Classification of Stars Flashcards
Define the luminosity of a star
The luminosity of a star is the total amount of electromagnetic radiation it emits each second measured in watts
What is the Sun’s luminosity and how does this compare to that of the most luminous stars?
- The Sun’s luminosity is about 4*10^26W
- The most luminous stars have a luminosity about a million times that of the sun
Define the intensity (I) of a star
The intensity of a star is the energy each second from the star hitting 1m^2 perpendicular to the radiation on earth. It is measured in Wm^-2 (Watts per square metre)
What is apparent magnitude (m)?
Apparent magnitude (m) is based on how bright things appear from earth
What does the brightness of a star in the night sky depend on?
The brightness of a star in the night sky depends on two things:
- Its luminosity
- The distance of the star from us
Therefore the brightest stars will either be close to us or have a high luminosity
Describe the system invented by Hipparchus to measure the brightness of stars
An ancient Greek called Hipparchus invented a system where the very brightest starts were given an apparent magnitude of 1 and the dimmest visible stars an apparent magnitude of 6 with the other levels catering for the stars in between
How was Hipparchus’s original scale redefined using a logarithmic scale?
- A magnitude 1 star has an intensity 100 times greater than a magnitude 6 star
- This means a difference of one magnitude corresponds to a difference in intensity of 100^1/5 times
- So a magnitude 1 star is about 2.51 times brighter than a magnitude 2 star
On the latest apparent magnitude scale, the lower the magnitude…
the brighter the star
On the latest apparent magnitude scale, the brightest objects in the sky have a…
negative apparent magnitude
How can you calculate the brightness/intensity ratio between two stars?
- I2/I1 ≈ 2.51^m1-m2
- I1 is the intensity of star 1
- I2 is the intensity of star 2
- m1 is the apparent magnitude of star 1
- m2 is the apparent magnitude of star 2
What is parralax?
Parallax is the apparent change in position
What is parallax measured in terms of?
Parallax is measured in terms of the angle of parallax. The greater the angle, the nearer the object is to you
How can the distance to nearby stars be measured?
The distance to nearby stars can be measured in parsecs
How can parsecs be used to measure the distance to nearby stars?
The distance to nearby stars can be calculated by observing how they move relative to very distant stars when the Earth is in different parts of its orbit. This gives a unit of distance called a parsec (pc)
When is a star exactly one parsec away from the Earth?
A star is exactly one parsec (pc) away from Earth if the angle of parallax (θ) is: θ = 1 arcsecond = 1/3600 degrees
How many arc seconds is 1 second?
1 second = 60 arc seconds
How do you convert between parsecs and metres?
1 parsec = 3.08*10^16m
Define a parsec
One parsec is defined as the distance to a point in space where the radius of the Earth’s orbit of the Sun subtends an angle of 1 arcsecond
What is absolute magnitude based (M) on?
Absolute magnitude (M) is based only on the luminosity of the star. It does not depend on its distance from Earth
Define absolute magnitude
The absolute magnitude of a star or galaxy is defined as what its apparent magnitude would be if it were 10 parsecs away from Earth
State the formula showing the relationship between m and M
- m-M = 5log(d/10)
- d is the distance in parsecs
- m is the apparent magnitude
- M is the absolute magnitude
If you know the absolute magnitude of a star, how can you calculate its distance from earth?
By using the formula m-M = 5log(d/10)
What is a standard candle?
- Standard candles are objects in the sky whose absolute magnitude are known
- You can calculate the luminosity of standard candles directly
How can distances in the solar system be measured?
Distances in the solar system can be measured in Astronomical Units (AU)
Define an Astronomical Unit
One astronomical unit (AU) is defined as the mean distance between the Earth and the Sun
When was the size of the astronomical unit measured?
The size of the astronomical unit wasn’t known until 1769 when it was carefully measured during a transit of Venus
What is another measure of distance apart from parsecs and astronomical units?
Light years (ly)
Define a light year
The distance that electromagnetic waves travel through a vacuum in one year is called a light-year (ly)
How do we see the light from a star in relation to its distance?
If we see the light from a star that is 10 light-years away then we are actually seeing it as it was 10 years ago. The further away the object is the further back in time we are actually seeing it
What is 1 light year in metres and parsecs?
- 1 ly = 9.46*10^15m
- 1pc = 3.26 ly
Why do objects emit electromagnetic radiation?
Objects emit electromagnetic radiation due to their temperature. At everyday temperatures this radiation lies mostly in the infrared part of the spectrum
How do pure black surfaces emit radiation?
Pure black surfaces emit radiation strongly and in a well-defined way. It is known as black body radiation
Define a black body
A black body is defined as a body that absorbs all wavelengths of electromagnetic radiation and can emit all wavelengths of electromagnetic radiation
What does the graph of intensity against wavelength for black body radiation vary with?
The graph of intensity against wavelength for black body radiation varies with temperature
What can we approximate stars as behaving as?
To a reasonably good approximation stars behave as black bodies and their black body radiation produces their continuous spectrum
Sketch a general graph of intensity against wavelength for stars
See page 180 in the revision guide
- The curve is steeper on the shorter wavelength side and tends to zero on the right hand side
What is the peak wavelength (λmax) ?
For each temperature there is a peak in the black body curve at a wavelength called the peak wavelength (λmax)
State the equation given by Wien’s law
- λmaxT = constant = 2.9*10^-3 mK
- T is the temperature in kelvin
- mK is a metre-kelvin
What does the power output of a star depend on?
The power output of a star depends on its temperature and surface area
What is the power output of a star?
The power output of a star (its luminosity) is the total energy it emits per second and is related to the temperature of the star and its surface area. It might be shown as P or L
State Stefan’s law
The power output of a star is proportional to the fourth power of the star’s temperature and is directly proportional to the surface area of the star
State the equation given by Stefan’s law
- P = 𝜎AT^4
- P is the power output of the star in W
- A is the surface area of the star in m^2
- T is the star’s surface temperature in K
- 𝜎 is Stefan’s constant
What is the intensity of radiation?
The intensity is the power of radiation per square metre
When can the equation used to calculate the intensity of radiation from a star be used?
If the radiation/energy has been emitted from a point or a sphere (like a star) then it obeys the inverse square law equation
State the equation used to calculate the intensity of radiation from a star
- I = P/4πd^2
- P is the power output of the star in W
- d is the distance from the star in m
Is it true that in some questions you may have to use all 3 of the wien’s, stefan’s and intensity of radiation equations to solve certain questions?
Yes
What are the problems preventing us from getting accurate measurements of stars properties from Wien’s displacement law, Stefan’s law and the inverse square law?
1- The atmosphere only lets through certain wavelengths of electromagnetic radiation - visible light, most radio waves, very near infrared and a bit of UV. Its opaque to the rest
2- Dust and man-made light pollution are problems. Observatories are placed at high altitudes away from cities and in low humidity climates to minimise the problem. The best solution is to send up satellites that can take measurements above the atmosphere
3- The measuring devices that astronomers use aren’t perfect since their sensitivity depends on the wavelength
4- For example, glass absorbs UV light but is transparent to visible light so any instruments that use glass affect UV reading straight off
What is the Balmer series?
The Balmer series is a set of lines in the spectrum of hydrogen
Why do lines in emission and absorption spectra occur?
The lines in emission and absorption spectra occur because electrons in an atom can only exist at certain well-defined energy levels
In atomic hydrogen, which energy level is the electron usually in?
In atomic hydrogen the electron is usually in the ground state but there are lots of energy levels that the electron could exist in if it was given more energy
What causes the Balmer series?
The wavelengths corresponding to the visible bit of hydrogen’s spectrum are caused by electrons moving from higher energy levels to the first excitation level (n=2). This leads to a series of lines called the Balmer series
How do spectral lines show the temperature of a star?
The strengths of the spectral lines show the temperature of a star
What needs to happen for a hydrogen absorption line to occur in the visible part of a star’s spectrum?
1- For a hydrogen absorption line to occur in the visible part of a star’s spectrum, electrons in the hydrogen atoms already need to be in the n=2 state
2- This happens at high temperatures where collisions between the atoms give the electrons extra energy
3- If the temperature is too high though the majority of the electrons will reach the n=3 level or above instead which means there won’t be so many Balmer transitions
4- So the intensity of the Balmer lines depends on the temperature of the star
How do astronomers get around the fact that for a particular intensity of the Balmer lines two temperatures are possible?
For a particular intensity of the Balmer lines two temperatures are possible. Astronomers get around this by looking at the absorption lines of other atoms and molecules as well
State the order of the spectral classes for stars from hottest to coolest
O, B, A, F, G, K and M
- Use the mnemonic “oh be a fine girl kiss me”
Give the characteristics for the O spectral class of stars
- Blue stars
- Temperature: 25000 - 50000K
- The strongest spectral lines are helium ion and helium atom absorptions since these need a really high temperature
- They have weak hydrogen Balmer lines too
Give the characteristics for the B spectral class of stars
- Blue stars
- 11000- 25000K
- These spectra show strong helium atom and hydrogen absorptions
Give the characteristics for the A spectral class of stars
- Blue-white stars
- 7500-11000K
- Visible spectra are governed by the strongest Balmer hydrogen lines but there are also some metal ion absorptions
Give the characteristics for the F spectral class of stars
- White stars
- 6000-7500K
- These spectra have strong metal ion absorptions
Give the characteristics for the G spectral class of stars
- Yellow-white stars
- 5000-6000K
- These have both metal ion and metal atom absorptions
Give the characteristics for the K spectral class of stars
- Orange stars
- 3500-5000K
At this temperature most spectral lines are from neutral metal atoms
Give the characteristics for the M spectral class of stars
- Red stars
- < 3500K
- Molecular band absorptions from compounds like titanium oxide are present in the spectra of these stars, since they’re cool enough for molecules to form
Draw a general Hertzprung-Russel diagram (H-R) diagram
See page 183 in the revision guide
What goes on the axes on a H-R diagram?
- Absolute magnitude goes on the y-axis and it decreases up the y-axis which means brightness is increasing
- Temperature goes on the x-axis and it goes the wrong way along the x-axis: from hotter to cooler
In what position is the sun on a H-R diagram?
It moves along the main sequence
What is the long diagonal band on a H-R diagram called?
The long diagonal band is called the main sequence. Main sequence stars are in their long-lived stable phase where they are fusing hydrogen into helium. The sun is a main sequence star
Which stars are found in the top right corner of a H-R diagram?
Stars that have a high luminosity and a relatively low surface temperature musty have a huge surface area because of Stefan’s law. These stars are called red giants and red supergiants and are found in the top right corner of the H-R diagram. These are stars that have moved off the main sequence and fusion reactions other than hydrogen to helium are also happening in them
Which stars are found in the bottom left corner of a H-R diagram?
Stars that have a low luminosity but a high temperature must be very small, again because of Stefan’s law. These stars are called white-dwarfs and are about the size of the earth. They lie in the bottom left corner of a H-R diagram. White dwarfs are stars at the end of their lives where all of their fusion reactions have stopped and they are just slowly cooling down
Explain what starts begin as and how they become main sequence stars
1- Stars are born in a cloud of dust and gas most of which was left when previous stars blew themselves apart in supernovae. The denser clumps of the cloud contract very slowly under the force of gravity
2- When these clumps get dense enough the cloud fragments into regions called protostars that continue to contract and heat up
3- Eventually the temperature at the centre of the protostar reaches a few million degrees and hydrogen nuclei start to fuse together to form helium
4- This releases an enormous amount of energy and creates enough radiation pressure along with the star’s gas pressure to stop the gravitational collapse
5- The star has now reached the main sequence and will stay there relatively unchanged while it fuses hydrogen into helium
Explain how main sequence starts develop into red giants
1- Stars spend most of their lives as main sequence stars. The pressure produced from hydrogen fusion in their core balances the gravitational force trying to compress them. This stage is called core hydrogen burning
2- When all the hydrogen in the core has fused into helium, nuclear fusion stops and with it the outward pressure stops. The helium core contracts and heats up under the weight of the star. The outer layers expand and cool and the star becomes a red giant
Explain what happens after a star has become a red giant
1- The material surrounding the core still has plenty of hydrogen. Heat from the contracting helium core raises the temperature of this material enough for the hydrogen to fuse. This is called shell hydrogen burning
2- The helium core continues to contract until eventually it gets hot enough and dense enough for helium to fuse into carbon and oxygen. This is called core helium burning. This releases a huge amount of energy which pushes the outer layers of the star further outwards
3- When the helium runs out the carbon-oxygen core contracts again and heats a shell around it so that helium can fuse in this region - shell helium burning
Explain how a white dwarf is formed
1- In low-mass starts the carbon-oxygen core isn’t hot enough for any further fusion and so it continues to contract under its own weight. Once the core has shrunk to about Earth-size electrons exert enough pressure (electron degeneracy pressure) to stop it collapsing any more
2- The helium shell becomes more and more unstable as the core contracts. The star pulsates and ejects its outer layers into space as a planetary nebula leaving behind the dense core
3- The star is now a very hot, dense solid called a white dwarf which will simply cool down and fade away
How do stars aging affect their position on a H-R diagram?
As stars age their position on the H-R diagram changes
Explain how the position of the sun on the H-R diagram will change over time as it evolves
- The sun won’t stay in the main sequence forever, its position on the H-R diagram will drift to the top-right as it becomes a red giant. It will be colder and appear brighter than it was on the main sequence
- Once it has run out of helium to burn in its core it will then become a white dwarf and its position will move to the bottom left of the H-R diagram. It will be hotter but will also be dimmer than it was on the main sequence
Explain how high mass stars can either form a neutron star or a black hole
