COSMOLOGY The Universe what is its age and origin?

Transcription

1 COSMOLOGY The Universe what is its age and origin?

2 REVIEW (SUMMARY) Oppenheimer Volkhoff limit: upper limit to mass of neutron star remnant more than 1.4 M à neutron degeneracy Supernova à extremely dense neutron star If mass above 2 3 M, the star collapses into black hole Chandrasakhar limit upper mass limit of star remnant less than 1.4 M à electron degeneracy Outer layers blow off planetary nebulae Core collapses further white dwarf

3 CGR\Why is it Dark at Night_ - YouTube [720p].mp4 NEWTON S UNIVERSE Newton thought the Universe to be Infinite Uniform static If this were true, the night sky should be bright where ever you look should be a star

4 OLBER S PARADOX In a given volume of space imagine an average number of stars N with density ρ Imagine stars in a thin shell of thickness d at a distance R Volume of shell: 4π R 2 d and # of stars N in shell = n 4π R 2 d But brightness b= L/4π R 2 Amount of Volume of shell increases from shell with R 2, but luminosity does not decreases with 1/ R 2 Total brightness we receive from any shell should shell be is 1/ R 2 B=Nb #Stars R 2 light received depend upon how far away B=n4π R 2 d L/4π R 2 =ndl R Thickness d Overall brightness: add up all shells Since assumed Universe is infinite, there are an infinite # of shells There should be an infinite bright night sky

5 POSSIBLE SOLUTIONS Is the 1. Universe Universe not infinite or it is not Infinite uniform and à but Uniform? there is no edge à it must be infinite 2. Light is absorbed by something Has all light à s.th. Should warm up reached us? and radiate energy à not observed 3. Not static à we know it is expanding from red and blue shift à it is expanding Is the now, but Universe what does it imply about static? the past?

6 Big Bang Universe was created ~ billion years ago Has the known Universe changed? We only could see light that was less than 15 billion ly away If we receive light from a finite # of stars, the night sky would be dark

7 BIG BANG MODEL Doppler effect causes redshift for sources moving away à longer λ à lower f Light sources are compared in their spectrum against the spectrum of a stationary hydrogen source Galaxies show redshift à they move away from each other à they must have been much closer together in the past

8 AT THE BEGINNING there was a point of infinite density called singularity Big Bang Explosion Time and space was created some billion years ago It is the space in which galaxies are situated that expands Balloon analogy, but à no outside à no center

9 QUESTIONS Questions are meaningless they can t be asked What is outside the Universe? What was there before the Big Bang?

10 REDSHIFT Due to photons traveling through space Space expands causing the λ of photons to expand The longer a photon travels, the more its λ will increase The photons originating from the furthest distance will be redshifted most

11 COSMIC BACKGROUND RADIATION CMB Isotropic the same in all directions

12 DICKE AND PEEBLES IN 1960 Proposal: CGR\Cosmic Origins clip_ Arno Penzias and the Expanding Universe - YouTube [720p].mp4 During early Universe sufficient high temperature to produce helium by fusion (24% of the Universe is helium) High energy photons were produced They have a BB spectrum corresponding to the temperature at that time As Universe expanded and cooled, photon spectrum would also cool and max λ would change in accordance with Wien s Law Today they should have a max λ corresponding to 3K

13 PENZIAS AND WILSON No matter where they pointed their aerial, it picked up a steady continuous background radiation All space is filled with radiation corresponding to a BB spectrum of 2.76K Evidence for the Bing Bang Model

14 BIG BANG MODEL Space is expanding and within space distribution of galaxies is not uniform Universe is not uniform or static Resolution to Olber s paradox

15 EXAMPLE This question is about the Big Bang model and red-shift. (a) Describe what is meant by the Big Bang model. Solution space and time originated from a single point in a large explosion (b) In the 1960s, Penzias and Wilson discovered a uniform cosmic background radiation (CMB) in the microwave region of the electromagnetic spectrum. (i) Explain how the CMB is consistent with the Big Bang model. Solution temperature of the universe immediately after the Big Bang was very high; as it expanded it cooled down; the wavelength of the CMB corresponds to a temperature consistent with this cooling down (ii) State why the red-shift of light from galaxies supports the Big Bang model. indicates that the universe is expanding;

16 EXAMPLE This question is about Olbers paradox. (a) Newton assumed that the universe is static and that the stars are uniformly distributed. State one further assumption of the Newtonian universe. Solution universe is infinite (b) Explain how Newton s assumptions led to Olbers paradox. Solution number of stars in shell increases as R 2 intensity decreases with 1/ R 2 ; hence brightness of shell is constant; adding all shells to infinity; sky would be uniformly bright;

17 HUBBLE S LAW (1929) Estimating the distance to galaxies, Hubble showed that the recession speed is proportional to the distance of galaxies to Earth Hubble s Law v= H 0 d v = recession speed d = distance to galaxy H 0 = Hubble s constant

18 VALUE FOR H 0 An accurate value for Hubble s constant is difficult to measure Units are important: v = km s 1 d = Mpc H 0 =km s 1 M pc 1 From the gradient of the graph of Hubble s data the original value for H 0 = 500 km s 1 M pc 1 Modern values state H 0 = 70 km s 1 M pc 1 Still contains uncertaint y

19 NEWEST VALUES FOR H 0 December 2012 NASA s Wilkinson microwave Anisotropy Probe (WMAP) gave a value of H 0 = (69.32±0.80) km s 1 M pc 1 March 2013 Planck mission provided a value of H 0 = (67.80±0.77) km s 1 M pc 1

20 EXAMPLE The value of the Hubble constant H 0 is accepted to be in the range of 60 km s 1 M pc 1 to 90 km s 1 M pc 1. A) state and explain why it is difficult to determine a precise value for H 0 Solution The further galaxies away, the more difficult it is to determine the distance accurately You need a standard candle to accurately measure its luminosity

21 EXAMPLE B) State one reason why it would be desirable to have a precise value of H 0 Solution We could get an accurate value of the rate of expansion of the Universe We could get an accurate value of the distance to the galaxy We could find an accurate value for

22 LIMITATIONS OF HUBBLE S LAW Cepheid Variable Standard candle Up to 60Mpc Brightest globular clusters 250Mpc < d < 900Mpc Red and blue super giants 60Mpc < d < 250Mpc Remember: as d error in measurement Supernova 900Mpc < d < 1000Mpc

23 AGE OF THE UNIVERSE AND H 0 Assume the Universe is expanding at constant rate. Two galaxies are separated by a distance d. How long did it take to get this distance apart? Solution Let the age or expansion time of the Universe be T, the Hubble time will be T= distance/speed T = d/ H 0 d T= 1/ H 0 But v = H 0 d This means the Universe has an age changing depending on H 0 d

24 CALCULATING THE AGE OF THE UNIVERSE Assume H 0 =70km s 1 M pc 1. T= 1/70km s 1 M pc 1 T= 10 6 x9.46x x3.26/70x 10 3 T= 3.1x /70x 10 3 = 4.4 x s ~1.4x years 1ly=9.46x m 1pc = 3.26ly 14 billion years

25 ASSUMPTION Galaxies and Earth are moving at constant speed of light c WRT each other There is nothing in their way to slow them down

26 HUBBLE TIME Assume à galaxies have traveled at constant speed If rate of expansion is slowing down, actual age of the Universe would be less than the Hubble time

27 THE ACCELERATING UNIVERSE To trace expansion history of the Universe, a supernova needs to be used as standard candle A 1990 supernova was used to find distance for about 1000Mpc It was found that at redshifts of 0.5 the supernova was fainter than expected for a constant expansion Conclusion: it must accelerate as it moves further away Energy density that acts in opposition to gravity causes expansion to accelerate

28 BUT...Supernovae at redshifts between 0.5 and 1 were decelerating Whether Universe will expand forever or will collapse is something that cosmologists are trying to answer in terms of dark energy

29 REDSHIFT: LENGTHENING OF WAVELENGTH What can cause redshift? Relative motion of source and observer Doppler effect Relativistic time dilation A photon losing energy as it climbs out a gravitational field

30 COSMOLOGICAL REDSHIFT Z Only used for redshift caused by overall expansion of space z= λ ob λ rest / λ rest z= λ/ λ 0 ~ v/c v= velocity of source c = speed of light

31 EXAMPLE The wavelength of the blue line in the spectrum of atomic hydrogen as measured in the lab on Earth is 486nm. In the spectrum from a distant galaxy the same blue line measures 498nm. Estimate the recession speed of the galaxy from Earth Solution λ= =12 nm λ/ λ 0 = v/c v= λ/ λ 0 c= 12/ = m s 1 d= v/ H 0 d= 7407km s 1 /65 =113.95~114Mpc Assume H 0 =65km s 1 M pc 1

32 THE COSMIC SCALE FACTOR R As the Universe expands, all distances are stretched by the cosmic scale factor R If radiation was λ 0 when emitted, but λ when it was detected, the cosmic scale factor would have changed from R 0 to R Space has stretched by an amount R in the same time λ has stretched by λ Hubble s law holds because space is expanding, not galaxies receding

33 SCALE FACTOR R z= λ/λ = R/R = R R 0 / R 0 = R/ R 0 1 z= R/ R 0 1 R = present scale factor R 0 = scale factor when radiation was emitted R/ R 0 = factor by which Universe has expanded since time presently observable radiation was emitted

34 EXAMPLE For a Quasar of redshift 4, we are seeing it as it was when the Universe was how big? Solution z+1= R/ R 0 1/z+1 = R 0 /R R 0 = 1/4+1 R= 1/5 R The Universe was 1/5 of its present value

35 EXAMPLE A distant Quasar is detected to have a redshift value z of 5.6 a) find the speed of the Quasar WRT Earth b) estimate the ratio of its current size to the Universe s size when the Quasar emitted the photons that were detected Solution a) z= λ/ λ 0 = v/c =5.6 v = 5.6c b) R/ R 0 1=5.6 R/ R 0 =5.6+1=6.6 R 0 /R = 1/6.6 R 0 =0.15R The Universe was 15% of its current size