Astro 1050     Mon. Oct. 7, 2002
   Today:  Discuss HW #4
                Finish Chapter 7 -- The Sun
                Start Ch. 8, Properties of Stars

Homework #4
Q1 The moon remains in Aries!
Q2 1 kg of mass transformed into energy:
E = mc2 so E=1 kg x (3x108m/s)2 = 9x1016 J
Q3 Sunspot brightness, use E = σT4
(T1/T2)4 = (5800/4200)4 = 3.6 times brighter
Q4 Radio Wave same speed as Gamma Ray
Q5 P. 123, flares up to a billion H-bombs so
The Traitor dies like the dog he is!

Fusion Energy Released in Proton-Proton Chain
Use E=mc2 to do accounting
Mass is a measure of the energy stored in a system
Loss of mass from a system means release of energy from that system
Compare mass of four 1H to mass of one 4He
6.693 ´ 10-27 kg   -  6.645 ´ 10-27 kg   =  0.048 ´ 10-27 kg       drop in mass
E = mc2 = 0.048 ´ 10-27 kg ´ (3 ´ 108 m/s)2 =  0.43 ´ 10-11 kg m2/s2 = 0.43 ´ 10-11 J (note == a Joule is just shorthand for kg m2/s2)
So 4.3 ´ 10-12 J of energy released
This is huge compared to chemical energy:  2.2 ´10-18 J to ionize hydrogen

How long will Sun’s fuel last?
Luminosity of sun:  3.8 ´ 1026 J/s
H burned rate:
H atoms available:
In reality not all the atoms we start with are H, and only those near the center are available for fusion.  The structure of the sun will change when about 10% of the above total have been used, so after about 10 billion years.

Testing solar fusion model
Does lifetime of sun make sense?
Oldest rocks on earth ~4 billion years old
Oldest rocks in meteorites ~4.5 billion years old
Other stars with higher/lower luminosity
Causes for different luminosity
Lifetimes of those stars
Look for neutrinos from fusion
Complicated story – due to neutrino properties
Example of how astronomy presents “extreme” conditions

Generated by “weak” force during   p+® n + e+ + n
“Massless” particles which interact poorly with matter
In that first respect, similar to photons
Can pass through sun without being absorbed
Same property makes them very hard to detect
Davis experiment at Homestake Mine in Black Hills
100,000 gallon tank of C2Cl4 dry cleaning fluid
in Cl nuclei   n + n ® p+ + e-   so Cl (Z=17) becomes Ar (Z=18)
Physically separate out the Ar, then wait for it to radioactively decay
Saw only 1/3 the neutrinos predicted

Missing Neutrino Problem
Lack of solar neutrinos confirmed by Kamiokande II detector in Japan.  (Using different detection method)
Possible explanation in terms of Neutrino physics
3 different types of Neutrinos:
electron, muon, and tau neutrinos
Sun generates and Cl detectors see only electron neutrinos
Can electron neutrinos can change to another type on way here?
These “neutrino oscillations” are possible if neutrino has non-zero mass
Kamiokande II evidence of muon neutrinos becoming electron ones
Read “Window on Science 7-2”  on “scientific faith”
Neutrino mass may have implications for “cosmology”
Neutrinos also used to study supernova 1987A

Chapter 8: Properties of Stars
How much energy do stars produce?
How large are stars?
How massive are stars?
We will find a large range in properties!

Distances to Stars

Parallax: Really just the small angle formula

Intrinsic Brightness of Stars
Apparent Brightness:  How bright star appears to us
Intrinsic Brightness:   “Inherent” – corrected for distance
How does brightness change with distance?
Flux = energy per unit time per unit area:   joule/sec/m2   = watts/m2
Example:  100 watt light bulb (assume this is 100 W of light energy)
        spread over 5 m2 desk gives  20 Watts/m2
Sun’s flux at the Earth
Luminosity = 3.8 ´1026 Watts
It has spread out over sphere of radius 1 AU = 1.5 ´ 1011 m
Surface area of sphere = 4 p R2 = 2.8 ´1023 m2
FSun = 3.8 ´1026 Watts / 2.8´1023 m2 = 1,357 W/m2
Inverse Square Law:   Flux falls of as 1/distance2
Double distance – flux drops by 4
Triple distance – flux drops by 9

Inverse-square law for light:

Correcting Magnitudes for Distance
To correct intensity or flux for distance, use Inverse Square Law
Up to now we have used “apparent magnitudes”  mv
Define absolute magnitude Mv as magnitude star would have
 if it were at a distance of 10 pc.
This gives us a way to correct Magnitude for distance, or find distance if we know absolute magnitude
Note:  the book writes mv and Mv:  The “V” stands for “Visual”
Later we’ll consider magnitudes in other colors like “B=Blue” “U=Ultraviolet”

Let’s work some examples:
Problem #4:
mV MV d (pc) P (arcsec)
___ 7 10 _______
11 ___ 1000 _______
___ -2 ____ 0.025
4 ___ ____ 0.040

Let’s work some examples:
Problem #4:
m MV d (pc) P (arcsec)
7 7 10 0.1
11 1 1000 0.001
1 -2 40 0.025
4 2 25 0.040

How to recognize patterns in data
What patterns matter for people – and how do we recognize them?
Weight and Height are easy to measure
Knowing how they are related gives insight into health
A given  weight tends to go with a given height
Weight either very high or very low compared to trend ARE important
Plot weight vs. height and look for deviations from simple line
Example of cars from the book
Note “main sequence” of cars
Weight plotted backwards
Just make main sequence a line
which goes down rather than up
Points off main sequence are
“unusual” cars

Stars:  Patterns of L, T, R
The Hertzsprung-Russsell (H-R) diagram
Plot L vs. backwards T.      (We can find R given L and T)

How are L, T, and R related?
L = area ´sT4 = 4 p R2 sT4
Stars can be intrinsically bright because of either large R or large T
Use ratio equations to simplify above equation
(Note book’s symbol for Sun is circle with dot inside)
Example:  Assume T is different but size is same
A star is ~ 2 ´ as hot as sun, expect L is 24 = 16 times as bright
M star is ~1/2 as hot as sun, expect L is 2-4 = 1/16 as bright
B star is ~  4 ´ as hot as sun, expect L is 44 = 256 times as bright
Example:  Assume T same but size is different
If you have a G star 4 ´ as large as sun, expect L would be 42=16 times as bright

L, T, R, and the H-R diagram
L = 4 p R2 sT4
The main sequence consists very roughly of similar size stars
The giants, supergiants, and white dwarfs are much larger or smaller

Lines of constant R in the H-R diagram

Slide 21

Different “types” of H-R diagrams

Luminosity Classes

Spectra of Different Luminosity Classes

Spectroscopic “Parallax”

What fundamental property of a star
varies along the main sequence?

Masses of Binary stars

Masses of Binary stars

Masses of Binary stars

Measuring a and P of binaries
Two types of binary stars
Visual binaries: See separate stars
a large, P long
Can’t directly measure component of a along line of sight
Spectroscopic binaries:  See Doppler shifts in spectra
a small, P short
Can’t directly measure component of a in plane of sky
If star is visual and spectroscopic binary get get full set of information and then get M

Masses and the HR Diagram
Main Sequence position:
M:    0.5 MSun
G:        1 MSun
B:       40 Msun
Luminosity Class
Must be controlled by something else

The Mass-Luminosity Relationship
L = M3.5

Eclipsing Binary Stars
System seen “edge-on”
Stars pass in front of each other
Brightness drops when either is hidden
Used to measure:
size of stars (relative to orbit)
relative “surface brightness”
area hidden is same for both eclipses
drop bigger when hotter star hidden
tells us system is edge on
useful for spectroscopic binaries