1. Distance and Magnitude Black body Curves & Color HR Diagrams
The Nature of Stars
Distance and Magnitude
Black body Curves & Color
HR Diagrams

2. Choose Something Like a Star
O Star (the fairest one in sight),
We grant your loftiness the right
To some obscurity of cloud--
It will not do to say of night,
Since dark is what brings out your light.
Some mystery becomes the proud.
But to be wholly taciturn
In your reserve is not allowed.
Say something to us we can learn
By heart and when alone repeat.
Say something! And it says, 'I burn.'
But say with what degree of heat.
Talk Fahrenheit, talk Centigrade.
Use language we can comprehend.
Tell us what elements you blend.
It gives us strangely little aid,
But does tell something in the end.
And steadfast as Keats' Eremite,
Not even stooping from its sphere,
It asks a little of us here.
It asks of us a certain height,
So when at times the mob is swayed
To carry praise or blame too far,
We may choose something like a star
To stay our minds on and be staid.
~Robert Frost

3. Distances Nothing can prepare people for the distances to the stars.
The nearest star (Alpha Centauri) is 40 trillion kilometers away.
The fastest spacecraft ever built would take 800,000 years to reach it.
Space in the solar neighborhood is % empty

4. How Does One Measure Distance?
The foundation of all distance measurements is a simple geometric method called Parallax or Stellar Parallax

5. Background tan(0.5q) = 0.5r/d q 0.5 = 0.5r/d  = r/d .5q d = r/ d1 2 r

6. Stellar Parallax
Earth is on the opposite side of the sun every 6 months.
Close stars appear to shift because of this.
The amount of shifting is inversely proportional to distance

7. Proper Motion
Stars have their own drift motions through space called proper motions.
Most stars are so distant we cannot measure this drift. But the ones close enough for a parallax measure are also close enough to detect proper motion!
We must observe them for several years to first measure proper motion before getting a parallax.

8. Inverse Square Law
To measure to greater distances, we use more indirect methods which are calibrated by stellar parallax.
All other methods, except cosmological redshift, use the 1/r2 dimming of light.
We measure apparent brightness or magnitude and compare it with absolute brightness or magnitude.
We can get absolute brightnesses from HR diagrams. These are a fundamental tool that will reappear throughout the semester. It is critical that you understand how they work!

9. HR Diagram It is stellar magnitude plotted against spectral type.
So what, exactly, is a magnitude?
What exactly is a spectral type?

10. Apparent Magnitude
The measure of how bright a star appears in the night-time sky.
Symbolized by m or m.
This is the system given to us by Hipparchus
The brightest stars are 1st magnitude.
The faintest stars visible to the naked eye are 6th magnitude.
1st to 6th magnitude is a factor of 100 times in brightness.
It is a logarithmic scale just like the response of the human eye. m = -2.5log(brightness)
Each step in magnitude is times brighter.

12. Examples
When carefully calibrated, a few stars ended up being brighter than 1st magnitude.
Sirius A (brightest in the sky)
Canopus
Arcturus
Alpha Centauri -0.01
Vega
Capella
Rigel

13. Other Objects Sun = -26.7 Full Moon = -12.6 Eye Limit = +6.0
Pluto = +14.0
Faintest object seen with Keck 10m telescope = +30.0

14. What Affects Apparent Magnitude?
1) How bright it really is
2) Its distance
Examples m Distance
Sirius A ly
Canopus ly
Alpha Centauri ly
Rigel ly
If we can measure the apparent magnitude of a star and somehow discover what its real brightness is, we can infer its distance!

15. Absolute Magnitude The measure of how bright a star really is.
Symbolized by M or M.
We define absolute magnitude as being the brightness an object would have if it were placed 10 parsecs away.
Some examples are:
The Faintest Stars = +20.0
The Sun = +4.8
The Brightest stars = -9.0
Exploding stars = -16.0
Average galaxies = -20.0
Giant galaxies = -23.0

16. Colors
A Color Index is the difference between two magnitudes taken in two different filters
Examples: (B-V), (U-B), (b-y)
Color measures the shape of the blackbody curve.
This gives us the star’s temperature! That is the main goal!
The more negative the index, the bluer the light.
The bluer the light, the hotter the object.

17. Star Colors

18. Spectroscopy
But if we want the blackbody curve, would it be better to just measure the entire spectrum?
A good idea! But it takes a lot of telescope time.
Photometry is the study of magnitudes and is best for studies of lots of objects at once.
Spectroscopy is the detailed study of the entire spectrum and is best for Doppler shifts, chemical analysis, and exploring weirdos.

19. Temperature Sequence
No. All stars have essentially the same amount of hydrogen. Temperature greatly affects the strength of spectral lines.
In time the spectral sequence was rearranged according to other line strengths and redundant types were eliminated to end up with a temperature sequence going hot to cool as:
“OBAFGKM” (LT)
‘Oh Be a Fine Girl, Kiss Me’

20. HR Diagrams (finally!)
Using the earliest distance determinations from parallax, in 1911 Ejnar Hertzsprung (Danish) plotted the absolute magnitude of stars versus a color index for each star.
In 1913 Henry Norris Russell (U.S.) plotted the absolute magnitude versus the spectral type.
The results were the same, the Hertzsprung-Russell diagram.

21. Nearby Stars Notice how the stars do NOT distribute randomly.
We can infer a great deal from where they are located.

22. Diameters
If a star is intrinsically bright but cool, it must be large.
If it is intrinsically faint but hot, it must be small.

23. Most of the stars are on the main sequence: a line from the upper left to the lower right on the diagram.
Red Giants and Supergiants are in the upper right. Blue Giants to the upper left.
White Dwarfs are in the lower left.

24. Masses
Mass increases from lower right to upper left along the main sequence.
Found from binary star systems.
M1+M2 = a3/P2

25. Luminosity Class
In the 1930’s Morgan and Keenan developed a system to help define the regions within the HR diagram.
The system was based on subtle differences in the spectral features caused by different surface gravity strength.
Giants have lower surface gravity
Dwarfs have higher surface gravity

26. Luminosity Classes Ia - Luminous Supergiants
Ib - less Luminous Supergiants
II - Bright Giants
III - Giants
IV - Subgiants
V - Main Sequence or Dwarfs
VI - Subdwarfs

27. By carefully examining a star’s spectral lines, astronomers can determine whether that star is a main-sequence star, giant, supergiant, or white dwarf

28. The Sun The Sun is a G2 V star Any star which is a G2 V will …
have the same absolute magnitude as the Sun
have a surface temperature of about 5800º K
have the same radius as the Sun
have the same mass as the Sun.
By the same token, all stars of the same spectral type and class will have the same absolute magnitude, surface temperature, radius and mass.

29. Back to Distance
Suppose we take the spectrum of a star and find it is a K5 II. We then know it
is a red giant with a surface temperature of 4000º K
has a luminosity about 1100x that of the Sun or an absolute magnitude of about -2.0
We then can measure the apparent magnitude and find the distance.
This is called “spectroscopic parallax” (although perhaps spectroscopic distance would have been a better name).