Download Lecture 4 January 31 - Center for Astrophysics and Space

ASTR 1020
First Homework Due Today
Second Homework due Feb 9
Next Observatory Session Tonight at 7pm
Website
http://casa.colorado.edu/~wcash/APS1020/APS1020.html
Escape Velocity
R
Fall from Large Height
1 2 GMm
mv 
2
R
Same Energy Needed to Reverse and Fly Away
2GM
ve 
R
G=6.7x10-11 in mks units
Escape velocity is the speed
at which object must be thrown
upward to escape and never come
down.
The Sun
The Sun
Falls into “Disk Stability”
99.9% Ended in Sun (0.1% in Jupiter)
Probably the Same Around All Stars -- Planets are Common
Shoots Planet-Size
Bullets into Space
Most of Mass Forms Ball
in Center
A Star Is a Hot
Ball of Hydrogen
(plus 11% Helium)
One Million Miles
What Stops the Fall?
Gravity Gets Stronger As Material Gets More Dense
GMm
Fg 
R2
R smaller implies F greater
The smaller it gets, the faster it falls in!
Why doesn’t it just become a black hole?
Or worse yet, a point-like singularity of mass?
Scaling
Scientists often do “scaling” do avoid all those
large numbers.
For example, the Sun is ABOUT a million times
the mass of the Earth and a hundred times the
size.
6
10
Vescape  11
 1000km / s
100
Question
What is the surface gravity of the Moon in
gees? R=.01Re, M=.25Me?
a).04
b)4
c)16
d).16
Answer
d
.01
g  11
 0.16
2
.25
Temperature
Temperature is a Measure of the
Random Kinetic Energy per Particle
The faster the atoms move, the higher the temperature.
But we’re talking about random motion.
If they all move together, then the object moves.
Thermal Pressure
Thermal Gas Pressure Balances Gravitational Pressure
Balloon
Every Time An Bounces Off
Edge of Balloon It Keeps It From
Collapsing
That’s Pressure
Pressure is Force per Unit Area
Pressure is Proportional to Temperature
Low Temperature
Atoms Move Slowly
High Temperature
Atoms Move Fast
A Star Is Held Up By
Thermal Pressure From Below
Gravity
Outer Mass
Individual Atoms Don’t
Orbit Entire Inside of
Star Like This
They Jostle Each Other
But Effect Is The Same
Temperature Scales
• Fahrenheit –
–
0=salt water freeze 100=human body
• Celsius
–
–
0=pure water freeze 100=water boil (sea level)
C=(F-32)x5/9
• Kelvin
–
–
–
0=absolute zero 100 degrees between freeze and boil
K=C+273
-273C = 0K = Absolute Zero
At Absolute Zero Atoms Stop Moving
Thermal Pressure
PV  nRT
PV  NkT
Ideal Gas Law
Chemistry Style
Ideal Gas Law
Physics Style
P
V
n
R
T
Pressure
Volume
# moles
Constant
Temperature (K)
P
V
N
k
T
Pressure
Volume
# atoms
Constant
Temperature (K)
Pressure Is Proportional to Temperature x Density
Pressure Balance
A Star Always Balances Gravitational Pressure with Thermal Pressure
At Each Point Inside
Thermal Pressure (Jostling)
Gravity
But We Have a Problem
The Sun is Luminous
Radiates Energy Into Space
Luminosity is Power Radiated -- ergs/second
The Energy Comes From Motion of the Atoms
Temperature Drops
What Happens When T Drops?
Luminosity Effect
When T Drops Thermal Pressure Can’t Hold Off Gravity
The Sun Shrinks -- Radius Drops
Energy is Released as Gas Falls Deeper Into Gravity Field
Temperature Rises
Note – Loss of Energy Results in
a) Temperature Rise
b) Radius Decrease
But Wait A Minute…
Isn’t the Sun Stable?
The Sun has been remarkably stable for 4 billion years
as evidenced by geological records.
This collapse is the process by which the Sun coalesced.
But then it stopped. Why?
The Sun collapsed until a new source of energy offset the losses
to radiation.
NUCLEAR FUSION --- IT’S BURNING HYDROGEN
As long as it burns H at this rate, it will be stable.
Fusion Increases with T
As T in core of Sun increases so does energy production
Sun shrank steadily, with T rising until, about 10 million years
after it started to form, it reached its current size
There is a VERY fast increase in nuclear energy production
above 1,000,000K.
At 15,000,000K in the core nuclear power generated finally balanced
the luminosity from the surface.
That’s the equilibrium we are still in.
The Nuclear Core
Envelope
1 Million K
core
15x106K
Photosphere 5000K At Surface
Cosmic Composition
•
•
•
•
•
H
He
O
C
N
hydrogen
helium
oxygen
carbon
nitrogen
89% by number
11%
0.1%
0.06%
0.015%
Pretty much the composition of the entire universe.
Sun and Jupiter have this composition
Earth does not.
Fusion vs. Fission
Fusion: Atoms unite and release energy (Fuse)
New atom must be no heavier than iron z=26
Fission: Heavy atoms split to release energy
Initial atom must be heavier than iron
WWII Nukes were fission bombs made of U and Pu
Sun works on FUSION of H into He
Proton-Proton Chain
Bottom Line: H+H+H+H  He
1H
1+
1H
2He
3+
1H
2+
2He
1
 1 H 2 + e+ + n
1H
3
1
 2He3 + g
 2He4 + 1H1 + 1H1
5x106 < T < 2x107K
CNO Cycle
6C
12 +
7N
13
6C
7N
13 +
15
15 +
1
 7N13 + g
 6C13 + e+ + n
14 +
8O
7N
1H
1H
1H
1
1
 7N14 + g
 8O15 + g
 7N15 + e+ + n
1H
1
2x107 < T < 108K
 6C12 + 2He4
Net: 1H1 +1H1 + 1H1 +1H1  2He4 + 2e+ + 4g +2n
hydrogen -> helium + energy
Triple-a Reaction
2He
4Be
4+
8+
2He
2He
4
4
 4Be8 + g
T < 108K
 6C12 + g
Must be very dense for this to work
Be8 decays back into helium very quickly
unless struck by another He4
Net: 2He4 +2He4 + 2He4 +2He4  6C12 + 2g
helium -> carbon + energy
Too low density
in Big Bang
Solar Schematic
Sunspots
Seen by Ancient Persians
(and me!)
Groups of Sunspots
Solar Corona Visible in Eclipse
The Sun Viewed in X-rays
X-ray Movie
X-ray Loops
Magnetic Structure
Dynamic Structure
Solar Turbulence
Differential Rotation
Rotates in 25 days at Equator
28 days Mid Latitude
30 days Poles
Rapidly Twists Up
Sunspots Erupt in Groups
Sunspot Cycle
During mid 1600’s sunspots became non-existent
Maunder Minimum
Solar Wind 5x105K
Corona 2x106K
Transition Region 105K
Chromosphere 104K
Photosphere 5500K
Solar Wind Passes Earth
Summary: Sun as a Star
• Formed from cloud 4.6x109 years ago
• Collapsed to present size
– stabilized by nuclear reactions
•
•
•
•
•
•
•
Emits 4x1026 W
Runs on proton-proton chain and CNO cycle
Now 20% brighter
Turbulent upper envelope
Magnetic Fields from Differential Rotation
Sunspots, Corona, Solar Wind
Activity Cycle 11 years
STARS
Stars are grouped in Galaxies
• Sun and all the stars we see are part of
Milky Way Galaxy
• We all orbit a common center
• Sun is 3x1020m from center of MW
You are here
Each star orbits
center
Disk Stability Again
Distances to the Stars
• Closest Star, Proxima Centauri is 4x1016m
away. (Alpha Cen ~4.3x1016m)
• Need a more convenient unit
The Light Year
Light Travels at 300,000km/s (186,000miles/s = 3x108m/s)
That’s one foot per nanosecond
One Year is 3.15x107 seconds long
In one year light travels 3.15x107x3x108 = 1016m
This is the definition of a light year. Prox Cen is at 4ly.
Question
• There’s a big black hole in the Center of
the Milky Way at a distance of 3x1020m.
How long does it take for its light to reach
us?
• A) 3years
• B) 30 years
• C) 300 years
• D) 3000 years
• E) 30,000 years
Question
• There’s a big black hole in the Center of
the Milky Way at a distance of 3x1020m.
How long does it take for its light to reach
us?
• A) 3years
• B) 30 years
• C) 300 years
• D) 3000 years
• E) 30,000 years
The Parsec
Astronomers use the parsec as a measure of distance
1pc = 3ly
1pc = 3x1016m
Origin of parsec comes from method of measuring
distance
Each Star Orbits the Center
How Long does that Take?
r3
P  2
GM
P  6.28
3x10 
20 3
6.7 x1011 x 2 x10 42
30 x1060
29
 6.3

6
.
3
2
.
5
x
10
13x1031
P  6.3 25x1028  6.3x5x1014  3x1015 sec
3x1015 sec
8
P

10
years
7
3x10 s / yr
Takes about a hundred million years to circumnavigate the galaxy
2r 2 x10 21 m
v

 6 x105 m / s  600km / s
15
P
3x10 s
Star Names
• Arabic Names
– Antares, Capella, Mira, etc.
• Constellations
a Orionis, b Cygni, … then 49 Ori, 50 Ori, etc.
• Catalogues HD80591, SAO 733421, etc
• RA and Dec – just position in the sky
Proper Motion
2003
All stars move
Nearby stars move faster
Appear to move against fixed field
1900
Can Take Many Years
Use Old Photographic Plates
Parallax
I year cycle
The Parsec
1 parsec
1AU
1 arcsecond
360 degrees in circle
60 arcminutes per degree
60 arcseconds per arcminute
200,000AU = 1 parsec = 3x1016m
parsec ---- parallax second
Question
• Based on the definition of a parsec , if star A has
a parallax of 0.5 arcseconds and star B has a
parallax of 0.75 arcseconds which one is farther
from the Earth?
• A. Star B is farther away because it has a
higher parallax
• B. Star A is farther away because it has a lower
parallax
• C. All stars are the same distance away from
the Earth
• D. It is impossible to tell from this information.
Question
• Based on the definition of a parsec , if star A has
a parallax of 0.5 arcseconds and star B has a
parallax of 0.75 arcseconds which one is farther
from the Earth?
• A. Star B is farther away because it has a
higher parallax
• B. Star A is farther away because it has a lower
parallax
• C. All stars are the same distance away from
the Earth
• D. It is impossible to tell from this information.
Measure Parallax
distance to a star in parsecs = 1/(parallax in arcseconds)
e.g. measure .04” parallax, then distance is 25pc
Measuring Parallax was first successful way to measure
distances to stars after centuries of trying
Took high speed photography in 1890’s to do it.
Question
• The parallax of an observed star is 0.1
arcseconds, how many lightyears is it
away from Earth?
• a. 1 light year
• b. 3 light years
• c. 10 light years
• d. 30 light years
• e. 75 light years
Question
• The parallax of an observed star is 0.1
arcseconds, how many light years is it
away from Earth?
• a. 1 light year
• b. 3 light years
• c. 10 light years
• d. 30 light years (10parsecs)
• e. 75 light years