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Measuring stellar radiation

F.1.1

Galaxies - Giant assemblies of stars, gas, and dust held together by the gravitational forces they have on each other. Our Galaxy is called the Milky Way.

Clusters -gravitationally bound system of galaxies/stars.

Constellations - group of galaxies/stars given a specific name. The 12 zodiacs are examples on such. (Pisces, Aries, Taurus, Gemini, Cancer,…)

Nebulae - from the Latin ‘cloud’. Used to label all sorts of stuff in space, that now are known as star cluster or galaxies. It is sometimes still used for a concentration of gas and dust.

Red Giants - luminous stars with low surface temperature. These stars are produced when the hydrogen in the core of the star has fused into the more heavy helium. Gravity forces the star to contract, but at the same time it heats up. The hydrogen around the core now burns more fiercely and causes the outer envelope of the star to expand and thus cool. This low surface temperature produces light at longer wavelength.

White Dwarfs - are developed as all fuel in a star is exhausted. Gravity forces the star (with a mass lower than 1.4 solar masses) to contract, heat up, at a high pressure. The atoms loose some of their electrons. It becomes a small hot White Dwarf.

Neutron stars - a very dense star, consisting only of uncharged neutrons. They are created when very massive stars explode, leaving this neutron ‘ball’ behind.

Black holes - are not proved to exist. If they do they are created by enormous gravitational forces, that doesn’t even allow light to leave.

Supernovae - are gigantic stellar explosions. These occur when very massive stars explode. Because of Einstein’s law, E=mc2, fusion can not take place after that iron is created. The star collapses since there is no force that can upweigh the gravitational force. When it is impossible to compress it further it explodes violently giving out extremely luminous light.

Pulsars - send out sharp, strong burst of radio waves at regular intervals ranging between milliseconds and 4 seconds. They appear to be rapidly rotating highly magnetic neutron stars. The pulses are very energetic charged particles. The rotation and pulse rates slow gradually down as energy is radiated away.

Quasars - small extraordinarily luminous extragalactic objects with high ,redshifts. They do not seem to conform to Hubble’s Law. They are as bright as nearby stars, but display very large redshifts. According to Hubble’s law the quasars must be either extremely distant and incredibly bright -- thousands of times brighter than ordinary galaxies; or that they are closer than the redshift suggests. There’s either and unresolved brightness problem of an unresolved redshift problem. A theory is that quasars could be powered by black holes.

F.1.2

Parallax, the apparent motion of a star against the background of a more distant star, due to the motion of the Earth around the Sun. The angle is measured at different times during the year. The distance of the Sun to the Earth is known. Distances are specified in parallax angle in seconds of arc (parsec). At large distances the uncertainty becomes too large and it can’t be applied. Ex: angle = (6 x 10^-5)° = (6 x 10^-5)° (3600) = 0.22`` of arc (seconds of arc) in parsecs: 1/0.22´´ = 4.5 pc.

F.1.3

Apparent magnitude is a measure of observed brightness of a star seen from Earth. Absolute magnitude is a measure of luminosity, how much light a star radiates into space. (Astronomers define absolute magnitude as the apparent magnitude a star would have 10 pc away from Earth) A star seeming just as bright as one close to us, but being further away has a greater absolute magnitude.

F.1.4

A black body is a theoretical perfect radiator. Stars radiate energy practically as these. The luminosity, energy distribution over the total area, is only dependent on temperature and the size of the star, described by the Stefan-Boltzmann’s law: , where is the Stefan-Boltzmann constant: 5.67 x 10^-8 Wm^-2K^-4.

F.1.5

Wien’s Law states that the peak wavelength in spectrum of light emitted by a black body is inversely proportional to the surface temperature: l max=2.9 x 10^-3/T.

F.1.6

The spectra of light emitted by a source can reveal the chemical composition of the source since the ‘emission spectrum’ is the material’s characteristic since excited gases emit light of only certain wavelengths.

Types of stellar objects

F.2.1

The Hertzsprung-Russel diagram links luminosity with temperature. The horizontal axis displays temperature, (but it’s the hottest at the left and coolest at the right!!!!) and the vertical axis is the luminosity. The stars fall basically into 3 regions, the Main sequence, the Red Giants and the White Dwarfs. The main sequence is like a backward tilted S. The hottest and most luminous stars are to be found in the top left-hand corner, having a bluish color. Stars with low temperature and low luminosity are found in the bottom right-hand corner, having reddish color. The red giants are top right, the white dwarfs bottom left.

Two types of Cepheid variables: RR Lyrae pulsating blue-white giants with periods of less than a day, and Long-period Myra red giants with periods between 80 and 1000 days, turning from brightest to dimmest.

Thomas Jacobsson comments:

First of all: Cepheids are Cepheids. RR Lyrae and Mira variables are something else, but the RR Lyr stars are very similar to the Cepheids (I believe that they can be used for the same purposes as the Cep's).

Secondly: Mira variables haven't got _anything_ to do with Cepheids. Miras are red giants pulsating with semiregular periods. Cepheids have _very_ regular periods - in fact I'm doing the Extended Essay in Cepheids, so I'll soon see for myself just how regular their periods are. The Miras have also got way too long periods to be considered among the Cepheids.

The three types of variable stars that can be associated with Cepheids are the classical cepheids (Delta Cephei variables), RR Lyrae variables and W Virginis variables (a good source for such information would be Patrick Moore: "The New Atlas Of The Universe").

F.2.2 see notes in F.1.1 and F.2.1

F.2.3

A variable star is any star whose luminosity is not constant with time. It is assumed that red giants turn into pulsating variable stars before they finally die. Red variables?????????????????????? Novae/Supernovae????????????

F.2.4

A binary star is formed when two stars revolve around a common center of gravity. Masses can be determined by angular size, and period of orbits.

A visual binary can be seen through a telescope, where two separate stars can be seen.

A spectroscopic binary can not be resolved by a telescope, only by its spectrum. There’s a varying Doppler shift in the spectral lines as it approaches and recedes from Earth

An eclipsing binary is situated so that one star passes in front of its companion and cuts off light at regular intervals, changing in brightness regularly.

The Expanding Universe

F.3.1

The formula is l ’ = l Ö ((1+v/c)/(1-v/c)) , where l ’ is the wavelength measured on Earth, l the wavelength in the source’s reference frame (on star), v is the speed of the source and c the speed of light (radiation).

If the source moves towards us, the frequency is higher and wavelength longer, moving away the opposite.

F.3.2

Redshift occurs when the source is moving away from us, since the wavelength of the light emitted appears longer to us, shifting towards the red end of the visible spectrum.

F.3.3

Hubble’s law: , where is the speed, is the Hubble parameter, and is the distance. It describes Hubble’s observation, that most lines in the spectra of other galaxies were redshifted, and the amount of shift was approximately proportional to the distance of the galaxy from us. So the velocity is proportional to the distance. H is approx. 50km/s/Mpc. It does not work well for nearby galaxies.

F.3.4

The fact that with increasing distance the velocity increases, suggests that there was a huge explosion ‘some’ years ago that accelerated the particles and that the universe is expanding.

F.3.5

The U.S. physicists A. Penzias and R. Wilson detected in 1956 microwave radiation coming equally from all directions in the sky, day and night. This radiation is like the one radiated by a black body at a temperature of 3 Kelvin, thereof the name 3K radiation.

This discovery supports the theory of Big Bang, where strong shortwave radiation was supposed to be sent out. The radiation spread filling the expanding universe uniformly. With time it cooled, to the now observed temperature of 3K, and strike Earth as a microwave.

The Big Bang model of the creation of the universe

F.4.1

Olber’s paradox: If the universe is infinite, how come then that we observe a black night sky? Shouldn’t such a universe provide an infinite number of stars so that wherever we looked it would be bright?

F.4.2

One solution could be that the universe is not infinitely old, so light from distant galaxies that are travelling very fast with respect to Earth, has yet not reached us. This contradicts Newton’s assumption of a static infinite universe, since in this case the universe is evidently expanding. The faster stars travel the greater is the redshift, so we could perhaps not even se the electromagnetic waves the most distant stars emit, since they don’t appear in the visible spectrum.

F.4.3

The matter and radiation of our present time was initially all packed together into and extremely hot and dense fireball, that exploded giving rise to the Big Bang. Within seconds matter was accelerated through 3 dimensions, expanding and developing very rapidly. Time became a measure of the rate of that expansion, the necessary 4th dimension.

F.4.4

Curvature of space (also called four-dimensional space-time): According to Einstein’s general theory of relativity light is also affected by gravity. This means that light can be bent ‘around’ planets, and follow a curved path. Light must travel through the shortest distance available between two points, meaning that the curved path is the shortest distance, hence space itself is curved.

Open universe - the universe will continue to expand forever because the curvature of the universe is negative.

Flat universe - the curvature is zero, the universe is infinite

Closed universe - the curvature is positive, to the universe is finite.

This can all be showed through non-Euclidean mathematics, where the sum of angles in a triangle either subtends of exceeds 180° .

F.4.5

Antimatter is the opposite of matter, with nucleus of antiprotons and orbiting positrons around it.

The Inflationary Epoch is the time after the Big Bang when two of the four forces of nature (gravity and strong nuclear forces) subsequently singled out, and the universe expanded very rapidly due to energy release.

As the universe gradually cooled (still talking about fractions of seconds) there was an excess production of matter over antimatter as they annihilated, when temperature dropped to the point where they could no longer be created

This excess forms electrons, neutrinos and hadrons (protons and neutrons). 3 minutes after the Big Bang, the hadrons start to form atomic nuclei such as deuterium and helium.

After 10 000 years at a temp. of 105 K, atoms are formed.

300 000 years after the explosion electrons began to bind to the nuclei, and the dense ‘fog’ of particles cleared. Gas clouds formed and due to the pull of gravity they contracted into stars. The contraction also provides energy for nuclear fusion, so that the stars ‘burn’. There two theories on how galaxies and clusters of galaxies formed, one stating that one was created before the other, the other the inverse, we can only say that they exist.

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