Download PHYS3380_110415_bw - The University of Texas at Dallas

PHYS 3380 - Astronomy
The second exam will be next Monday, November 9 at the
regular class time. It is closed book but you may bring in
one 8 1/2 X 11 inch “cheat sheet” with writing on both
sides. It will cover everything I have covered in class up
through last Wednesday’s class (excluding what I
covered on the first exam – i.e., starting with the class on
9/28/15). It will not cover anything from today’s or
Monday’s class. The homework solutions up to
assignment #8 are on line.
PHYS 3380 - Astronomy
Homework Set #9
11/4/15
Due 11/16/14
Chapter 12
Review Questions
6,8
Problems
3, 7
Learning to look
1
Chapter 13
Review Questions
2, 6
Problem
1
PHYS 3380 - Astronomy
Atacama Large Millimeter/submillimeter Array (ALMA)
ALMA - an astronomical interferometer of radio telescopes in the Atacama desert of
northern Chile
- on the Chajnantor plateau at 5,000 meters altitude
- high and dry site - crucial to millimeter wavelength operations
- 66 12-meter , and 7-meter diameter radio telescopes - up to 16 km baseline
PHYS 3380 - Astronomy
The principal sources of atmospheric
attenuation are molecular resonances of
water vapor, oxygen and ozone. The
resonances of water vapor and oxygen
are pressure broadened and cause
attenuation far from the resonance
frequencies.
Below 30 GHz the absorption is
dominated by the weak transition of H20
at 22.2 GHz, and rarely exceeds 20% in
the zenith directions. The oxygen bands
in the 53-67 GHz band are considerably
stronger, and no astronomical
observations can be made from the
ground in this band. A similar effect
happens with the isolated 118 GHz O2
line, which makes observations
impossible in the 116-120 GHz band.
There is a series of strong water vapor
lines at 183, 325, 380, 448, 475, 557,
621, 752, 988 and 1097 GHz and
higher. Observations can be made in
the windows between these lines at dry
locations like the Chajnantor plateau.
PHYS 3380 - Astronomy
Composite image of
the young star HL
Tauri and its
surroundings using
data from ALMA
(enlarged in box at
upper right) and
Hubble (rest of the
picture). This is the
first ALMA image
where the image
sharpness exceeds
that normally attained
with Hubble.
PHYS 3380 - Astronomy
Incredible fine detail never been seen before in the planet-forming disc around a young
star. These are the first observations that have used ALMA in its near-final configuration
and the sharpest pictures ever made at submillimetre wavelengths. Show substructures
within the never been seen before - possible positions of planets forming in the dark
patches within the system.
PHYS 3380 - Astronomy
Star Clusters
NGC3293 - Open cluster
47 Tuc – Globular cluster
10 - 1000 stars
About 25 pc in diameter
Open, transparent
appearance - stars are not
crowded together
105 - 106 stars
10 - 30 pc in diameter
Nearly spherical and much
closer together than open
clusters
PHYS 3380 - Astronomy
Open Cluster HRD
•MS turn off point varies massively,
lowest is consistent with globulars
•Maximum luminosity of stars can
get to Mv-10
•Very massive stars found in these
clusters
Globular Cluster HRD
•MS turn-off points in similar position.
Giant branch joining MS
•Horizontal branch from giant branch to
above the MS turn-off point
•Horizontal branch often populated only
with variable RR Lyrae stars
PHYS 3380 - Astronomy
Open vs. Globular Clusters
Differences are interpreted due to age – open clusters lie in the disk of the
Milky Way and have large range of ages. The Globulars are all ancient,
with the oldest tracing the earliest stages of the formation of Milky Way (~
12 109 yrs)
Globular clusters are old and
metal poor - produce a horizontal
branch
• Mass-loss dependent on
metallic content - drives
bluewards evolution
Open clusters are metal rich produce a red clump
• More metal rich stars
appear towards red
• Clump stars  extreme red
end of HB
PHYS 3380 - Astronomy
PHYS 3380 - Astronomy
Modelling star clusters
Best way to check stellar evolutionary calculations
is to compare calculated and observed tracks. But
can’t observe stars as they evolve - need to use
star clusters.
Isochrones:
A curve which traces the properties of stars as a
function of mass for a given age.
Be clear about the difference with an evolutionary
track - which shows the properties of a star as a
function of age for a fixed mass.
Isochrones are particularly useful for star clusters all stars born at the same time with the same
composition. Consider stars of different masses
but with the same age . Make a plot of Log(L/L)
vs. LogTeff for an age of 1Gyr. The result is an
isochrone.
Important - When we observe a cluster, we are seeing a “freeze-frame” picture at a
particular age. We see how stars of different masses have evolved up to that fixed
age (this is not equivalent to an evolutionary track).
PHYS 3380 - Astronomy
NGC6231 young cluster
Age~ 6Myrs
47 Tuc : globular cluster. Age=
8-10Gyrs
Pleiades young open cluster
Age~ 100Myrs
NGC188: old open cluster .
Age= 7Gyrs
PHYS 3380 - Astronomy
Evidence for Stellar Evolution: Variable Stars
Some stars show intrinsic brightness variations not
caused by eclipsing in binary systems.
Most important example: d Cephei
Cepheid stars - oscillate between two states
1. star is compact - large temperature and
pressure gradients build up in the star. These
large pressures cause the star to expand.
2. When the star is in its expanded state, there is a
much weaker pressure gradient in the star.
Without the pressure gradient to support the
star against gravity, the star contracts and
returns to its compressed state.
Light curve of
d Cephei
PHYS 3380 - Astronomy
Pulsating Variables: The Valve Mechanism
Partial He ionization zone is opaque and
absorbs more energy than necessary to
balance the weight from higher layers.
=> Expansion
Upon expansion, partial
He ionization zone
becomes more
transparent, absorbs
less energy => weight
from higher layers
pushes it back inward.
=> Contraction.
Upon compression, partial He ionization zone
becomes more opaque again, absorbs more
energy than needed for equilibrium => Expansion
PHYS 3380 - Astronomy
Cepheid Variables: The Period-Luminosity Relation
The variability period of a Cepheid
variable is correlated with its luminosity
- most recent empirical formula
produced using data from the
Hipparcos satellite, to calculate the
distances to many Galactic Cepheids
via trigonometric parallax.
Mv = -2.81 log(P) - (1.43  0.1)

(P is in days)
Cepheids have masses between five and
twenty solar masses. More massive
stars are more luminous and have more
extended envelopes. Because these
envelopes are more extended and the
density in their envelopes is lower, their
variability period, which is proportional to
the inverse square root of the density in
the layer, is longer.
 the more luminous it is, the more
slowly it pulsates.
PHYS 3380 - Astronomy
Population I - Type I Cepheids - metal-rich stars
• common in the spiral arms of the Milky Way galaxy
• extreme Population I - youngest stars found farther in
• intermediate Population I stars are farther out, etc.
• Sun is considered an intermediate Population I star
• have regular elliptical orbits of the galactic centre, with a low relative
velocity
• more likely to possess planetary systems, since planets, particularly
terrestrial planets, thought to be formed by the accretion of metals
• intermediary disc population - between the intermediate populations I and
II
Population II - type II Cepheids - metal-poor stars
• more primitive. formed during an earlier time of the universe
• intermediate Population II - common in the bulge near to the centre of the
galaxy
• halo Population II - in the galactic halo
• believed that Population II stars created all the other elements in the
periodic table, except the more unstable ones.
Type II Cepheids not as opaque as type I
• energy escapes more easily
• less luminous for same period of pulsation
PHYS 3380 - Astronomy
Population III - metal-free stars
• hypothetical population of extremely massive and hot stars with virtually
no metal content, except for a small quantity of metals formed in the Big
Bang, such as Lithium-7
• believed to have been formed in the early universe.
RR Lyrae - older, less massive, and fainter (~45 L) than Cepheids
• little over half the Sun’s mass
• from speed at which RR Lyraes pulsate (~0.2 - 2 days) know that size
cannot be changing enough to cause the change in brightness that we
see.
- surface of the star would have to move in and out so fast that the
star would blow itself apart.
• as the RR Lyrae shrinks and expands, the surface heats up and cools
down.
-change in brightness accounted for by temperature change
• often found in globular clusters - allow better determination of distance
and metallicity
PHYS 3380 - Astronomy
Cepheid Distance Measurements
Measuring a Cepheid’s period, we can determine its absolute magnitude.
Comparing absolute and apparent magnitudes of Cepheids, we can measure
their distances.
The Cepheid distance
measurements were
the first distance
determinations that
worked out to
distances beyond our
Milky Way.
Cepheids are up to
~ 40,000 times more
luminous than our sun
 can be identified in
other galaxies - Edwin
Hubble first identified
some Cepheids in the
Andromeda galaxy, thus
proving its extragalactic
nature
PHYS 3380 - Astronomy
Pulsating Variables: The Instability Strip
For specific
combinations of radius
and temperature, stars
can maintain periodic
oscillations.
Those combinations
correspond to locations
in the Instability Strip
Cepheids pulsate
with radius changes
of ~ 5 – 10 %.
PHYS 3380 - Astronomy
Period Changes in Variable Stars
Periods of some Variables are not constant over time
because of stellar evolution.
 Another piece of evidence for stellar evolution.
PHYS 3380 - Astronomy
The End of a Star’s Life
When all the nuclear fuel in a star is used up, gravity will win over pressure
and the star will die.
High-mass stars will
die first, in a gigantic
explosion, called a
supernova.
Less massive stars will
form planetary nebula
and die as white dwarfs
or in a less dramatic
event than a supernova,
called a nova
PHYS 3380 - Astronomy
The Final Breaths of Sun-Like Stars: Planetary Nebulae
Remnants of stars with ~ 1 – a few M
Radii: R ~ 0.2 - 3 light years
Expanding at ~10 – 20 km/s (Doppler shifts)

Less than 10,000 years old
Have nothing to do with planets.
The Helix Nebula
PHYS 3380 - Astronomy
The Formation of Planetary Nebulae
Two-stage process:
The Ring Nebula
in Lyra
Slow wind from a red giant blows
away cool, outer layers of the
star
Fast wind from hot, inner
layers of the star overtakes
the slow wind and excites it
=> Planetary Nebula
PHYS 3380 - Astronomy
Planetary Nebulae
Often asymmetric, possibly due to
• Stellar rotation
• Magnetic fields
• Dust disks around the stars
The Butterfly
Nebula
Globe
The Ring Nebula
The Helix Nebula
Knots in the
Helix Nebula
Knots in the
Helix Nebula
PHYS 3380 - Astronomy
PHYS 3380 - Astronomy
The Remnants of Sun-Like Stars: White Dwarfs
Sunlike stars build up a
Carbon-Oxygen (C,O)
core, which does not
ignite Carbon fusion.
He-burning shell keeps
dumping C and O onto
the core. C,O core
collapses and the matter
becomes degenerate.
 Formation of a
White Dwarf
PHYS 3380 - Astronomy
Equation of State of a Degenerate Gas
At high densities, gas particles may be so close, that interactions between them
cannot be neglected.
What basic physical principle will become important as we increase the density
and pressure of a highly ionised ideal gas ?
The Pauli exclusion principle - the e– in the gas must obey the law:
No more than two electrons (of opposite spin) can occupy the same
quantum cell
The quantum cell of an e– is defined in phase space, and given by 6 values:
x, y, z, px, py, pz
The volume of allowed phase space is given by
xyzpxpypz  h
3
The number of electrons in this cell must be at most 2
PHYS 3380 - Astronomy
White Dwarfs
Degenerate stellar remnant (C,O core)
Extremely dense:
1 teaspoon of WD material: mass ≈ 16 tons!!!
Chunk of WD material the size of a beach ball would
outweigh an ocean liner!
White Dwarfs:
Mass ~ M
Temp. ~ 25,000 K
Luminosity ~ 0.01 L
PHYS 3380 - Astronomy
White Dwarfs
Low luminosity; high temperature => White dwarfs are found in the lower
left corner of the Hertzsprung-Russell diagram.
PHYS 3380 - Astronomy
Example of WD discovered in Globular
cluster M4
Cluster age ~ 12Gyrs
WDs represent cooling sequence
Similar intrinsic brightness as mainsequence members, but much hotter
(hence bluer)
PHYS 3380 - Astronomy
The Chandrasekhar Limit
The more massive a white dwarf, the smaller it is.
 Pressure becomes larger, until electron degeneracy pressure can
no longer hold up against gravity.
WDs with more than ~ 1.4 solar
masses can not exist!
PHYS 3380 - Astronomy
Summary of 1 M evolution
･On Main Sequence, Sun evolves slowly due to the changing chemical composition of
its core - the Sun gets hotter and increases in luminosity (moving to the left and up in
the HR diagram).
･After the hydrogen is used up in the core, the helium core contracts, and heats the
hydrogen rich layer just outside of the core. The hydrogen ignites in the shell around
the core and the Sun moves to the right in the HR diagram.
･When the outer layers of the Sun become convective, the luminosity of the Sun
shoots up and the Sun becomes a Red Giant.
･The core continues to contract until it reaches the ignition temperature for helium
･At the point of helium ignition, the core of the Sun is supported by the hot (normal)
gas of helium nuclei produced by the hydrogen burning and by degenerate electrons;
the electrons already occupy many of the available energy levels up to very high
energies - it will take a lot of heat in order to increase the energy of even 1 electron.
The fractional increase in the kinetic energy of the electrons will be very small for a
given amount of heat input. So, the pressure due to the electrons does not change
very much for a given amount of heat input -the core of the Sun will not expand
strongly in response to the ignition of the helium.
PHYS 3380 - Astronomy
･The temperature of the core rises (really the temperature of the helium nuclei gas
rises) as the reactions turn-on - the reaction rate goes up - the temperature of the
helium nuclei in the core goes up - the rate of reactions goes up - and so on.... Until
ignition of helium burning - helium flash lasts for a few minutes or less with a peak core
luminosity of up to 1 x1011 L.
･The helium flash shuts down because, eventually, as you add enough heat to the gas,
you can excite electrons to higher energy states and you eventually spread the
electrons out over a large enough range of states to make the gas normal. (obey the
perfect gas law).
･The helium flash occurs in stars less massive than around 2.25 M.
･After the helium flash, the star quiescently burns what is left of the helium in its core
(for a time ~ 10 - 20 % as long as its Main Sequence lifetime).
･When the helium is converted into carbon and oxygen, the core again contracts,
ignites helium burning in a shell around the core, expands, cools, and moves to the
right in the HR diagram.
PHYS 3380 - Astronomy
･When the star becomes convective, it moves up the AGB greatly increasing in
luminosity at roughly constant temperature. Low mass stars are not, however,
massive enough to reach the ignition temperature of carbon before the core becomes
completely supported by degenerate electron pressure (which halts the contraction).
･The nuclear evolution of the Sun ends at this point and the star is now ready to enter
into its final stages of evolution; at this time the star is AGB star characterized by a
carbon-oxygen core, surrounded by a helium burning shell and a hydrogen burning
shell.
• For stars whose mass is greater than 2.25 M, the electrons in their cores are not
degenerate at the time of helium ignition and so there is no helium flash and they
settle into a stage of quiescent helium burning before they approach the AGB.
•Star cools and moves left on the H-R diagram possibly generating a planetary nebula
•He-burning shell keeps dumping C and O onto the core. C,O core collapses and the
matter becomes degenerate.
•Star becomes a white dwarf
PHYS 3380 - Astronomy
Summary of 1 M evolution
Approximate typical
timescales
Phase
Main-sequence
Subgiant
Redgiant Branch
Red clump
AGB evolution
PNe
WD cooling
 (yrs)
9 x109
3 x109
1 x109
1 x 108
~5x106
~1x105
>8x109