1. Previous Classes: The Sun This Class Greenhouse Effect Stars
Phys 1830: Lecture 27
NASA’s Solar Dynamics Observatory: Extreme UltraViolet wavelengths
Image Workshop!
Dec 3 at 7-10pm
Allen Building
Previous Classes:
The Sun
This Class
Greenhouse Effect
Stars
Luminosity
Upcoming Classes
Radii, Mass
Lifetime
Stellar Populations
ALL NOTES COPYRIGHT JAYANNE ENGLISH
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This is a lengthy ppt that I will quickly go through.

2. New IPCC report – trends continue
Check the King’s Centre for Visualization in Science for interactives on climate change:
Melting ice caps could disrupt ocean currents. If the Gulf Stream is responsible for heating Europe and it is disrupted, then Europe could experience an “ice age”.
Currently needs more research and monitoring of ocean currents.
(conclusions P 31).
There is an American Institute of Physics article on ice ages and they know that the usual causes can’t be used now to predict an ice age. They are measuring CO2 variations in ice cores tp find matches with Earth’s elliptical orbit and Earth’s tilt. However now CO2 is out of range that it ever was in the past.

3. Stars: Their Characteristics
Luminosity: energy output
Temperature
Size

4. Stars: Their Characteristics
Recall Inverse Square Brightness Law
Recall that luminosity is the intrinsic power of a star.
Luminosity, or absolute brightness, is a measure of the total power radiated by a star.
Apparent brightness is how bright a star appears when viewed from Earth; it depends on the absolute brightness but also on the distance of the star.

5. Luminosity and Apparent Brightness
Therefore, two stars that appear equally bright might be a closer, dimmer star and a farther, brighter one:
Figure Luminosity Two stars A and B of different luminosities can appear equally bright to an observer on Earth if the brighter star B is more distant than the fainter star A.
Finished here.

6. More Precisely 17-1: More on the Magnitude Scale
Apparent brightness when measured using a logarithmic, magnitude scale, which is related to our perception is called apparent magnitude.
Absolute magnitude is the apparent magnitude that a star would have if it were placed 10 parsecs from Earth.
A reduction of 5 in magnitude corresponds to an increase in a factor of 100 in luminosity.
Magnitudes are inverted in scale, such that bright stars have low magnitudes.
Converting from magnitude to luminosity in solar units: This graph allows us to perform this conversion simply by reading horizontally.

7. Question 5
In the stellar magnitude system, a smaller magnitude indicates a _____ star.
1) brighter
2) hotter
3) cooler
4) fainter
5) more distant
Click to add notes

8. Question 5
In the stellar magnitude system, a smaller magnitude indicates a _____ star.
1) brighter
2) hotter
3) cooler
4) fainter
5) more distant

9. Question 7
1) one million km.
2) one astronomical unit.
3) one light year.
4) ten parsecs.
5) ten light years.
The absolute magnitude of a star is its brightness as seen from a distance of
Click to add notes

10. Question 7
1) one million km.
2) one astronomical unit.
3) one light year.
4) ten parsecs.
5) ten light years.
The absolute magnitude of a star is its brightness as seen from a distance of
Astronomers use a distance of 10 parsecs (about 32 light years) as a standard for specifying and comparing the brightnesses of stars.

11. Stars: Their Characteristics
Let’s now look at the properties of a star if you were at its surface.
Then “distance” is the radius of the star.

12. Stars: Their Characteristics
We have vaguely been calling this “brightness” or “intensity” when we’ve been at a distance and viewing stars as point sources.
The flux (F) of energy radiated through a centimetre square patch on the surface per second.

13. Star: Their characteristics
Blackbody curves
Wavelength (nm)
500° K
1000° K
2000° K
5000° K
10,000° K
20,000° K
X-Ray Ultraviolet Visible Infrared Microwave Radio
Intensity
Recall that stars radiate very similarly to ideal blackbodies.
Their flux (F) is related to their temperature (T). ( is a constant.)
Stefan’s Law relating flux and temperature is well-known from experiment.
Sigma is a constant.

14. Stars: Their Characteristics
Luminosity (L): The total energy radiated per second, at all wavelengths.
L = surface area * flux
Surface area of a sphere is 
Luminosity is proportional to the radius squared times surface temperature to the 4th power.

15. Stars: Why Temperature is useful.
Notice that if we know the temperature of a star, then if we know the radius, we can calculate the luminosity.
Alternatively, if we know the temperature and the luminosity we can determine the radius. 

16. Stars: Surface Temperatures
Black body curves
Wavelength (nm)
500° K
1000° K
2000° K
5000° K
10,000° K
20,000° K
X-Ray Ultraviolet Visible Infrared Microwave Radio
Intensity
Judiciously select filters and image the star in each of the filters using a CCD.
Measuring the magnitude of the star is called photometry.
Example of stars in HST data in .xcf file.
To measure the magnitude we surround the star with an aperture (circle) and count the number of photons within that aperture.

17. Stars: Surface Temperatures
Black body curves
Wavelength (nm)
5000° K
10,000° K
Intensity
“Colour” is a proxy for temperature
The cool, red star will have a higher intensity (lower magnitude) in the red filter compared to its blue filter.
The hotter, blue star will have a higher intensity (lower magnitude) in its blue filter compared to its red filter.
We can then reconstruct the black body curve.
The black body curve  temperature.
Can do this roughly with only 2 filters, more accurately with more filters.

18. How do we determine the temperature?
One way is to do photometry on images of stars in different filters.
This gives points on the black body curve.
“Connecting the dots” of intensity can trace the black body curve.
the peak of the black body curve tells us the temperature of the star.
this procedure does not take much observing time.

19. Can do this roughly for 2 filters but more filters trace the black body curve better.
hotter star
cooler star

20. has a reddish colour and is cool.
Review:
You are measuring the apparent magnitude of a star by doing photometry. You find that more light comes through the red filter than through the visual filter. Also more light comes through the visual filter than through the blue filter. (Hint draw the black body curve.) This means that the star
has a reddish colour and is cool.
has a greenish colour and is about the same temperature as our sun.
has a bluish colour and is very hot.

21. Stellar Temperatures
Stellar spectra are much more informative than the blackbody curves. However they take more observing time.
There are seven general categories of stellar spectra, corresponding to different temperatures.
From highest to lowest temperature, those categories are:
O B A F G K M
This classification is called Spectral Type or Spectral Class.
Traditional mnemonic is Oh Be A Fine Girl Kiss Me.

22. Stellar Temperatures Here are simplified diagrams of their spectra:
If we can classify a star by this system, then we know its temperature.
Careful – horizontally these diagrams are organized by increasing energy.
Figure Stellar Spectra Comparison of spectra observed for seven different stars having a range of surface temperatures. These are not actual spectra, which are messy and complex, but simplified artists’ renderings illustrating a few spectral features. The spectra of the hottest stars, at the top, show lines of helium and multiply ionized heavy elements. In the coolest stars, at the bottom, helium lines are absent, but lines of neutral atoms and molecules are plentiful. At intermediate temperatures, hydrogen lines are strongest. All seven stars have about the same chemical composition.

23. Stars: Plot Luminosity versus Spectral Class
Plots:
Plot astronomer’s height versus astronomer’s weight.
Plot astronomer’s height versus astronomer’s IQ.
Plot Luminosity versus Temperature (Spectral Type)
As if there were no relationship.
As if there is a 1-to-1 correlation.
Shows a correlation … almost 1-to-1.
This is a scatter plot.
What would you expect?

24. Stars: Hertzsprung-Russell Diagram
Because of the equation for Luminosity with radius and temperature, we can plot dashed lines for radii.
Sun has 1 solar luminousity and 1 solar radius. Circle with dot in centre is the symbol for sun.
This is the sort of diagram we get when we plot data.
20,000 stars.
Note that the sun is a G star.

25. The Hertzsprung-Russell Diagram
These are the 80 closest stars to us; note the dashed lines of constant radius.
The darkened curve is called the main sequence (MS), as this is where most stars are. 90% of all stars are on the MS.
Also indicated is the white dwarf (WD) region; these stars are hot but not very luminous, as they are quite small. 1% of all stars are WD.
Figure H–R Diagram of Nearby Stars Most stars have properties within the long, thin, shaded region of the H–R diagram known as the main sequence. The points plotted here are for stars lying within about 5 pc of the Sun. Each dashed diagonal line corresponds to a constant stellar radius, so that stellar size can be indicated on the same diagram as stellar luminosity and temperature.

26. The Hertzsprung-Russell Diagram
These 100 stars are all more luminous than the Sun. Two new categories appear here—the red giants and the blue giants.
Figure H–R Diagram of Brightest Stars An H–R diagram for the 100 brightest stars in the sky is biased in favor of the most luminous stars—which appear toward the upper left—because we can see them more easily than we can the faintest stars. (Compare with Figure 17.14, which shows only the closest stars.)

27. Stars: Hertzsprung-Russell Diagram
Be able to draw the HR diagram later in this class!
(Including the ranges on the axes.)
Notice the luminosity and the temperatures.
General regions:
Main Sequence (MS)
White Dwarfs (WD)
Giants
Supergiants

28. Stars: Hertzsprung-Russell Diagram
The highest density of stars is in the Main Sequence (MS).
Colour scale gives the number of stars in that point.
Notice in this version they plot “observables” – the things that astronomer measure. From these temperature and luminosity can be calculated. For temperature they plot the magnitude difference in colour between filters. Recall that the ratio between intensities in filters (i.e. this colour difference) gives the spectral class and hence temperature. For luminosity they plot the absolute magnitude.
Roughly stars from the ESA Hipparcos mission.
HIPPARCOS measured
precise positions, parallaxes and motions
2.5 million stars in 3.5 years
Out to about 200 pc
2 colour photometry for 400,000 stars

29. Stars: Hertzsprung-Russell Diagram
If we know only the temperature, can we use the H-R diagram to know the luminosity of a star?
Yes.
No.
We need to know their radii.

30. Stars: Hertzsprung-Russell Diagram
Colour scale gives the number of stars in that point.
Notice in this version they plot the magnitude difference in colour between filters. Recall that the ratio between intensities in filters (i.e. this colour difference) gives the spectral class.
Notice that there isn’t a 1-to-1 correlation between temperature and luminosity.

31. Stars: Hertzsprung-Russell Diagram
If we know only the temperature, can we use the H-R diagram to know a unique luminosity for a star?
Yes.
No.
We need to know their radii.

32. Stars: Hertzsprung-Russell Diagram
Because of the equation for Luminosity with radius and temperature, we can plot dashed lines for radii.
Given the temperature we need to know the radius to get the luminosity.
Similarly if we know the luminosity we need the radius to get the temperature.
How do we get the radius of a star?

33. Stars: Hertzsprung-Russell Diagram
This is an important diagnostic tool that allows us to find radii, distances, and other characteristics of stars. We can even trace a star’s evolution from birth to death on the diagram.
Draw the HR Diagram and include and label the following:
4 axes and their ranges
General regions where stars reside
The location of the sun
Notice the luminosity and the temperatures.

34. Stars: Hertzsprung-Russell Diagram
Notice the luminosity and the temperatures.
General regions:
Main Sequence (MS)
White Dwarfs (WD)
Giants
Supergiants

35. Stars: Hertzsprung-Russell Diagram
Because of the equation for Luminosity with radius and temperature, we can plot dashed lines for radii.
Given the temperature we need to know the radius to get the luminosity.
Similarly if we know the luminosity we need the radius to get the temperature.
How do we get the radius of a star?