Introduction P 1 Introduction P 2 PART II ETP — Asteve/astrophysics_07/handouts/intro2.pdf ·...
Transcript of Introduction P 1 Introduction P 2 PART II ETP — Asteve/astrophysics_07/handouts/intro2.pdf ·...
Introduction P 1
PART II ETP — ASTROPHYSICS
22 Lectures Prof. S.F. Gull & Prof. A.N. Lasenby
• 16 lectures this Term. First, an introduction (2 lectures) to astrophysics
and the content of the visible universe. Prof. Lasenby will then deal
with the large-scale structure and evolution of the universe and give an
introduction to General Relativity (8 lectures).
• I will then describe the astrophysics of (more or less) normal matter
from scales of stars to clusters of galaxies, using ordinary physics and
Newtonian gravitation theory. There are 6 lectures nest Term, the last
few of which will concentrate on the qualitative understanding of
astrophysical “test cases”, such as supernovae and their remnants,
radio galaxies and quasars, and the amazing detective story told by
meteorites.
• HANDOUT — Syllabus; books; essential astronomical facts and
jargon; orders of magnitudes; how we measure distances, velocities,
masses; basic information about astrophysical objects we will meet;
states of condensed matter. Please report any errors or typos.
• NOTES — Provisional hardcopy available in advance. Definitive copies
of overheads available on web.
• SUMMARY SHEETS — 1 page summary of each lecture.
• EXAMPLES — 4 in all, 3 sheets this Term — 2 examples per lecture.
• WORKED EXAMPLES — Will be available on the web later.
• WEB PAGE — For feedback, additional pictures, movies etc.
http://www.mrao.cam.ac.uk/∼steve/astrophysics/
Introduction P 2
THE OBSERVABLE UNIVERSE
• Astrophysics is the extension of laboratory physics to large-scale
structures in the universe.
• “Large” means bigger than the Earth (radius 6400 km) — the nearest
external object is our Moon (distance 400, 000 km radius 1738 km).
• The universe seems to organise itself preferentially into stars, which
are objects of size 109 m and 1030 kg.
• The nearest star is the Sun at distance 1.5 × 1011 m (8 light min).
• Sun is a fairly typical star: radius 7× 108 m; mass (M�) 2× 1030 kg.
• Next nearest stars are 30, 000 times further away at about 5 light
years 5 × 1016 m).
• Stars organise themselves into various scales, but there is another
preferential scale: galaxies (1021 m, 1042 kg).
• Other larger scales: clusters, superclusters.
• Universe originated from hot, dense state 15 billion years ago.
• Finite observable universe 2 × 1026 m containing 1012 galaxies.
• And that’s just the stuff we can see. . .
Introduction P 3
ASTROPHYSICS AND ASTRONOMY
• Universe contains wide range of exotic phenomena: stars; star
formation; supernovae; galaxies; radio galaxies; quasars; clusters;
cosmic microwave background.
• Laws of physics governing the behaviour of astrophysical objects is
exactly the same as here on Earth (we keep an open mind on this, but
would need a lot of convincing otherwise).
• Extreme conditions found in the cosmic laboratory can provide tests of
our understanding of physics.
• Astronomy is an observational science: we have to make do with the
objects Nature provides, and we can only see them from one viewpoint.
• Astrophysical timescales can be very long (e.g. dynamics of radio jets
in galaxies: 107 years). Can often only see a snapshot of a long
evolutionary process; have to infer evolution from many examples.
• Inevitable selection effects: we can only see objects that emit radiation;
we have limited dynamic range of instruments; we can only see rare,
very luminous phenomena to the greatest distances; some objects
emit anisotropically – interstellar masars, pulsars, relativistic jets.
Introduction P 4
PHYSICS NEEDED FOR ASTROPHYSICS
• We will need almost everything you have been taught – and a bit more.
• Gravity The glue of the universe — makes all objects tend to attract
and collapse. Needed throughout the course: particle orbits in globular
clusters, galaxies and clusters; Hydrostatic equilibrium of stars and
cluster gas; star formation; evolution and death of stars; formation of
galaxies and other structures from the expanding universe; dark matter.
• Fluid dynamics and plasma physics Many astrophysical
phenomena involve jets, turbulence, shocks, explosions. Hot gas in
clusters of galaxies.
• Nuclear and Statistical physics Needed to understand the
physics of normal and degenerate stars; end points of evolution of
stars; supernovae and synthesis of post-Fe elements; nucleosynthesis
in the early universe.
• Radiation mechanisms and radiative transfer This is how
we see astrophysical objects; also important for energy transport in
stars; cooling and determining the evolution of objects.
• Exotic physics General relativity and Black holes; dark matter;
dark energy; the epoch of inflation.
Introduction P 5
STUDYING ASTROPHYSICS
• Overall aim We will try to develop an intuitive view of the various
astrophysical phenomena we observe, and be able to apply simple
physical models to explain them quantitatively.
• Realistic goal I’d like you enjoy astrophysics, to be able to do the
problems on the question sheet and to do well in the Exam.
• Astronomical context We have to have some appreciation of the
observational data: wavebands used; resolution achieved relative to
scale of the object; nature of radiation processes; spectral and velocity
information (if any). The is the necessary astronomical legwork. You
can’t progress in astrophysical research without building telescopes,
doing surveys and studying sources in gruesome detail.
• Theoretical treatment This is very difficult. Theories we can
compute with are approximate (no one knows how to do the 2-body
problem in GR. Even numerical N -body Newtonian gravitational work
and 3-d fluid dynamics are fraught with difficulties, though can give
insight. Analytical treatments are usually worse, but can still be very
useful. We use approximate theory and imperfect simulations to try to
educate our physical intuition. We iterate round the loop of theory,
observation and simulation and eventually hope to progress.
• Method This course will consist of generally applicable theoretical
ideas, a necessary minimum of astronomical facts, illustrated by
examples of astrophysical test cases which will be described in more
detail.
Introduction P 6
ASTRONOMICAL FACTS AND JARGON
• Angles are measured in degrees, arc minutes and arc seconds:
π/180 radians = 1 degree = 60 arcmin = 3600 arcsec
• 1 AU (astronomical unit) = 1.5 × 1011 m
• 1 pc (parsec) = 1 AU subtends 1 arcsec = 180 × 3600/π AU
= 3 × 1016 m
• 1 M� (Solar mass) 2 × 1030 kg
• Redshift: z ≡λobs − λrest
λrest
• m = apparent magnitude = −2.5 log10
(
Flux(ν)
StandardFlux(ν)
)
M = absolute magnitude = m − 5 log10
(
Distance
10 pc
)
m M
Sun −27 +5
Full Moon −13 +32
Sirius −1.5 +1.5
A0 star at 10 pc 0 0
White dwarf at 100 pc +20 +15
Galaxy at z = 1 +22 −22
Type Ia SN at z = 1 +24.5 −19.5
Introduction P 7
THE EXPANDING UNIVERSE AND HUBBLE’S “CONSTANT”
• In 1929 Edwin Hubble found that all galaxies seemed to be mov-
ing away from us, with velocity v proportional to distance D: v = H0D.
• He determined the constant H0 to be 500 km s−1 Mpc−1.
• In real units this is 1/H0 = 1.5 Gyr.
• This caused a huge problem, because the age of the Earth is 4.5 Gyr.
• Cosmologists were resourceful and invented lots of crazy theories to
account for this impossible observation.
• Hubble’s calibration had underestimated the luminosity of Cepheid
variables. When corrected, the problem disappeared.
• The value of H0 is still uncertain.: H0 = 75 km s−1 Mpc−1 is
currently popular.
Introduction P 8
EVOLUTION OF HUBBLE’S CONSTANT
• Published values of Hubble’s constant up to 1980.
Introduction P 9
THE BIG BANG
• Although the Hubble constant settled down so that the universe was
older than the Earth, people still didn’t like the idea that the universe
had a definite “beginning” in a hot, dense state 10–15 billion years ago.
• Fred Hoyle (one of the originators of the“Steady-State” theory) said:
“You might as well say it all started in a big bang!”
• The discovery of the relic 2.7 K cosmic microwave background
radiation and the clear evidence of evolution in the radio source counts
(radio source were much more common at z = 2 than they are today)
largely settled the matter, though there were persistent pockets of
resistance for many years afterwards.
• So now we call the dense, hot early universe the “Big Bang”.
• A version of the “Steady-State” theory is now popular again (for the
very early universe). . .
Introduction P 10
DETERMINATION OF THE DISTANCE SCALE
Traditional “step by step” approach: the distance ladder
• Solar system: planetary radar, tracking of spacecraft and pulsar timing
gives value of AU to a few metres.
• Nearby stars: use parallax. Hipparchos satellite measured parallaxes
to 0.001 arcsec (expect a further factor of 100 improvement soon).
Thus establish luminosity as a function of spectral type for main
sequence stars.
• Apply to more distant stars, especially clusters. Find luminosity of
bright “standard candles” (in particular Cepheid variables, for which the
absolute luminosity is well correlated with the period of oscillation).
Introduction P 11
THE DISTANCE SCALE II
• Observe Cepheids in nearby galaxies to establish distances to them
and thus obtain the absolute luminosity of still brighter objects: globular
clusters, H+ regions and whole galaxies.
• Extend these to find distances to galaxies that are sufficiently far away
that the overall expansion of the universe dominates over random
motions. This should provide the value of the Hubble constant H0.
• Beyond that the recession velocity is used as the indicator of distance,
though the true form of the distance–redshift relation remains to be
determined.
• The brightest standard candles available are Type Ia supernovae. They
arise from the ignition of a white dwarf star following accretion of matter
from its normal companion in a binary system. Ignition occurs at a
definite mass 1.4 M�, and there is usually not much absorbing material
in the way, since the lifetime of these stellar systems is very long and
they are likely to have moved away from the dense regions in which
they were formed. These standard candles have extended the distance
scale to high redshift, but calibration will continue to require refinement.
Introduction P 12
HUBBLE DIAGRAM FROM TYPE IA SUPERNOVAE
• Hubble diagram from Perlmutter & Schmidt (2003).
• A distance modulus of 40 corresponds to a distance of 1 Gpc, and
increase of 5 in the distance modulus is equivalent to an factor of 10
increase in distance. (There are lots of technical issues here.)
Introduction P 13
COSMIC ABUNDANCES OF THE ELEMENTS
• Only hydrogen and helium were formed in the Big Bang.
• Binding energy graph shows that Li, Be, B will be rare.
• C, O, Ne are formed in normal stars, post-Fe arise from supernovae.
Introduction P 14
THE SOLAR SYSTEM
• The Sun
- Contains 99.9% of the mass of the solar system
- Rotation period: 25 days at equator, 30 days at poles.
- The angular momentum of the rotation is only 2% of that of the
solar system (most is in the orbital motion of Jupiter).
- The differential rotation creates magnetic field, typically 10−4 T, but
0.3 T in sunspots.
- Optical photosphere has Teff = 6000 K (emits continuum).
- Chromosphere has T = 4500 K (absorption lines).
- Whiplash effect of convection cells heats the low density corona to
T = 106 K.
- Generates solar wind 400–700 km s−1, with spiral sector structure.
- Heat is generated by conversion of hydrogen to helium in the
centre, where the temperature is 1.5 × 107 K and the density is
1.6 × 105 kg m−3.
- Heat is transported outwards by radiative diffusion, except for the
outer 1%, where the decreasing density makes the fluid develop
convection cells.
- Clues to interior: solar oscillations; neutrinos. Has enabled us to
make very detailed measurements of the solar structure and
elemental composition.
Introduction P 15
THE SOLAR SYSTEM II
• Planetary system
- Orbits are approximately circular and lie in a plane — must have
been formed from a gaseous disc.
- Composition shows temperature gradient: inner planets have
ρ ≈ 5 × 103 kg m−3; outer gas giants have ρ ≈ 103 kg m−3
• Earth
- Differentiated: Iron/Nickel core; silicate mantle and crust.
- Heated by radioactive decay, causing geological activity.
- Age of oldest surface rock is about 3.8 Gyr.
• Mars and Venus
- Similar histories to Earth.
- Differences in atmosphere can be understood from temperature and
gravity.
• Moon and Mercury
- Geological activity ceased before the end of asteroid bombardment.
- Age of oldest Moon rock is 4.5 Gyr.
Introduction P 16
THE SOLAR SYSTEM III
• Asteroids
- Smaller bodies, mostly lying between Mars and Jupiter, sizes from
< 1 km to a few hundred km..
- Total mass < 10−3 that of the Earth.
- Interactions and collisions generate meteors which we can study
directly. Differentiated: stony; stony/iron; irons. Some stony
meteors contain “chondrites” — appear to be pre-solar material
(contain SiC which cannot form in the presence of O).
• Outer planets
- Formed from “ices” — H2O, NH3, CH4.
- Massive enough to keep most of the H and He.
- Systems of moons — formation similar to planetary system as a
whole?.
- Ring systems: dust to bolder-sized particles inside the Roche limit.
• Comets
- Made from“Dirty ices”. There are probably about 1010 comets.
- Highly eccentric orbits — regular visitors must have had interaction
with planets that circularised their orbits.
- Probably originate in the Oort cloud at 105 AU
Introduction P 17
STARS AND THEIR CONSEQUENCES
• There are large clouds of molecular hydrogen orbiting in the plane of
the Galaxy. As compression takes place in the shocks of the spiral
density waves, star formation can occur.
• Stars are born when a hydrogen gas cloud collapses under gravity.
Newly formed stars (T Tauri) have jets and other outflows.
• A collapsed gas cloud becomes a star when the temperature in its core
becomes high enough to ignite nuclear burning (107 K).
• The mass range for stars is 0.075 M� to 100 M� and their initial
luminosity is approximately L ∝ M 3.
• Main-sequence stars burn hydrogen in their cores and remain stable
until the fuel is exhausted. This takes 10 Gyr for a solar-mass star.
• Red giants, planetary nebulae, white dwarves, Type II supernovae and
neutron stars are later stages in the evolution of stars.
• Many star systems are binaries and there can be very interesting
consequences as a result of mass transfer. These include novae and
other variable stars, Type IA supernovae, X-ray binaries and other
exotics.
• Supernovae and other mass loss from stellar systems recycle material
into the gas of the Galactic disc and enrich the interstellar medium with
heavy elements.
Introduction P 18
STAR CLUSTERS, GALAXIES AND CLUSTERS
• Star clusters
- Globular clusters: massive (106 M�); old; dynamically relaxed.
- Open clusters: smaller; younger; dynamically evolving and
evaporating.
- Particularly important because all stars are at about the same
distance and presumably of about the same age.
- Massive stars form in clusters.
• Galaxies Limited range of types:
- Ellipticals: similar to globular clusters; masses range from 108 M�
to 1014 M� (found in clusters – arise through cannibalism). Some
galaxies have active nuclei, arising from accretion onto massive
black holes.
- Spirals: pattern is a density wave in the interstellar gas — moves
with respect to the stars; gas and dust are concentrated in the spiral
arms; find that young stars emerge from the arms.
- Irregulars: disruption by interactions, mergers; huge burst of star
formation.
• Clusters of galaxies
- Large aggregations (thousands) of galaxies, often with a very large
elliptical in the centre. Contain hydrostatic X-ray emitting hot gas
(108 K), which strips out the gas from the individual galaxies as
they travel through it.
- There are also larger superclusters and immense voids in the
expanding universe.
Introduction P 19
ASTROPHYSICAL OBJECTS — MASS VERSUS RADIUS PLOT
• Over a very wide range of masses (factor of 1054) objects have a
density of order 103 kg m−3.
• Narrow range of masses (1027–1031 kg with wide range of densities.
• On larger scales see dynamical groups of stars.
Introduction P 20
THE FATE OF COLD MATTER IN THE UNIVERSE
• Gravity tries to concentrate matter.
• Other forces resist:
1) Coulomb force can do the job for M < 2 × 1027 kg
2) Degeneracy pressure i.e. Pauli principle for identical fermions
a) Electrons in white dwarf stars
are sufficient for 2 × 1027 kg < M < 2 × 1030 kg
b) Neutrons in neutron stars (pulsars)
manage for 2 × 1030 kg < M < 1031 kg
• Above this limit gravity must win in the end.
• Collapse is postponed by:
3) Entropy
a) Compression + opacity → heat → pressure.
b) Compression + turbulence → heat → pressure.
c) If temperature T > 107K → nuclear fusion.
Introduction P 21
HOW COMPRESSIBLE ARE ATOMS?
• Recall Bohr model for hydrogen atom:
Forces:e2
4πε0r2= meω
2r
⇒ ω2 =e2
4πε0mer3
Quantum: h̄ = meωr2⇒ ω =
h̄
mer2
• Hence radius of orbit a0 is given by a0 =4πε0h̄
2
e2me
= 5 × 10−11 m.
• Energy is (using Virial theorem):
E = −12
e2
4πε0a0
= −e4me
32π2ε20h̄2
= −13.6 eV
.
• Atoms contain a large amount of
energy and resist compression
very strongly.
• We can estimate the pressure that
atoms can resist as approximately
equal to the energy density ∼ E/(2a0)3∼ 2 × 1012 Pa.
• This estimate is an upper limit: if exceeded the electrons will certainly
not be bound to the protons.
Introduction P 22
HOW COMPRESSIBLE ARE ATOMS? II
• We can make a simpler model of an atom: ignore the proton and
suppose the electron is in a box of side πa, so that its momentum is
p =h̄
aand the kinetic energy is
p2
2me
=h̄2
2mea2.
• Now remember the proton and find the total energy
E(a) =h̄2
2mea2−
e2
4πε0a
E(a)
a
• Treat a as a variable parameter
and locate the minimum energy
as a is varied:
amin =4πε0h̄
2
e2me
= a0.
• The minimum energy itself is Emin = −e4me
32π2ε20h̄2
as before.
• I admit I fiddled that — you can also invoke the uncertainty principle if
you like. . .
• The general point is that, as you try to compress an atom, the kinetic
energy will increase and eventually the total energy will be positive. At
this point the electrons are not bound to individual protons and the
hydrogen becomes metallic (predicted in 1935).
• According to our simple model this occurs when a = 12a0; i.e. when
compressed by a factor of 8.
Introduction P 23
GRAVITY: THE ATOM-CRUSHER
• The gravitational energy of neighbouring atoms in hydrogen is about
Gm2p
2a0
∼ 10−35eV — a factor of 1036 times weaker than the
electrostatic energy.
• But gravity is always attractive and, as you add more atoms,
gravitational effects become more important. . .
• Suppose we have a body containing N atoms.
• The electrostatic forces on an atom are no
stronger than before — the electric field is
shielded on scales larger than a0.
• An atom will feel the gravitational effect of all the other atoms in the
body, but we have to allow for the increased separation.
• For an incompressible body the average separation is ∼ a0N1/3.
• The gravitational energy of the atom is nowNGm2
p
2a0N1/3; i.e. ∝ N2/3
• Although gravitation is 1036 times weaker than electromagnetism at
the atomic level, it will dominate when the number of atoms exceeds
(1036)3/2 = 1054.
• This is a mass of1054mp ≈ 1027 kg — about the size of Jupiter.
Introduction P 24
PROPERTIES OF SOLID HYDROGEN
• Density of solid hydrogen is low: the molecular volume is 22.7 cm3.
• As solids go it is rather weak – it compresses by a factor of two in
volume under a pressure of “only” 2 × 104 atmospheres (3 GPa).
• Resistivity and molecular volume have now been measured up to
pressures of 300 GPa, which is about the central pressure of Jupiter.
• The resistivity drops dramatically and hydrogen becomes “metallic”
when compressed by a factor of 9.