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Revision:Edexcel Astrophysics

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TSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > Edexcel Astrophysics

Recording star images

CCD - Charged Couple Devices

Advantages Over Film:

Higher quantum efficency ~70% (number of bits of info recorded / number of photons x 100)
More linear response (output is more directly proportional to light intensity received)
No need to replace
Can be used repeatedly
Faster Operation

Disadvantages

Smaller field of view
Need to be kept cool (about 120K)
Not portable
Resolution is not as good

Made from slices of silicon that store electons from photons and build an image (in pixels) from this. Pixels are from 5-50 micrometers, and pixels where larger quantities of light land (higher light intensity) have more electons.

A voltage is applies to pixels so that the computer can "read" the image.

Film

Advantages Over CCD:

Cheap
Good resolution
Permanent record
Easily transported

Disadvantages

Not as efficent
Not as linear
Have to be replaced
Slower to use ( up to 2 hours while CCD is about 1 minute) Because of this, also more expensive because telescope time is expensive.
Grain Size is 0.1 - 1 micrometer (large grains are sensitive to light but produce a grainy image while small grains are less sensitive but produce a sharper image)

Benefits of observing from above the Earth's atmosphere

Light Pollution reflects off gaseous atmosphere (known as scattering)
Pollution reflects and absorbs light
Light passing thrhough atmosphere experiences different refractive indeces
Diffraction limits resolving power of telescopes
Some wavelengths are absorbed by atmosphere

There are 2 "windows" in atmosphere. They let radio and optical waves through.

Where d is diameter of particle in atmosphere, and w is wavelength.

d > w particles act like mirrors

d = w scattering is proportional to 1/w (blue more scattered than red)

d < w amount of scattering is (1/(w^4)) called Rayleigh scattering.

Telescopes

Hubble Space Telescope
IRAS - For infrared
COBE - infrared and micrwave
ROSAT - X-Ray

Need details about these 'scopes...

Information from wavelengths of different stars

By observing different stars we find that:

The spectrum given off can tell us the chemical composition of the gases which make up the star
The star emits a range of wavelengths and as the temperature of a star increases i) the light intensity of the radiation increases at all wavelengths ii) the spectrum of radiation shifts towards higher frequencies.

Wien's law

These observations lead to Wien's displacement law.

This states that for a star there is a simple connection between the temperature of the star (k) and the wavelength (λmax - lander max) which is the maximum intensitywithin the spectrum.

Note: If a frequency is given Velocity/Frequency = Wavelength

Wien found:

$\displaystyle \lambda _{\mathsf{max}} \times T = \mathsf{constant} = 2.898 \mathsf{x} 10^{-3}\ (m.K)$

Luminosity of stars

Luminosity is the total power radiated by a star.

Total power depends on temperature and surface area.

Stefan-Boltzman found that the luminosity is directily proportional to the temperature (k) to the power of 4.

$\displaystyle L \propto T^4$

$\displaystyle L = \sigma (T^4) \times \mathsf{surface\ area\ of\ sun}$

Where $\sigma$ is a constant called the Stefan constant and has a value of:

$\sigma = 5.67 \mathsf{x} 10^{-8} Wk^{-4}m^{-2}$

Measuring Distances

For large distances:

1 Light year = 9.46 x 10^15 m (Speed of light is 3 x 10^8 m/s)

1 AU - the average distance between the earth and the sun. (may not be in syllabus)

Parallax Method

Only suitable for relatively close stars

ok...so E is earth at opposite times in the year (6 months apart), S is Sun and T is the star you are looking at...

....E-------S-------E

.....x.........|.........x

.......x.......|.......x

.........x.....|.....x

...........x...|...x

.............x.|.x

...............T

Imagine an angle at E(T)S..call it d

because the angle is small, (less than 1 degree) ET can be assumed to be the same as ST.

So: tan d =~ sin d = 1AU/D.

Method for annual parallax method:

From a position on earth line up the nearby star with a more distant star observed from earth.
Exactly 6 months later repeat the process in number 1, by varying the angle.
Measure the distance between the angle of 1 and 2.
Knowing the average diameter from the earth's orbit radius, the Distance D = 1AU/tan d

Hertzprung - Russel diagram

For a star LANDERmax is proportional to 1/Temperature (from Wien's law whcih is LANDERmax.T= constant.

The further the star is away fro earth, the lower its intensity (I).

Intensity is directly proportional to luminosity

Intensity on earth can be measured, and then Luminosity can be calculated by using the following equation:

$\displaystyle I = \frac{L}{(4\pi D^2)}$ , where D is the distance from earth, adn can be calculated using the parallax method.

Using this value of L, the star can now be put on the HR diagram.

The HR diagram can also be used to measue distances ( for nearby or far away stars?):

Measure the temperature T by using Wien's law, then use the HR diagram to estimate a luminosity. Then the luminosity can be used to calculate the distance. [ $\displaystyle I = \frac{L}{(4\pi D^2)}$ ]

Cepheid Variables

These are stars that pulsate. They have used up their main supply of hydrogen.

Cepheid variables go from being very dim, to being very bright in a time range of anything between about 1-50 days.

The period of a Cepheid is related to its luminosity:

........ I....................x

10^4..I..................x

.........I...............x

.........I.............x

10^3..I...........x

.........I.........x

.........I.......x

10^2..I.....x

.........I...x

.........I_____________________

.......... 1....3....10.... 30....100

Astonomers have found that over a period of pulsations that the time period of pulsation depends on Luminosity. (Almost a direct proportionality based on a relative luminosity)

So astronomers measure the time period T and use it to find the luminosity. then they can use I = L/(4piD^2), to work out the distance.

There are also RR Lyrae variables, but their period is less than 1 day, and they do not follow the same pattern.

Stars=

Stars are born as interstellar gas clouds collapse under their own gravitational contraction.

They are made up of Hydgrogen a small amount of Helium and about 1-2% of heavier elements. If the mass of the cloud is large enough (100x that of the sun supposedly?) Hydogen nuclei all move towards the centre, and their gravitaional potential energy is converted into kinetic energy. This causes the protostar to heat up and begin fusion where it then becomes a star and settles into a main sequence star. Pressure outwards (radioactive and caused by heat I think) matches pressure inwards of gravity.

Fusion - p-p chain is where Hydrogen is converted to Helium (I think). But for edexcel details of p-p chain are not neccessary.

Mass of sun is 2 x 10³⁰kg

For energy conversions in stars E=mc^2 .

Main Sequence stars

Large stars have large gravitational forces acting on them. They therefore have a large inwards pull. They reach higher temperatures faster, and have higher luminosity. Top left of the H-R diagram. SHORT LIFETIMES

Small stars: have small gravitational forces, so lower temps and luminosity. Bottom right of H-R. LONG LIFETIMES

What happens after...just gets messy and complicated in my opinion, but I'll try...

Ms = Mass relative to sun.

White Dwarves

Less than 1.4 Solar Masses When the main sequence star has finished its hydrogen burning [which is very slow due to the low mass] it is not large enough to have the gravitational forces requires for outer layers to be drawn inward and implode. The outer layers are cast off slowly leaving a molten core of what is mainly Iron, and still retains a lot of heat. No burning is occurring so the star begins to cool, and will continue to do so until it becomes a black dwarf.

Red Giants

The stars between 1.4 and 8 Ms become Red Giants when most of the H is converted to He. This is because the outwards pressure is no longer balanced with the inwards pressure. This causes the core to heat up, and increases energy flow to gases around the outside of the star. The outside gases begin fusion, which makes the outward forces unbalanced again, meaning that the sun begins to expand (by about ~100x) to become a Red Giant or a Super Giant. (Red giants then go on to become white dwarfs)

Now more and more fusion of heavier and heavier elements occurs at the core (in layers around the centre).

When the fusion reaches Iron, the red giant cannot fuse anymore (because the star has run out of lots of energy, and Iron is very hard to fuse)

Supernovae

The rapid implosion of stars greater than 8 solar masses, [supergiants] Caused mainly due to the massive gravitational inward pull of the core pulling the outer layers inward when hydrogen burning stops so no outward force is created.

All the outer layers are drawn inward and energy is released as a shockwave as the outer layers are then rapidly cast off.

Neutron Stars

If Ms of core of a superovae is >1.4, the central core of neutrons will form a neutron star. They are highly dense (10^15 x normal matter). Are about 20km in diameter and have a mass of 10^30kg.

AS the neutron star rotates it it emits high frquency radio signals. (Is this a pulsar?)

Black Holes

If the core remnants of a supernovae are greater than 2.5Ms a black hole is formed. The supernova collapses to an infinite density called a singularity.

Can be dected by noticing strong X-ray sources near stars