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Stars Comparison of ground-based observation of the globular cluster M4 with an HST image showing white dwarfs. (Produced with the Wide-Field Planetary Camera 2 ... – PowerPoint PPT presentation

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Title: Stars

Comparison of ground-based observation of the
globular cluster M4 with an HST image showing
white dwarfs. (Produced with the Wide-Field
Planetary Camera 2, Hubble Space Telescope.)
  • The stars in the sky appear to be objects much
    like the sun although much, much further away.
    Can we get some kind of idea of how far away?
  • In the lab we will do an experiment demonstrating
    the parallax method for determining distances.
    This method actually works for the nearer

  • The basic idea behind parallax is trig using
    known distances and angles to get unknown

Line of sight to background stars very, very far
2 AUs
Change in angle of star from 6 months previous
Line of sight to background stars very, very far
  • We actually have a unit of distance defined by
    the parallax method. It is called a parsec. A
    parsec is the distance a star is away if it has a
    change of angle of 1 arc second (which is 1/60th
    of an arc minute, which is 1/60th of a degree).
    A parsec can be converted into AUs and another
    common unit of distance, the light year 1
    parsec 3.26 lt. yrs 200,000 AUs.

  • The nearest star has a parallax angle of about ¾
    of a second of arc, and so is about 4/3 1.3
    parsecs away (about 4 light years away, or about
    266,000 AUs away). Recall that Pluto was about
    40 AUs away, and the Oort Cloud is thought to be
    about 50,000 AUs away.
  • We can effectively measure distances this way for
    about several thousand stars that are within
    about 90 parsecs (300 light years) from the earth.

Binary Stars Get Mass
  • Because gravity is the force that keeps smaller
    objects going around bigger objects, we can
    determine the mass of the bigger object by
    measuring the radius and period of the smaller
    orbiting objects.
  • We use this in determining the masses of the
    planets by looking at their moons or by putting
    our own moons (satellites) in orbit around them.

Binary Stars Get Mass
  • We use this same system to get the mass of the
    sun since we have the planets orbiting the sun.
  • We are only now being able to see other planets
    orbit other stars since those stars are so far
  • However, we notice that there are lots of stars
    that orbit each other and we can use that to
    get the mass of the bigger (central) star.

Binary Stars
  • The most direct way of seeing binary stars is to
    really see them. This is possible for the nearer
    stars. We can actually see both stars
    individually and watch one orbit the other.
    These are called visual binaries.
  • We need to be careful here, since some stars only
    appear to be close due to our perspective. These
    are called optical doubles and not real binary
    systems at all. We can tell the difference by
    watching these over time or by noting that the
    distance to each of the two is quite a bit

Binary Stars
  • A second way is to look at the spectra. When the
    orbiting star comes toward us, its spectral lines
    are shifted (Doppler effect) a little towards the
    blue, and when it goes around and away from us,
    the spectral lines are shifted a little towards
    the red. This works well for binary systems that
    we view edge on.

Binary Stars
  • A third way of detecting binary stars is to
    notice the brightness of a star over time (light
    curves). When the orbiting star goes in front of
    the more massive central star, a bit of the
    central star will be covered by the orbiting
    star and the total light from the star system
    will decrease. A similar thing happens when the
    orbiting star goes behind the central star.
    These are called eclipsing binaries.

Binary Stars
  • For these eclipsing binary star systems, we can
    then determine it as binary and get some
    interesting information about the systems from
    these light curves.

Binary Systems
  • A fourth way of detecting binary systems is to
    notice that a star is wobbling as if it is
    swinging another heavy object around it even if
    the heavy object cant be seen. This can occur
    if the star is swinging a dark star or perhaps
    a burned out star. These are called
    astrometric binaries. This will have to be
    considered when looking at the birth and death of
    stars (stellar evolution).

Binary and Multiple Star Systems
  • By having these various methods available to
    detect binary systems, we notice that most stars
    are not single stars like the sun, but instead
    are either binary star systems or are in star
    groups with multiple stars mutually orbiting each
    other. We will have to take this fact of
    multiple star systems into consideration in
    looking at theories of stellar formation and

What we can measure
  • 1. Parallax (but only for the nearer stars)
  • 2. Brightness
  • 3. Spectra - how much red versus blue
  • 4. Spectra - emission and absorption lines
  • 5. Binary systems orbits of less massive stars
    around more massive stars
  • a) by direct viewing (seeing the stars orbit)
  • b) by spectroscopy (seeing alternating blue and
    red shifts)
  • c) by light curves (seeing dips in light output
    due to stars eclipsing one another).
  • d) astrometric (by observing the wobble of a

Relations between quantities
  • Spectra amount of red versus blue gives surface
    temperature (T)
  • Brightness (B) depends on luminosity (L) and
    distance (d) B ? L/d2
  • (Here the symbol ? means proportional to.)
  • Luminosity (L) depends on temperature (T) and
    area (A) L ? AT4

For the nearer stars
  • 1. Get distance (d) from parallax.
  • 2. Get temperature (T) from amount of red versus
    blue in spectra.
  • 3. From brightness (B) and distance (d), use
  • L ? B/d2 to get luminosity (L).
  • 4. From luminosity (L) and temperature (T), use
    L ? AT4 to get area (A).
  • For the nearer stars, we then know their surface
    temperature and size.

Farther stars
  • For the farther stars, we cannot use parallax to
    determine the distance.
  • Since we dont know the distance, we cant
    determine their luminosity.
  • Since we dont know their luminosity, we cant
    determine their area.

Stellar Classifications
  • Since there are several thousand stars close
    enough to use parallax, perhaps we can classify
    these stars, and then apply these classifications
    to further stars to try and get their
    luminosities based on their classifications.
  • If we can determine their luminosities, we can
    use B ? L/d2 to determine their distances, and
    we can use L ? AT4 to get their areas.

The H-R diagram
  • One way to try and see relations between
    quantities for the purpose of developing a
    classification system is to plot one quantity
    versus another and see what it looks like.
  • It turns out that plotting Luminosity versus
    Temperature gives a very useful graph. This is
    called an H-R diagram. (The diagram name is
    actually the Hertzsprung-Russell diagram, but it
    is called the H-R diagram for short.)

  • Apparent Magnitude is a measure of brightness and
    came from the attempt to classify stars by their
    brightness 1 brightest, 5 dimmest (to the
    unaided eye).
  • Luminosity is often expressed in terms of
    Absolute Magnitude the brightness (in Apparent
    Magnitude) a star would have if it were located
    at a standard distance of 10 parsecs away.

  • When we started using the telescope, we had to
    extend the apparent magnitude system to cover
    even lower brightnesses. In doing so and in
    using more sophisticated measuring devices than
    the eye, we noted that the original five units of
    apparent magnitude corresponded to 100 times in
    brightness. Thus we could extend the brightness
    system (apparent magnitude) down in brightness
    but up in value from 1 to 5 all the way to 1 to
    15. (At this point, we about reach the limit of
    telescopes based on the light scatter in the
    atmosphere.) With the Hubble, we can extend it
    even lower still.

  • But after we started using this scale for
    Absolute Magnitude (Luminosity) we saw that we
    needed even higher luminosities and so we needed
    even lower numbers. This meant we had to go
    below 1 (and even below 0) to reach as low (as
    high a luminosity) as -10 !
  • On this scale, our sun is rated as 4.8 . That
    is, at 10 parsecs (about 32 light years away), it
    would be just barely visible to the naked eye.

Spectral Classification (due to temperature)
  • We measure temperature of the stars surface by
    measuring how much red versus how much blue there
    is in the spectra of the star. Thus we refer to
    the cooler stars as red stars and the hotter
    stars as blue stars. But we have developed a
    letter scale for this as well From hotter to
    cooler we have
  • O B A F G K M (O stars are the hottest and
    bluest, M stars are the coolest and reddest).
  • (Memory device Oh Be A Fine Guy/Girl Kiss Me)

  • We even got good enough that we could identify
    subclasses of these temperatures, with 0 being
    the hottest and 9 being the coolest in any letter
    category. According to this, an O0 star is the
    hottest and an M9 star is the coolest.
  • According to this scale, our sun is a G2 star (as
    far as temperature/color is concerned).

The H-R diagram
  • The vertical axis of the H-R diagram is
    Luminosity, with the lower luminosity at the
    bottom (15 in Absolute Magnitude) and the higher
    luminosity at the top (-10 in Absolute
  • The horizontal axis of the H-R diagram is
    temperature/color, with the hottest/bluest stars
    (O) on the left and the coolest/reddest stars (M)
    on the right.

The H-R Diagram
  • Everything else being equal, we might expect that
    the stars would fall on a diagonal line from the
    upper left (high luminosity and high temperature)
    to the lower right (low luminosity and low
  • Detailed H-R diagrams can be found on the web if
    you search for H-R diagrams. Many stars do fall
    on a more or less diagonal line like we expected,
    and this line is called the Main Sequence.

H-R Diagramexpected results

Luminosi ty
Sun G2 at 4.8 Magnitude
Temperature / Color
H-R Diagramresults for nearest stars

Luminosi ty
Temperature / Color
H-R Diagrambrightest stars

Luminosi ty
Temperature / Color
H-R diagram
  • The nearest stars should give us a good
    representation since it should count all the
    stars in the area. We can see that many if not
    most of the stars do fall on the predicted line.
    Well call this predicted line the Main
  • There are significant number of stars that fall
    below the Main Sequence. Since they have lower
    luminosities than their temperature would
    normally suggest, we infer that they are much
    smaller. We call them white dwarfs.

H-R diagram
  • When we add in the brightest stars, we realize
    that this is NOT a representative sample because
    we can see those brighter stars at much greater
  • Some of the bright stars do seem to fall on the
    expected Main Sequence line. But many of these
    stars have much higher luminosities than their
    temperature suggests, they much be much larger
    stars. We call these stars giant stars.

Size classification
  • The stars furthest above the Main Sequence are
    called Super Giants, and are classified as I or
    II (with I being the biggest).
  • The stars above but close to the Main Sequence
    are called Giants, and are classified as III (or
    IV for sub-giants).
  • The stars on the Main Sequence are classified as
  • Stars below the Main Sequence are sometimes
    called Dwarf stars, but they have low
    luminosities and so are hard to see.
  • Hence our sun is a G2-V star since it is on the
    Main Sequence.

Mass-Luminosity Relation
  • By using binary stars, we can get the mass of the
    central star. As we noted earlier, over half of
    the stars in the sky are part of binary or
    multiple star systems, so we have lots of stars
    to relate luminosity with brightness.
  • We find that higher mass stars on the main
    sequence also have higher luminosities.

Mass and Luminosity
  • This makes sense
  • higher mass means more gravity
  • more gravity means more compactness and more
  • more heat and compactness means more energy
    production by fusion
  • more energy production means more luminosity.

Mass and Main Sequence Stars
  • The place a star has on the main sequence can be
    related to its mass.
  • We still have the problem with the stars that are
    off of the main sequence why would they have
    different temperatures and different sizes when
    they have the same mass as other stars? Is this
    related to their age or development? This leads
    to the next topic stellar evolution.

Brightest stars in North basic info
  • Star constellation class App. Mag Abs. Mag
    dist in ly
  • Sirius Canus Major A1 V -1.46 1.4 9
  • Arcturus Bootes K2 III 0 -0.2 36
  • Vega Lyra A0 V 0 0.5 26
  • Capella Auriga G8 III 0.1 0.3 42
  • Rigel Orion B8 Ia 0.1 -7.1 900
  • Procyon Canus Minor F5 IV 0.4 2.6 11
  • Betelgeuse Orion M2 Iab 0.5 -5.6 310
  • Altair Aquila A7 IV-V 0.8 2.2 16