Astrophysics and Cosmology
7/24/2016
Lecture
#26
Lecture XXVI
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Concepts
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Parsec, light year
Curved space
Hubble’s law
Big Bang
Early universe
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Units to measure large distances
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Light second = cx1s=3x108 m = 3x105 km
Earth circumference = 40,000 km = 0.13 light seconds
Earth – Moon = 1.28 light seconds
Light minute = cx60s=1.8x1010 m
Earth – Sun = 8.3 light minutes
Earth – Pluto = 311 light minutes
Light year = cx1y=9.46x1015 m
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Scales of the universe
Distance from Earth
• Proxima Centauri (next door neighbor) – 4.3 ly
• Center of our Galaxy (Milky Way)
3x104 ly
• Our galaxy (Milky Way) is a disk
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D=100,000 ly
thickness 2,000ly
total number of stars in Milky Way ~1011
• Nearest galaxy (Andromeda nebula)
2x106 ly
• Farthest galaxies
1010 ly
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How to measure heavenly distances?
Cannot clock the light, cannot use a ruler…
Parallax – apparent motion of a star against the
background of more distant stars
f
D
d
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q
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f=90-q
D=d/tan(f)
d=1.5x108km
Parallax angle in seconds
– distance to the star in
Parsec = 3.26 ly
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Other information from the sky
• Apparent brightness  on average related to distances
• Spectrum  temperature
– Red shift – related to relative velocity  distances
• High energy radiation
• Neutrinos (m=~0, weak interaction) – propagate great
distances
• Experiment  observation
• SLOAN digital sky survey: http://skyserver.fnal.gov/en/
• Hubble telescope:
http://www.stsci.edu/ftp/science/hdf/hdf.html
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Hubble deep field
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Hertzsprung-Russel (H-R)
diagram
• Luminosity increases with
star’s mass
• Temperature related to the
wavelength lT=2.9x10-3mK
• By measuring l we can find T,
then using H-R diagram we
can predict the absolute
brightness (L).
• The apparent brightness (l) is
related to L and the distance
to the star:
L
l=
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Evolution of the stars-I
• Stars are born when gaseous clouds (mostly hydrogen) contract
due to gravity
• Gravity accelerates the particles of the star inward  kinetic
energy is increasing, could be large enough (1keV~107K) to
overcome coulomb repulsion and start nuclear fusion HHe (In
our Sun – yellow dwarf)
• Pressure from the energy released in fusion keeps the star from
collapsing
• When the hydrogen in the core burns out the core contracts and T
goes up  the outer envelope expands and cools down (Red giant)
• The core continues to heat up and He starts burning in fusion and
continue to higher Z’s ending nucleosynthesis at Fe and Ni
• No pressure from fusion – gravitational collapse – white dwarf
• Pauli principle for orbital e keeps the star from further collapse
• T goes down white draft becomes black dwarf (cloud of ash)
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Evolution of the stars-II
• Heavier stars continue to burn beyond Fe and Ni in
endoergic reactions
• In addition the following process can occur
e-+pn+n
Neutrons are formed in abundance – neutron star (>~1.5
mass of Sun, D~10km) Pauli principle for neutrons limit
the size
No electrostatic repulsion – leads to a catastrophic collapse
– supernova explosion
If mass of neutron star >2-3xSolar mass – black hole – not
even light can escape
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Gravity and curvature of space
• Einstein’s general relativity: No observer can determine
by experiment if he is accelerating or is rather in a
gravitational field
• Explain gravity (interaction) through curvature of space
(geometry)
• Establish equivalence between gravitational and inertial
mass
• Experimental proof: Curving light: straight line
becomes curved in gravitational field
• Extreme curvature – black hole: black because not even
light can escape it
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Expanding universe
• Redshift – spectral lines shifted – object is moving
• In 1929 Edwin Hubble, measured the redshifts of a
number of distant galaxies. the redshift of distant
galaxies increased as a linear function of their distance
• Hubble’s law
v=Hd
• v- velocity of galaxies, d – distance
• H=80km/s/Mpc
• The universe is expanding.
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Age of the universe
v=Hd
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v- velocity of galaxies, d – distance
H=80km/s/Mpc = 20km/s/million ly
Farthest galaxy 1010ly
t=d/v=d/(dH)=1/H=15x109yr
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Universe evolution
Age of the universe 1010 years
Cosmic Microwave background – echo of the Big Bang
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1.4 10-23 J / K  3K
-4
KE = kT =
=
2
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6

10
eV
-19
1.6Lecture
10XXVIJ / eV
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Cosmic microwave background
• Discovered in 1964 by Arno Penzias and Robert Wilson
as a “noise” in radio telescope
• Cosmic microwave background at l=7.35 cm
• Blackbody radiation at T=~3K
• Present precise measurement 2.7K
• Echo of the Big Bang, predicted in 1940 by George
Gamow
• Radiation “decoupled” from matter when atoms were
formed and there were no free electrons to scatter light
(~3000K, 0.3 Myears after birth)
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Fate of the Universe
• Gravity slows down the expansion
• Depending on the density the universe might
– Continue to expand infinitely
– Collapse back to a point
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WMAP Launched from cape Canaveral on June 30 2001
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Phasing loops
Lunar swingby
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days to L2, 1.5e6 km from
Earth.
Trajectory
Official arrival date:
Oct 1, 2001 18
COBE 1992
Bennett et al 2003
WMAP 2003
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Facts first, then the conclusions!
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BEYOND LCDM model
FLATNESS
Riess et al. 2001
+ HST meas. of Ho
de Bernardis et al 2000
Verde et al 2002
 = 1.02  0.02
(Spergel et al 2003)
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After
We (and all of chemistry) are a
small minority in the Universe.
Compare gravitational rotation of galaxies with luminous matter
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