Download Wien`s law - Uplift Education

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Constellation is a group of stars that form a pattern as seen from the Earth, not bound by
gravitation.
Stellar cluster is a group of stars held together by gravitation in same region of space, created
roughly at the same time.
Galaxy is a huge group of stars, dust, and gas held together by gravity, often containing billions of
stars, measuring many light years across.
Star is a massive body of gas held together by gravity, with fusion going on at its center, giving off
electromagnetic radiation. There is an equilibrium between radiation pressure and gravitational
pressure.
• Comet: A small body composed of mainly ice and dust that orbits the sun in an elliptical orbit.
Option E: Astrophysics
L = AT
4
𝜆max(meters) =
d(parsec) =
b =
2.90×10-3
T (kelvin)
1
p (arc-second)
L
4𝜋𝑑 2
m – M = 5 log (
d
)
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Stars’ and planets’ radiation spectrum is approximately the same as
black-body radiation/ Plank’s law.
Intensity as a function of wavelength depends upon its temperature
Wien’s law: Wavelength at which the intensity
of the radiation is a maximum λmax, is:
max (m) 
2.9×10-3
T(K)
Luminosity (of a star) is the total power (total energy per second) radiated by an object (star).
If we regard stars as black body, then luminosity is:
4
2
L = A σT = 4πR σT
4
(Watts)
Stefan-Boltzmann’s law
A is surface area of the star, R is the radius of the star,
T surface temperature (K), σ is Stefan-Boltzmann constant.
(Apparent) brightness (b) is the power from the star received per square meter of the Earth’s surface
b=
L
2
(W/m )
4π𝑑 2
L is luminosity of the star; d its distance from the Earth
Magnitude Scale: Magnitudes are a way of assigning a number to a star so we know how bright it is
Apparent magnitude (m) of a celestial body is a measure of its brightness as seen from Earth. The brighter the object appears the
lower its apparent magnitude. Greeks ordered the stars in the sky from brightest to faintest… Later, astronomers accepted and
quantified this system.
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• Every one step in magnitude corresponds to a factor of 2.51 change in brightness. Ex: m1 = 6 and m2 = 9, then b1 = (2.51) b2
Absolute magnitude (M) of a star is the apparent magnitude that a star would have if it were at distance of 10 pc from Earth.
It is the true measurement of a star’s brightness seen from a set distance.
d
m – M = 5 log (
)
10
m – apparent magnitude
M – absolute magnitude of the star
d – its distance from the Earth measured in parsecs.
• If two stars have the same absolute magnitude but different apparent magnitude they would have the same brightness
if they were both at distance of 10 pc from Earth, so we conclude they have the same luminosity, but are at different
distances from Earth !!!!!!!!!!!!!!
• Every one step in absolute magnitude corresponds to a factor of 2.51 change in luminosity.
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Ex: M1 = – 2 and M2 = 5, then L1 / L2 = (2.51)
Binary star is a stellar system consisting of two stars orbiting around their common center of mass.
The ONLY way to find mass of the stars is when they are the part of binary stars. Knowing the period of
the binary and the separation of the stars the total mass of the binary system can be calculated (not in this course).
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Visual binary: a system of stars that
can be seen as two separate stars with
a telescope and sometimes with the
unaided eye.
Spectroscopic binary: A binary-star
system which from Earth appears as a
single star, but whose light spectrum
(spectral lines) shows periodic splitting
and shifting of spectral lines due to
Doppler effect as two stars orbit one
another.
Eclipsing binary: (Rare) binary-star
system in which the two stars are too
close to be seen separately but is
aligned in such a way that from Earth
we periodically observe changes in
brightness as each star successively
passes in front of the other, that is,
eclipses the other.
They are sufficiently close to Earth and
the stars are well enough separated.
Sirius A, brightest star in the night sky
and its companion first white dwarf
star to be discovered Sirius B.
The Hertzsprung–Russell (H – R) diagram(family portrait) is a scatter graph of stars
showing the relationship between the stars' absolute magnitudes / luminosities
versus their spectral types(color) /classifications or surface temperature.
It shows stars of different ages and in different stages, all at the same time.
L = sun luminosity = 3.839 × 10 W
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main sequence stars: fusing hydrogen into helium, the difference between them
is in mass: left upper corner more massive than right lower corner.
white dwarf compared to a main sequence star: • has smaller radius • more dense
• higher surface temperature • energy not produced by nuclear fusion
Techniques for determining stellar distances: stellar parallax, spectroscopic parallax and Cepheid variables.
 Stellar parallax
• two apparent positions of a close star with respect to position of distant stars
as seen by an observer from two widely separated points are compared and recorded;
• the maximum angular variation from the mean, p, is recorded;
• the distance (in parsecs) can be calculated using geometry
tan p =
Sun-earth distance
Sun-star distance
=
astronomical unit
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1 AU = 1.5 x 10 m
1 AU
d
• for small angles: tan θ ≈ sin θ ≈ θ (in radians):
d (parsecs) =
1
p(arcseconds)
d=
1 AU
p
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1 pc = 3.08x10 m
• limit because of small parallaxes: d ≤ 100 pc
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(p = 1 sec of arc, d = 3.08x10 m defined as 1 pc)
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 Spectroscopic parallax: no parallax at all!!!! (a lot of uncertainty in calculations)
• light from star analyzed (relative amplitudes of the absorption spectrum lines) to give indication of stellar class/temperature
• HR diagram used to estimate the luminosity • distance away calculated from apparent brightness
limit: d ≤ 10 Mpc
 Cepheids as distance indicators
Cepheid variables are stars with regular variation in absolute magnitude (luminosity) (rapid brightening, gradual dimming) which is
caused by periodic expansion and contraction of outer surface (brighter as it expands). This is to do with the balance between the
nuclear and gravitational forces within the star. In most stars these forces are balanced over long periods but in Cepheid variables
they seem to take turns, a bit like a mass bouncing up and down on a spring.
Left: graph shows how the
.
apparent
magnitude (the
brightness) changes, getting
brighter and dimmer again with a
fixed, measurable period for a
particular Cepheid variable.
•
•
•
•
•
There is a clear relationship between
the period of a Cepheid variable and its
absolute magnitude. The greater the
period then the greater the maximum
luminosity of the star. Cepheids
typically vary in brightness over a
period of about 7 days. Left is general
luminosity – period graph.
So, to find out how far away Cepheid is:
Measure brightness to get period
Use graph absolute magnitude M vs. period to find absolute magnitude M
Measure maximum brightness
2
Calculate d from b = L/4πd
Distances to galaxies are then known if the Cepheid can be ascertained to be within a specific galaxy.
Newton assumptions about the nature of the universe:
•
•
•
•
universe is infinite in extent
contains an infinite number of stars uniformly distributed
is static and exists forever
these assumptions led to Olber’s paradox
Olber’s paradox
density of stars n = N/V = number of stars per unit volume
• divide the whole universe into concentric shells around Earth of constant thickness t
• look at one shell of thickness t at distance d from the Earth
2
• since stars are uniformly distributed the number of stars seen from Earth increases as d :
2
number of stars in shell = density x volume = n 4πd t
2
2
• brightness of one star decreases as 1/d ; b = L/4 πd
• brightness of shell is constant; assuming that luminosity L is the same for all stars, the received energy per sec per unit area
(brightness) from all stars in the thin shell is:
L
4π d2
•
•
•
•
•
× 4π d2 nt = Lnt = const.
amount of light we receive from shell does not depend upon how far away the shell is
adding all shells to infinity; each contributing a constant amount of energy
the total energy is infinite
sky would be uniformly bright
but it’s dark in night
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Solutions to Olber’s paradox
• Perhaps the Universe is not infinite. But current model of the Universe is that it is infinite.
• Perhaps the light is absorbed before it gets to us. But then Universe would warm up and eventually reradiate energy.
Real help: the Big Bang model leads to the idea that the observable universe is not infinite and to the idea of the expansion
of the universe;
• Universe is not static, it is expanding, hence the most distant stars/ galaxies are strongly red - shifted, out of the visible
part of the spectrum.
• There is a finite time since the Big Bang. Some 12 to 15 billion years. That means we can only see the part of it that lies within 12
to 15 billion light-years from us. And the observable part of the universe contains too few stars to fill up the sky with light.
Calculation shows that the helium produced by nuclear fusion within stars cannot account for the real amount of helium in Universe
(24%). In 1960 it was proposed that sometime during the early history of the Universe, long before any star, Universe was at a
sufficiently high temperature to produce helium by fusion. In this process many high energy photons would be produced. The CMB
(Cosmic Microwave Background Radiation) radiation was emitted only a few hundred thousand years after the Big Bang, long before
stars or galaxies ever existed. The photons would have a black body spectrum corresponding to the then temperature of the Universe.
As the Universe expanded and cooled the photon spectrum would also change with their maximum wavelength shifting in
accordance with Wien’s law. It is estimated that at the present time the photons should have a maximum wavelength corresponding
to a black body spectrum of an extremely cold object of temperature of 2.7 K.
Cosmological background radiation / Cosmic microwave background radiation (CMB) is microwave radiation - left over from the
Big Bang that fills the universe roughly uniformly in all directions. The Big Bang predicts an expanding universe that had a very high
temperature at the beginning; during the expansion the universe is cooling down and the temperature of the radiation should fall to
its present low value of about 2.7 K.
That radiation corresponds to a black body spectrum of about 2.7 K.
The other way of explaining CMB is: Big Bang producing initially produced very short wavelength photons /EM radiation. As the
universe expands, the wavelengths become red shifted to reach current value.
█ Explain how knowledge of the spectrum of a black body and the existence of cosmological background radiation is consistent with
the “Big Bang” model of the universe.
► Big Bang predicts a low temperature radiation at 2.7 K (i.e. CMB radiation). The Big Bang theory also predicts an expanded
universe which we observe through red- shifting of the galaxies and the lowering of CMB radiation temperature. This expanding
universe is the result of the initial energy released in the Big Bang
█ State one piece of evidence that indicates that the Universe is expanding.
► light from distant galaxies/stars is red-shifted (which means they move away from us – as the red-shifting occurs in all direction,
the universe must be expanding)
► existence of CMB
► the helium abundance in the universe which is about 25 % and is consistent with a hot beginning of the universe;
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The eventual fate of the Universe is determined by the amount of mass in the Universe.
Critical density is the density of the Universe which produces a flat universe, i.e. it would take an infinite amount of time
to stop expansion of it.
Critical density is the density of the Universe that would be necessary to stop the expansion after an infinite amount
of time.
• Closed Universe A model of the universe in which density of the Universe is such that gravity will stop the universe
expanding and then cause it to contract. Eventually the contraction will result in a ‘Big Crunch’ after which the whole
creation process could start again.
• Open Universe A model of the universe in which density is such that gravity is too weak to stop the Universe expanding forever.
• Flat Universe means that the density is at a critical value whereby the Universe will only start to contract after an
infinite amount of time.
non-coincident starts (not at beginning);
correct shapes and correctly labelled;
coincident at appropriate place;
Dark matter is the matter that makes up for most of the mass in the universe, but cannot be detected because it does not emit
radiation. Its existence is inferred from techniques rather then direct visual contact (gravitational effects on visible matter, radiation
and the large-scale structure of the cosmos).
Examples of dark matter.
► two of Neutrinos / WIMPS / MACHOS / black holes / exotic super symmetric particles / grand unified predicted particles /
magnetic monopoles etc.;
or maybe our current theory of gravity is again not correct
Precision Cosmology
“…as we know, there are known knowns; there are things we know we know.
We also know there are known unknowns; that is to say we know there are some things we do not know.
But there are also unknown unknowns -- the ones we don't know we don't know.”