Atoms to Astronomy 2 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 a ID: 542769
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Story of the UniverseSlide2
Atoms to Astronomy
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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. Slide3
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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!Slide5
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Gravity - 1
Gravity is the attractive force that attracts two bodies of mass M and m with a force which is given by
where i is the 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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Lagrangian points
8The Lagrangian
points libration points are five positions between 2 gravitating bodies, where a small object affected only by gravity can theoretically be stationary relative to two larger objects (such as a satellite with respect to the Earth and Moon). The Lagrange points mark positions where the combined gravitational pull of the two large masses provides precisely the centripetal force required to rotate with them.Equipotential surfaces
Balanced potential point:
Object will be balanced
Mass transfer occurs from here
ROCHE LOBESlide9
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.Atoms to Astronomy
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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.Slide11
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Super massive black hole in the galaxy NGC4258
MCG-6-30-16 - 400 ks long XMM observation
Iron line in compact objects
Quasi periodic oscillations of 0.01 to 500 Hz and direct evidence of BHSlide13
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Quantum Mechanics
When the measuring method is of the same order as what is being measured, there are some fundamental complications and the observer and the observed are intermixed!
Since energy and mass are equivalent, one can imagine mass as having energy and wavelength.
Inversely, light which is a packet of energy can be considered as if it was a solid object and can be traded only in fundamental units!
The wavelength of a matter object is in fact the probability of finding the object somewhere etc.
It also produces some interesting effects such as:
tunnelling
stable electron orbits.Slide14
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blue
yellow
red
blue
yellow
red
Doppler Shift
Light from stationary star
Light from star moving away from us (red shift)
Light from object moving towards us (blue shift)
red
blue
yellowSlide17
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Northern Sky
Southern SkySlide18
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Difference in brightness can arise because
The stars are at different distances
Stars are of different intrinsic brightnessSlide19
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FOR NORMALISED AREASlide21
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For stars at an angle, an additional cos(
) factor has to be consideredSlide23
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16 D
sunSlide24
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700 D
sun
1 AUSlide25Slide26
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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 parallax and ism by extinction.Slide27
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Variable Stars as distance indicators
The period-luminosity relation for Cepheids
Constant luminosity
Note the logarithmic scale for the graph
(type 1)Slide28
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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)-1Slide31
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Planck Value: 67.3 km/s/MpcSlide33
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36Gamma raySlide37
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WMAP
PlanckSlide38
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3 min
380,000 yearsPresent
A conspiracy of Gravity and Nuclear forces
Time
EntropySlide39
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39Star formation through timeMadau plot (Cole et al. 2001)
Cosmic timeSlide40
Wonders of the Universe
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41Gravity dominatedExpansion dominatedSlide42
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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.Slide44
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Dense clouds of gas collapse into the first (Pop III) massive stars and probably produce the first GRBs. GRBs can then precede the formation of the first galaxies, which in turn precede that of active galactic nuclei (AGN) powered by supermassive
black holes. Thus, GRBs could probe the first structures and galaxies to emerge after the 'dark ages' of the Universe. The narrow beaming of GRBs, best defined by GRB 080319B (not shown to scale), makes them the most luminous back-lights for mapping the far-distant visible Universe.Slide47
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Inflation
10-35 sProton 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!Slide48
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Maxwell’s Electromagnetic Theory
Abdul Salam’s Electroweak TheoryStandard Model
String Theory?
Theory of Vacuum fluctuations???Slide52
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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 Slide56
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56This is an artist’s impression of the galaxy Z8-GND-5296. Image credit: V. Tilvi / S.L. Finkelstein / C. Papovich
/ the Hubble Heritage TeamZ8-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 clockEvent
timeredshift
H and He formation
3 min.
10
9
Recombination
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
0Slide58
Dark
Energy58Slide59
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61~ 2 billion years agoSlide62
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62MatterStrength of the repulsive force in the UniverseSlide63
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634%21 %
75%Slide64
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Origin of elements in the UniverseSlide66
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Synthesis of elementsSlide68
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Limits to production of heavy elements in the Universe: The Binding energy curveSlide69
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Abundance of matter in the UniverseSlide72
How will the universe end?Slide73
Dark is more important than brightSlide74
Distance from Centre
Rotational velocity (km/s)Slide75Slide76Slide77Slide78Slide79Slide80
Cosmic clock
Event
timeredshift
H and He formation
3 min.
10
9
Recombination
400,000 yr
1,500
The first stars
400 Myr
10
Reionization
500 Myr
9
The first galaxies
0.8 Gyr
6.5
Today
13.7 Gyr
0Slide81
Star formation through time
Madau plot (Cole et al. 2001)
Cosmic timeSlide82Slide83Slide84
~ 2 billion years agoSlide85
4%
26 %
60%Slide86Slide87
I should have stopped long back
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END