II Light http://sgoodwin.staff.shef.ac.uk/phy111.html
0. Light Light is the main tool we have in astronomy. We detect light from distant objects and can determine the temperature, density, composition, kinematics etc. of the body that emitted that light. If the light passes through any intervening material (e.g. gas and dust) it can tell us about the properties of that material as well.
0. Light Light is shorthand for electromagnetic radiation and it is both a wave and a particle. Light can be thought of as a wave with a particular frequency or wavelength. Light can be thought of as a particle a photon with a particular energy that corresponds to a particular frequency/wavelength.
0. Light Light can be described by its wavelength (λ) or frequency (f), and speed (c=3x10 8 m s -1 ) λf = c And the energy of a photon is E = hf = hc/λ (where h is Planck s constant = 6.6x10-34 J s -1 ).
1. Blackbodies Temperature is a measure of the thermal energy (random kinetic energy) of a system. Hot bodies contain more thermal energy so compared to a cold body we would expect them to a) Give-out more energy (higher luminosity) b) Give-out higher-energy light (shorter wavelengths) And this is what they do emitting as a blackbody.
1. Blackbodies These are the blackbody curves of objects at T=3500K to 5500K (y-axis is energy per unit wavelength)
1. Blackbodies The luminosity (L energy emitted per unit time) depends on the temperature (T) and the surface area (for a sphere 4πr 2 ): L = 4πr 2 σ SB T 4 Where σ SB is the Steffan-Boltzmann constant=5.67x10-8 W m -2 K -4. Hotter objects give out more energy, and larger objects give out more energy. So a small, hot star can be as luminous as a large, cool star.
1. Blackbodies The peak wavelength of the light emitted by a blackbody is given by Wein s Law: λ max = 0.29 cm / T Where T is in K. So hotter bodies have peaks at shorter wavelengths.
1. Blackbodies The Sun has T=5800K, so λ max ~500nm the middle of the visible (and why it is the visible to our eyes). The Earth has T~300K, so λ max ~10µm everything in this room is emitting radiation at about 10µm. The coldest gas in the Universe is at about 10K, so λ max ~100µm. Note: you might see wavelengths given in Ångströms (units of 10-10 m), so 1nm=10Å.
2. Atoms and lines An atom has a nucleus of protons and neutrons with electrons orbiting the nucleus (the Bohr model). The electrons have specific energy levels they can inhabit, and they cannot have energies in-between. If an atom absorbs a photon of exactly the right energy it can cause an electron to jump to a higher energy level. Electrons in higher levels can fall to a lower level emitting a photon with the energy difference.
2. Atoms and lines The energy differences between levels change from element to element (or molecule). So particular energy differences are a finger print of the particular atom that caused them. Atoms can gain energy by a) Absorbing a photon of exactly the right energy. b) Being hit by another atom and extracting energy from the impact. Once the electron is excited it will want to de-excite by emitting a photon in a random direction.
2. Atoms and lines The most common element is hydrogen. Energy levels are always numbered from n=1 (ground state) to n=2,3 Transitions to-and-from n=1 have high energy (UV) and are Lyman series lines. Tranisitions to-and-from n=2 are Balmer series lines in the visible. And for n=3 they are the Paschen series in the IR.
2. Ionisation If you give an electron enough energy you can unbind it from its atom ionisation. The bigger the atom, generally the easier this is to do. So as temperature increases first metals like iron become more-and-more ionised, then atoms like carbon and oxygen, then hydrogen, and finally helium. Astronomers tend to use roman numerals to denote ionisation levels: so FeVI is 5x ionised Fe. HI is neutral hydrogen, HII is singly (the most it can be) ionised H.
2. Atoms and lines Electrons do not have to de-excite to the ground state at once. An electron could be excited from n=1 to n=4 by a collision, and then dexcite from n=4 to n=2 (emitting a Balmer series photon), and then from n=2 to n=1 (Lyman series).
3. `Types of light Solid bodies tend to emit as blackbodies giving out all wavelengths of light according to their BB curve. But if that light passes through gas, atoms and molecules in the gas can absorb or emit various lines. Almost all of our understanding of astronomy comes from analysing the light we see, looking at BB curves and lines.
3. Blackbodies If a body is at high density light will scatter internally and become thermalised and we will see a continuum (light of all wavelengths/energies). The distribution of energies will be a blackbody spectrum that depends on the temperature (to the power 4) of the object. [Technically this is cavity emission, but this explanation will do for now.]
3. Emission lines A low-density gas will excite atoms inside it by collisions. The atoms will then emit light at particular wavelengths so we see a few bright emission lines. Which lines depend on the temperature and composition of the gas.
3. Absorption lines A low-density gas with a background source will absorb light of particular energies and then re-emit it randomly. So we see less light at particular wavelengths absorption lines. Which lines depend on the temperature and composition of the gas.
4. Light from the Sun Light from the Sun as seen from the Earth is roughly a blackbody with T~5800K, but with absorption lines due to (a) the Sun s atmosphere, and (b) the Earth s atmosphere.
Summary Dense bodies will emit blackbody radiation. The total luminosity depends on r 2 and T 4. The peak wavelength depends on T. Atoms have quantised electron energy levels. Lowdensity gas can absorb lines of background light, or emit lines from themselves. The energy of those lines tells us the atoms that are present (as well as their temperature and density). So the light we see can be a mixture of any or all of three sources: blackbody (continuum), emission lines, absorption lines.
Key points Know that f, λ, and E for light are equivalent. Know the relationships between L, r, T and λ max for a blackbody (the Steffan-Boltzmann law, and Wein s law). Be able to describe if and why something will show a blackbody continuum, emission line, or absorption line spectrum.
Quickies The luminosity of the Sun is 7.0x10 26 W, and its surface temperature is 5800K. What is the radius of the Sun? What type of spectrum would the following sources show: a) Sodium street light? b) Tungsten filament lightbulb? c) A star? d) A neon sign? e) An energy-saving lightbulb? (Not obvious.) What would the luminosity of a 10000km diameter star of temperature 10 5 K be? What strikes you as odd about this? (We ll see what it is later.) Star A and Star B have the same temperature, but star B is 25 times more luminous. How much bigger is star B than star A? A cold molecular cloud is observed. What type of spectrum will it show and why?
Notes The reason for most of the behavior of light and atoms is quantum. The quantum world is very strange, but at very small scales things like electrons and photons show both wave- and particle-like behavior. Experiments show they act like this and quantum mechanics seems to be an extremely good description of the microscopic world. Electrons don t really orbit the nucelus, rather there is a messy and undefined electron cloud, but this orbital picture is OK for understanding the energy levels. Understanding blackbodies was impossible before quantum mechanics (and it was a problem wrestled-with by many scientists). Physicists and chemists will get to do quantum mechanics in great detail from second year, but there is a fairly serious level of maths needed to solve the equations.
Notes Rather annoyingly H 2 (molecular hydrogen) and HII (ionised hydrogen) and both said out-loud the same way aitch-two. This can get confusing in molecular cloud which have a massive star because they contain both types of aitch-two. Depending on the part of the electromagnetic spectrum being observed astronomers work in frequency, wavelength or energy. In the X- and γ-ray energy is used (kev or MeV usually where ev is an electronvolt a useful measure of energy in particle physics). In the visible and IR people tend to work in wavelength (nm, micron or sub-mm for example). In the radio people tend to talk about frequency (MHz of GHz for example).