Mass and the Properties of Main Sequence Stars

1
Mass and the Properties of Main Sequence Stars

• Mass is the most important properties of the
  main-sequence stars. It determine their
  luminosity, surface temperature, radius, and
  lifetime.
• Nuclear fusion requires high temperatures and
  densities in the core, and the stars internal
  conditions are determined by the equilibrium
  condition between the inward pull of gravity and
  the outward push of pressure.
• In a star that has high mass, the greater weight
  of its overlying layers means the star must
  sustain a higher nuclear fusion rate to generate
  the additional pressure needed to maintain
  gravitational equilibrium.
• The higher nuclear fusion rate makes the star
  more luminous.
• The high luminosity requires a star to have
  either high temperature or large size, or both.
• The higher luminosity also means that it will run
  out of fuel faster than less massive stars.

10 Rsun
3 Rsun
1 Rsun
0.1 Rsun
2
The Lifetime of Main-Sequence Stars

• The lifetime of a star is determined by how
  fast it burns its supply of hydrogenThis
  hydrogen burning rate can be inferred from the
  luminosity of the star.
• The Mass-Luminosity Relation
• Once we have observationally determined the
  luminosity and mass of many main sequence stars,
  we find that the higher the mass M of a star is,
  the higher is its luminosity (L).
• L/L? (M/M? )3.5
• Note The Mass-Luminosity relation applies to
  main-sequence stars only!
• For example,
• A 10 M? star is roughly (103.5 ) 3,000
  brighter, or burning its hydrogen times 3,000
  faster.
• We know that the lifetime of the Sun is about 10
  billion years.
• The more massive star would have a lifetime of
  about
• 10 10 billion years 3,000 30 million
  years.

3
Giant and Supergiants

• Giants and supergiants are stars nearing the
  ends of their lives.
• Giants and supergiants do not follow the
  relationship between surface temperature and
  luminosity for hydrogen-burning, main-sequence
  stars.
• The supply of hydrogen fuel in the core of the
  giants is running out, and they respond to this
  fuel shortage by releasing fusion energy at a
  furious rate. Thus, in order to radiate away this
  huge amount of energy, the surface of a dying
  star must expand to an enormous size (Chapter 12)
• Because giants and supergiants are so bright, we
  can see them even if they are not especially
  close to us.
• Many of the brightest stars visible to the naked
  eye are giants or supergiants.
• They are often identifiable by the reddish color
  produced by their cool surfaces.
• Giants and supergiants are considerably rarer
  than main-sequence stars. When we look at the
  sky, most of the stars we see are main sequence
  stars.
• Betelgeus M2 I

Betelgeuse and R Doradus
4
White Dwarf

• White dwarfs are the exposed core of the dead
  low-mass main-sequence stars, supported against
  gravity by electron degenerate pressure (Chapter
  12).
• Properties
• Hot surface (not long after the formation),
  comparable or higher than the surface of the Sun.
• Low luminosity (0.0001L? to 0.1L? )
• High mass comparable to the Sun
• White dwarfs have high surface temperature and
  low luminosity
• ? Small size comparable to the size of the
  Earth.
• White dwarfs are small in size, but high in mass
  
• Very high density

5
Summary of Sizes of Stars From Supergiants to
White Dwarfs
Supergiant 100 1000 Rsun
Giant 10 100 Rsun
Main-Sequence Star 0.1 10 Rsun
White Dwarf 0.01 Rsun About the size of Earth!
6

• Properties of Stars
• Classifying Stars
• Star Clusters
• Open and Globular Clusters
• Dating the Age of the Universe by Globular
  Clusters

7
Star Clusters
The Pleiades

• Most stars are formed from giant clouds of
  gas with enough material to form many stars. When
  we look into the sky, we often find clusters of
  stars. There are two types of clusters
• Open Clusters
• Found in the disk of the galaxy.
• Contains a few thousand stars.
• Span about 30 light-years.
• Globular Clusters
• Found in the halo of the galaxy.
• Up to one million stars.
• Spans about 60 to 150 light-years.
• Because
• Stars in the same cluster lie at about the same
  distance from Earth
• Stars in the same cluster are formed roughly at
  the same time.
• They are useful as a cosmic clock

8
HR Diagram of Star Cluster

• Pleiades is an open cluster that contains
  thousands of stars
• The H-R diagram of Pleiades shows that most of
  the stars fall in the main sequence curve.
• However, it is missing the O and B type stars.
• The high-luminosity end of the curve moves away
  from the main-sequence curve
• If the stars in Pleiades were all formed at the
  same time, then higher mass stars would move off
  the main sequence curve first. Therefore, the
  theoretical lifespan of the most massive star of
  the cluster remaining in the main sequence tells
  us about the age of the cluster.

H-R Diagram of Pleiades
9
Dating the Age of Star Clusters

• When a star cluster is born, it contains stars
  spanning the entire range of the H-R diagram.
• As the cluster ages, the high-luminosity, hot,
  blue stars move away from the main sequence curve
  first.
• The point where the curve of the H-R diagram
  deviates from the main sequence curve (the
  main-sequence turn-off point) indicates the age
  of the cluster.

Evolution of the H-R Diagram of Star Cluster
100 million years
10 billion years
New-born
Luminosity
Luminosity
Luminosity
Main sequence curve
Temperature
Temperature
Temperature
Time
10
Examples of H-R Diagram of Star Clusters
We have only being plotting the H-R diagrams for
about 100 years. Therefore, we do not have a time
sequence of H-R diagrams to show the evolution of
any cluster. However, if we plot the H-R diagrams
of several star clusters with different age, we
should see the evolutionary effect
11
Dating the Age of the Universe with Globular
Cluster

• The age of the oldest star cluster should give us
  an lower limit of the age of the universe, since
  no star can form before the universe was born!
• Most of the open clusters are relatively young.
  Very few are older than 5 billion years.

• The age of some of the oldest globular cluster,
  such as M5 below, is about 13 billion years.
  Therefore, the age of the universe must be more
  than 13 billion years.

H-R Diagram of M4 Age 10 billion years.
Image of M5, in Constellation Serpentis, with
apparent brightness magnitude of mv 12
12
Chapter 12 Star Stuff

• Star Formation
• Evolution of Low-Mass Stars
• Evolution of High-Mass Stars

13
From Clouds to Protostar

• Stars form in cold (10-30 K), dense (although
  still very low density compared with the density
  we are used to) molecule clouds composed of
  mostly hydrogen and helium.
• The low temperature allows the formation of
  hydrogen molecule H2 hence molecule clouds.
• Low temperature and high density allow gravity
  to compress the clouds without resistance from
  thermal pressure.
• Because of the low density, the gas can radiate
  away its thermal radiation quickly. The
  temperature of the gas remain low ( 100 K), and
  emits in the infrared wavelengths.
• As the cloud undergoes gravitational contraction,
  density increases, making it increasingly
  difficult for radiation to escape.
• The gas heats up as the density increases,
  eventually forms a dense, hot protostar!

Molecule cloud glows in the infrared, but is dark
in the visible light image!
14
Disks and Jets

• The random motion of the molecule can contain a
  net angular momentum, as the cloud contract,
• this angular momentum is conserved, and results
  in the fast rotation of the protostar and the
  subsequent formation of a disk and jets
• Details of how the jets are formed is still
  unknown. Magnetic field probably plays an
  important role!

Image of jet and disk of a protostar!
15
Jet in Neutron Stars

• Similar to the core of the low-mass stars,
  electrons degeneracy pressure will resist the
  gravitational pressure. However, because of the
  high mass, it cannot hold off the gravitational
  collapse like in the case of the white dwarfs.
• As gravity overcomes electron degeneracy
  pressure, and the core collapse rapidly, the
  electrons and protons recombine to form neutrons,
  and releasing neutrinos and energy at the same
  time ? Supernova explosion.
• Eventually the neutron degeneracy pressure will
  balance the gravitational pressure (if the star
  is not too massive) to form a neutron star.
• The estimated of the neutron stars are about 10
  km in diameter, with a mass of about 1 M? ? Too
  small to be directly observed!
• However, the strong gravity of the neutron stars
  pull surrounding materials in, forming an rapidly
  rotating accretion disk. The high speed
  collisions between the materials and the neutron
  stars generate strong X-ray, as the image of crab
  nebula from Chandra X-ray Observatory has shown.

Conbined Hubbles visible (red) and Chandras
X-ray (blue) images.
16
More Example of Astronomical Jets

• Jets are found in many different spatial
  scales. In this composite picture of x-ray (blue)
  picture from Chandra X-ray Observatory, visible
  (white) image from Hubble Space Telescope, and
  radio (red) image from the Very Large Array radio
  telescope, jets (seen in radio emission in red)
  are ejected from a supermassive black hole in
  galaxy cluster MS 0735.67421 in constellation
  Camelopardus.

http//chandra.harvard.edu/photo/2006/ms0735/
17
Examples of Star Forming Molecular Clouds and EGGs

• The Eagle Nebula is a star forming region in the
  constellation Serpens.
• Evaporating Gaseous Globules (EGGs) are dense
  regions of molecular hydrogen (H2) clouds that
  have gravitationally collapsed to form stars.
• UV radiation from hot bright star (off the image)
  evaporates the outer layer of the dense H2 cloud,
  revealing the denser regions that are forming
  stars.

EGGs in Eagle Nebula in constellation Serpens
http//antwrp.gsfc.nasa.gov/apod/ap061022.html
18
Star-Forming Region in W5

• This picture of the star forming region W5 in
  constellation Cassiopeia was obtained by the
  Spitzer Space Telescope. The insert at the
  lower-left-hand corner is the same region taken
  in the visible wavelength. Dusts and dense H2
  cloud blocks visible radiation, and the region
  looks dark in the visible image.
• Infrared radiation are emitted by the cold and
  dense H2 clouds.
• Additionally, infrared radiation can propagates
  through the gas and dust, allowing us to see
  inside the clouds.

http//www.spitzer.caltech.edu/Media/releases/ssc2
005-23/index.shtml
19
Star Forming Region in NGC 2467

• This picture of NGC 2467 shows stars at
  different stages in star formation process.
• The bright stars on the left of the image are
  stars that have already formed and the winds
  probably have dispersed the planetary nebulae
  around them.
• The star at the lower left is emerging from its
  planetary nebula.
• The deep dark lanes near the center are dense
  regions that are probably forming new stars
  inside.
• The bright walls of gas on the right are gases
  been evaporated by some newly-formed hot stars.

http//antwrp.gsfc.nasa.gov/apod/ap050131.html
20
The Mass Limits of Main Sequence Stars

• Usually a single group of molecular clouds can
  give birth to a star cluster containing thousands
  of stars. The mass distribution of the stars is
  such that there are a whole lot more low mass
  stars than high mass stars.
• Upper limit of stellar mass 100 Msun
• The core temperature becomes so high that
  radiation pressure (pressure exerted by photons)
  upsets the equilibrium between the thermal
  pressure and the gravitational pull. The star
  becomes unstable
• No star with mass greater than 100 Msun has been
  observed.
• Lower limit of stellar mass 0.08 Msun
• The core temperature of objects with mass less
  than 0.08 Msun is not hot enough to trigger
  hydrogen burning.
• Jupiter is 0.001 Msu

21
Brown Dwarfs

• Brown dwarfs are objects that does not have
  enough mass to maitain core hydrogen fusion, with
  mass less than 0.08 Msun.
• Brown dwarfs are supported by electron degenerate
  pressure (like white dwarfs).
• Brown dwarfs and large planets are similar in
  size
• Distinction between brown dwarfs and planets is
  fussy
• Support mechanism?
• Deuterium fusion (gt13 Mjupiter)?

22
The Origin of Degenerate Pressure1. Fermions and
Bosons.

• In quantum physics, particles are divided
  into two types fermions and bosons. In quantum
  physics, one of the intrinsic properties of
  particles are called spin. Spin is associate with
  the angular momentum of the particle around its
  center of mass. In quantum physics, spin can only
  have values equal to multiple of 1/2, such as ½,
  1, 1 ½ , 2, it is a quantized quanty.
• Fermions are particles with half-integer spin,
  such as
• Electrons,
• Protons,
• Neutrons
• Bosons are particles with integer spin, such as
• Deuterium isotope of hydrogen, containing one
  proton and one neutron in its nuclei.
• Helium-4 (superconductivity).
• Photons

23
The Origin of Degenerate Pressure2. Paulis
Exclusion Principle and Heisenbergs Uncertainty
Principle

• Degenerate pressure arises from two fundamental
  laws of quantum physics
• Paulis Exclusion Principle for the fermions
• No two particles (fermions) can occupy the same
  quantum mechanical state simultaneously.
• Heisenbergs Uncertainty Principle
• The product of the uncertainty in the position
  of a particle and its momentum is always greater
  than the Planck constant
• ?x ?p h
• where ?x is the uncertainty in the position of
  the particle, ?p is the uncertainty in the
  momentum of the particle, and h 6.626 ? 10-27
  gm cm2/sec is the Plancks constant.

24
Paulis Exclusion Principle

• Under normal conditions, electrons in atoms can
  occupy a large number of energy states, like
  students in a mostly-empty class room there are
  more seats available than people. In this
  situation, we do not need to worry about the
  exclusion principle.
• When atoms are compressed, like in a white dwarf
  where thermal pressure is no longer able to
  resist the gravitational force of the matter, the
  number of available energy states is reduced,
  similar to a packed classroomin which only one
  person is allowed in each seat (the exclusion
  principle).
• The reduced number of energy level available in
  the compressed atoms is equivalent to confined
  space allowed for the electrons, or small ?x in
  the uncertainty principle.

25
Uncertainty Principle and Degenerate Pressure

• According to Heisenbergs Uncertain Principle,
• ?x ?p h
• very small ?x requires that ?p h / ?x be very
  large.
• Very large uncertainty in the momentum of the
  electrons means that their velocity varies over a
  very large range (recall the definition of
  momentum p mv)
• A very large range in the possible range of
  velocity of a large collection of particles is
  equivalent to saying that this collection of
  particles have a very high temperature (Recall
  the definition of temperature in Chapter 5.)
• High temperature means high pressure!

26
Important Properties of Degenerate Pressure

• Degenerate pressure becomes appreciable only
  when the atoms are compressed by a tremendous
  pressure. This is because the Planck constant is
  a very small number
• and
• h 6.626 ? 10-27 gm cm2/sec
• Thermal pressure depends on the temperature. A
  gas cloud at a temperature of 0 K does not posses
  any thermal pressure. However, degenerate
  pressure does not depend on temperature. The
  temperature of the white dwarfs can be at
  absolute zero, its electron degenerate pressure
  will be the same as it is at 25,000 K.
• There are different kind of degenerate pressure
• Electron degenerate pressure (in white dwarfs and
  brown dwarfs chapter 12).
• Neutron degenerate pressure (in Neutron Stars
  Chapter 13).

27

• Star Formation
• Evolution of Low-Mass Stars
• Evolution of High-Mass Stars

28
Evolution of Low Mass Stars I

• Low Mass Stars M lt 8 10 M?
• Evolutionary History for a typical low-mass
  star like the Sun
• During the main-sequence phase, helium produced
  by the proton-proton chain (hydrogen burning)
  accumulates at the core. As a main sequence star
  exhausts its core hydrogen supply, its energy
  output is reduced.
• Without the thermal pressure of the hydrogen
  fusion, gravitation contraction continue, and the
  core temperature rises.
• Because the temperature required to start helium
  burning is much higher ( 100 million degrees),
  there isnt enough thermal pressure at the core
  to resist the gravitational contraction (just
  yet).
• The core temperature rises, as well as the outer
  layer of the star where there are still
  substantial supply of hydrogen, triggering shell
  hydrogen burning, at a much higher temperature
  than the core temperature in the main sequence
  stars.
• The high temperature shell hydrogen burning
  produces more energy than the same star in its
  main sequence core hydrogen burning stage ?
  Higher luminosity.
• The high thermal pressure of the shell hydrogen
  burning push the envelop of the star outward,
  much larger than its size at the main sequence
  stage ? giant.
• The large surface area of the giant cools off
  fast ? red giant.
• From sub giant to red giant few hundred million
  years.

29
Structure of Red Giants

• Inert Helium core ? Most of the mass of the star
  is concentrated at the helium core.
• The electron degeneracy pressure of the inert
  helium core balance the gravitational
  contraction.
• Hydrogen-burning shell.
• Hydrogen envelop.

30
Evolution of Low-Mass Star II

• The time it takes to reach the red giant state
  depends on the mass of the star
• For star with lower mass then the Sun, it takes
  longer.
• As the shell hydrogen fusion stops, the helium
  core of the low mass stars may never a
  temperature high enough for helium fusion to
  start.
• As fusion stops, the gravitational collapse
  continue, eventually stopped by the electron
  degenerate pressure of the helium core.
• The star become a helium white dwarf.
• For star more massive than the Sun, it takes less
  than 10 billion years.
• As the shell hydrogen fusion exhausts its fuel,
  gravitational collapse continue. However, the
  high mass of the star means that the core
  temperature can reach 100 million degrees,
  sufficient for helium fusion to start.

31
Evolution of Low-Mass Star III

• Triple alpha process in helium burning stars
• Helium fusion converts three helium atoms into
  one carbon, and generating energy.
• Theoretical model suggests that before core
  helium fusion phase, the star is supported by the
  electron degenerate pressure of the helium core.
  This degenerate pressure does not increase with
  the increasing core temperature as the star
  contracts.
• However, once helium fusion starts, it releases a
  large amount of energy in a short time, causing
  the star to expand rapidly. This is referred to
  as the Helium Flash.

32
Evolution of Low-Mass Star IV

• After helium flash, the star settles into a
  helium burning stage, the energy of the star
  decreases
• The helium burning stars are smaller, hotter, and
  less luminous than the star in the red giant
  state.
• The helium core of the low-mass stars fuse helium
  into carbon at about the same rate. Therefore,
  they appears on the HR diagram as a horizontal
  line.
• This state is represented in the HR diagram as
  the horizontal branch.
• Low-mass stars spend about 100 million years in
  this stage.

33
Evolution of Low-Mass Star V

• The helium fuel in the core eventually runs
  out, and core fusion ceases.
• The carbon core will begin to contract due to
  gravity.
• The increased temperature due to the contraction
  will cause shell helium burning around the carbon
  core.
• Further out, a shell hydrogen burning continue on
  top of the helium shell double-shell buring,
  1 million years.
• Both shells contract with the carbon core,
  driving the increase in temperature and fusion
  rate.

• The star expands further, becomes larger and more
  luminous than its red giant phase.
• Fusion of carbon requires high temperature, 600
  million degrees. This is unlikely to happen for
  low-mass stars.

Click to start animation
34
The end of Low-Mass StarsPlanetary Nebulae

• As the stars luminosity and radius increase, its
  wind will grow stronger as well. The star ejects
  its outer layer to form the beautiful planetary
  nebula.
• The exposed core will be hot for a long time,
  emitting UV radiations.
• The UV radiation will ionize the gas in the
  expanding shell, making it grows brightly.