Download May 2013 - Otterbein

Welcome to
Starry Monday at Otterbein
Astronomy Lecture Series
-every first Monday of the monthMay 6, 2013
Dr. Uwe Trittmann
Today’s Topics
• Understanding the Stars II
• The Night Sky in May
Reminder: Last Starry Monday
• Limitations:
Astronomy is not an
experimental Science –
It is an observational
science
• We observe (largely)
the electromagnetic
radiation we receive
from an object
Two Interwoven Strands
• If we can measure distances to stars we
might be able to understand how they work
• If we understand how stars work, we might
be able to use this knowledge to measure
(larger) distances
Appearance vs. “the real thing”
• Angular size of an object cannot tell us its actual size –
depends on how far away it is
• Sun and Moon have very nearly the same angular size (30' =
½) when viewed from Earth
• They APPEAR to have the same size, but ARE of different
size
Understanding the Stars?
• What does understanding mean?
– We can predict their brightness from other
properties?
– We can calculate their masses from other
properties?
– We understand how energy is being produced?
– We understand how stars from, live and die?
– Something else/ All of the above?
Brightness is not Brightness?!
• Must not confuse:
– apparent brightness B
– intrinsic brightness L (luminosity)
• Only the latter is a property of the star
– Cf: the sun and the moon have the same size?!
Luminosity and Brightness
• Luminosity L is the total power
(energy per unit time) radiated
by the star, actual brightness of
star, cf. 100 W lightbulb
• Apparent brightness B is how
bright it appears from Earth
– Determined by the amount of
light per unit area reaching Earth
– B  L / d2
• Just by looking, we cannot tell
if a star is close and dim or far
away and bright
Distance Determination Method
• Understand how bright an object is
(L)
• Observe how bright an object appears (B)
• Calculate how far the object is away:
B  L / d2
So
L/B  d2 or
d  √L/B
Distances to the Stars
• Parallax can be used out to about
100 light years
• The parsec:
– Distance in parsecs = 1/parallax (in
arc seconds)
– Thus a star with a measured
parallax of 1” is 1 parsec away
– 1 pc is about 3.3 light years
• The nearest star (Proxima
Centauri) is about 1.3 pc or 4.3
lyr away
– Solar system is less than 1/1000 lyr
How are temperature and color
related?
• Thermodynamics has a clear answer from
the lab
– Physics is an experimental science!
• Do an experiment: heat up an iron rod and
see how its color and luminosity changes!
Color of a radiating blackbody as a
function of temperature
• Think of heating an iron bar in the fire: red
glowing to white to bluish glowing
• Every THING radiates roughly like a BB
Understand Star Brightness:
Classify Stars by their
Temperature (Color)
Class
O
B
A
F
G
K
M
Temperature
30,000 K
20,000 K
10,000 K
8,000 K
6,000 K
4,000 K
3,000 K
Color
blue
bluish
white
white
yellow
orange
red
Examples
Rigel
Vega, Sirius
Canopus
Sun,  Centauri
Arcturus
Betelgeuse
The hotter  the bluer!
Color “=“ Temperature!
•
•
•
•
What about the other properties?
Temperature “=“ Luminosity?
Mass “=“ Luminosity?
Size “=“ mass?
 Observe!
– Measure properties of many stars, plot them
against each other
ColorLuminosity
Correlation
• Hertzprung-Russell
Diagram is a plot of
absolute luminosity
(vertical scale)
against spectral type
or temperature
(horizontal scale)
• Most stars (90%) lie
in a band known as
the Main Sequence
Indirect Measurement of Sizes
• Distance and brightness can be used to find
the luminosity:
L  d2 B
(1)
• The laws of black body radiation also tell us
that amount of energy given off depends on
star size and temperature:
L  R2  T4 (2)
• We can compare two values of absolute
luminosity L to get the size
Sizes of Stars
• Dwarfs
– Comparable in size, or
smaller than, the Sun
• Giants
– Up to 100 times the
size of the Sun
• Supergiants
– Up to 1000 times the
size of the Sun
• Note: Temperature
changes – no clear
correlation between
size and temperature
Main Sequence Sizes
Two Ways to Continue
• Take this “understanding” of stars’
properties as new baseline to develop
distance measurement methods that work
farther out  Cosmology
• Try to “explain” these empirical findings by
uncovering the physical mechanism
generating all this energy  Astrophysics
First Path: Energy Generation in
Stars
• Use nuclear physics and thermodynamics to
understand energy production
• Then go on to uncover the lifecycle of stars
How do we know how much energy
the Sun produces each second?
• The Sun’s energy spreads out in
all directions
• We can measure how much
energy we receive on Earth
• At a distance of 1 A.U., each
square meter receives 1400 Watts
of power (the solar constant)
• Multiply by surface of sphere of
radius 149.6 bill. meter (=1 A.U.)
to obtain total power output of the
Sun: 4  1026 Watts
The Sun
Diameter: 100  that of Earth
Mass: 300,000  that of Earth
Density: 0.3  that of Earth
Temperature of visible surface
= 5800 K (about 10,000º F)
• Conclusion:
•
•
•
•
– The sun is big, hot, massive
– But not crazy big, or insanely hot,
or grotesquely massive
Where does the Energy come from?
• Anaxagoras (500-428 BC): Sun a large hot
rock – No, it would cool down too fast
• Combustion?
– No, it could last a few thousand years
• 19th Century – gravitational contraction?
– No! Even though the lifetime of sun would be
about 100 million years, geological evidence
showed that Earth was much older than this
What process can produce so much
power?
• For the longest time we did not know
• Only in the 1930’s had science advanced to
the point where we could answer this question
• Needed to develop very advanced physics:
quantum mechanics and nuclear physics
• There is virtually only one type of process
that can do the job
Atom: Nucleus and
Electrons
The Structure of Matter
Nucleus: Protons and
Neutrons (Nucleons)
Nucleon: 3 Quarks
| 10-10m |
Atomic Energy:
1 eV,
Visible light
| 10-14m |
Nuclear energy:
10000 x atomic energy!
|10-15m|
Nuclear fusion reaction
–
–
–
In essence, 4 hydrogen nuclei combine (fuse) to
form a helium nucleus, plus some byproducts
(actually, a total of 6 nuclei are involved)
Mass of products is less than the original mass
The missing mass is emitted in the form of energy,
according to Einstein’s famous formulas:
E=
2
mc
(the speed of light is very large, so there is a
lot of energy in even a tiny mass)
Hydrogen fuses to Helium
Start: 4 + 2 protons  End: Helium nucleus + 2 protons
Hydrogen
fuses to
Helium
Hydrostatic Equilibrium
• Two forces compete: gravity (inward) and energy
pressure due to heat generated (outward)
• Stars neither shrink nor expand, they are in
hydrostatic equilibrium, i.e. the forces are equally
strong
Gravity
Heat
Gravity
More Mass means more Energy
• More mass means more gravitational
pressure
• More pressure means higher density,
temperature
• Higher density, temp. means faster reactions
& more reactions per time
• This means more energy is produced
Understanding the Stars
• Stars are “suns”: hot glowing gas balls made up of
hydrogen and helium initially
• Some stars have more mass than others, hence:
–
–
–
–
Some are hotter, some are cooler
Some look blue, some red
Some live shorter, others longer
Some end up as black holes, some as neutron stars,
some as white dwarfs
Lifecycle
• Lifecycle of a
main sequence G
star
• Most time is
spent on the
main-sequence
(normal star)
250 million years
Baby Stars
Gas cloud becomes smaller,
flatter, denser, hotter  Star
A Newborn Star
• Main-sequence star;
pressure from nuclear
fusion and gravity are
in balance
– Duration ~ 10 billion
years (much longer
than all other stages
combined)
– Temperature ~ 15
million K at core, 6000
K at surface
– Size ~ Sun
Mass Matters
• Larger masses
– higher surface
temperatures
– higher luminosities
– take less time to form
– have shorter main
sequence lifetimes
• Smaller masses
– lower surface
temperatures
– lower luminosities
– take longer to form
– have longer main
sequence lifetimes
Mass and the Main Sequence
• The position of a star
in the main sequence
is determined by its
mass
All we need to know
to predict luminosity
and temperature!
• Both radius and
luminosity increase
with mass
Stellar Lifetimes
• From the luminosity, we can
determine the rate of energy
release, and thus rate of fuel
consumption
• Given the mass (amount of
fuel to burn) we can obtain
the lifetime
• Large hot blue stars: ~ 20 million
years
• The Sun: 10 billion years
• Small cool red dwarfs: trillions of
years
The hotter, the shorter
the life!
Main Sequence Lifetimes
Mass (in solar masses)
Lifetime
10 Suns
10 Million yrs
4 Suns
2 Billion yrs
1 Sun
10 Billion yrs
½ Sun
500 Billion yrs
Luminosity
10,000 Suns
100 Suns
1 Sun
0.01 Sun
Old Stars
• Leave the main
sequence when they
run out of hydrogen
fuel
• For sun-like stars
(0.08-8 Msun): puff
up into Red Giant,
etc.
• Explode into white
dwarf (ex core) and
planetary nebula
The life of
Stars –
pretty well
understood
Second Path: Distance
Measurements lead to Cosmology
• Apparent brightness B is obvious – it’s what
we “see”
• We use some additional insight (“This is a
blue MS star”, “This is a Cepheid variable
star”) to deduce the absolute brightness or
luminosity
• Then, from the apparent brightness
compared to absolute luminosity, we can
determine the distance (d2  L/B)
Use Insight to come up with another
Method: Spectroscopic Parallax
• From the color of a
main sequence star we
can determine its
absolute luminosity
• Then, from the apparent
brightness compared to
absolute luminosity, we
can determine the
distance (B  L / d2 )
• Good out to 3000 ly or
so; accuracy of 25%
More Insight: Understanding
Variable Stars yields another
Method
• Two useful types:
– Cepheids
– RR Lyrae
• Again, method uses insight to get absolute
brightness, then concludes distance from
apparent brightness
Cepheids
• Henrietta Leavitt (1908) discovers the
period-luminosity relationship for
Cepheid variables
• Period thus tells us luminosity, which
then tells us the distance
• Since Cepheids are
brighter than RR Lyrae,
they can be used to
measure out to further
distances
Properties of Cepheids
• Period of pulsation: a few days
• Luminosity: 200-20000 suns
• Radius: 10-100 solar radii
Cepheids and RR Lyrae: Yard-Sticks
• Normal stars undergoing a
phase of instability
• Cepheids are more massive
and brighter than RR Lyrae
• Note: all RR Lyrae have
the same luminosity
• Apparent brightness thus
tells us the distance to
them!
– Recall: B  L/d2
• Extends the cosmic
distance ladder out
as far as we can see
Cepheids – about 50
million ly
• In 1920 Hubble used
this technique to
measure the distance
to Andromeda
(about 2 million ly)
• Works best for
periodic variables
Distance Measurements
with variable stars
Last Rung of Distance Ladder
• This one works differently!
• Due to the expansion of the universe, we
expect distances between objects to increase
with time
• Also, the “speed” of objects should be
proportional to the distance of the object
Aside: The Expanding Universe
•
Except for a few nearby galaxies (like Andromeda), all the
galaxies are seen to be moving away from us
•
Generally, the recession speed of a galaxy is proportional to
its distance from us; that is, a galaxy that’s twice as far away
is moving twice as fast (aside from local motions within
galaxy clusters)
The Expanding Universe
This expansion pattern (speed proportional to distance)
actually implies that galaxies are all moving away from each
other
Milky Way
Expansion
The Expanding Universe
This expansion pattern (speed proportional to distance)
actually implies that galaxies are all moving away from each
other
Milky Way
Expansion
Twice as far away,
so moves twice as fast
The Expanding Universe
This expansion pattern (speed proportional to
distance) actually implies that galaxies are all
moving away from each other
Start:
A while later:
d
d
2d
The Expanding Universe
• Each galaxy sees the others moving away with
the same pattern (further → faster)
• As though the galaxies ride on a rubber band
that is being stretched!
Start:
A while later:
The Red Shift
• We know distance of galaxies
from variable star or TullyFisher measurements
• Now measure spectrum of
galaxies and compare to
laboratory measurement:
lines are shifted towards red
• This is the Doppler effect:
Red-shifted objects are
moving away from us
Hubble’s Law
Velocity = H0  Distance
Distance = Velocity /H0
• H0 = (65 ± 15) km/sec/Mpc is Hubble’s constant
• Compare to distance = velocity  time
• Appears the universe “exploded” from a single point in
the past – the Big Bang
• Age of the universe is 1/H0 or about 14 billion years
The Cosmic Distance Ladder
The Latest Surprise
• Type Ia Supernovae are
standard candles
• Can calculate distance
from brightness
• Can measure redshift
• General relativity gives us distance as a
function of redshift for a given universe
Supernovae are further away than
expected for any decelerating (“standard”)
universe
The Night Sky in May
• Nights are getting shorter!
• Spring constellations: Leo, Virgo, Big Dipper,
Bootes, Canes Venatici, Coma  lots of galaxies!
• Saturn is visible all night
Moon Phases
• Today (Waning Crescent)
• 5 / 9 (New Moon)
• 5 / 18 (First Quarter Moon)
• 5 / 25 (Full Moon)
• 5 / 31 (Last Quarter Moon)
Today
at
Noon
Sun at
meridian,
i.e.
exactly
south
10 PM
Typical
observing
hour,
early May
Saturn
Zenith
Big Dipper
points to the
north pole
SouthEast
Spring
constellations:
– Leo
– Virgo
– Coma
Messier 3
Saturn
East
• Canes
Venatici:
– M51
• ComaVirgo
Cluster
• Globular
Star
Clusters
– M3, M5
Messier 3 – A globular Star Cluster
South
Virgo and
Coma
with the
Virgo-Coma
galaxy
cluster
VirgoComa
Cluster
• Lots of
galaxies
within a
few
degrees
M87, M88
and M91
Low in
the South
– Virgo
– Corvus
– Libra
Globular Star
Cluster:
•M5
Centaurus
Mark your Calendars!
• Next Starry Monday: September 2, 2013, 7 pm
(this is a Monday
)