|
|
|
Stars and Slopes |
Day 2
Day 2 delves into how to use log-log plots to gain insight into certain
celestial objects of interest to X-ray astronomers.
Day 2 is still under development!
Materials
Engagement
Now we are ready to apply our knowledge of log-log plotting to investigate
various celestial objects, and the physical differences between them.
The sources that you see listed below are defined by certain properties
that might be new to your students. For them to fully understand these
objects, select from the following:
Guided Activity
For those interested in understanding the physics behind why certain kinds
of celestial objects have certain kinds of spectral slopes, this section is
for you! You may skip directly to the section on "What am I?",
however we encourage the investigation and discussion of
some of the physics within these sources to begin with you and your
students.
X-ray measurements provide the most direct probes of astrophysical
environments with temperatures above 1,000,000 K. The field of X-ray
spectroscopy, or looking at the X-ray emission of celestial objects as a
function of energy, has come into its own in the past decade or so as an
extremely powerful tool in understanding our Universe. In the following
discussion, we will greatly simplify the real world by ignoring factors
such as the presence of strong magnetic fields, the limited resolving
powers of X-ray telescopes, and so on. Instead, we will take a simplified
look at the Universe and focus only on the following idea:
Slope has to do with the physical mechanism which is responsible for the
emission of the X-ray photon, and different kinds of celestial objects can
be dominated by different emission mechanisms.
We will examine the following emission mechanisms in this lesson:
Synchrotron Emission/ Compton Scattering, Bremsstrahlung, and Blackbody
Radiation.
Bremsstrahlung
Bremsstrahlung is radiation associated with the acceleration of electrons
in the electrostatic fields of the ions and the nuclei of atoms in the
material through which the electron is passing. In the 1930s,
scientists noticed that the ionization loss rate that was expected for an
electron underestimated the true value as the electron became relativistic.
It was realized that an additional loss mechanism was present and
associated
with the radiation of electromagnetic waves because of the acceleration of
the
electron in the electrostatic field of the nucleus. This radiation is
called
'braking radiation' or, in German, bremsstrahlung. In fact, whenever a
charged
particle is accelerated or decelerated, it emits bremsstrahlung radiation.
There are two kinds of bremsstrahlung, thermal and non-thermal, which are
reflective of the number distribution of the electrons. For hot gases, the
number distribution is Maxwellian and thermal bremsstrahlung results. For a
power law distribution of electrons, non-thermal bremsstrahlung results.
In certain astrophysical contexts, such as the hot (T~108 K )
intergalactic gas in clusters of galaxies, the X-ray emitting plasma is
very low in density. This results in the emitted X-rays getting "out
" of the
plasma without interacting with the gas, which is to say the gas is
"optically thin". Thus, the X-ray spectrum we detect is a true
representation of the emission process occurring in the plasma. In very hot
plasmas (T>108 K), almost all of the elements are fully ionized
and the X-ray emission is dominated by bremsstrahlung from hydrogen and
helium. The thermal bremsstrahlung radiation spectrum is characterized by the
equation:
Blackbody Radiation
So what is a blackbody? Let us think of it this way. All objects radiate
energy (unless they have a temperature of absolute zero). The maximum
energy
which can be radiated by an object is called blackbody radiation. A
blackbody
is a theoretical object which is a perfect absorber and emitter. The
radiation
given off by a blackbody occurs over a broad spectrum of energies, but has
a
peak in the emission at a wavelength which is mathematically determined by
the
temperature of the body. The equation which reflects this relationship is
called Planck's Law, which gives the energy density as
Real objects such as stars and planets can, in fact,
closely approximate a theoretical blackbody. Each such object can be
treated as a blackbody, giving off energy at a rate determined by its
temperature.
One of the most exciting uses of X-ray spectroscopy is as a probe of the
extreme physical environments associated with objects such as accreting
white dwarfs, neutron stars, and black holes. In such cases, the X-ray
emission is derived from the release of gravitational potential energy by
accreting matter. Here, the gas flows will most likely be optically thick,
i.e., the X-ray will most likely scatter off something before it exits the
plasma. This results in the X-ray spectrum containing not only clues about
the
primary emission mechanism, but also about the material flow which feeds it
.
Thus, understanding the observed spectrum requires understanding how X-ray
spectra are modified by passage through an optically thick medium.
One of the two temperatures which occur naturally in accretion flows is the
blackbody temperature. For white
dwarfs, kTBB is usually less than 0.2 keV, while for neutron
stars it is of order 2 keV. For a stellar mass black hole, it is typically
around 1 keV.
Synchrotron Radiation / Compton Scattering
Highly relativistic electrons moving through a magnetic field with a
component perpendicular to the electron velocity will produce X-rays by
synchrotron radiation in most astrophysical sources. Inverse Compton
radiation, in which a low energy photon is scattered by a relativistic
electron, also can produce photons with energies above 1 keV.
Synchrotron and inverse Compton scattering are formally very similar. Both
produce power law spectra with spectral index a = (GAMMA-1)/2, if the
relativistic electron number spectrum is a power law with number index GAMMA.
Specifically,
for synchrotron radiation
and for inverse Compton radiation
Synchrotron radiation and Compton scattered radiation are major components
of the diffuse X-ray background and emission from active galaxies.
What am I?
Below is a spectrum taken by the A2 experiment aboard the HEAO 1 satellite.
Using the knowledge gained from the above discussion, the students should be
able to determine whether the source of this X-ray emission is an accreting
neutron star, diffuse galactic emission, or a cluster of galaxies.
Independent Activity
The students are now ready to determine the object types of several cosmic
sources. They will apply the concepts learned in this lesson to data
received from high-energy satellites.
COMING SOON !
Extensions
What is the Equation?
Using the plot below, determine the equations of lines A, B, and C.
What is the Crab?
You found, in your Materials list for today, a sample set of data from the
Crab. Students should plot these data using the log-log format discussed
on Day 1.
- What class of source do you think the Crab could be?
- What reasoning do you have for choosing that kind of object?
Now, check to see if you are correct!
|
