Astro 1050     Mon. Oct. 14, 2002
   Today:  HW #5 review
                Finish Ch. 8, Properties of Stars
            Chapter 9: Formation & Structure

Homework #5
1. Mass of the Binary stars:  1.8 solar masses
2. Parsecs & Parallax: d = 1/p, so 1/12 of an arcsec
3. Most of the nearby stars are cool K and M stars.
4. m=-1.5, M=1.4.  Recall 10 pc is about 30 lt. yrs.
Hard method: m – M = -5 + 5log(d/1pc), so less than 30 years
5. d =145 pc, M = -5.2, so m = 0.6 (other answers bad)
6. Same M, one star is type G, one is type B.  G is bigger.

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

Starting Ch.9: Interstellar Medium
Since stars die, new ones must somehow be born
They must be made out of material like star:
H, He, plus a little heavier elements
Three types of interstellar “nebulae” or clouds
Emission nebulae -- Glow with emission lines
Reflection nebulae -- Reflect starlight
Dark nebulae -- seen in silhouette

Emission nebulae
The red glow is Hydrogen Balmer a   (Ha ) emission
Could be from hot gas but –
relative strength of emission lines not always right
Can also get fluorescence:
UV photon from bright star boosts electron to high level (or ionizes it)
Emission lines created as electron cascades back down through H energy levels
The “horse” is a dark cloud in front of the glowing gas.

Reflection nebulae – The Pleiades
Cluster of new stars
Visible to unaided eye
in western Taurus
Stars form in clusters – most of which slowly spread apart.
Reflection nebula is reflected sunlight
Can see stellar-like spectra with absorption lines
Blue light scattered more efficiently than red
Pleiades didn’t form here – just moving through this cloud of dust.

Dark Nebula

Spectral Measurements
Use spectra of stars
Ignore broad (“high pressure” stellar lines
Very narrow (low pressure) lines from interstellar gas
This one Ca II  = Ca+1
Stronger in more distant stars
Stronger when looking through interstellar gas clouds
Hydrogen hard to measure
remember Balmer rules

Measurements at other Wavelengths
Infrared “Cirrus”
really slightly warm dust
X-Rays of hot gas near exploded stars (supernova)
Radio observations of “Molecular Clouds”
Called that because cool and dense enough for molecules to form
H2 also hard to detect
CO common and easy to detect
Densest have 1000 atoms/cm3
T as low as 10 K
Location of star formation

Collapse of
 Molecular Clouds
Barely stable against collapse:
Imagine slightly compressing cloud
Gravity goes up because material is packed more tightly (R in 1/R2 is smaller)
Tends to make cloud want to collapse
Pressure goes up because material is packed more tightly (P µ rT) and r higher
Tends to make cloud want to expand
For smaller clouds Pressure wins (stable)
For larger clouds Gravity wins (collapse)
As it collapses and becomes denser, smaller and smaller parts become unstable
Shock wave can trigger collapse

What will a forming star look like in HR diagram?
Temperature changes relatively simple
Starts out large and relatively cool Must be on red side of diagram
It heats up as it contracts Must towards the blue
Luminosity more complicated because it depends on T and R
Not much energy to start with Luminosity must start out low
Collapse releases grav. energy Luminosity will rise
Fusion begins, releases more energy Luminosity at a peak
Collapse slows, only have fusion now Luminosity declines
Finally stabilizes on the main sequence

How does mass affect collapse?
More massive protostars have stronger gravity
Collapse speed will be much faster
Fast collapse and short lifetime means massive stars reach end of lifetime while low mass stars in cloud are just forming
Supernova shocks may come from earlier generation of stars
Sequential Star Formation
Energy from supernova and other effects eventually disrupts cloud – prevents further collapse.

Observations of collapse
Young cluster “NGC 2264”
Few million years old
High mass stars have reached
main sequence
Lower mass stars are still approaching main sequence
T Tauri stars
Naming of classes of stars:  Usually named after first star in class:  T Tauri
Stars with letters (RR Lyrae) are typically “variable” stars
Earlier stages hidden by dust

More details of stellar structure and energy generation
Alternatives to the proton-proton chain
Fusion of Helium to heavier elements
Proton-proton reaction slow because:
Need two rare events at once
High energy collision of 2 protons
Conversion of p Ţn during collision

The CNO Cycle
Gives way around need for p ®n during the collision
Still must happen later – but don’t need to rare events simultaneously
Trade off is need for higher energy collisions  (T>16 million K)
Add p to some nucleus where new one is still “stable”
Wait for p ® n while that nucleus just “sits around”
The net effect is still   4  1H ®  4He
C just acts like a “catalyst”

Heavy Element Fusion
Triple Alpha process
4He + 4He ® 8Be + g
8Be + 4He ® 12C  + g
Similar type reactions create heavy elements above 600 Million K
Plot to left gives:
x:   # of neutrons
y:   # of protons
Right one – add neutron
Up     one – add proton
Diagonal    p ® n or reverse
Jumps:        add 4He or more

Models of Stellar Structure
Divide star into thin shells,calculate how following vary from shell to shell
 (i.e. as function of radius r)
P (Pressure)
T (Temperature)
r (Density)
To do this also need to find:
M (Mass) contained within any r
L (Luminosity) generated within any r
P example:

Numerical Stellar Models

Why don’t stars collapse?
Limiting case:  Assume no nuclear fusion so only energy source is gravity.
Star is “almost” in hydrostatic equilibrium
Star radiates energy:  If nothing else happened T would drop, P would drop, star would shrink.
Star does shrink, but in doing so gravitational energy is converted to heat, preventing T from continuing to drop.
In fact, since star is now more compact, gravity is stronger and it actually needs higher P (so higher T) to prevent catastrophic collapse
As star shrinks, ˝ of gravitational energy goes into heating up star, ˝ gets radiated away
Rate at which it radiates energy, so rate at which it shrinks, is limited by how “insulating” intermediate layers are

Why do we get steady fusion rates?
Strange counterintuitive result:
As star radiates away thermal energy it actually heats up
(because as it shrinks gravity supplies even more energy)
Star continues to shrink till it gets hot enough inside for fusion (rather than gravity) to balance energy being radiated away.
Nuclear thermostat
If fusion reactions took place in a “box” with fixed walls:
Fusion Ţ more energy Ţhigher T Ţ more fusion    (explosion)
If fusion reactions take place in sun with “soft gravity walls”:
If fusion rate is too high T tries to go up but star expands and actually ends up cooling off – slowing down fusion.  (steady rate)

Mass-Luminosity relationship
L µ M3.5 Why?
Higher mass means higher internal pressure
Higher pressure goes with higher temperature
Higher temperature means heat leaks out faster
Star shrinks until T inside is high enough for
fusion rate (which is very sensitive to temperature)
to balance heat leak rate

Lifetime on Main Sequence
L µ M3.5 T µ fuel / L = M/M3.5 = M-2.5
Example:  M=2 MSun      L = 11.3 LSun        T =1/5.7  TSun

How about a 0.5 solar mass star?
M = 0.5 Msun
Time =
Luminosity =

How about a 0.5 solar mass star?
M = 0.5 Msun
Time = 5.7 times solar lifetime
Luminosity = 0.09 solar luminosity

Width of Main Sequence – and Stellar Aging
As star converts H to He you have more massive nuclei
Pressure related to number of nuclei
Gravity related to mass of nuclei
Pressure would tend to drop unless something else happens
Temperature must rise (slightly) to compensate
Luminosity  must  rise (slightly) as heat leaks out faster

Orion Nebula: A Star-Forming Region
Red light = Hydrogen emission
Blue light = reflection nebula
Dark lanes = dust
Astronomy Picture of the Day:

Protoplanetary Disks in the Orion Nebula
Dusty disk seen in silhouette
Central star visible at long wavelengths

Herbig-Haro objects: The angular momentum problem
As clouds try to collapse angular momentum makes them spin faster
A disk forms around the protostar
Material is ejected along the rotation axis

Herbig-Haro 34 in Orion
Jet along the axis visible as red
Lobes at each end where jets run into surrounding gas clouds

Motion of Herbig-Haro 34 in Orion
Can actually see the knots in the jet move with time
In time jets, UV photons, supernova, will disrupt the stellar nursery