Stefan-Boltzmann's Law Wien's

. Constellation is a group of stars that form a pattern as seen from the Earth, but not bound by gravitation. Option E: Astrophysics Stellar cluster is a group of stars held together by gravitation in same region of space, created roughly at the L = AT4 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. 휆max(meters) = 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. d(parsec) = - Stars’ an planets’ radiation spectrum is approximately the same as black-body radiation/ Plank’s law. b = Intensity as a function of wavelength depends upon its temperature m – M = 5 log ( ) Wien’s law: Wavelength at which the intensity -3 of the radiation is a maximum λmax, is: 2.9×10 max(m) 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: 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-Boltzmann constant. (Apparent) brightness (b) is the power from the star receive per square meter of the Earth’s surface 2 b = (W/m ) 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 or ere the stars in the sky from brightest to faintest… Later, astronomers 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 istance. m – apparent magnitude M – absolute magnitude of the star m – M = 5 log ( ) d – its distance from the Earth measured in parsecs. • If two stars have the same absolute magnitu e but ifferent apparent magnitu e they woul 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 !!!!!!!!!!!!!! 7 • Every one step in absolute magnitude corresponds to a factor of 2.51 change in luminosity. 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 here). Visual binary: a system of stars that can be Spectroscopic binary: A binary-star system Eclipsing binary: (Rare) binary-star system seen as two separate stars with a telescope which from Earth appears as a single star, in which the two stars are too close to be and sometimes with the unaided eye. but whose light spectrum (spectral lines) seen separately but is aligned in such a shows periodic splitting and shifting of way that from Earth we periodically spectral lines due to Doppler effect as two observe changes in brightness as each star stars orbit one another. 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. 26 L = sun luminosity = 3.839 × 10 W 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 Sun-earth istance astronomical unit tan p = = for small angles: tan θ ≈ sin θ ≈ θ (in ra ians) 11 Sun-star istance 1 AU = 1.5 x 10 m d = if p = 1 sec of arc, d = 3.08x1016 m defined as 1 pc d (parsecs) = p(arcsecon s) limit because of small parallaxes: ≤ 00 pc Spectroscopic parallax: no parallax at all!!!! (a lot of uncertainty in calculations) • light from star analyze (relative amplitu es of the absorption spectrum lines) to give indication of stellar class/temperature • HR iagram use to estimate the luminosity • istance away calculate from apparent brightness limit: ≤ 0 Mpc 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. There is a clear relationship between the Left: graph shows how the apparent period of a Cepheid variable and its magnitude. (the brightness) changes, absolute magnitude. The greater the period getting brighter and dimmer again then the greater the maximum luminosity with a fixed, measurable period for a of the star. Cepheids typically vary in brightness over a period of about 7 days. particular Cepheid variable. 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/4π 2 • 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 istribute • is static an exists forever • these assumptions le to Olber’s para ox 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 = ensity x volume = n 4π 2 t • brightness of one star ecreases as / 2 ; b = L/4 π 2 • 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: = Lnt = const. • amount of light we receive from shell oes not epen upon how far away the shell is • a ing all shells to infinity; each contributing a constant amount of energy • the total energy is infinite • sky would be uniformly bright • but it’s ark in night 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 cha g w th th r max mum wa gth sh ft g accorda c w th W ’s aw It s st mat d that at th pr s t t m th photons should have a maximum wavelength corresponding to a black body spectrum of an extremely cold object of temperature of 2.7 K.

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