The h r diagram
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The H-R Diagram. In 1913, the American astronomer Henry Russel plotted the luminosities of stars versus their spectra class (related to the temperature). Similar to work done in 1911 by Danish astronomer Ejnar Hertzsprung They found that the luminosities and temperatures of star are related

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The h r diagram
The H-R Diagram

  • In 1913, the American astronomer Henry Russel plotted the luminosities of stars versus their spectra class (related to the temperature)

  • Similar to work done in 1911 by Danish astronomer Ejnar Hertzsprung

  • They found that the luminosities and temperatures of star are related

    • H-R Diagram

Lecture 18

Features of the h r diagram
Features of the H-R Diagram

  • Note that the luminosity is plotted on a logarithmic scale and the temperature is plotted backwards

  • The majority of these stars are located along a narrow sequence from the upper left (hot, bright) to the lower right (coll, dim)

    • Main sequence

    • Hotter stars are more luminous that cooler stars

  • Stars above and to the right of the main sequence are giants and supergiants

  • Stars below and to the left of the main sequence are white dwarfs

Lecture 18

More h r diagram
More H-R Diagram

  • The previous H-R Diagram was plotted for stars whose distances are well known

  • Instead, we could plot intensities and temperatures for all stars

  • Astronomers find that 90% of all stars are on the main sequence

  • Models of stellar evolution show that the main sequence is a sequence of stellar mass

Lecture 18


  • There are superluminous stars in the top left of the H-R diagram

  • The cool supergiants in the upper right corner are as much as 10,000 times a luminous as the Sun and are very much larger than the Sun

  • The red, cool, low-luminosity stars in the lower right hand corner are about 80 times denser than the Sun

  • The white dwarfs in the lower left have very high densities

Lecture 18

White dwarfs
White Dwarfs

  • The first white dwarf was discovered in 1862 which is a binary star with Sirius

  • Hundreds of white dwarfs are now known

  • A typical white dwarf is 40 Eridani B

    • 12,000 K temperature

    • L = 1/275 Lsun

    • 1.4% the diameter of the Sun

    • Density = 200,000 g/cm3

    • 1 teaspoon has a mass of 50 tons

Lecture 18

Imaging of stars using optical interference
Imaging of Stars using Optical Interference

  • In 1996, the highest resolution picture of 2 binary stars was taken using the Navy Prototype Optical Interference (NPOI) (from Scientific American, March, 2001)

Lecture 18

Units of distance
Units of Distance

  • The first sets of measurements were based on human dimensions

  • The metric system of measurements was adopted in France in 1799 and is now used by every country in the world EXCEPT the US

  • The basic unit of length was defined at the meter and was based on a bar of platinum-iridium metal

  • In 1960, the definition of the meter was changed to be 1,650,763.73 wavelengths of an atomic transition in krypton-86

  • In 1983, the meter was again redefined in terms in terms of the frequency of a cesium-133 clock and the speed of light

    • 1 light second = 299,792,458.6 m

Lecture 18

Distances in the solar system
Distances in the Solar System

  • Copernicus and Kepler established the relative distances of the planets

  • Absolute distances are measured with radar telescopes

  • Radar measurements have been made of the distance to Venus, Mercury, Mars, satellites of Jupiter, the rings of Saturn, and several asteroids

  • The distance from the Earth to the Sun is taken as 1 astronomical unit (AU)

    • 500 light seconds (LS)

    • 8.3 light minutes (LM)

    • 1.5 x 1011 m

    • 150 million km

Radar Telescope

Lecture 18


  • Measuring the distance to stars cannot be done by radar

  • A good method is triangulation

    • Your brain does triangulation to get depth perception using your two eyes

  • Triangulation is consists of using a baseline and two angles

  • Parallax is the angle that lines AC and line BC make

  • Measuring the angles at A and B allow the calculation of a triangle and the distance to the tree

  • To study the distances to stars, the baseline becomes the diameter of Earth’s orbit around the Sun

Lecture 18

Distance to stars
Distance to Stars

  • As the Earth travels around the Sun, it provides us with a baseline of 2 AU or 300 million km

  • Even with this baseline, the parallax for stars is still too small to see with the naked eye

    • Early (Greek) observers were confused by the lack of parallax for the stars

      • They could not conceive how far way the stars are

  • The first successful measurement of the parallax of stars were done in 1838

Lecture 18

Units of stellar distance
Units of Stellar Distance

  • We define the unit parsec as the distance a star would be if it had a parallax of 1 arcsec and a baseline of 1 AU

    • “the distance at which we have a parallax of one second”

    • pc

    • 3.1 x 1013 km

    • 1 pc = 3.26 LY, 1 LY = 0.31 pc

  • The distance of a star is just the reciprocal of its parallax

    • R = 1/p

Lecture 18

The nearest stars
The Nearest Stars

  • No star is within 1 LY or even 1 pc

  • The closest stars are three stars the make up a multiple system in the constellation of Centaurus

    • Alpha Centauri

      • Not visible in the northern hemisphere

      • A binary system

      • 4.4 LY from Earth

    • Proxima Centauri

      • 4.3 LY

  • The closest stars visible without a telescope from the US is Sirius

    • 8 LY

    • Binary system

  • Even with the Hipparchus we can only measure distances out to 300 LY, which is only 1% of the size of own galaxy and very small on the scale of the universe

Lecture 18

Standard bulbs revisited
Standard Bulbs Revisited

  • Stars come in many luminosities

  • If astronomers could tell what the luminosity of a star was, they could calculate the distance to the star knowing the apparent brightness

  • Most stars shine steadily but some star have variable brightness

  • The amount of light as a function of time is called the light curve

Cepheid Light Curve

For Delta Cephei

Lecture 18

Variable stars
Variable Stars

  • There are two type of variable stars

    • Cepheids

    • RR Lyrae

      • Both types of variable stars actually change their diameters with time

  • Cepheids are large, yellow, pulsating stars

    • Named for the constellation in which they were first found, Delta Cephei (confusing!)

    • Several hundred cepheids are known

    • Polaris is a cepheid varying 10% in visual luminosity with a period of 4 days

Lecture 18

The period luminosity relationship
The Period-Luminosity Relationship

  • The period and average luminosities of cepheid variables are related

  • The period is easy to measure and give the astronomer the luminosity of the star

  • Using the luminosity and the apparent brightness, the astronomer can calculate the distance to the star

  • The relationship between period and luminosity was discovered by Henrietta Leavit in 1908

  • Leavit found that the brighter cepheids always had longer periods

  • These cepheids were all in the Large Magellanic Cloud and so were all about the same distance

Lecture 18

Cepheids in the large magellanic cloud
Cepheids in the Large Magellanic Cloud

  • The cepheids that Leavit found were all in the Large Magellanic cloud

  • Later the distance to the Large Magellanic cloud was measured by other means and absolute distances were attached to the period-luminosity-apparent brightness distances

Lecture 18

Very distant cepheids
Very Distant Cepheids

  • Image of part of M100 galaxy taken with HST

  • Inset shows single cepheid going through its cycle of brightness

Lecture 18

H r diagram and cosmic distances
H-R Diagram and Cosmic Distances

  • Variable stars are useful but not all stars are variable

  • We can use the H-R Diagram to measure the distance to non variable stars

Lecture 18

Luminosity classes
Luminosity Classes

  • Knowing the the spectra index gives the astronomer the luminosity and thus the distance using the variable star information

  • We can also get the pressure so we know whether we are dealing with giant stars or main sequence stars

  • 6 luminosity classes

  • Ia: Brightest supergiants

  • Ib: Less-luminous supergiants

  • II: Bright giants

  • III: Giants

  • IV: Subgiants

  • V: Main-sequence stars

Lecture 18

Rr lyrae stars
RR Lyrae Stars

  • A related group of stars is the RR Lyrae variables

  • More common but less luminous than cepheids

    • Thousands are known in our galaxy

    • Periods are less than a day

    • Brightness changes by less than a factor of two

  • All RR Lyrae stars have the same luminosity

    • 50 Lsun

  • RR Lyrae stars can be detected out to about 2 million LY

Lecture 18