Download Lecture 5: Stars

V.
Stars
http://sgoodwin.staff.shef.ac.uk/phy111.html
0. The local HR diagram
We saw that locally we can
make an HR diagram of
absolute luminosity against
temperature.
We find a main sequence,
giants and white dwarfs.
1. Going further
We only know the absolute luminosity if we know the
distance, but we only know the parallax distances out to
about 100 pc (further to some bright stars).
The problem is that if we see a star with a surface
temperature of 3000K – is it a nearby red dwarf, or a distant
red giant? Without more information than colour and
apparent brightness we just can’t tell.
And what are their physical properties – mass and radius?
1. Spectral types
We saw that spectra can be used to classify stars into
‘types’ – from hot to cool:
OBAFGKM
Simply – at low temperatures very little material is ionised
and molecules can even exist.
The easiest elements to ionise are metals (e.g. Fe), then
things like O or C, then H, and finally He.
1. Spectral types
So what lines of an element we see vary with surface
temperature.
1. Spectral types
The Sun is a G-star and we see lots of neutral and ionised
metal lines. (The O2 lines below are due to the Earth’s
atmosphere.)
1. Spectral types
Important to remember:
What we see is the ‘surface’ (photosphere).
The lines we see do not directly tell us about abundances.
In the Sun’s photosphere we see lots of iron lines, but the
Sun is 98% H-He – as are most stars. Its just that iron has
lots of lines in the visible.
1. Spectral types
So why are some stars so much more luminous than
others?
To be more luminous they must be producing more energy,
and it turns-out that this depends on their mass.
More massive stars produce more energy per unit time –
and so are more luminous.
(Only on the main sequence though – as we’ll see red
giants can be low-mass stars.)
2. Surface gravity
Exactly what we see in a spectrum (lines, line shapes,
ionisation state) depends on temperature and pressure.
Exactly how is a mix of thermodynamics and quantum
mechanics, but the upshot is that from the spectra we can
measure both.
Pressure depends on the gravity – which depends on mass
and radius (small and massive = high gravity).
So spectra give us surface temperature and surface gravity
(a mix of radius and mass).
3. Physical properties of stars
We need to calibrate our models using some stars for
which we know the absolute luminosity, temperature, mass
and radius.
The Sun is one calibrator – we know all of these in detail.
We also calibrate using binary stars.
3. Binaries and mass
If we can observe a close binary and measure the orbital
velocities of the components we can get their masses from
Kepler’s laws
3. Binaries and mass
If we can observe a close binary and measure the orbital
velocities of the components we can get their relative
masses from Newton’s laws.
If the system eclipses then we can get absolute masses
and also measures of their radii.
3. Binaries and mass
But the upshot is we can calibrate our models and so
use spectra to get the stellar surface temperatures,
pressures, gravity, and so their masses and radii.
4. Metallicity
From spectra we can also get the relative abundances of
different elements.
Almost all stars are about ¾ H and ¼ He.
The Sun is about 2% other elements (other stars vary from
almost no other elements to around 5%).
Confusingly astronomers call ALL elements other than H
and He ‘metals’. (Fe is a ‘metal’, but so are O and N.)
We’ll come back to this quite a few times later as it turnsout to be really important.
5. Stellar properties
We find that stars range in mass from about 10-2M to
about 102M.
(Technically ‘stars’ less than about 0.1M are ‘brown
dwarfs’ not stars as they do not burn H.)
About 90% of stars lie on the main sequence (as we’ll see
this is where they spend most of their lives burning H in
their cores).
The ‘’ is for Solar values (M is a Solar mass =
2x1030kg).
5. Stellar properties
On the main sequence we find fairly good relationships
between mass and luminosity (also temperature and radius
as they all all related):
This is true for roughly Solar-mass stars – the power-law
varies a bit (you might see it as 3 or 4, it depends on the
range). For very high-mass stars its roughly linear – but
we’ll go with this…
5. Stellar properties
On the main sequence this mass-luminosity relationship
means that there is a mass-spectral type relationship.
On the HR diagram:
O-stars are hot and very luminous (top left): very
luminous means very massive (>20 M).
M-stars are cool and very faint (bottom right): so lowmass (<0.5 M).
G-stars are in-between (the Sun sits in the middle): so
intermediate-mass (1 M).
Summary
From spectra we can get the surface temperature,
pressure, and gravity. Spectra also give the composition
(metallicity).
Binary stars allow us to calibrate our models by giving the
masses and radii of some stars.
We find a mass-luminosity relationship on the main
sequence – more luminous stars are more massive.
The main sequence OBAFGKM spectral sequence is a
temperature sequence (from high to low temperature), and
a mass sequence (from high to low mass).
Key points
To know the OBAFGKM sequence is both a temperature
and mass sequence – on the main sequence.
To be able to describe very broadly what elements and their
ionisation states that we see in different spectral types and
why.
To know the mass-luminosity relationship for the main
sequence.
Quickies
A main sequence star shows lines of ionised He, is it a high- or low-mass star? Briefly
justify your answer.
Two stars are observed with the same apparent brightness. One shows lines of ionised
H, the other lines of TiO. Which star is closer? Briefly justify your answer.
Two M-stars are observed: one is a giant, the other a dwarf. Give ONE way of telling the
difference.
A star has a luminosity of 104 L. Give a rough estimate of its mass.
Suggest ONE spectral line you might look for to distinguish an G-star from an O-star.
Notes
For ease (and space) I will use the symbols for various elements:
By far the most common elements:
H – hydrogen
He - helium
Other reasonably common elements:
C – carbon
O – oxygen
N – nitrogen
Fe – iron
Si – silicon
S – sulfur
K – potassium
Ca – calcium
P – phosphorus
Ar – argon
Na – soldium
Mg – magnesium
Ni – nickle
Ti – titanium
Notes
When writing down an element sometimes the atomic number is added so: 12C (spoken
aloud as ‘carbon 12’).
The atomic number is the total number of protons and neutrons in the nucleus, so 12C is
lighter than 14C.
What defines the element is the number of protons in the nucleus – carbon always has 6.
So 12C has 6 protons and 6 neutrons, and 14C has 6 protons and 8 neutrons.
Because the nucleus of 14C is so much larger it is unstable and will decay to 12C (it is
created in the atmosphere by impacts with cosmic rays, 14C has a half-life of 5730 years
and is the ‘carbon’ in ‘carbon dating’).
Notes
When classifying stars the star is given one of the OBAFGKM spectral classifications.
Within this a number 0-9 says how hot it is, so an M0 is hotter than an M9 (the coolest
type of star). The Sun is a G2 star (at the hot-end of the Gs).
Roman numerals are used to distinguish sizes as determined by the surface pressure
measured by the lines. ‘V’ is a main sequence star, and I, II, III types of giant star.
So the Sun is formally a G2 V star. (To add an extra layer of confusion main sequence
stars are often called ‘dwarfs’, so the Sun is a G-dwarf.)
For even more complication stars <0.01M are not really stars as they can not burn H.
They are ‘brown dwarfs’ and are very cool and have spectral types LTY (although it is
arguable if the Y subtype even exists). So you might see a spectral sequence as
OBAFGKMLTY. I won’t ever talk about types LTY.