Flashcards in Classification of Stars (Unit 5) Deck (47):
the distance to an object subtending 1 second of arc to the radius of the Earth’s orbit.
(1 second of arc (arcsecond) = 1/3600 of a degree).
Definition light year
Distance light travels in a vacuum in 1 year.
(number of seconds in 1 year = 365 x 24 x 60 x 60 = 3.15x107s
Units light year
Definition astronomical unit
The mean distance between the Earth and the Sun
Units astronomical unit
Definition of absolute magnitude
The brightness an object would appear if it was 10 parsecs from the Earth.
Definition of apparent magnitude
The brightness of an object as seen from Earth
What is black body radiation?
The electromagnetic radiation emitted by an object because of its temperature
General shape of black body curves
Definition of lambda(max)
The wavelength at which maximum emission occurs.
Assumption about a star to use Wein’s displacement law (lambda max)
Star is acting as a black body.
Effect of atmosphere on estimate of a star’s temperature
• Ozone in atmosphere preferentially absorbs UV part of spectrum
• This increases observed lambda max (longer wavelength)
• Resulting in an underestimate of the star’s temperature
Definition of intensity
energy arriving every second on a 1 m2 surface orientated perpendicular to the direction of radiation
Units of intensity
Relation between intensity and apparent magnitude
Each change in magnitude of 1 (on the magnitude scale) corresponds to a change in intensity of 2.5 (actually 2.51).
So a star which has a magnitude that is 5 times brighter than another star, has an intensity which is 100 times greater (2.55 = 100).
Inverse square law and assumptions in its application
the intensity I at a distance r from a star with a total power output P, is given by
Intensity I = P/(4 x pi x r2)
Inverse square law assumes that:
• no light is scattered or absorbed between source and observer
• the source can be treated as a point
Spectral class information
How are Hydrogen Balmer lines produced?
• The atmosphere of the star has hydrogen atoms with electrons in the n=2 state
• Light from the star passes through the atmosphere of the star
• Electrons (at the n=2 level) are excited into higher energy states
• They can only absorb certain amounts of energy
• These certain energies are related to specific frequencies (E=hf)
• The electrons then de-excite
• The electrons may de-excite through different energy level changes
• When the electrons de-excite the light is radiated in all directions
• This means that the intensity of the light at particular frequencies is reduced, resulting in absorption lines
Hertzsprung Russell (HR) diagram
Spectral class and magnitude of our sun
G5 (it’s like a, like a, like a G6 – but not a G6)
Stellar evolution of our sun
• Our sun is currently a main sequence star (G5)
• As it uses up Hydrogen fuel and starts fusing Helium its core gets hotter and expands - it becomes a giant star.
• As it expands, the outer surface of Sun will cool
• Outer parts of sun are pushed away (by continued Helium fusion) to form planetary nebula.
• Leaving extremely hot but small core - it becomes a white dwarf.
• Fusion has finished and the white dwarf cools eventually to a brown dwarf.
Neutron star composition and properties
Neutron stars consist of neutrons and have the density of nuclear matter
Properties of a neutron star
• very dense
• powerful radio source
• spinning (usually very quickly)
• strong magnetic field
Definition of a supernova
Where the absolute magnitude of a star increases rapidly and enormously due to it exploding
Light curve of a type 1a supernova
Definition of a black hole
an object whose escape velocity is greater than the speed of light
Properties of a black hole
• Large gravitational field strength
• Nothing, including light, can escape
Definition event horizon
The boundary (or surface) where the escape velocity equals the speed of light
Schwarzschild radius, Rs, on formula sheet is the radius of the event horizon
What is at the centre of galaxies?
Super massive black holes
How are type 1a supernovae used as standard candles to determine distances
• All type 1a supernovae have the same peak absolute magnitude (M).
• Apparent magnitude, m, (of supernovae) can be measured
• Distance to galaxy, d, (supernova) can be calculated using m-M=5log(d/10).
Controversy surrounding accelerating universe
• The absolute magnitude of type 1a supernova is known, so they can be used as standard candles
• Using m-M=5log(d/10) the distance to the galaxy can be calculated
• Supernovae are very bright so they can be seen in very distant galaxies
• It has taken billions of years for the light from the most distant galaxies to reach Earth; these supernovae were therefore produced when the Universe was young
• Measurement of red shift (to measure velocity) and use of Hubble’s Law shows that these supernovae are fainter than expected
• This indicates that the Universe is expanding faster now than when the supernovae exploded as the light has had to travel further to reach us than expected by a constant rate of expansion.
What is causing accelerating expansion of universe?
Binary star system
Two stars orbiting a common centre of mass
Eclipsing binary star system
Binary star system whose orbit lies in same plane as the line of sight from the Earth
(so one star passes in front of the other as observed from Earth)
Light curve from binary star system
Explain light curve from binary star system
• Brightest magnitude (3.30) occurs when both stars can be seen.
• First (smaller) dip (3.45) occurs when brighter star is in front of dimmer star.
• Second (large) dip (3.60) occurs when dimmer star is in front of brighter star.
Definition of Doppler effect
Change in wavelength (of em radiation) due to relative velocity between observer and source
How can Doppler effect be used to calculate relative velocity?
• From spectrum obtain change in wavelength, lambda, for a spectral line
• Using known wavelength measured on Earth, lambda,
• Calculate v from
lambda/lambda = v/c
Assumption for Doppler equation
Definition of red shift
Increase in wavelength (of em radiation) due to relative recessive velocity between observer and source
Interpretation of red shift in terms of expanding universe
Hubble observed that:
• (virtually) all galaxies are red shifted – means they are moving away from us (and each other)
• the more distant galaxies have greater red shifts – meaning more distant galaxies are travelling faster
• Hubble discovered that the (recessional) velocity of a galaxy was directly proportional to its distance.
Estimation of age of universe
• If in time, t, a galaxy has moved a distance, d, at velocity v, then
• as , v = d/t, t = d/v
• But from Hubble’s Law, v = Hd
• Time (age of Universe) = d/v = d/Hd = 1/H
Assumption for estimating age of Universe from Hubble’s Law
Hubble’s constant, H, has been constant since the Big Bang.
Features of Big Bang
• Expanding universe
• from an extremely hot and dense single point
• Suggest about 15 billion years ago (from Hubble’s constant)
• “explosion” – creation of space/matter and time
Evidence for Big Bang
Redshift of distant galaxies
• In keeping with Hubble’s law (see Hubble observations above).
• Hubble’s law can be used to age universe.
Cosmological microwave background radiation
• If Universe is about 15 billion years old and has been expanding and cooling since Big Bang.
• would estimate temperature of “empty space” to be a few Kelvin after this time.
• black body curve of “empty space” corresponds to temperature of about 2.7 Kelvin (appropriate max)
• consistent with temperature universe would have cooled to after 15 billion years
Relative abundance of Helium and Hydrogen
• short time after Big Bang universe hot enough to fuse matter
• Hydrogen fused to form Helium
• Universe continued to expand, and cool
• making fusion of helium into heavier elements impossible
• creating predicted ratio of 3:1 (Hydrogen to Helium)
• consistent with observation of matter in Universe.