1. Cepheids
Lab 7

2. Cepheid Variables
All stars, late in their lifetime, change from being average stars for their mass (main sequence stars) to becoming swollen red giants
Most stars change from the swollen red giant phase to pulsating variable stars before they finally die, all reactions ceasing
These are Cepheid Variables, which expand and contract, glowing brightly and fading every so often

3. How Does it Do it??
Cepheid is a star of several solar masses and ~104 solar luminosities whose luminosity changes periodically
As radiation streams out, some He+ in the atmosphere of the star is ionized to He2+, making the atmosphere opaque

4. Then……
This decreased transparency of the stellar material blocks the energy flux and heats the gas, so the increased pressure pushes the envelope out, which increases the star's size and luminosity
As the star expands, it cools, and He2+ gains an electron, converting back to He+
The enhanced transparency causes the atmosphere to shrink again

5. So… Cepheids are … pulsating stars
have used up their main supply of hydrogen fuel are unstable and pulsate
have a relationship between the period of a Cepheid and its luminosity
Type I Cepheids are population I stars whose brightness periods fluctuate from 1 to 100 days

6. Cepheids as Distance Markers
This relationship allows us to work out how much brighter than the Sun the star is
From there we can calculate how much further away the star must be than the Sun to make it the brightness we see from Earth
Delta Cephei shows has a period of about 5 days
This is a reasonably bright star in the constellation of Cepheus
Cepheids are in other galaxies also, and used similarly, to find distance

7. calculations
The brightness at the distance of 1 light-year > than the observed brightness …..due to the fact that brightness drops like the square of the distance
From these numbers one can extract the distance to the stars
This method works up to 13 million light-years when Earth-bound telescopes are used

9. Example
Population 1 Cepheid in the cluster with a period of 11 days and average apparent magnitude of 2.3
From a graph we can see that the star's luminosity must be 10,000 times that of the Sun. This corresponds to a magnitude difference of 10
Since the Sun's absolute magnitude is 4.8, the absolute magnitude of the star must be = -5.2
We can now use a simple equation (Inverse Square Law) connecting absolute and apparent magnitude with distance to find that the distance of the star and also its cluster is about 320 parsecs

10. Inverse Square Law
The relationship between intensity of light coming from a source and the distance of the observer from that source
It states that the intensity is inversely proportional to the square of the distance (i.e. if you are twice as far from a light, it will appear four times as dim)

11. Definitions
period The length of time between successive peaks in the brightness of a variable star
apparent magnitude A measure of the brightness of a star as seen by the observer. Based on a system set up by the Greek astronomer Hipparchus
absolute magnitude A measure of the inherent brightness of a star independent of any observer. Equivalent to the apparent magnitude of a star seen from a distance of 10 parsecs.
luminosity Gives the total amount of radiation being given off by a star in 1 second
parsec The distance at which a star would have a parallax angle of 1". (~3.26 light years)

12. Two Magnitude Systems
One gives the brightness of a star as observed from here on Earth. This is the apparent magnitude.
The other - absolute magnitude - gives a measure of the total amount of light being given out by the star in all directions
Both systems are logarithmic with a difference in magnitude of 5 being equivalent to a factor of 100 in brightness

13. More Defs
logarithmic Applied to measures that increase by 1 whenever the factor they depend on is multiplied by a certain number. For example, if a value increased from 10 to 100 to 1000, then a logarithmic measure of that value could increase, say, from 1 to 2 to 3.
red giant After a star has finished burning the hydrogen in its core, it enters this stage before dying. The star swells up and turns red.
Doppler Effect The apparent change in the wavelength of waves due to the relative movement of the source of the waves relative to the observer.

14. More Defs contd
Hertzsprung-Russell diagram A graph plotting absolute magnitude against spectral type. Shows the correspondence between temperature and luminosity
Hubble's Law Relationship between a galaxy's distance and its speed of recession
v = H * d where v is the speed, d is the distance, H is Hubble's constant
Hubble graph A graph plotting a galaxy's recession speed against its distance
Stefan's Law The relationship between luminosity, surface area and surface temperature of a star