, we can
solve for the masses of both the normal star and the compact object.
This has important consequences for theories of stellar evolution, which
predict a relatively narrow range of masses that neutron stars are allowed
Neutron Star Spin-down and Age
Many pulsars have now been observed for decades. It turns out that
isolated neutron stars are not spinning at a constant rate but are
instead slowing down very gradually. This slowing is called the spin-down rate,
and it is a measure of the amount of energy the pulsar is losing as a
function of time, and hence the age of the pulsar. Different models
of the magnetic structure of pulsars predict different spin-down
rates. Through long-term monitoring of the spin-down rates of isolated
pulsars, astronomers can determine which of the models best predicts
the observed behavior.
Variability that appears more random on a variety of timescales is
even more common, and may even be universal, in X-ray binary systems.
Changes on the order of months might represent changes in the
accretion rate or evolution of the accretion disk. Flares of a few
seconds may indicate differences in the accretion flow, or
thermonuclear flashes on the surface of the neutron star.
Some sources show surprisingly erratic variations, sometimes with flares
as short as milliseconds. The underlying physics governing this
process is still not well understood. On the right is a light curve
showing aperiodic variation in X-ray intensity.
QPOs and X-ray Binaries
Some X-ray binary systems display a complicated variation which is termed
"quasi-periodic oscillations" or QPOs for short. When astronomers study
these systems, they find variations over a close range of periods, usually
centered around one value. The mechanism giving rise to this almost,
but not quite, periodic behavior is still a mystery. Many
researchers believe they are caused by the interaction of the accretion
disk around a compact object and the magnetic field near the object.
Material at different distances from the compact object would
explain why an entire range of periods is observed. Continued
monitoring of QPOs in various types of X-ray binary systems will allow
astronomers to refine the models which give rise to this behavior.
Use Hera to try your hand at timing
analysis with modern data.