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Home , Black body, Radiation

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Constellation is a group of that form a pattern as seen from the , not bound by Option E: Astrophysics gravitation. 4 L = AT Stellar cluster is a group of stars held together by gravitation in same region of , created

2.90×10-3 roughly at the same . 휆 (meters) = max T () Galaxy is a huge group of stars, , and gas held together by , often containing billions of stars, measuring many years across. 1 d(parsec) = is a massive body of gas held together by gravity, with fusion going on at its center, giving off p (arc-second) electromagnetic . There is an equilibrium between radiation pressure and gravitational L pressure. b = 2 4휋푑 • Comet: A small body composed of mainly ice and dust that orbits the in an elliptical orbit. d m – M = 5 log ( ) 10

Stars’ and ’ radiation spectrum is approximately the same as

-body radiation/ Plank’s law.

Intensity as a function of depends upon its

Wien’s law: Wavelength at which the intensity 2.9×10-3 of the radiation is a maximum λ , is: max(m) max T(K)

Luminosity (of a star) is the total power (total per second) radiated by an object (star). If we regard stars as , then is: L = A σT4 = 4πR2σT4 (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-.

(Apparent) brightness (b) is the power from the star received per square meter of the Earth’s surface L b = (W/m2) 4π푑2 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 . Greeks ordered the stars in the sky from brightest to faintest… Later, accepted and quantified this system. 3 • 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 – apparent magnitude M – of the star m – M = 5 log ( ) 10 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. 7 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 Spectroscopic binary: A binary-star Eclipsing binary: (Rare) binary-star can be seen as two separate stars with system which from Earth appears as a system in which the two stars are too a telescope and sometimes with the single star, but whose light spectrum close to be seen separately but is unaided eye. (spectral lines) shows periodic splitting aligned in such a way that from Earth and shifting of spectral lines due to we periodically observe changes in as two stars orbit one brightness as each star successively another. 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

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 / versus their spectral types(color) /classifications or surface temperature. It shows stars of different ages and in different stages, all at the same time.

26 L = sun luminosity = 3.839 × 10 W 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

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

Sun-earth distance 1 AU astronomical unit tan p = = 11 Sun-star distance d 1 AU = 1.5 x 10 m

1 AU • for small angles: tan θ ≈ sin θ ≈ θ (in radians): d = p 1 d (parsecs) = 1 pc = 3.08x1016 m (p = 1 sec of arc, d = 3.08x1016 m defined as 1 pc) p(arcseconds) • limit because of small parallaxes: d ≤ 100 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 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.

There is a clear relationship between Left: graph shows how the the period of a Cepheid variable and its apparent. magnitude (the absolute magnitude. The greater the brightness) changes, getting period then the greater the maximum brighter and dimmer again with a luminosity of the star. Cepheids fixed, measurable period for a typically vary in brightness over a particular Cepheid variable. 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 • Calculate d from b = L/4πd2 • Distances to galaxies are then known if the Cepheid can be ascertained to be within a specific galaxy.

Newton assumptions about the of the : • 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 • since stars are uniformly distributed the number of stars seen from Earth increases as d2: number of stars in shell = density x volume = n 4πd2 t • brightness of one star decreases as 1/d2 ; b = L/4 πd2 • 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 d2nt = Lnt = const. 4π d2 • 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 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 - 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 would be produced. The CMB (Cosmic ) 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 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 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 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 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 / WIMPS / MACHOS / black holes / exotic super symmetric / grand unified predicted particles / magnetic monopoles etc.; or maybe our current theory of gravity is again not correct

Precision “…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.”