Download in search of antimatter in the universe

IN SEARCH OF ANTIMATTER IN
THE UNIVERSE
BY CHRIS HERRON
It is believed that when the universe was
forged during the Big Bang, equal amounts
of matter, and its intrinsic opposite, antimatter, should have formed. But look
around today. Matter surrounds us almost
everywhere we could think to look. The
whereabouts of this ‘missing’ antimatter is
one of the great physical mysteries of
modern science, demanding new and
innovative methods of detection.
The Standard Model of
Particles
What is Antimatter?
In 1928, Paul Dirac predicted the existence
of an ‘anti-electron’, a particle that had the
same mass as an electron, but opposite
charge; an antiparticle1. Today, under the
Standard Model of particles (Figure 1),
every particle has a corresponding
antiparticle; protons have antiprotons,
neutrons have antineutrons, and so on.
Each antiparticle has the same mass, but
opposite charge of the ‘normal’ particle.
Perhaps the most mystifying feature of this
relationship is the complete annihilation
that occurs whenever a particle and its
corresponding antiparticle collide.
Figure 1: All fundamental particles have a
corresponding antiparticle. In particular, the
electron has the positron as its antiparticle.
Particles known as baryons, such as protons
and neutrons, are composed of quarks, and
their antiparticles are composed of the
corresponding anti-quarks.
From:
http://theta13.lbl.gov/neutrinos_universe/neutrinos
_11.html (accessed 10/10/10) Credit: The Diablo
Canyon Neutrino project.
When annihilation occurs, no mass from
either particle remains. This is to say, that
the mass of both particles is converted to
energy in the form of photons, and the
amount of energy released can be
determined by Einstein’s famous equation,
E = mc2.
Positronium and Hydrogen
Positronium: Exotic Atom
One form in which antimatter can be found
is the short-lived atom known as
Positronium. Similar to the Hydrogen
atom, Positronium involves an electron
orbiting a positively charged core;
however in Positronium, Hydrogen’s
proton has been replaced by a positron, the
anti-electron2,3. (Figure 2)
Because the electron and positron are so
close together in Positronium, it is only a
(very short) matter of time before they
annihilate4. When para-Positronium
annihilates, it releases two gamma ray
photons that have a characteristic energy
of 511 keV. One method of detecting
Positronium is by detecting this emission,
using Gamma ray telescopes such as
INTEGRAL. Experiments observing this
emission have shown that Positronium is
forming and annihilating near the Sun, and
at the centre of our own Milky Way
galaxy.5,6
However, one limitation of Gamma ray
telescopes is that they have poor
resolution. This means that using this
emission to search for Positronium only
gives a rough idea of where it is; we can’t
pinpoint its location.
Figure 2: On the left is the Hydrogen atom,
consisting of an electron and a proton, and
on the right, is Positronium, consisting of
an electron, and its antiparticle, the
positron. Positronium comes in two
forms, para- and ortho-Positronium,
depending on the spin of the electron
and positron. Para-Positronium has both
spins anti-parallel (singlet state),
whereas ortho-Positronium has both
spins parallel (triplet state). Because of
the number of ways these states can
occur, the ortho- state outnumbers the
para- state by 3:1. Ortho-Positronium is
more stable than para-Positronium,
generally living for 1.41 x 10-7s,
whereas para-Positronium generally
lives for 1.26 x 10-10s.4
http://www.stolaf.edu/academics/positron/intro.
htm (accessed 2/10/10), property of the Positron
Research Group at St Olaf College, Northfield,
MN.
One way of overcoming this barrier is to
apply a form of emission that occurs in the
Hydrogen atom, based on the Bohr model
of the atom. In this model, when the
electron transits between certain quantised
energy levels, a photon is emitted with
energy equal to the energy difference
between the levels (Figure 3). This causes
Hydrogen to have a characteristic series of
emission lines at optical wavelengths,
known as the Balmer series. Positronium
has a similar series of unique emission
lines, which lie near visible wavelengths of
light. By detecting the Ps-alpha emission
at 1.3µm, we can take advantage of the
higher resolution of optical telescopes, and
detect point sources of Positronium for the
first time.
Birthplaces of Positronium
We aim to determine where Positronium is
likely to form in the universe, and test
whether its emission is bright enough to be
detectable from Earth.
Balmer Emission of Hydrogen
As mentioned previously, Positronium has
been detected near the Sun, and at the
centre of the Milky Way, implying that
Positronium forms in high energy
environments. Other high energy
environments where Positronium may
form in our galaxy include supernovae,
pulsars, Low Mass X-Ray binaries and
micro-quasars, the weird and wonderful
extremes of the universe.
An extragalactic source of Positronium
may include the jets of Active Galactic
Nuclei (AGN) (See title, Figure 4,5) These
colossal jets originate from the central
super-massive black hole of the galaxy,
flying through the galaxy around them at
speeds close to the speed of light. It is
possible that these jets contain electrons
and positrons, meaning it is likely that
Positronium will form somewhere along
the jet.
Figure 3: When an electron transits from a
higher energy state to a lower energy state,
as in the Bohr atom, a photon with the
same energy as this difference is emitted.
Positronium can undergo similar
transitions. However, as its reduced mass is
half that of the hydrogen atom, the
wavelengths of the same transitions are
double that of Hydrogen. This means that
the H-alpha line (red in the picture) occurs
at 1.3 µm for Positronium, and this is
known as the Ps-alpha line.
http://outreach.atnf.csiro.au/education/senior/as
trophysics/spectroscopyhow.html, (accessed
3/10/10). Credit: HyperPhysics, and CSIRO
Australia
Figure 4: The jet of M87 is shown at
visible wavelengths to stretch into the
Active Galactic Nucleus at the centre of
the galaxy.
http://fermi.gsfc.nasa.gov/public/science/agn.
jpg (accessed 12/10/10). Credit: NASA, HST
The high velocity of the jet means that the
constituent particles are at high energies,
higher than the ionisation energy (energy
required to remove an electron) of
Positronium. This means that even if a
positron and electron are close enough to
form Positronium, they will not bind
together4. On the other hand, if a jet were
to collide with a star, the remnant of a star
(such as a Planetary nebula or a supernova
remnant), or a molecular cloud, then the
particles in the jet would collide with the
particles of the body, and slow down.
Once a particle has undergone enough
collisions, and has less energy than the
ionisation energy, then it can combine to
form Positronium. As the time required for
thermalisation is relatively small, we can
assume that thermalisation occurs
instantaneously.4,7
Spiral galaxies do not often feature AGN,
and so instead, we consider elliptical
galaxies, which have stars evenly
distributed throughout the volume of an
ellipse. One such galaxy is Centaurus A,
which is the closest galaxy to us with an
AGN jet, at 3.7 Mega parsecs (1 parsec is
3.1x1016 m). This means its jet can be
studied in greater detail than is possible in
more remote sources. (Figure 5). This has
allowed ‘knots’ in the jet to be resolved in
x-ray and radio wavelengths (Figure 6).
The cause of these knots has remained
unknown for many years, although recent
evidence suggests that they may be caused
by collisions of the jet with stars, or other
large gaseous objects, and thus they may
be sites of Positronium formation.8,9
Figure 5: This is a composite image of
Centaurus A, using visible, x-ray and
submillimetre wavelengths. The streamer
of gas coming out of the centre is the jet
of the galaxy, which remains well
structured until eventually dispersing into
a plume of gas. The jets of these Active
Galactic Nuclei can erupt into enormous
lobes of gas larger than the galaxy itself!
http://chandra.harvard.edu/photo/2009/cena/ ,
accessed 1/10/10
Credit: X-ray: NASA/CXC/CfA/R.Kraft et al.;
Submillimeter: MPIfR/ESO/APEX/A.Weiss et
al.; Optical: ESO/WFI.
Probability of Collision
To determine the chance that a jet does hit
a star, we need to know how the stars are
distributed throughout the galaxy. By
observing galaxies, we can see that the
intensity of light emitted by the galaxy
decreases with radius, and as we would
expect, the brighter a region is, the more
stars are in that region, and hence more
mass. This fact can be used to determine
an expression for how the mass density of
the galaxy varies with radius. (See
Equation 1, Figure 7) 10
In order to convert this mass density to a
stellar density (number of stars per unit
volume), we need to divide the mass
density by the average mass of a star. This
can be calculated to be 0.35 times the mass
of the sun,11,12 allowing us to graph how
the stellar density changes across an
elliptical galaxy, and hence how the
number of stars varies. As seen in the
graphs (Figures 8,9), stellar density
decreases with radius, and the number of
stars reaches a maximum relatively close
to the centre of the galaxy. The total
number of stars calculated from the graph
is 8.4 x 1011, similar to that observed in
most galaxies, so our model of the galaxy
is realistic.
It is also important to consider what the
average size of a star is. By looking at
what percentage of main sequence stars
have a certain mass, and weighting this by
the radius of a star of that mass, we can
determine the average cross-sectional area
of a star. To make this more
comprehensive, we also include the size of
Planetary Nebulae, supernova remnants
and Asymptotic Giant Branch stars,
weighted by how common these are in a
galaxy, and what length of time they
remain in a condensed form. This gives an
average area of 6 x 10-6 square parsecs.
The final quantity to consider is the area of
the jet itself. If we assume a conical
expansion of the jet, then it is possible to
relate the cross-sectional area of the jet to
the angle formed at the base of the jet.
(Equation 2).
Combining these quantities allows us to
determine the number of stars that the jet
will collide with at a given radius. This is
simply calculated by finding the volume of
the jet at this radius, and multiplying by
the density of stars. (Equation 3) Summing
the values for the probability of hitting a
star at a given radius gives a total
probability of 1.6 x 1011%, corresponding
to 1.6x109 stars being hit. (Figure 10)
So we expect the AGN jet to collide with
very many stars as it moves through the
galaxy.
Impacting Positrons and the
Formation of Positronium
In order to determine how many Positrons
are colliding with a star per second, we
first consider the positron flux (number of
positrons passing a given area per second)
of an AGN jet. If we assume that all of the
positrons that are initially injected into the
jet remain in the jet along its length (a
reasonable assumption as the annihilation
of positrons and electrons in the jet is quite
small)4,7 then the positron flux in the jet is
approximately constant. (Equation 4)
When the jet hits a star, the ratio of the
area of the star to the area of the jet shows
what fraction of the positrons in the jet
will thermalise by collision. This allows us
to calculate the positron flux that would
occur if the jet hits a star at a certain
radius, and thus the rate of Positronium
formation.
The number of Positronium atoms that are
formed on collision is proportional to the
number of positrons incident on the
surface of the star. It turns out that the
proportionality constant depends on the
temperature of the medium in which the
positrons thermalise, and if we take T =
106 K (a high enough temperature to allow
thermal X-ray emission), then this
proportionality constant is 41%. This
allows us to plot the rate of Positronium
formation if the jet hits a star at a certain
distance (Figure 11). As expected, this
decreases with distance, as the incident
flux of positrons decreases with distance. 4
Figure 6: A 0.8 – 3 keV unsmoothed image of the Centaurus A jet at X-ray wavelengths
using the Chandra X-ray observatory. Each bright spot represents a ‘knot’. From Worrall et al
2008, ApJ, 673, L135.
Equations and Results
Equation 1: This equation is for the mass density in solar masses, derived from the brightness
profile of a galaxy.10 Here, r is the distance from the centre of the galaxy, Re is the effective
radius of the galaxy (both in parsecs), b and p are parameters that depend on the Sersic index,
n, of the galaxy, M/L is the mass to luminosity ratio of the galaxy in terms of the solar M/L,
and I0 is the central intensity in solar L pc-2.
Figure 7: Mass density (solar masses per cubic parsec) of a theoretical elliptical galaxy as a
function of distance from the galactic centre. The total mass is 3x1011 solar masses.
Figure 8: Stellar density
(stars per cubic parsec) as
a function of distance
from the galactic centre.
The average density is
0.002 stars per cubic
parsec.
Figure 9: Number of stars in the galaxy as a function of distance from the galactic centre.
There is a clear maximum at about 500 parsecs. The total number of stars is 8.4x1011, close to
the expected number for Centaurus A. This graph is formed by calculating the number of
stars in a shell of width 5 parsecs, in 5 parsec intervals from the centre of the galaxy.
A = πr2 = π(rb + R tanθ)2
Equation 2: Cross-sectional area of the jet at distance R parsecs from the centre of the galaxy.
rb is the radius of the base of the jet in parsecs, and θ is the half angle of the jet, in degrees.
N = A η ΔR
Equation 3: Number of stars hit at a certain radius from the galactic centre. A is the crosssectional area of the jet in square parsecs, η is the star density in stars per cubic parsec, and
ΔR is the increment in radius, taken to be 5 parsecs.
Figure 10: Number of
stars hit by the jet as a
function of distance
from the galactic
centre. There is a clear
maximum at 500
parsecs, where most of
the stars are. The total
number of stars hit is
1.6x109.
F(e+) = π R02 ρ v f
Equation 4: Formula for the positron flux of the jet. R0 is the initial radius of the jet, ρ is the
particle density of the jet (particles per cubic parsec), v is the velocity of the jet (parsecs per
second) and f is the fraction of particles that are positrons.13
Figure 11: The rate of Positronium formation as a function of distance from the galactic
centre if the jet hits an average sized star, and thermalises at 106 K.
Equation 5: Formula for the flux of observed photons emitted by Positronium. r is the
positron flux, fPs is the fraction of positrons that form Positronium, α, β are parameters
regarding the emission line observed, DL is the distance to the source in metres, A is the
absorption coefficient, Δλ is the width of the emission line. 4
Figure 12: The observed brightness of the Positronium Ps-alpha line if the jet collided with
the gas shell left by a supernova remnant, of cross-sectional area 20 square parsecs. This
requires a slightly wider jet, and a large increase in the density of positrons at the gas-jet
interface due to shock formation as the jet ploughs into the gas, compared to the jet hitting an
‘average star’. The emission should just be visible out to 600 pc for a galaxy at 3.7 Mpc, if
these requirements are met.
Positronium Emission
Once the rate at which Positronium forms
has been determined, we can finally
determine how bright the Ps-alpha
emission would appear from Earth, using
Equation 5. If we consider a galaxy as far
away from us as Centaurus A, then we
obtain a graph similar to Figure 12 for our
theoretical galaxy. The brightness of the
emission line decreases with distance, as
we would expect, based on the decrease in
positron flux.
Unfortunately, we see that the peak
brightness is 3x10-10 photons s-1 m-2 µm-1.
This means that if we had a telescope with
an area of 1 m2, then it would collect 1
photon every 100 years. Obviously, this
will not be visible.
But this is the brightness we would expect
if the jet hits the ‘average star’. If we
instead consider a much larger object, such
as the gas shell of a supernova, then we
obtain Figure 12.
In this case, the emission line is just visible
up to 600 parsecs, after which the
brightness drops below 0.1 photons s-1m-2,
and the emission line will be hard to
distinguish from background noise.
Considering future optical telescopes that
may be 25m in diameter, this corresponds
to 150 photons s-1.
Conclusion
We have found that the jets of Active
Galactic Nuclei will collide with very
many stars in elliptical galaxies, and thus
are a potential source of Positronium
formation. Centaurus A, being the closest
galaxy with an AGN, is likely the best
galaxy in which to search for the Ps-alpha
emission of Positronium, as the brightness
of the emission decreases strongly with
distance.
Furthermore, if the knots in the Centaurus
A jet (Figure 6) are due to jet-gas
collisions, then these may provide a bright
source of Ps-alpha emission, particularly
as they are estimated to have a radius of
0.5-2.5 pc.8 On calculating the number of
stars in the Centaurus A jet, the number of
planetary nebulae and supernovae should
be about 15, comparable to the number of
knots in the jet.
As we have also found that objects with
radii close to 2.5 pc may be bright enough
sources of Positronium alpha emission to
be visible from Earth, we conclude that
likely visible sources of Ps-alpha emission
are the larger knots in the Centaurus A jet,
found closer to the centre of the galaxy.
If this emission is detected from these
knots, then it will be the first time
antimatter has been detected outside our
own galaxy, and it will provide strong
evidence for the mechanism responsible
for the formation of knots in AGN jets.
Acknowledgements
Thank you to Dr Simon Ellis and Prof Joss
Bland-Hawthorn for their guidance and
thorough help in this project. Thanks also
to Prof Dick Hunstead and Dr Michael
Biercuk for directing and managing the
Physics TSP, and insightful feedback.
Title picture from
http://www.dailygalaxy.com/photos/uncategori
zed/2007/07/30/supermassive_black_holejpg_
1_2.jpg (accessed 10/10/10). Credit: The Daily
Galaxy and Casey Kazan.
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