Topic 2 Spectral Universe Flashcards
Electromagnetic waves definition
Wave like disturbances to electric and magnetic fields. The wave length or frequency of waves can he used to identify which category of the electromagnetic spectrum a wave belongs to.
Wave length definition
The distance from one peak to the next peak of a wave, represented by lambda (λ)
Frequency definition
The number of wave lengths to pass a fixed point in one second, represented by (f).
Wave quantities equation
c = fλ
Where c is speed, f is frequency and λ is wavelength.
Photon model of light equation
ε = hf
Where ‘ε’ is the energy of the photon, ‘f’ is the frequency and h is the Planck’s constant 6.63x10^-34 J s (4.14x10^-15 eV s).
What wavelengths of light are absorbed by the atmosphere?
Gamma rays to ultra violet undergo photoelectric absorption by nitrogen or oxygen atoms, removing electrons and creating the earths ionosphere of charged particles.
Ultraviolet light also breaks up molecular oxygen to form ozone, and is then absorbed by ozone.
Many bands of infrared light are absorbed by water, CO2 and other molecules to form the green house effect.
Low frequency radio waves are absorbed or reflected by the ionosphere.
Black body sources definition
Black body sources are objects that produce a continuous spectra of electromagnetic radiation with a characteristic shape called a Planck curve.
Wien’s law
Wien’s law describes the relationship between temperature in kelvin (T), and peak wavelength in meters (λpeak).
(λpeak / m) = (2.90x10^-3) / (T / K)
Photosphere definition
The relatively transparent outer layers of a star from which nearly all the radiation we observe is omitted.
The effective surface temperature is the temperature of that region of a stars photosphere from which a majority of its light is emitted.
Stefan - Boltzmann law (equation)
This is the relationship between power, l, radiated by a unit area of a black body source and its temperature, T.
l = σΤ^4
Where σ is the Stephan Boltzmann constant, 5.67x10^-8 W m^-2 K^-4
Calculate the total power emitted by the surface of a black body.
Submit the equation for the surface area of a sphere into the stephan- Boltzmann law.
L =4πR^2σT^4
Total power is equivalent to luminosity, so the temperature and radius can be used to calculate luminosity. These three measures are known as LTR relationship.
Normalised LTR expressions
Normalised expressions allow us to compare stars using convenient solar units.
L / L sol = (R / Rsol)^2 x (T / Tsol)^4
Or
R / Rsol = sqrt(L / Lsol) x (Tsol / T)^2
Synchrotron radiation definition
This is electromagnetic radiation with a continuous non-thermal spectrum that is released wile electrically charged particles, usually electrons, pass through magnetic fields at near the speed of light.
The electrons experience sideways force causing them to move helically around magnetic field lines.
Inverse Compton scattering definition
This is a continuous non-thermal spectrum that is emitted by electrons traveling near the speed of light (relativistic) collide and scatter photons. This removes energy from the electron and energises the photon, which is equivalent to the emission of radiation.
What effect does interstellar dust have on electromagnet waves?
Dust is around 10^-6 to 10^-7 and will scatter light with comparable wavelengths (visible and ultraviolet). The spectrum will appear reddened.
Some photons may be absorbed by the dust and heat it up, causing the dust to emit infrared.
Broadband spectrum definition
A spectrum covering a wide range of wavelengths or frequencies which represent the energy distribution of a source. Doesn’t typically show absorption lines.
Spectral energy distributions
A form of broadbrand spectrum of an astronomical source that shows quantity lambda F lambda against frequency.it shows contributions to total luminosity emitted in different wave lengths.
What is an absorption spectrum?
This is a spectrum in which absorption lines are prominent (the main spectrum of light that passes directly through gas cloud).
What is an emission spectrum.
An emission spectrum shows the light that is emitted from a gas cloud indirectly (the photons that were scattered by a gas cloud).
What is the chromosphere?
This is the outer layer of a star, a shell of thin gas surrounding the photosphere.
What is the ground state?
The ground state is the lowest energy state of an atom, molecule or other quantum system.
How to calculate the energy associated with the excited state of hydrogen. (Equation)
Use the formula
En = (-13.6 eV) / n^2
Where n is the energy level ( 2,3,4, etc.)
-13.6 eV is the ground state of hydrogen
Equation for frequency of exciting hydrogen.
A hydrogen atom has an initial amount of energy, Ei. The hydrogen atom can absorb a photon with exactly the right amount of energy, ε, to allow the hydrogen to make the transition to a higher energy state where Ef is the final energy. The frequency of light associated with this transition can be given by:
f = (Ef - Ei) / h
What is ionisation energy?
This is the maximum amount of energy an atom can absorb without being split apart.
What do absorption lines tell us about a stars temperature?
To measure a stars temperature from absorption lines you can look at the size of the absorption lines and at what wavelength they occur. An absorption lines strength is calculated via the peaks area, meaning a long narrow peak and short wide peak can have the same strength.
What do absorption lines tell us about a stars luminosity?
The width of on absorption line can indicate a stars luminosity. More luminous stars have nationier narrower absorption lines than less luminous stars of the same temperature. A smaller star has a more dense atmosphere, so more light is absorbed meaning its less luminous.
What is the Harvard spectral classification scheme?
A classification of stars based on the strength of there absorption lines. This categorises them based on their photospheric temperatures in order of depending temperature from O, B, A, F, G, K and M.
What is the morgan-keenan spectral classification system?
This supplement the Harvard system with luminosity classes ranging from I to V or in extreme cases VII.
I can be split to Ia and lb.
What is disassociation energy?
The energy required for an atom to become unbound from a molecule.
What is disassociation energy?
The energy required for an atom to become unbound from a molecule.
What is a vibrational transition?
These are the changes associated with different vibrational energies of a molecule, which can be represented by the stretching and compressing of the bond between the atoms.
What are rotational transitions?
These are the transitions associated with different rotational speeds of a molecule (how fast a molecule rotates about some axis.
Diatomic molecules with identical atoms have very weak rotational lines.
What is quantum mechanical spin?
This can be thought of as the subatomic particles rotation about its axis.
In hydrogen the the lowest energy form of spin is called anti parallel which is where to rotational axis of the proton is up and the axis of the electron is down.
Collisions with other atoms can increase the energy level, causing the electrons rotational axis to flip, so the electrons and protons axis become parallel.
What is the spin flip transition?
This is when the rotational axis of a sub atomic particle flips 180°.
Related to the 21cm (0.211m) absorption line of HI with an energy of 5.87x10^-6 eV.
What is an absorption line?
When continuum light passes through a gas cloud, atoms in the gas absorbs photons with the amount of energy required for the electronic transition to a higher energy level.
f = (Ef - Ei) / h
Where Ei and Ef are the initial and final energy levels
What are emission lines?
Those are formed when atoms in an excited state undergo spontaneous electronic transition to a lower energy level. Emitting a photon in a random direction with frequency given by
f = (Ei - Ef) / h
Where Ei and Ef are the initial and final energy levels
What is a absorption spectrum?
A spectrum where absorption lines are prominent.
What is an emission spectrum?
A spectrum where emission lines are prominent.
What is the ground state of an electron?
It is the lowest energy level an atom or molecule can be.
What is equivalent width?
The measure of strength of a spectral line. If a spectrum is platted as spectral flux density against wavelength it is the width of an area bounded by the spectral flux density of the continuum that was the same area as that between the actual spectral flux line and the continuum.
What is the 21 cm line?
A spectral feature produced by electromagnetic radiation with a wavelength of 21cm, in the radio part of the spectrum, which is emitted or absorbed by a hydrogen atom when it undergoes spin- flip Transition.
What is the Lyman series?
Electronic transitions in hydrogen that involves a change to/from the n=1 state. Associated with spectral lines in the ultraviolet.
What is the balmer series?
Electronic transitions in hydrogen that involves a change to/from the n=2 state. Associated with spectral lines in the visible spectrum.
What is the Paschen series
Electronic transitions in hydrogen that involves a change to/from the n=3 state. Associated with spectral lines in the infrared.
What is the Brackett series?
Electronic transitions in hydrogen that involves a change to/from the n=4 state. Associated with spectral lines in the infrared.
What is radial velocity?
It is the component of an objects velocity that is in the direction of coming towards in away from you.
What is the Doppler effect?
It is the effect whereby wavelengths are shifted to longer or shorter values as a result of relative motion between a source and an observer.
The perceived frequency is higher if the source is moving towards an observer, lower frequency if the source is moving away.
Equation for relating observed and emitted wavelengths to radial velocity?
νr = (c(λobs - λem)) / λem
Where νr is radial velocity, c is the speed of light and λ is wavelength of observed and emitted.
Space velocity equation
v = sqrt(vt^2 + vr^2)
Where v is space velocity, vt is transverse velocity and vr is radial velocity.
What is space velocity?
This is an objects overall motion through space with respect to us. Its components are radial velocity and transverse velocity.
Redshift for galaxies equation.
z = (λobs / λem) - 1
Where z is the redshift of a galaxy, λ is for the wavelength observed and emitted.
What is cosmological redshifts?
Cosmological redshifts are produced by the expansion of the universe itself as opposed to the Doppler shifts which are caused by objects moving through space.
What is the barrycentre?
This is the centre of mass between a orbiting objects (binary system).
What is an orbital period?
The length of time taken for an orbiting body of binary system to complete one orbit.
What is the degree of eccentricity (non circlitarity, e)?
A numerical measure of the extent to which an elipse/eliptical orbit differs from a circle.
Keplers third law
Porb^2 = (4π^2 a^3) / G(M + m)
Where G is the universal gravity constant 6.67x10^-11 N m^2 kg^-2
a is half the length of the longer dimension of an ellipse
And M and m is the masses of the larger and smaller objects respectively
Keplers third law (normalised)
(Porb / y)^2 = (a / AU)^3 / ((M / M(sun)) + (m / M(sun))
Where a is half the semi major axis in AU
M and m are the bodies masses in solar masses
Calculating semi major axis from radial velocity amplitudes for a stars
VrM = 2πdM / Porb
Vrm = 2πdm / Porb
M / m = dm / dM
What is keplerian rotation?
This is a pattern of rotation arising when the mass of a gravitating system is dominated by a single body. In the case of our solar system, the single body would be the sun. This would not apply in the case of a disc of a galaxy.
Equation for keplerian rotation
ν = sqrt((GM) / r)
Where G is newtons gravitational constant (6.67x10^-11), M is the mass of the central large body and r is the radius the object is from the sun.
What is rigid body rotation?
A pattern of rotation where all parts of the rotational system have the same period. A plate for example.
Rigid body rotation equation.
ν = 2πr / P
Where P is the period of rotation.
V is speed
What is an extended mass system?
A system containing a large number of objects but no central mass. The generalised keplerian rotation equation can be used.
Generalised keplerian equation
ν(r) = sqrt((GM(r)) / r)
Where ν(r) is speed at r and M(r) is mass enclosed within r.
What is the equation for velocity dispersion?
Δν ~ sqrt(2kT / m)
Where k is the Boltzmann constant (1.38x10^-23)
What is bulk motion?
The movement of significant volumes of gas due to rotation, inflow or outflow relative to a centre or large scale turbulence.
Why may a star show emission and absorption lines for the same atom?
This is because the atom would be present in both the expanding gas shell (emission) and near the surface of the star (absorption).
Velocity dispersion and Doppler broadening equation.
Δλ / λ = Δν / c
Where c is the speed of light
What is the Tully - fisher relation?
The relationship between the luminosity of a spiral galaxy and its maximum rotational speed, measured from the width of its 21cm H emission line.
This relationship can be used to determine the luminosities and hence distances of spiral galaxies.
L ~ νmax^4
What is the faber - Jackson relation?
For elliptical galaxies the velocity dispersion can be used to characterise the motion of stars within the galaxy (random rather than rotational).
The luminosity and velocity dispersion is related by
L ~ Δv^4
What are global oscillations?
This is where parts of the surface of a star rise and fall which can be measured by photometric and spectroscopic observations.
Distance of 2 bodies to their centre of mass equation
M / m = dm / dM
Where M is the mass of the more massive body, and m is the mass of the smaller body.
What is pressure broadening?
In a very dense gas the proximity of so many atoms to one another affects the energy levels in all of them this shows-up as a broadening of spectral lines.
Now does a stars size affect its absorption spectra?
Larger stars have a decrease in the width of their absorption lines as their atmosphere is less dense so less of the rotation radiation is absorbed.
