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Dark Matter and the Universe
Topic 4
Hunting for Baryonic Dark Matter
Black Holes, Dead Stars, Neutrinos & the Primordial Soup
Why is the dark matter not ordinary matter we can not see?!
Contents of Topic 4
In this Topic we move to consider the possible Baryonic
candidates for dark matter, their nature and the arguments
that eventually lead to the conclusion that dark matter can
not be composed of hidden Baryons. We cover:
‣ Gas, dust, rocks and smaller material as dark matter
‣ Massive Astronomical Compact Halo Objects (MACHOs),
Brown Dwarfs, Dead Stars and Stellar Remnants
‣ Hunting for MACHOs with Gravitational Microlensing
‣ Microlensing theory, Amplification Factor and Einstein Time
‣ Very Massive Objects (VMOs), Black Holes, & Neutron Stars
‣ Big Bang Nucleosynthesis, the CMBR and ΩB
‣ The death of Baryonic Dark Matter
‣ First ideas on particle dark matter - Antimatter and Neutrinos
Baryonic Dark Matter Candidates
‣ It is clear from the evidence shown that there are copious
amounts of Missing Matter or Dark Matter in the Universe.
‣ Whatever this material is it must not give off light or interact
with light, otherwise we would see it!
‣ A first step to unravelling this huge mystery,
investigated
by the first scientists involved, is to consider objects or
classes of ordinary material, i.e. Baryonic Material, that
are known to exist but that might be hidden from us. An
example is Hydrogen Gas:
‣ The term Baryon basically
refers to protons and neutrons.
Strewn throughout the Universe are "trees"
of H gas that absorb light from distant
objects. For instance they leave absorption
lines in distant quasar's spectra.
Baryonic Dark Matter Candidates
‣ A more complete list of possible Baryonic Candidates,
roughly in order of size, is as follows:
(1)! Gas - hot and cold gas, hydrogen and helium
(2)! Snowballs - particles of frozen gas
(3)! Dust - particles that include heavier elements like Si
(4)! Rocks and Small Planets - including asteroid size objects
(5)! Dim Stars - including Brown Dwarfs and Black Dwarfs
(6)! Neutron Stars - remnants of supernovae
(7)! Black Holes - remnants of bigger supernovae
‣ Candidates labelled (5) have been the subject of intense
searches in the halo of our galaxy. They are often called:
Massive Astronomical Compact Halo Objects (MACHOs)
‣ Candidates (6) and (7) come under the heading
Very Massive Object (VMO)
Gas, Dust and Smaller Material
‣ This type of material is actually hard to hide in the Universe.
It can produce spectral lines if hot or absorption lines due to
background stars.
Gas as Baryonic Dark Matter
‣ A first obvious Baryonic Candidate might be objects made
of hydrogen or helium gas, the most abundant elements in
the Universe. But each class of this has a problem:!
(1)!so called “Snowballs” (small lumps of frozen hydrogen) –
it turns out that these would be expected to evaporate.
(2)!Hot Gas - this is expected to emit x-rays, but very little
such radiation is seen.
(3)!Cool Neutral Hydrogen Gas – this should absorb
background light from distant objects like quasars, but not
much of this absorption is seen either.!
Dust, Rocks and Small Planets
‣ So what about material with
elements more complex than
hydrogen, forming dust, rocks,
asteroids or even small planets.
It certainly exists, here is an
example Porous Chondrite
interplanetary dust particle.
‣ But if the Universe is filled with a lot of this stuff then stars
should be contaminated with significant abundance of
“Metals”. This is not seen. We see mainly hydrogen again.
‣ Also rocks and dust can be observed by obscuration of
background light. It is actually hard to hide in the Universe.
It can produce spectral lines if hot or absorption lines due
to background stars. Not enough of this phenomena is
seen. None of this can explain the dark matter problem.
MACHOs
‣ MACHOs are another possibility, basically Very Low
Luminosity Stars, sometimes called Dead Stars or Stellar
Remnants, stars known as Brown Dwarfs and Jupiter-like
Objects. These objects
would have mass < ~0.08 M⦿.
‣ Below this mass they never attain
a high enough central
temperature for the fusion
reactions that convert H into He
normal in larger mass stars to
start and produce high luminosity.
‣ The only energy they can radiate comes from
Gravitational Energy as they slowly contract to a final
dense state. There is an initial fairly fast contraction which
can cause significant luminosity but it does not last long.
Hunting for MACHOs
‣ So MACHOs can not be seen with telescopes but it is
possible to use so-called Gravitational Microlensing (GM).
This exciting method to search for faint stars in the halo of
our galaxy was first proposed by Bohdan Paczynski in 1986.
‣ GM is a variant of the lensing described earlier but here the
lens is a MACHO in the halo of our galaxy (a much smaller
object than considered before) and the source is a star in a
nearby galaxy, usually the Large Magellanic Cloud (LMC).
Bohdan
Paczynski
MACHO
Star in nearby
galaxy
Earth
Gravitational Microlensing Theory
‣ We can use the same equations for GM as previously used
for Gravitational Lensing. However, in Microlensing there
are a few interesting differences to what is happening:
(1)!For a small lens like a Brown Dwarf we might expect an
Einstein Ring or Multiple Images, but in practice the light
bending is too small for this to be resolved in a telescope on
Earth. Instead we see a general brightening resulting from
the multiple images being superposed on each other.
(2)!Another vital difference is that
we expect the MACHO to be
moving in the halo such that the
alignment between Observer,
MACHO and Lens that produces
this brightening will only occur for
a timescale of ~days to months.
STAR IN
LMC
MOVING MACHO
OBSERVER
ON EARTH
Microlensing Example
‣ The image here shows an actual
example candidate MACHO Event.
We see a sequence of pictures of a
small section of a star field taken
over a period of a few weeks. Note
how one of the stars in the centre
gets brighter and then dims.
‣ A plot of the brightness
vs. time gives us a
characteristic Light
Curve for the event as
opposite. We see a
Transient Brightening
of the background star as
the MACHO passes by.
Microlensing Theory?
‣ We can use the same equations to describe Microlensing
as we examined for general lensing previously.
r here is distance of the
MACHO from the line-of-sight
r
source
observer
MACHO (lens)
‣ The MACHO moves across the line-of-sight so r changes
with time, i.e. r(t). We can call it the angular separation of
the lens from the observer-source line-of-sight vs. time.
‣ The Impact Parameter b, as defined
previously, is effectively the
instantaneous value of r.
The Amplification Factor
‣ The source brightness is amplified by an Amplification
Factor A that depends only on how close the alignment, r(t),
is between observer, lens, and source. It is given by:
here u(t) is defined in terms of r(t), the angular separation of
the lens from the observer-source line-of-sight, divided by
the Einstein Radius θE and is given by:
where t0 is the time at Peak Brightness and u0 = u(t = t0). τE
is the Einstein Time, the time taken by the lens to travel the
angular distance θE. u = 0 corresponds to perfect alignment.
The Amplification Factor
‣ So when t = t0, we have Peak Brightness.
‣ The smaller u becomes, the bigger the amplitude A, and
also the smaller the value for u0 = u(t = t0), the bigger is the
value that the Amplification Factor A can achieve.
‣ In the extreme case that u0 = 0, which corresponds to a
situation where we get perfect alignment of source, lens and
observer at t = t0, then A would become infinite.
‣ Here is an example light curve
for a point like MACHO for
different values of u0 vs. time.
‣ The vertical axis is logarithmic
multiplied with 2.5 to obtain the
astronomical logarithmic
brightness measure Magnitude.
u0
How to Identify a MACHO
‣ Microlensing differs from Macrolensing (the Strong and
Weak Lensing with galaxies) in that the value of u changes
significantly in a short period of time, ~days to months.
‣ Note also that observation of a MACHO Event can allow
us to determine a value for the Einstein Time τE, but this is
not sufficient to allow the MACHO mass to be determined
because we also need to know the distance D and the
velocity of the MACHO vM.
‣ In other words the main observable, the Einstein Time,
is a degenerate function of the lens mass, distance and
velocity. We can not determine them from a single event.
‣ So in practice to get at the masses we need multiple
events and estimates of the distances and velocities.
How to Identify a MACHO
‣ Another issue is that many stars naturally have variability.
It
is important to distinguish such stars from MACHO Events.
‣ This can be done because MACHOs have three particular
characteristics:
(1)!A MACHO Event should never repeat (they are too rare).
(2)!The Light Curve for a MACHO should be symmetric in
! time, i.e. rising and falling with the same shape.
(3)!The magnitude of the Light Amplification should be the !
! same in all wavelengths e.g. the blue and red wavebands
! as typically measured in astronomical observations.
‣ This difference arises because the change in light for a
MACHO concerns purely gravitational effects, whereas in a
variable star, such as a Ceyfert Variable, the changes are
due to physics processes to do with the star itself.
MACHOs Found! or Not
‣ Several extensive searches have been undertaken for
MACHOs in the halo of our galaxy by observing many stars
in the LMC over several years.
‣ The most important work
has been by the EROS,
OGLE and MACHO
collaborations.
‣ Here are examples for the
first few candidate events
seen by the MACHO
Collaboration.
Red and blue light curves of the
first three microlensing candidates
of the MACHO collaboration.
THE ASTROPHYSICAL JOURNAL!
479, 119 È146 (1997)
MACHOs Found! or Not
‣ The MACHO Collaboration identified about 45 lensing
candidates towards the bulge of our own galaxy and 4
lensing candidates towards the Large Magellanic Cloud.
OGLE identified about 500 events in the Galactic Bulge.
‣ As mentioned there are difficulties with interpretation. It is
difficult to tell exactly where along the line-of-sight the lens
is located, e.g. the LMC events could also perhaps be in our
own Galactic Halo or an intervening Dwarf Galaxy.
Candidates in our own bulge are less convincing due to th
known populations of dim stars there.
‣ Nevertheless the number of events observed can be used
to infer the fraction of dark matter in galactic halos.
‣ Unfortunately, it turns out to be nothing like enough to
solve the dark matter problem as explained next:
MACHOs Found! or Not
‣ Here are results from the EROS team, given as an
Exclusion Plot of the fraction of our halo that could be
made of MACHOs vs. mass. The curves refer to different
observations. Regions above the curves are excluded at
95% confidence. The full black line is the sum of all results.
‣ The conclusion here is that MACHOs can at most make
about 15% of the halo.
‣ As we will see, there are
theoretical reasons to
believe the fraction to be
much less. It is hard to
create enough baryons in
the early Universe to
make the number of
MACHOs needed for DM.
Direct Observation of Brown Dwarfs
‣ Microlensing provides a powerful tool for searching for
MACHOs but there are other techniques that have been
used, for instance to look for Brown Dwarfs, seen as the
most likely candidate object in the class of MACHOs.
‣ Do Brown Dwarfs at least exist? A few appear to have been
detected but the evidence is not clear. They are very dim
<10-4 L⊙ so can easily be confused with distant bright stars and
they will only ever be seen nearby. Several techniques exist:
‣ One possibility is to use their Proper Motion. i.e. there
should be candidates near to us so these will have a motion
against the background sky over a few years.
‣ An example is Epsilon Indi B - a Brown Dwarf object less
than 12 light-years from the Sun, discovered from the
comparatively rapid motion across the sky.
Direct Observation of Brown Dwarfs
‣ Probably most Brown Dwarfs are in Binary Systems like
most stars. However, usually the pair of stars in binaries
are found to have similar masses, so this might be true for
Brown Dwarfs as well, making them difficult to see.
Nevertheless there are two techniques with binaries:
(1) Look for Irregularity in the motion of the companion star
(2) Direct Observation
‣ For (2) the companion must not be too bright. We look for
Infrared Emission, where BDs emit most strongly.
‣ However, note that even if Brown Dwarfs are seen in
binaries, and even if every star had a Brown Dwarf
companion, there would still not be enough to form all the
Dark Matter. !
!‣ i.e. if Brown Dwarfs are the Dark Matter they must be
mainly single stars and in large numbers.
Direct Observation of Brown Dwarfs
‣ Here is one example of Brown Dwarf found in a Binary
System.
These two false-colour telescope images show the first unambiguous
detection of a Brown Dwarf, called GL229B. It is in orbit around the Red
Dwarf star Gliese 229, located approximately 18 light-years away in the
constellation Lepus. The Brown Dwarf is about 20-50 times the mass of
Jupiter, but is so dense it is about the same diameter as Jupiter.
Very Massive Objects (VMOs)
‣ Another potential Baryonic Candidate are so-called Very
Massive Objects (VMOs) - the remnants of a hypothetical
population of very heavy stars that formed in early Galactic
history - predicted to have masses of 103 - 106 M⊙.
‣ Such objects might lead to a large population now of:
(1) Neutron Stars
(2) Massive Black Holes
Neutron Stars (NS) as Dark Matter
‣ Neutron Stars usually result from Supernovae.
So if these
are the Dark Matter then a most of the present mass of the
galaxy would have had to go through a Supernovae Stage.
visualisation of a
neutron star
Supernova remnant
N49 shown in x-ray
and optical together
‣ This seems very implausible because Supernovae produce
Heavy Elements and so there should be lots of heavy
elements around in the Universe. But this is not seen.
‣ Also a conventional Neutron Star ends up with mass
<2 M⊙, so there would need to be a huge number of them.
‣ These factors rule out Neutron Stars as the Dark Matter.
Black Holes (BH) as Dark Matter
‣ Stars larger than ~50M⊙ likely collapse into a Black Hole
with almost all mass going to form Black Hole (unlike the
Neutron Star case where there is a supernova ejecting
material into space). This is all unlikely but not completely
ruled out. There are three ways to search for Black Holes:
(1) Direct Detection of Black Holes - most likely the BHs
would have to be single to account for the dark matter. They
might be detected because accretion of gas and dust would
cause emission lines as the gas atoms collide with each other.
(2) Disruption of Binaries - if there are a large number of BHs
they would be expected to gravitationally disrupt Wide
Binaries. i.e. we would not expect there to be many “loose” or
wide ordinary binary systems. So finding lots of wide binaries
would be a clear sign of the non-existence of large BHs.
(3) Quasar Microlensing - described as follows:
Detection of BH by Quasar Microlensing
‣ Black Holes might be detectable also by Gravitational
Microlensing. BUT if they make a large fraction of the halo
then because their mass is so high it means: (i) the lensing
will be infrequent, and (ii) the lensing time will be very long,
proportional to M1/2.
Remember the Opening Angle
of the Einstein Ring:
‣ For a given lensing angle
so the Cross Section
for lensing or a given mass
, goes UP with D. So
in principle if we look for lensing of halo objects in a distant
galaxy by an even more distant quasar we would expect a
much higher probability of lensing!
‣ However, note that here the timescale for events is years
or decades.
‣ There is little evidence that such Quasar Lensing exists.
Conclusion so far on Baryons
‣ So observation of spectral emission and absorption rules out
‣
Gas, Dust and Smaller Candidates as the Dark Matter.
Microlensing and the other observations essentially rule out
MACHOs (massively compact halo objects), including Brown
Dwarfs, as being a dominant Dark Matter component.
‣ The various calculations and observations above seem to
indicate that the total contribution from VMO objects,
Neutron Stars and Black Holes gives Ωo < ~0.03.
So direct searches conclude that normal baryons
do not appear to account for the dark matter
‣ But this conclusion is made far stronger by two further
pieces of evidence from studies of the “Primordial Soup”:
(1) from Big Bang Nucleosynthesis (BBNS)
(2) from the Cosmic Microwave Background (CMBR)
Big Bang Nucleosynthesis (BBNS)
‣ BBNS is the process by which the Light Elements (H, D,
He, Li etc) get formed in the Early Universe. Calculations
of this can also tell us the total number of baryons expected
in the Universe, or rather the Baryon Number Density, ΩB.
‣ By comparing the value of ΩB we get
from BBNS with our measurements of
Ω0 we can tell what fraction of the
Universe we expect to be Baryons.
‣ The nuclear reactions that occur
in the early Universe are very
interesting. It is covered more
fully in other courses. Here we
just show the main reaction
equations (opposite) and give the
most important details:
Big Bang Nucleosynthesis (BBNS)
‣ Nucleosynthesis, by which the protons and neutrons (the
Baryons) formed in the Big Bang start to do the reactions
shown, begins when the Universe is about 1 minute old.
‣ The details of how the reactions work out, depend critically
on the total Density of Baryons B, the ratio of the number
of neutrons to protons, the p-n Ratio, and the Neutron
Lifetime. It is these factors that determine the eventual
Relative Abundances of the light elements.
‣ If we were confident of the particle physics in the early
Universe then we could fully predict both B and the p-n
Ratio. Instead we look at the effect on abundances of
changing the Baryon Number and p-n Ratio and compare
this with astronomical observation of the abundances now.
‣ The relative abundances are very sensitive to Baryon
Density.
BBNS vs. Time
‣ This plot shows how the abundances might evolve with time
(or temperature) for one particular set of assumptions for B.
The abundance (y-axis) is given relative to hydrogen:
Abundances vs. ΩB
‣ Based on such data we
can plot the Relative
Abundances vs. the
Baryon Density now,
because we know how the
Universe expands
(obviously the density will
be less now than it was).
‣ We can do this in terms of
ΩB, the contribution to the
total density of the
Universe, noting that if ΩB
= 1 then all the matter in
the Universe would be
Baryonic.
He-4
D
the circles
indicate the
values
measured
Li-7
He-3
BBNS and ΩB
‣ The plot shows us how the Light Elements Abundances
depend on the value ΩB. Measuring those abundances
thus provides a powerful means to find the real value of ΩB.
‣ The3 circles in7 the plot indicate typical values found for 4He,
D, He and Li. They line up as indicated on the grey band.
‣ Amazingly the result is Ωb = 0.044 ± 0.004, in other words:
The data are consistent with only about 4% of the
matter density of the Universe being baryonic!
‣ So BBNS, based on simple nuclear physics and observation
of the Light Element Abundances, tells us we should
expect only 4% of the Universe to be ordinary matter.
‣ This is a startling result, but it is in clear agreement with the
previous conclusions on searches for Baryonic Objects in
the Universe, like MACHOs etc.
CMBR and ΩB
‣ Studies of the Cosmic Microwave Background Radiation
(CMBR), thanks to the satellite missions COBE, WMAP and
PLANCK, have revolutionised cosmology in recent decades.
In particular, this has also provided further independent
measurements of the Baryon Density ΩB.
‣ As indicated in Topic 1, the CMBR is a smooth radiation we
seen now at 2.7K, arising from the time of “Decoupling” in
the early Universe when matter ceased to be ionised and
photons were thus first free to travel.
‣ But taking a closer look
we find fluctuations at
about one part in 10,000.
A plot from Planck showing the
Universe in Galactic coordinates. Colours
show the temperature with blue being the coldest.
CMBR and ΩB
‣ It turns out that the size of the
temperature fluctuations
depends on what Angular
Scale you look at on the plot,
the biggest being at a scale
of ~1 degree. This “Power
Spectrum” is shown here:
‣ There is huge cosmology information in this plot but most
importantly we see a characteristic Acoustic Oscillation
due to conflict in the Photon-Baryon Plasma at the time.
The size and shape of this is very sensitive to the mixture
of material and energy in the early Universe (baryons,
neutrinos, dark matter). This is because photon pressure
tends to erase anisotropies while Baryon gravitational
attraction tends to enhance them.
CMBR and ΩB
‣ The beautiful data on the plot well fits the theoretical
derived black curve and yields the following results:
Hubble!
constant:
Matter!
abundance:
Baryon!
abundance
Age of!
universe:
Age of!
microwave!
background:
!
‣ Here again we see the startling result that ΩB ~4%
‣ We also see for the first time a conclusion that the total
matter content, ΩM is ~30%. Matter is missing!
Summary on Baryons so far
‣ What we conclude from this astonishing set of data,
spanning many different, independent, techniques is:
We do not see enough baryonic matter as gas or dust
to account for the missing matter
There are nothing like enough MACHOs, VMOs or any
other types of baryonic candidate
Big Bang Nucleosynthesis predicts that we should
anyway not expect more than 4% as baryons
CMBR measurements also tells us that we don’t expect
more than 4% as baryons
‣ We are starting to run out of any explanations that involve
“normal” matter. However, there are perhaps two
remaining possibilities we should examine before moving
on to more exotic possibilities, these are:
ANTIMATTER
NEUTRINOS
Why Not Antimatter?
‣ We know at least that Antimatter and Neutrinos exist.
So
could these explain the Dark Matter?
‣ Every type of particle has a corresponding Antiparticle,
Antimatter feels gravity like matter, and it definitely exists.
‣ Particle and antiparticle pairs have the same spin and mass
but are opposite in all other ways (charge, colour charge,
quantum numbers). So when they collide, given that charge,
energy & momentum are conserved, they must Annihilate
leaving something neutral and energetic, like Gamma Rays,
Quark/Antiquark or Neutrino/Antineutrino Pairs.
‣ But we do not see enough of this annihilation. In fact it is
a great mystery in science why matter dominates.
‣ And anyway Antimatter still counts as part of the atomic
Universe, part of the ~4% baryons. So even if it existed
much in nature it could at most explain half of that.
Neutrinos as Dark Matter
‣ What about Neutrinos as the Dark Matter?
They at least
exist!. They feel gravity and the Weak Force.
‣ They don’t actually count as an atomic component because
neutrino reactions have stopped before Nucleosynthesis
occurs, so they don’t influence the atomic abundance.
‣ Hot Big-Bang Theory also tells us that we expect a lot of
neutrinos in the Universe, about as many cosmic ”BlackBody Neutrinos” as there are microwave photons. So if
neutrinos have even a small mass they can contribute to
the dark matter. The density of neutrinos is given by:
3
ρ v = nγ ∑ mυ
11
sum extends over the masses of all!
the neutrino flavours
present-day density in microwave background photons
‣ We now know there are 3 neutrino flavours so
.
Neutrinos as Dark Matter
‣ From this we can estimate the actual number density of
neutrinos now from the energy in radiation in today's
Universe using the Stefan-Boltzmann Law, considering
that the Universe is filled with blackbody radiation at 2.7 K.
in this equilibrium radiation is given by:
‣ The Energy Density
4
u(T) = const × T const ~ 7.56 x 10-15 erg cm-3 k-4
‣ From this the Number Density of Photons expect is:
u(T)
~ 1080 cm-3 so:
nγ =
kT
cm-3
‣ Allowing for possible errors in the Hubble Constant and for
the possibility that neutrinos might contribute anything from
some of the Dark Matter to all of it, we predict a reasonable
range of mass for the neutrino as: 4eV ≤ mν ≤ 40eV
‣ Note the point here that if the neutrino mass is too large
then we might “Over-Close” the Universe.
Dark Matter and Neutrino Mass
‣ We do not yet know the mass of neutrinos but the Ray
Davis experiment that first observed neutrinos from the Sun,
subsequently confirmed by many others, eventually showed
that Neutrinos Oscillate between their 3 flavours and so do
have mass. !
‣ These result plus cosmology data indicate that the combined
mass must be <1 eV. !
‣ So neutrinos are simply too light and at most add to 0.5% of
the mass in the Universe. !
‣ Note that this is about the same amount as all the stars in
the Universe! an amazing conclusion in itself..
‣ As we will see in Topic 5 there are many other reasons to
disfavour neutrinos as dark matter. We reach a final overall
conclusion here:
Dark Matter is highly likely to be NON-BARYONIC
and furthermore probably new physics
Summary of Topic 4!
A guide for the exam
‣ A first explanation for dark matter is that it is hidden baryonic
material - understand the various possible candidates and
the arguments that make each one unlikely to be correct.
‣ Understand MACHOs and the basic equations that govern
Microlensing searches for them in our galaxy. Know about
searches for Brown Dwarfs, VMOs and other candidates.!
‣ Big Bang Nucleosynthesis theory and observation of the
Cosmic Microwave Background Radiation provides
important evidence for the lack of baryons in the Universe understand the arguments that lead us to believe ΩB ~0.04.!
‣ We are forced to conclude that normal baryonic matter can
not explain the dark matter - know the arguments about
antimatter and neutrinos that lead us to believe also that no
known subatomic particles can be the explanation either.!
Terms to know from Topic 4 !
A guide for the exam
‣ Baryons, Baryonic Materials, Interstellar Gas, Snowballs, Dust, Rocks
‣ Dim Stars, Brown Dwarfs, Stellar Remnants, Dead Stars, MACHOs
‣ Cool Neutral Hydrogen Gas, Hot Gas, Jupiter-like Objects
‣ Gravitational Microlensig, LMC, Light Curve, Transient Brightening
‣ Amplification Factor, Einstein Radius, Einstein Time, Peak Brightness
‣OGLE, EROS, MACHO Collaborations, Halo Fraction, Exclusion Plot
‣ Proper Motion, Binary Systems, VMO, Neutron Star, Black Hole
‣ Quasar Microlensing, Wide Binary, Big Bang Nucleosynthesis, BBNS
‣ Baryon Number Density, ΩB, p-n Ratio, Light Element Abundances,
‣ Cosmic Microwave Background Radiation, CMBR, Angular Scale
‣ Power Spectrum, Acoustic Oscillation, Photon-Baryon Plasma
‣ Antimatter, Neutrino Mass, Stefan-Boltzmann, Universe Over-Closure
Questions on Topic 4 !
to help with exam revision
‣
Use the gravitational lensing equations to show that we do not expect to
be able to resolve an Einstein Ring in the case of a MACHO event.
‣
What three characteristics of a MACHO event allow it to be distinguished
from a variable star.
‣
‣
Why is antimatter not the solution to the dark matter problem?
‣
What is the theoretical value for the Amplification Factor A in gravitational
microlensing when there is perfect alignment?
‣
Explain how Brown Dwarfs might be observable, other than by
microlensing.
‣
How much more 6Li would there need to be than is observed to make
us believe that the Universe had enough baryons for closure?
What is the peak angular scale seen in the CMBR?
‣
‣
How does the Einstein Time of a MACHO event depend on the MACHOs
velocity and mass.
What mass would neutrinos need to have to explain all the dark matter?
Equations from Topic 4 !
Equation reminders for the exam
u(T)
nγ =
kT
3
ρ v = nγ ∑ mυ
11
€
u(T) = const × T
€
4
u(T)
nγ =
kT