Download Part 9: Story of the Universe

Story of the Universe
Special theory of Relativity
It is a basic property of Nature that:
Velocity of Light in vacuum is constant.
All inertial frames are identical so if two objects are
moving with a constant velocity, it is impossible to do
any test which allows to measure the velocities in
absolute manner.
This has significant consequences.
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Consequences
• Because velocity of light is constant:
– space and time must contract.
– Acceleration must increase not just the velocity of
an object but also its inertia and hence objects
become heavier as they approach the velocity of
light
– No object with finite mass can move at velocity of
light and no object of zero mass can move at a
slower velocity!
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Gravity - 1
• Gravity is the attractive force that attracts two bodies of mass M
𝐺𝑀𝑚
and m with a force which is given by 𝐹 = 2 𝑖 where i is the
𝑟
unit vector in the line joining the centre of mass of the two
objects.
• From this, one can derive Kepler’s 3 laws:
– Each planet goes around the sun in an elliptical orbit with the Sun at one
focus of the ellipse.
– Planets cover equal area in equal times.
– The square of the period of the revolution (T) of the planet is proportional
to the cube of the semi-major access (a) of the orbit.
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Gravity - 2
• It also defines Keplerian Velocity. In order for an
object to remain in stable revolution around a
star, it must have a velocity so that gravity and
centrifugal force are balanced.
• The inverse square law implies that in general,
the orbit of an object experiencing the
gravitational attraction of another body will
undergo motion best explained by conic curves
(ellipse, parabola or hyperbola) defined by initial
conditions.
• Also, the centre of mass of the two objects going
around each other will be the stable point around
which both the objects will revolve.
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Problems
• However, this is not fully satisfactory and cannot
explain precession of orbits etc.
• This led Einstein to expand it into a larger
formulation called General Theory of Relativity.
• Newton’s laws are a special case of General
Theory of relativity when the masses and
speeds are small.
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General theory of Relativity
General Theory of relativity states that:
Influence of Gravity is identical to that of
sitting in an accelerated frame.
Identifying the curvature of space-time with
Gravity
It becomes important in the presence of
Strong gravitational fields such as those
existing near compact objects.
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Iron line in
compact objects
Super massive black hole in the
galaxy NGC4258
Quasi periodic oscillations of 0.01 to 500
Hz and direct evidence of BH
MCG-6-30-16 - 400 ks long XMM
observation
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 v  vo 

n'  n
 v  vs 
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red
yellow
Doppler Shift
Light from
1 stationary
vc
v
'

v
star
1 v c
blue
red
yellow
Light from star moving
away from us (red shift)
blue
red
yellow
blue
Light from object
moving towards us
(blue shift)
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Southern Sky
Northern Sky
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Difference in brightness can arise because
a) The stars are at different distances
b) Stars are of different intrinsic brightness
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u  d 
8hc

5
e
1
hc / kT

1
d
FOR NORMALISED AREA
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max T  0.29 cm K
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D pc 
1
parcsec
For stars at an angle, an additional cos() factor has to be considered
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16 Dsun
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1 AU
700 Dsun
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Measuring distances to galaxies involves
using some selected objects
STANDARD CANDLES
These are objects of known intrinsic brightness. Hence
a ratio of their apparent brightness to their intrinsic
(absolute) brightness gives their distance.
For objects inside our galaxy an additional parameter
comes from extinction where distance is measured by
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parallax and ism by extinction.
Variable Stars as distance indicators
The period-luminosity relation for Cepheids
Note the
logarithmic
scale for
the graph
(type 1)
Constant
luminosity
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Redshift (z) is defined as z =  /
z = 1+[(c+vrec)/(c-vrec)]1/2
Depth of Universe Visible (a) is
a = (1+ z)-1
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vH D
v  recessiona l velocity
H  Hubble Constant (73 km/s/Mpc)
D  Distance
Planck Value:
67.3
km/s/Mpc
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Gamma ray
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WMAP
Planck
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Entropy
A conspiracy of Gravity and
Nuclear forces
3 min
380,000 years
Present
Time
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Cosmic time
Star formation
through time
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Madau plot (Cole etAtoms
al. 2001)
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Wonders of the Universe
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Gravity dominated
Expansion dominated
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Inflation
• It seems that the nascent universe passed through a
phase of exponential expansion.
• Inflation answers the following problems of the big
bang cosmology:
– Why does the universe appear flat, homogeneous and
isotropic
– Origin of the large-scale structure of the cosmos. Quantum
fluctuations in the microscopic inflationary region, magnified
to cosmic size, become the seeds for the growth of structure
in the universe.
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Proton formation:
1 sec
The earliest galaxies
we have seen are at z
~ 7.51, i.e. about 10.7
billion years since the
birth of the Universe.
The earliest stars
were born 200 million
years after the
Universe was born!
Inflation
10-35 s
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String Theory?
Theory of
Vacuum
fluctuations???
Standard Model
Abdul
Salam’s
Electrowea
k Theory
Maxwell’s
Electromagnetic
Theory
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page 5 5 4 | N AT U R E | VO L 4 9 7 | 3 0 M AY 2 0 1 3
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This is an artist’s impression of the galaxy Z8-GND-5296.
Image credit: V. Tilvi / S.L. Finkelstein / C. Papovich / the
Hubble Heritage Team
Z8-GND-5296 is forming stars extremely rapidly –
producing each year about 300 times the mass of our
Sun. By comparison, our Milky Way Galaxy forms only 2
– 3 stars per year.
Even galaxies observed at a time when the Universe had
reached only 5% of its current age may already be
chemically enriched with dust and heavy elements, which
must have been produced by an earlier generation of
stars.
Finkelstein, S. L. et al. Nature 502, 524–527 (2013); see
also Riecher 24 October 2013, Nature, 502, 459
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Cosmic clock
Event
H and He formation
time
3 min.
redshift
109
400,000 yr
1,500
The first stars
400 Myr
10
Reionization
400 Myr
9
The first galaxies
0.7 Gyr
6.5
Today
13.7 Gyr
0
Recombination
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Dark Energy
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~ 2 billion years ago
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Matter
Strength of
the repulsive
force in the
Universe
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75%
4%
21 %
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Origin of elements in the
Universe
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Synthesis of elements
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Limits to production of heavy elements in the Universe: The Binding energy curve
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Abundance of matter in the Universe
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How will the universe end?
Dark is more important than bright
Rotational velocity (km/s)
Distance from Centre
Cosmic clock
Event
H and He formation
time
3 min.
redshift
109
400,000 yr
1,500
The first stars
400 Myr
10
Reionization
500 Myr
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The first galaxies
0.8 Gyr
6.5
Today
13.7 Gyr
0
Recombination
Star formation through time
Cosmic time
Madau plot (Cole et al. 2001)
~ 2 billion years ago
60%
4%
26 %
I should have stopped long back

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END