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Olbers Paradox

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Meaning that the Brightness B of a star is constant, so faraway stars should be ... So the brightness of the will decrease as we look at stars farther away. But ... – PowerPoint PPT presentation

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Title: Olbers Paradox


1
Olbers Paradox
  • Mike Collicutt and Ryan Marciniak

2
Whos Paradox?
  • Heinrich Wilhelm Matthäus Olbers lived from 1758
    to 1840.
  • Discovered Pallas (1802) and Vesta (1807)
  • Pluralist, firm believer of moon life

3
The line-of-sight argument
  • Requires infinite, homogeneous universe
  • Called Olbers paradox by Hermann Bondi in 1952
  • Every sight line from every point intercepts a
    star
  • Entire sky would be as bright as 180,000 suns

4
The Forest Analogy
5
Intensity
  • If we look at the flux of photons from the sun at
    radius d
  • If we double the distance d to the sun, then the
    solar flux decreases by a factor of 4.

6
Area Intensity
  • Solid angle subtended by the sun is given by
  • If we double the distance to the sun as before,
    the solid angle subtended by the sun also
    decreases by 4

7
  • This means that the intensity per unit area per
    unit solid angle is constant
  • Meaning that the Brightness B of a star is
    constant, so faraway stars should be as bright as
    nearby stars like the sun.

8
Is it Dust Extinction?
  • Dust particles in thick clouds absorb light
  • Does dust account for why we see a dark night
    sky?

9
Nope!
  • Light from stars behind the dust would heat it up

Good old Blackbody Radiation
10
Hubble to the Rescue
  • Hubbles discovery of an expanding universe
    allowed for red shift of light
  • Stars farther away from an observer have more
    expanding space in between, and hence more
    redshift
  • So the brightness of the will decrease as we look
    at stars farther away

11
But is that enough???
12
Solutions Finite visible universe
  • First proposed (poetically) by Edgar Allen Poe in
    1848, and Lord Kelvin Mathematically in early
    1900s
  • "Were the succession of stars endless, then the
    background of the sky would present us a uniform
    luminosity since there could be absolutely no
    point, in all that background, at which would not
    exist a star. The only mode, therefore, in which,
    under such a state of affairs, we could
    comprehend the voids which our telescopes find in
    innumerable directions, would be by supposing the
    distance of the invisible background so immense
    that no ray from it has yet been able to reach us
    at all."

13
Finite Visible Universe Contd
  • Even if our universe is indeed infinite with
    infinitely many stars, he argued that our visible
    universe is only finite in size the light from
    stars outside of this sphere hasnt had enough
    time to reach us yet
  • Kelvin calculated that in order to have a night
    sky as bright as the sun, wed need to include
    all starlight up to 3x1015 ly away
  • Were on the right track, but is there anything
    else?

14
Finite lifetime of stars
  • Typical lifetime of a star 10 billion years
  • Universe 13.7 billion years old
  • Stars in the early universe have since died out
  • At any given time we only see a certain amount of
    luminous matter
  • Not enough starlight has been emitted to make the
    night sky bright

15
Age vs. Expansion
  • Which factor contributes more to lack of observed
    radiation we see Finite age of galaxies or the
    expansion of the universe causing redshift?
  • Start by finding the intensity of visible light
    from all of the galaxies

16
All-sky intensity
  • no number density of galaxies now that formed at
    tf (big bang) usually
  • F spectrum of a galaxy as a function of
    wavelength time
  • RR(t) scale factor for the expansion of the
    universe Hubbles law
  • Ro radius of the universe in present epoch
  • Actually express ? as ?oR/Ro ?o is the observed
    wavelength, ? is the actual wavelength emitted by
    the galaxy
  • I(?o) is the intensity at wavelength ?o of all
    the radiation from galaxies within some imaginary
    sphere corresponding to the time of the galaxies
    formation
  • Units of I power/unit area/unit wavelength
    interval

17
Galaxy Spectrum
  • Simplest model assume the galaxies act as black
    bodies
  • As galaxies age, the luminosity of a galaxy
    decreases as spectrum becomes redder incorporate
    this by letting TT(t)
  • Whats C? Blackbody gt Use Stefans Law

18
Almost there
  • Fixes C as
  • Now can sub F into the expression for intensity
    to obtain

19
Now to the point Affect of Age of Galaxies
  • We can compare the intensity found under an
    expanding universe with that of a completely
    static one RoR, TTo
  • So the intensity directly proportional to the age
    of galaxies in the universe by to-tf

20
The point Effect of the expanding universe
  • From here we want to know I/Is. The best we can
    do is use a numerical integration technique to
    gather any numerical information
  • BORING
  • So Lets look at the results

21
The Affect of the Expanding Universe
  • Can vary different parameters such as density of
    galaxies, and redshift of galaxy formation (time
    of galaxy formation)
  • BUT Every time get roughly the same decrease in
    intensity I/Is 1/3
  • SO the expansion of the universe only reduces the
    observed intensity of light by 1/3, whereas the
    age of the galaxies determine the observed
    intensity by orders of magnitude to-tf

22
Summary/Conclusions
  • Olbers paradox states that in an infinite,
    static universe with infinitely many uniformly
    distributed stars (galaxies) the night sky would
    appear as bright as the surface of the sun
  • Resolutions
  • Redshift due to expansion
  • Finite visible universe
  • Finite age of the galaxies limits light produced
  • Most important effect that resolves the paradox

23
Zee Aind
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