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Booth 1
Alexander Booth
Physics 460
Professor Cowsik
17 December, 2014
ID: 425784
A Brief Summary and Guide to High-Energy Astrophysics
Dear Provost Blartlegoof of Martian University,
My name is Alexander Booth and I just finished an amazing and fascinating course about
high energy astrophysics at Washington University in St. Louis. It has come to my attention that
you do not offer such a course at Martian University and I wish to change your mind on the
matter. High energy astrophysics is immensely important to learning more about our universe
and especially what other objects are out there. There may be a myriad of stars in the universe,
but high energy astrophysics lets us see that they are all special. There are so many types of stars
that we would not know about without high energy astrophysics. We now know all about
accreting binary systems, pulsars, quasars, neutron stars, and even black holes. High energy
astrophysics has even given us an insight into dark matter! I hope after you read my brief guide
to high energy astrophysics that you will find it as fascinating as I do and offer it as a course at
your own university. My professor, Dr. Cowsik, was the one who made this material so
fascinating to me and I have used his lectures as a main emphasis on the guide, however it also
includes articles from Nature as well as an article on modern high energy research.
We can start by defining astrophysics as the study of the physics of astronomical systems.
The adjective “high energy is used with several different meanings: A) individual particles or
photons will have literal high energies where E >> kT. For example, cosmic rays have an
Booth 2
average energy of 1 Gev with certain gamma rays having about 10^12ev. X-rays from
supernovae explosions have energies ranging from 1-100Kev. Thus it is gamma and X-rays we
can mainly focus on in this course. A second meaning B) is non-thermal spectra while a third
meaning C) could be the huge amounts of energy involved in certain astrophysical interactions.
D) Sometimes a very high luminosity is encountered, for example a galactic x-ray source has a
luminosity greater than 10^38erg/s! E) We have observed some very intense explosions with jets
and fireballs being emitted with a bulk Lorentz factor reaching close to 100. F) The field of
elementary particle physics is also called high energy physics and we can encompass this in our
analysis too. Finally, G) we have observed extreme conditions of matter, for instance the density
of a neutron star is 10^15g/cm^3! We can discuss the following categories of objects: the sun
and normal stars, white dwarfs, cataclysmic variables, novae, pulsars and neutron stars, neutron
stars in binary stars, black hole binaries, supernova remnants and supernovae, galactic centers,
and finally the interstellar medium and cosmic background.
A brief history of astrophysics begins with discovery of the first cosmic rays in 1912. The
first interesting data however came from the first x-ray observations of a celestial body. Since the
Earth’s atmosphere absorbs a high percentage of x-rays, observations have to occur at altitudes
greater than 20km above the Earth’s surface. The first observations of x-rays came in 1949 when
Geiger counters from a v-2 rocket detected some coming from the corona of the sun. This
quickly led to the development of x-ray telescopes to observe other stellar corona in the 1960’s.
However, the field of x-ray astronomy did not get off the ground until a fortuitous and
serendipitous discovery. While some scientists were pointing their detectors at the moon, they
found a source of x-rays a million times brighter than the sun coming from the constellation of
Scorpius. Christened ScoX-1, scientists jumped on the chance to explain this phenomenon. The
Booth 3
neutron star had already been postulated and so it was conjectured that accretion from a binary
system onto the neutron star could power the emissions of this mysterious object as this would
produce copious amounts of x-rays due to shock heating of the accreted gas. Thus, neutron stars
became a proven reality thanks to x-ray astronomy. To showcase how strong efficient ScoX-1
emissions were, we can calculate its luminosity and divide by that of the sun, revealing a
staggering 10^9 more x-ray emitting efficiency than that of the sun! This led to the first x-ray
devoted satellite being launched in 1970 which subsequently discovered over 330 sources of x-
rays in the next 4 years! One of its most important discoveries was the fact that most galactic x-
ray sources were mass exchange binaries in which one of the objects was compact, e.g. a neutron
star or black hole. The rest seemed to come from the intergalactic medium and clusters of
galaxies, perhaps supernovae remnants? That is why we will delve into those objects in our study
of high energy astrophysics.
The first discovery of cosmic rays in 1912 was made with an electroscope, a device
charged with a rod make of ebony rubbed with fur that lifts a gold leaf. The time it takes for the
gold leaf to return to its vertical position is an indicator of how ionized the electroscope is which
in turn indicates what the level of ionization of the incoming radiation is. The physics behind this
revolves around the photoelectric effect where the photoelectric cross section equals the
Thomson scattering cross section times 64/Z^2(h-bar*c/e^2)^3(Ek/E)^7/2g(n). By looking at
these constants it can be seen that the photoelectric cross section is huge in comparison with the
Thomson scattering cross section. This led to the formation of the Geiger counter which could
detect the number of alpha particles from radioactive substances. How the Thomson scattering
and photoelectric effect factor in to the design of an instrument is important because it affects
how x-ray polarimetry of astronomical sources are detected. X-ray polarimetry is at the very
Booth 4
frontier of x-ray astronomy and astrophysics and thus many pioneering groups are striving to
take this field to new heights. Astronomical x-ray polarimetry is a probe of relativistic particles
in non-thermal sources, intense magnetic fields and their structure in neutron stars, strong gravity
effects near accretion powered black holes, and anisotropic radiation and matter distributions,
especially in x-ray sources where diffusive Comptonization operates.
Moving on from the history and descriptions of detectors, the first topic that should be
covered is accretion. Now, consider matter falling onto a compact star, in a symmetrically
spherical fashion, from rest at infinity. This matter will free fall onto stellar surface and the
impact will release kinetic energy with a resulting steady state luminosity of GMMx/Rx where M
is the mass accretion rate, Mx is the mass of the star and Rx is the radius of the star and G is the
Newtonian gravitational constant. From this, the efficiency of radioactive emissions in regard to
the accreted mass energy can be calculated, which is about .1 for a neutron star. This naturally
leads one to wonder what the maximum luminosity for a star is solely powered by accretion.
Assuming simple hydrogen plasma accreting on the star, radiation will interact with the electrons
via Thomson scattering. This results in an outer-radial force equal to Lx times the Thomson cross
section/(4pi*r^2*c). The only other force in this steady state system is the gravitational force
between the hydrogen and the star, GMHMx/Rx. Setting these equal to each other and solving for
the luminosity, we get Lx = 4pi*GcMHMx/ the Thomson cross section, which is about
1.3*10^38*(Mx/Msun) ergs/s. This is called the Eddington Limit. The maximum accretion rate
can similarly be solved for and is equal to 4pi*RxcMH/Thomson cross section. However, to
achieve an accretion rate this high, the objects must be in binary systems operating through a
Roche-lobe overflow. Nearly half the stars in our galaxy are binary or multiple systems.
Consider then a binary system where the separation is comparable to the radius of the larger star.
Booth 5
Under gravitational influence, a tear shape bulge emerges and the two behave like a damped
oscillator. This will result in synchronous and circular orbits for the stars once the tidal energies
have dissipated and the system proceeds as a steady state. The innermost equipotential which
connects up the two stars are said to comprise of the Roche lobes of the two stars. This is also
called the inner Lagragian point, given by a[.5-.227log10(M2/M1).
The accretion rate of collisionless particles however is slightly more complex. This will
be applicable to the accretion of stars by a massive black hole, with mass greater than 10^8 of
our sun, which is expected at the center of almost every galaxy. The best equation describing this
accretion states that in the absence of collisions, the rate of change of the phase space density at
any location is given by the negative G-divergence of the flow in phase space. One of the
consequences of this equation however is the phase space density is invariant along a dynamical
trajectory. Now for a given kinetic energy of a particle, there is a maximum angular momentum
where the particle will collide with the object, any higher and they will miss. By approximating
the velocity as c at the event horizon, we can find this angular momentum and consequently, the
capture rate and mass accretion rate. Thus, the Eddington accretion limit for a black hole with a
Schwartzschild radius and mass of 10^8 solar masses is about 10^-1 solar masses/year. The
accretion rate is limited by the spatial density of the surrounding stars in the center of the galaxy.
After a period of high luminosity, the black hole has to accrete from stars farther out. Since it
takes about 10^5-10^6 years on average to accrete a single star, this results in episodic emission
from the active galactic nuclei, providing us with ever more information about our universe.
Now, hydrodynamical flow differs from a collisionless flow of particles because in a
fluid flow there is only one velocity vector associated with any space-time point. In contrast, the
collionless particles at a given space-time point may be moving in every direction and we need to
Booth 6
specify that velocity distribution at each of these points. This aspect of the fluid flow has an
important bearing on the accretion rate, enhancing it by forcing the flow to be directed towards
the gravitating object. Luckily, interstellar gas and plasma behave like fluids, even though the
probability of a two body collision may be low, because of the presence of weak magnetic fields
and collective affects. The mathematical aspects of hydrodynamical accretion are identical to the
emission of stellar, including solar, winds. This has already been analyzed by Eugene Parker and
other renowned scientists. Their answer reveals that accretion of the gas can occur at either
subsonic or supersonic speeds, resulting in two scenarios. The matter could leave the star at
subsonic speeds, accelerate, and then accrete as a supersonic wind. Alternately, the matter leaves
the star at supersonic speeds before significantly reducing velocity and accreting at a much
slower pace.
When the accretion material carries angular momentum, an accretion disc will form. This
was realized when two notable scientists were contemplating black holes. If accretion material
just fell beyond the horizon, most of the kinetic energy of the particles would disappear, leading
to a negligible luminosity. Since this is not the case, an accretion disk must be the answer; with
kinetic energy being released as the materials hits the surface of the star as well as radiation
coming from the disk. In a semi-detached binary system, the atmosphere of the secondary star
flows through the inner Lagrangian point. If the distance between the two stars is far enough,
then this stream will not impinge directly on the stellar surface. It goes into orbit and spreads due
to the effects of viscosity into an accretion disk. This is also how pulsing neutron stars form. The
accreting material falls onto the star at two mirrored points; a dipole effect. This causes the
temperature of emission to be higher at these poles and the emitted radiation will be seen as a
pulse as the neutron star rotates the poles in and out of view.

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High Energy Astrophysics Dissertation

  • 1. Booth 1 Alexander Booth Physics 460 Professor Cowsik 17 December, 2014 ID: 425784 A Brief Summary and Guide to High-Energy Astrophysics Dear Provost Blartlegoof of Martian University, My name is Alexander Booth and I just finished an amazing and fascinating course about high energy astrophysics at Washington University in St. Louis. It has come to my attention that you do not offer such a course at Martian University and I wish to change your mind on the matter. High energy astrophysics is immensely important to learning more about our universe and especially what other objects are out there. There may be a myriad of stars in the universe, but high energy astrophysics lets us see that they are all special. There are so many types of stars that we would not know about without high energy astrophysics. We now know all about accreting binary systems, pulsars, quasars, neutron stars, and even black holes. High energy astrophysics has even given us an insight into dark matter! I hope after you read my brief guide to high energy astrophysics that you will find it as fascinating as I do and offer it as a course at your own university. My professor, Dr. Cowsik, was the one who made this material so fascinating to me and I have used his lectures as a main emphasis on the guide, however it also includes articles from Nature as well as an article on modern high energy research. We can start by defining astrophysics as the study of the physics of astronomical systems. The adjective “high energy is used with several different meanings: A) individual particles or photons will have literal high energies where E >> kT. For example, cosmic rays have an
  • 2. Booth 2 average energy of 1 Gev with certain gamma rays having about 10^12ev. X-rays from supernovae explosions have energies ranging from 1-100Kev. Thus it is gamma and X-rays we can mainly focus on in this course. A second meaning B) is non-thermal spectra while a third meaning C) could be the huge amounts of energy involved in certain astrophysical interactions. D) Sometimes a very high luminosity is encountered, for example a galactic x-ray source has a luminosity greater than 10^38erg/s! E) We have observed some very intense explosions with jets and fireballs being emitted with a bulk Lorentz factor reaching close to 100. F) The field of elementary particle physics is also called high energy physics and we can encompass this in our analysis too. Finally, G) we have observed extreme conditions of matter, for instance the density of a neutron star is 10^15g/cm^3! We can discuss the following categories of objects: the sun and normal stars, white dwarfs, cataclysmic variables, novae, pulsars and neutron stars, neutron stars in binary stars, black hole binaries, supernova remnants and supernovae, galactic centers, and finally the interstellar medium and cosmic background. A brief history of astrophysics begins with discovery of the first cosmic rays in 1912. The first interesting data however came from the first x-ray observations of a celestial body. Since the Earth’s atmosphere absorbs a high percentage of x-rays, observations have to occur at altitudes greater than 20km above the Earth’s surface. The first observations of x-rays came in 1949 when Geiger counters from a v-2 rocket detected some coming from the corona of the sun. This quickly led to the development of x-ray telescopes to observe other stellar corona in the 1960’s. However, the field of x-ray astronomy did not get off the ground until a fortuitous and serendipitous discovery. While some scientists were pointing their detectors at the moon, they found a source of x-rays a million times brighter than the sun coming from the constellation of Scorpius. Christened ScoX-1, scientists jumped on the chance to explain this phenomenon. The
  • 3. Booth 3 neutron star had already been postulated and so it was conjectured that accretion from a binary system onto the neutron star could power the emissions of this mysterious object as this would produce copious amounts of x-rays due to shock heating of the accreted gas. Thus, neutron stars became a proven reality thanks to x-ray astronomy. To showcase how strong efficient ScoX-1 emissions were, we can calculate its luminosity and divide by that of the sun, revealing a staggering 10^9 more x-ray emitting efficiency than that of the sun! This led to the first x-ray devoted satellite being launched in 1970 which subsequently discovered over 330 sources of x- rays in the next 4 years! One of its most important discoveries was the fact that most galactic x- ray sources were mass exchange binaries in which one of the objects was compact, e.g. a neutron star or black hole. The rest seemed to come from the intergalactic medium and clusters of galaxies, perhaps supernovae remnants? That is why we will delve into those objects in our study of high energy astrophysics. The first discovery of cosmic rays in 1912 was made with an electroscope, a device charged with a rod make of ebony rubbed with fur that lifts a gold leaf. The time it takes for the gold leaf to return to its vertical position is an indicator of how ionized the electroscope is which in turn indicates what the level of ionization of the incoming radiation is. The physics behind this revolves around the photoelectric effect where the photoelectric cross section equals the Thomson scattering cross section times 64/Z^2(h-bar*c/e^2)^3(Ek/E)^7/2g(n). By looking at these constants it can be seen that the photoelectric cross section is huge in comparison with the Thomson scattering cross section. This led to the formation of the Geiger counter which could detect the number of alpha particles from radioactive substances. How the Thomson scattering and photoelectric effect factor in to the design of an instrument is important because it affects how x-ray polarimetry of astronomical sources are detected. X-ray polarimetry is at the very
  • 4. Booth 4 frontier of x-ray astronomy and astrophysics and thus many pioneering groups are striving to take this field to new heights. Astronomical x-ray polarimetry is a probe of relativistic particles in non-thermal sources, intense magnetic fields and their structure in neutron stars, strong gravity effects near accretion powered black holes, and anisotropic radiation and matter distributions, especially in x-ray sources where diffusive Comptonization operates. Moving on from the history and descriptions of detectors, the first topic that should be covered is accretion. Now, consider matter falling onto a compact star, in a symmetrically spherical fashion, from rest at infinity. This matter will free fall onto stellar surface and the impact will release kinetic energy with a resulting steady state luminosity of GMMx/Rx where M is the mass accretion rate, Mx is the mass of the star and Rx is the radius of the star and G is the Newtonian gravitational constant. From this, the efficiency of radioactive emissions in regard to the accreted mass energy can be calculated, which is about .1 for a neutron star. This naturally leads one to wonder what the maximum luminosity for a star is solely powered by accretion. Assuming simple hydrogen plasma accreting on the star, radiation will interact with the electrons via Thomson scattering. This results in an outer-radial force equal to Lx times the Thomson cross section/(4pi*r^2*c). The only other force in this steady state system is the gravitational force between the hydrogen and the star, GMHMx/Rx. Setting these equal to each other and solving for the luminosity, we get Lx = 4pi*GcMHMx/ the Thomson cross section, which is about 1.3*10^38*(Mx/Msun) ergs/s. This is called the Eddington Limit. The maximum accretion rate can similarly be solved for and is equal to 4pi*RxcMH/Thomson cross section. However, to achieve an accretion rate this high, the objects must be in binary systems operating through a Roche-lobe overflow. Nearly half the stars in our galaxy are binary or multiple systems. Consider then a binary system where the separation is comparable to the radius of the larger star.
  • 5. Booth 5 Under gravitational influence, a tear shape bulge emerges and the two behave like a damped oscillator. This will result in synchronous and circular orbits for the stars once the tidal energies have dissipated and the system proceeds as a steady state. The innermost equipotential which connects up the two stars are said to comprise of the Roche lobes of the two stars. This is also called the inner Lagragian point, given by a[.5-.227log10(M2/M1). The accretion rate of collisionless particles however is slightly more complex. This will be applicable to the accretion of stars by a massive black hole, with mass greater than 10^8 of our sun, which is expected at the center of almost every galaxy. The best equation describing this accretion states that in the absence of collisions, the rate of change of the phase space density at any location is given by the negative G-divergence of the flow in phase space. One of the consequences of this equation however is the phase space density is invariant along a dynamical trajectory. Now for a given kinetic energy of a particle, there is a maximum angular momentum where the particle will collide with the object, any higher and they will miss. By approximating the velocity as c at the event horizon, we can find this angular momentum and consequently, the capture rate and mass accretion rate. Thus, the Eddington accretion limit for a black hole with a Schwartzschild radius and mass of 10^8 solar masses is about 10^-1 solar masses/year. The accretion rate is limited by the spatial density of the surrounding stars in the center of the galaxy. After a period of high luminosity, the black hole has to accrete from stars farther out. Since it takes about 10^5-10^6 years on average to accrete a single star, this results in episodic emission from the active galactic nuclei, providing us with ever more information about our universe. Now, hydrodynamical flow differs from a collisionless flow of particles because in a fluid flow there is only one velocity vector associated with any space-time point. In contrast, the collionless particles at a given space-time point may be moving in every direction and we need to
  • 6. Booth 6 specify that velocity distribution at each of these points. This aspect of the fluid flow has an important bearing on the accretion rate, enhancing it by forcing the flow to be directed towards the gravitating object. Luckily, interstellar gas and plasma behave like fluids, even though the probability of a two body collision may be low, because of the presence of weak magnetic fields and collective affects. The mathematical aspects of hydrodynamical accretion are identical to the emission of stellar, including solar, winds. This has already been analyzed by Eugene Parker and other renowned scientists. Their answer reveals that accretion of the gas can occur at either subsonic or supersonic speeds, resulting in two scenarios. The matter could leave the star at subsonic speeds, accelerate, and then accrete as a supersonic wind. Alternately, the matter leaves the star at supersonic speeds before significantly reducing velocity and accreting at a much slower pace. When the accretion material carries angular momentum, an accretion disc will form. This was realized when two notable scientists were contemplating black holes. If accretion material just fell beyond the horizon, most of the kinetic energy of the particles would disappear, leading to a negligible luminosity. Since this is not the case, an accretion disk must be the answer; with kinetic energy being released as the materials hits the surface of the star as well as radiation coming from the disk. In a semi-detached binary system, the atmosphere of the secondary star flows through the inner Lagrangian point. If the distance between the two stars is far enough, then this stream will not impinge directly on the stellar surface. It goes into orbit and spreads due to the effects of viscosity into an accretion disk. This is also how pulsing neutron stars form. The accreting material falls onto the star at two mirrored points; a dipole effect. This causes the temperature of emission to be higher at these poles and the emitted radiation will be seen as a pulse as the neutron star rotates the poles in and out of view.
  • 7. Booth 7 Among the binary stellar systems emitting x-rays, the binary pulsars form an important subclass. Based off of their observed character, very straight forward arguments can be made. The first is that the variability noted on very short scales in x-ray luminosity can be implied by the causality of very compact sources. Secondly, many systems were confirmed to be binary stellar systems, with one star emitting in the optical window, making possible further observations. Finally, mass accretion onto white dwarfs, neutron stars, and black holes proved to be an efficient way of converting gravitational potential energy into x-rays. Also, calculating the period of regular pulses by these objects gives us a chance to calculate their density. This lead a group of scientists to conclude that objects emitting radio pulses are neutron stars due to their density. It has been proven that the magnetic poles were not aligned with the rotational axis, thus the accreted material is channeled onto the poles by the strong magnetic fields. This is known because the observed spectrum shows a feature around 58Kev, which was interpreted a cyclotron line in a magnetic field of around 5*10^12 Gauss. One of the most interesting discoveries of x-ray astronomy is the black-hole, which emits x-rays by accreting mass from a companion star. The most studied black hole is the object Cygnus X-1 which emits x-rays not only from its accretion disk but also from its hot corona. Stellar mass black holes are formed when stars with mass greater than 10 solar masses explode in a supernova near the end of their evolution. These high massive x-ray binaries form in a binary system of two reasonably large stars. The mass transfer through the Lagrange point complicates evolution, thus when one inevitably explodes as a supernova, the system stays bound if the total mass ejected is less than one half of the sum of the masses of the stars of the binary system. This begs the question, how do we know that the compact object at the center of the accretion disk is a black hole? Part of this answer is that when we study the equilibrium configurations of neutron
  • 8. Booth 8 stars, we find that their mass cannot exceed 3 solar masses. Thus if we can prove that the compact object emitting x-rays exceeds the mass bound on stable neutron stars then by process of deduction it must be a black hole. By solving the two body gravitational problem, we can use certain equations to determine what this mass must be, and thus prove black holes exist. It is interesting to note that the three body problem, which helps in multi gravitational body systems, has been solved, but is far too complex to go into right now. It is also useful to calculate the velocity of stars in their orbits, for it is on this speed that the Doppler shifts we observe depend. For circular orbits, the speed is constant and is calculated fairly simply. Eccentric orbits, however, have their velocity as a periodic function of the position angle or equivalently, of time, with maximum speeds when they are closest to the center and slowest when they are furthest away. This satisfies Kepler’s law dA/dt = pi*ab/p = .5pi^2 times the angle. The math behind this equation, as well as the rest of his laws, is very interesting, as it involves mostly algebraic theorems as opposed to calculus, which everyone can enjoy. Using this information, we can calculate the ascending and descending nodes, granting us valuable insight into Doppler Shifts. Then, the observed Doppler shifts can be used to calculate eccentricity of the orbit and even the kopt parameter! Further calculations reveal that we can solve for the mass in the system. This was used with the compact object in Cygnus X-1, which came to a mass of 10.5 times greater than that of the sun; much too large to be a neutron star, leaving only a black hole as the answer. Other awesome phenomena in the universe are supernova explosions. These are one of the most energetic events in the Universe, releasing about 10^53 ergs of energy within 1 second! Occasionally left behind is a neutron star or a black hole. Each of these and the explosion itself are of considerable interest in astrophysics. The ejecta comprise of the unburnt nuclei in the outer
  • 9. Booth 9 region while the heavier synthesized are also dispersed into the interstellar medium. Have you ever heard the rumor that everything comes from star dust? It is true. The interaction this debris has with the interstellar medium heats up the matter to very high temperatures, emitting x-rays. X- rays are also generated during the shock wave when very high energy electrons emit synchrotron radiation. The neutron star or black hole also release x-rays as previously discussed. Thus x-ray astronomy is a necessity in supernovae research. There are two types of supernovae creatively named Type I and Type II, although there are a myriad of subclasses. The main difference is the presence or absence of the spectral line of hydrogen. Type II supernovae originate in young massive stars and it is generally believed that Type I supernovae originate in population-II objects. As the cores of the stars synthesize higher and higher elements, the kinetic material of the in-falling material on the core compresses the core to densities exceeding their nuclei. The chemistry and physics ongoing here result in the explosions. Interestingly, Fe is the highest element to fuse in the core, every other element in the universe is fused during the supernova. Type Ia supernovae are used as standard candles, due to their constant luminosity in cosmology. The expelling of these heavy metals into the interstellar medium is only one effect however. The shock causes heating of the gas which in turn is noticeable by the acceleration of cosmic rays. In the shell-like remnants after the supernova, instabilities generate turbulent motions which amplify an already large magnetic field, accelerating electrons at high energy. This in turn causes most of the various electromagnetic phenomena seen in these regions. Also, as I said previously, a neutron star is occasionally left behind, sometimes resulting in a magnificent pulsar. Finally, the remnants will slow down significantly after the explosion as the net mass of the explosion is dominated by the great maw that is the interstellar medium. This part
  • 10. Booth 10 of the life cycle is called the Sedov-Taylor phase. During this phase only a small fraction of the internal energy of the shell of matter is radiated away. The observation of polarization of optical emission from certain nebulas remaining after a supernova explosion reveals that some synchrotron radiation is at play. The high brightness temperatures of several astronomical objects seen at radio wavelengths were attributed to synchrotron emission by relativistic electrons. It has also been suggested that these cosmic ray electrons spiraling in the interstellar magnetic fields might be responsible for the Galactic radio emission. Specifically, an electron spinning with a cyclotron frequency in a strong magnetic field, after obtaining the Fourier transform of the shape of the pulse in the time domain, emits radiation, called the synchrotron radiation. It is also important to note here that the inverse Compton Effect and the auto-Compton effect result in scattering of the electrons that complicate these calculations, but result in a more accurate depiction of the cosmos. A natural question that arises after seeing the link between synchrotron radiation and radio waves is how exactly do the supernova remnants turn-on as radio sources? The answer is again complicated. As the debris propagates into the interstellar medium, it gathers the matter ahead of the shock like a snow-plough. This decelerates the debris, which is analogous to what the gravitational field did earlier. The material in the shell is dense and this is supported as it were against the gravity like force by the tenuous hot inner fluids driving the debris outward. This can be compared to the famous Rayleigh-Taylor instability where a heavier fluid when supported by one of lower density, induces a turn over by letting down fingers of the heavy liquid into its lighter one. The movement of the fingers drives the Kevin-Helmoltz instability. As a consequence, the debris becomes highly turbulent, eventually giving off radio waves.
  • 11. Booth 11 The two major sources of power which energize non-thermal emission from supernova remnants are Fermi acceleration and the active central pulsar. Fermi acceleration is mainly for shell like supernova remnants while the pulsar mainly powers plerions such as the Crab nebula. These non-thermal emissions associated with the supernova die away within a year. It is again interesting to note that we do not see any sources brighter than Cas-A, even though with the average rate of Type-II expected in our galaxy, we should have seen several. One of my esteemed professors, Ramanath Cowsik, researched the evolution of the radio spectrum of Cassiopeia A and wrote a fascinating dissertation on the topic. If this interests you more, you should contact him at my university. However, this does astoundingly mean that supernova remnants only turn on as radio objects about 2-300 years after the explosion! Another fascinating topic is cosmic ray electrons. The observations of the electron component of cosmic rays have to be demodulated for solar modulation effect which result in observed fluxes of about 2% of the proton flux at Ee < 5Gev. At higher energies the electron flux drops rapidly with increasing energy. Also, cosmic ray electrons lose energy in the interstellar medium due to two processes previously discussed, synchrotron radiation on the magnetic fields and Compton scattering on the radiation fields like starlight and the microwave background. These losses are proportional to the energy density in the magnetic and radiation fields and also increase quadratically with the energy of the electron. A quick analysis reveals that there are nearby sources of cosmic ray electrons. However, the steepening of the electron spectrum around 10-15eV could be intrinsic to the acceleration process in the sources. We can discuss a scenario in which the galactic disc is sprinkled with cosmic ray sources and the propagation effects including the energy loss by synchrotron radiation and where Compton processes lead to a cut-off in the electron spectrum
  • 12. Booth 12 around 1000GeV. Now the total electron spectrum is primarily made up of these electron from cosmic ray sources, however secondary electrons and positrons from interaction of matter from the sources with the interstellar medium. Thankfully today, new measurements provide means to distinguish amongst these various propagation models. We can calculate the total secondary e+ and e- spectrum expected by using the nested leaky box method. This obviously lets us determine the primary electron spectrum. The primary electron spectrum from the sum over discrete sources can be subtracted from the observed spectrum to determine the shape of excess. This is also done for the smooth fit through the total electron spectrum. Moving on to observations of the diffuse emissions of the radio continuum from the galaxy, it is known that considerable effort is needed to generate all-sky maps of the non-thermal emission of radio waves from the galaxy. From any single location on the earth, we have access to only a part of the sky, especially because high quality observations can only happen within a 45 degree wash from the local zenith. This means that to generate a map of the entire sky, we need to combine observations from various parts of the globe with telescopes located in the northern and southern hemispheres. Consequently, one has to calibrate the sensitivities of the different telescopes and normalize them. Furthermore, since the angular resolutions depend on the size of the dish, all the observations should be smoothed to the resolution of the broadest beam. This makes the image less distorted. The non-thermal emission from the general interstellar medium is mixed up with three things; the thermal bremsstrahlung from discrete sources, non-thermal emission from sources such as supernova remnants, and finally outer- galactic sources. Since the typical beam size is approximately 1 degree, faint sources at great distances blend together and appear to be a diffuse emission. Most galactic maps have some similarities. The galactic center is the approximate center of symmetry in these maps, the
  • 13. Booth 13 intensity drops off as we move away from the center, and loops and spurs are seen, perhaps remnants of an old supernova explosion. Nearly 90% of the emission comes from the thin disk around the galactic center and only 10% of the emissions from the thin disk are from sources and thermal contamination; the truly non-thermal thin disk is perhaps not there at all. A natural progression is to heating in galaxy clusters. The hot (10^7 to 10^8 Kelvin) X- ray interstellar medium is the dominant baryonic constituent of clusters of galaxies. In the cores of many clusters, radiative energy losses from the interstellar medium occur on timescales much shorter than the age of the system. Unchecked, this cooling would lead to massive accumulations of cold gas and vigorous star formations; in contradiction to observations. Various sources of energy capable of compensating for these cooling losses have been proposed, the most promising being the heating by the supermassive black holes in the central galaxies, through inflation of bubbles of relativistic plasma. Regardless of the original source of energy, the question of how this energy is transferred to the interstellar medium remains unsolved. Here we present a plausible solutions to this question based off x-ray data and a new data analysis method that enables us to evaluate directly the interstellar medium heating rate from the dissipation of turbulence. We find that turbulent heating is sufficient to offset radiative cooling and indeed appears to balance it locally at each radius. This may therefore be the key element is resolving the gas cooling problem in cluster cores and, more universally, in the atmosphere of x-ray emitting, gas-rich systems on scales from galaxy clusters to groups and elliptical galaxies. Let us now discuss pulsars. The strong electric fields have a quad-pole structure for a rotating magnetic dipole. These strong fields contract electrons and ions from the surface of the neutron star and the power dissipated by the current in the vxB fields is essentially equal to the energy lost through magnetic dipole radiation. Thus in either case, one finds that the energy
  • 14. Booth 14 losses are proportional to B^2R^6 =M^4 and w^4. The quad-pole electric fields of a rotating magnetic dipole of a neutron star are very strong so it can extract charges to fill the magnetosphere. Because of the quad-pole nature, these will have a tendency to generate electric fields parallel to the magnetic fields. The idea is that sufficient charges will flow out of the neutron star surface to nullify this parallel field as seen by an observer. The plasma can maintain itself only up to the light cylinder beyond which the fieldlines are distorted by the plasma into an open torroidal configuration. It is the plasma moving away with relativistic speeds that carries away energy and angular momentum. The radio flux from the pulsars is so high that we are forced to assume coherent effects to interpret them. Clouds of electrons or positrons with net charges thousands times the charge on a single electron are involved. Since the emission of synchrotron or curvature radiation is proportional to the square of the charge, bunching the charges helps us to understand the very high effective temperature of radio emissions. How exactly are these electrons or positrons produced you may ask. The loss of charge from the surface of the neutron star creates two types of gaps. One type is above each of the polar caps and the second type is at the interface between the magnetosphere and the velocity of light cylinder. In these gaps the electrostatic potentials are not balanced and potential differences exceeding about 10^12 volts/meter would be present, capable of accelerating electrons or positrons to high speeds. Occasionally a random event creates a few charges which we can say get accelerated in the electric field and in the gap emit gamma rays through curvature radiation. These gamma rays in turn will convert into an electron/positron pair in the magnetic field and repeated processes of these will generate an electro-magnetic cascade. Periodically our line of sight intercepts these polar regions we see x- rays, gamma rays, and other radiation. Part of the positron that is accelerated flows towards the
  • 15. Booth 15 neutron star surface also and these particles heat up the polar cap and add a small thermal component to the x-ray emission. There can also be some acceleration in the outer gap near the velocity of light cylinder. The polar cap model successfully accounts for the drifting sub-pulses, as due to correlation of charge clouds around the pole, motion develops. Whereas galaxies are self-gravitating systems containing 10^9-10^11 stars, they themselves form bound systems, pairs groups and clusters. Rich galaxy clusters may have up to ten thousand galaxies and contain hot x-ray emitting plasma whose mass exceeds the mass contained within the galaxies by a factor of ten or more. The study of this x-ray emitting plasma is of great importance to astrophysics and cosmology because there are astrophysical issues connected with the origin, heating, and dynamics of this plasma. It also is a probe of the gravitational potential of the cluster with the particular reference to the dominant contributions from the dark matter density. Finally, observations of the distortions in the spectrum of the microwave background caused by the Sunyaev-Zeldovich effect and their applications to cosmology can be found in these galaxy clusters. The first clues to some of the unusual aspects of cluster of galaxies came from observations in 1935 that showed about 10 galaxies in a cluster that each had velocities greater than 1000 km/second which gives an approximate mass of 5*10^14 solar masses. On the other hand, the mass contained within the visible matter in the galaxies is less than one tenth of this mass. This observation is generally referred to as the virial man discrepancy in clusters. This observation was confirmed in 1972 where some scientists observed the velocities of about 200 galaxies in the cluster. It was then suggested the virial discrepancy could be understood in terms of weakly interacting dark matter. This was the first suggestion that weakly interacting particles from the big bang would have a significant or indeed a dominant influence on the formation and
  • 16. Booth 16 subsequent dynamics of galactic systems. The temperature and the spatial distribution of the x- ray emitting gas is a tentative probe of the gravitational potential of the cluster to which the weakly interacting particles of dark matter are significant contributes. Recent observations, especially with the Hubble Space Telescope, sample the gravitational potential of the cluster. These studies have confirmed the presence of dark matter in clusters and map out the large scale profile of the gravitational potential. Thus the studies of x-ray emissions can be used as an effective probe in several aspects of the astrophysics of intra-cluster gas. The cosmic microwave background radiation, when viewed through the x-ray emitting gas in clusters, will show distortions with respect to a spectrum induced by scattering in the hot plasma. Even in this only the linear term in the Kompaneets equation dominates and can take recourse to the fact that the x-ray emitting plasma is tine to calculate the effect on the spectrum of the Cosmic Microwave Background. A decrease of effective temperatures has been observed in many clusters, and this provides an independent measure, not dependent on the x-ray luminosity. These clusters are very bright sources and can be observed up to red shifts of about 3-4 easily. Furthermore, their structure has virialized recently and in some cases that are just forming. Thus they provide a unique view as to the contents and dynamics of the universe. Consequently, a special x-ray satellite dedicated to this study called DUET has been proposed to NASA. This is a nice segue into our next topic, gamma ray astronomy. Gamma ray astronomical observations are conducted mostly from space platforms outside the atmosphere, except at energies exceeding 100GeV where ground based observations are possible. Because of the high energy of these photons, they give us a view of the most unusual and energetic objects in the Universe. The field of gamma ray astronomy was stimulated and perhaps initiated with the idea
  • 17. Booth 17 that objects emitting gamma rays would also be the sources of cosmic rays. This hope is only partially fulfilled as many sources of gamma rays have been discovered. These objects must contain substantial amounts of energetic protons and electrons in them; on the other hand it is not clear that it is indeed this population of energetic particles that leaks out of the sources and diffuses into the general interstellar medium giving rise to the observed cosmic rays. Almost all the types of objects that we have been discussing, from the sun, interstellar medium, pulsars, supernovae and supernova remnants, quasars and the active galactic nuclei, accreting neutron stars, and even black holes, all give off gamma rays. Gamma ray emission is essentially a non-thermal phenomenon as it is virtually impossible to heat and maintain thermal plasma at temperatures over a few hundred keV. Both line emission and continuum emission have been observed. The line emission occurs through the de-excitation of nuclear energy levels and the annihilation of positronium. The continuum is generated through bremsstrahlung and inverse Compton scattering. Absorption and scattering can reduce the gamma ray intensities. The physical processes responsible for these are Compton scattering, pair production in collisions, both with matter and with intervening radiation and magnetic fields. Spontaneous and induced radioactivity lead to production of a wide variety of line emissions, extending up to 12.7 MeV. Natural radioactivity is a major source of emission from planetary bodies. Satellites carrying gamma ray spectrometers have mapped this emission, especially of the lunar surface, to get the distribution of various elements and therefore deduce the types of rocks that constitute these surface layers. The most important naturally occurring elements are the products of Uranium and Thorium decay. The second important source of line emission is the induced radioactivity caused by neutron capture and scattering and by cosmic ray interactions. The cross section for this process
  • 18. Booth 18 is about 7.3 *10^-20/vn cm^2 where vn is the velocity of the neutron in centimeter per second. Thus a thermal neutron with a velocity of approximately 10^5 cm/sec gets captured with a cross section of .3! This is why we have to use heavy water as the modulator in nuclear reactors. This neutron capture reaction induces emission of the deuteron line at 2.2 MeV from solar flares and has been observed. One of the most fascinating phenomenon of gamma rays are gamma ray bursts. Intense pulse of about 1 MeV astronomical gamma rays discovered in the late 1960’s by the VELA satellites serendipitously. Understood only a few years ago, helped by the Beppo SAX Italian- Dutch satellite which helped isolate the location of the bursts in the sky to within a few arcminutes, thus allowing optical telescopes to be trained in that direction and identify the association of the gamma ray bursts with extreme galaxies. Crucial to this identification is the afterglow of the optical and x-ray bands. Ne we know that the afterglow extends down to the radii’s band on one side and to GeV gamma rays on the other. The BATSE instrument aboard CGRO has been responsible for the most detailed observation in the low energy gamma ray band. A typical observatory in any longitude band has a 10% chance of observing the afterglow. Information from up to 8 hours after the burst is available thanks to the pool of international efforts. The temporal structure is generally a power law of slope approximately -.7 which steepens after a few days to about -2.5 The afterglow of some bursts show no steepening even after 100 days, but evolve as a single power law in tie. The spectral distribution of the energy flux of afterglow is generally a power law f(v) = v^B where is B is the slope. This is reminiscent of non-thermal synchrotron spectra. Below 10^12 Hz, the spectrum turns over with positive exponent at lower frequencies. This may be either due to a cut-off in the spectrum of the
  • 19. Booth 19 electrons or due to synchrotron self-absorption. Again, there are relativistic effects in gamma ray bursts, but I will not go into detail of that here. Finally, I will attach and analyze an article about some modern research ongoing into high energy astrophysics. This particular article has to do with pulsars in binary systems. Pulsars that are powered by accretion give off high energy x-rays, while those powered by rotation emits radio waves. Some background information is as such: “Pulsars are the highly magnetised, spinning remnants of massive stars and are primarily observed as pulsating sources of radio waves. The radio emission is powered by the rotating magnetic field and focused in two beams stemming from the magnetic poles. As the pulsar rotates, the effect is similar to that of a rotating lighthouse beacon, resulting in distant observers seeing regular pulses of radio waves. The emission mechanism of pulsars transforms kinetic rotational energy into radiation, and as this energy is radiated over time, the rotation is slowed down. Whilst pulsars spin rapidly at birth, they tend to rotate more slowly – with periods of up to a few seconds – as they age. For this reason, astronomers in the 1980s were puzzled by the discovery of millisecond pulsars – old but extremely quickly rotating pulsars with periods of a few thousandths of a second.” The theory behind this was that an accreting pulsar gaining an accretion disk would also gain angular momentum, as discussed earlier, which would increase the spin. However, no accreting pulsars had been found that directly correlate to this theory. It was in the process of cataloguing a seemingly run of the mill radio pulsar when one of the group leaders noticed that its numbers, including period, positioning, etc., matched perfectly with a x-ray emitting pulsar seen here a few year ago. They then realized this must be the missing link between the two types of pulsars! It seems that the best astrophysical discoveries are made serendipitously. This has helped us learn more about how these work. As accretion de-intensifies, then the magnetosphere
  • 20. Booth 20 expands and pushes the matter away. This decreases the amount of x-rays emitted while increasing the number of radio waves emitted. Luckily, this also helped rejuvenate the INTEGRAL project; a high energy satellite that was rumored would be coming to an end. It once again proved how useful and fascinating high energy astrophysics is. Here are some astounding images of what this may look like; the first is radio while the second is x-ray: After perusing this guide I hope that I have convinced you about how fascinating this material is. High energy astrophysics lets us know of things we could not have even imagined and details of things we could. From supernovae remnants to neutron stars, black holes, gamma ray bursts, even the proof of the existence of dark matter and much more, high energy astrophysics informs us of what else there is in the universe. We should never stop questioning; curiosity is in our nature. High energy astrophysics is an outlet for this curiosity, one that sometimes raises more questions than it answers. Even so, we have learned so much from this discipline and there is so much left to learn. Yours, Alexander Booth B.S. Candidate Mathematics|Astrophysics|Drama Washington University in St. Louis, Class of 2016