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Notes 67 - Optional Topic E - Astrophysics

Notes 67 - Optional Topic E - Astrophysics - ------------------------------------------------------------------------------ E .3.9 Spectroscopic Parallax: Luminosity and Stellar Spectra E. 3.10 Stellar Distance with M and L E. 3.11 Spectroscopic Parallax (limited to 10 Mpc)

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Notes 67 - Optional Topic E - Astrophysics

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  1. Notes 67 - Optional Topic E - Astrophysics ------------------------------------------------------------------------------- E.3.9 Spectroscopic Parallax: Luminosity and Stellar Spectra E.3.10 Stellar Distance with M and L E.3.11 Spectroscopic Parallax (limited to 10 Mpc) E.3.12 Problems involving stellar distances, apparent brightness, and luminosity • The H-R Diagram is a graph of Luminosity and/or Absolute Magnitude as a function of decreasing surface temperature of a star; • If we assume the Main Sequence is a line, rather than a “fuzzy band,” and that all stars are Main Sequence stars, then we can plot a star’s Spectral Type on the H-R Diagram and can determine its L (or M) by reading it off the y-axis; • By using this estimate of L, and combining it with apparent brightness (b), we can derive an estimate for the distance to the star; this method is called Spectroscopic Parallax (even though no actual parallax is used); it is accurate to about +/- 25%; • The limit of Spectroscopic Parallax is about 10. million parsecs (10. Mpc); Spectroscopic Parallax http://staff.imsa.edu/science/astro/astrometry/stellarclass.html Example: The apparent brightness of Regulus is 5.2 x 10-12 compared to Sol and its luminosity is 140 times that of Sol. What is the approximate distance to Regulus? (show solution in NB) Given: Unknown: Equation:

  2. Notes 68 - Optional Topic E - Astrophysics ---------------------------------------------------------------------------- E.3.13 Cepheid Variables E.3.14 Period-Magnitude Function for Cepheids E.3.15 Cepheids as a “Standard Candle” E.3.16 Distance Determination with Cepheids • Distance estimation techniques learned to date: 1. Radar Ranging - out to 30.+ AU (solar system); 2. Trigonometric Parallax - out to 100. pc or 326 ly; 3. Spectroscopic Parallax - out to 10. Mpc or 33 Mly; How are distances beyond 10 Mpc to be estimated? • In 1784, John Goodricke (English amateur astronomer) discovered Delta Cephei (about 300 pc from earth)...a star whose luminosity varied regularly. Since then, hundreds of Cepheid Variables have been discovered. • A Cepheid Variable star is an “Intrinsic Variable Star” which actually pulsates...ie., its radius increases and decreases because of changing internal pressures causes by changes in the rate of fusion; • Cepheid Variables are located in the instability strip on the H-R Diagram between the Main Sequence and the Red Giant stars; Henrietta Leavitt 1868 - 1921 http://www.physics.sfsu.edu/~gmarcy/cswa/history/leavitt.html

  3. CEPHEID VARIABLES http://zebu.uoregon.edu/~soper/MilkyWay/cepheid.html • Henrietta Leavitt discovered that the period of the Cepheid variable stars was directly related to their luminosity...that is, the longer the period, the greater the luminosity. By determining the period of a cepheid variable, and consulting her graph, she could accurately estimate its luminosity!! • This historic discovery allowed scientists to accurately estimate the distance to truly far-off objects using the following scheme: 1. Observe a Cepheid variable in a distant galaxy; 2. Determine the period of the Cepheid variable; 3. Use the Leavitt Graph to estimate the luminosity (L) of the Cepheid; 4. Determine the Cepheids apparent brightness (b) using telescopic observations; 5. Substitute b and L into the apparent brightness equation (b = L/4 pi d2) and solve for d to determine the distance to the Cepheid and thus to the distant galaxy. • Henrietta Leavitt, in discovering the period-luminosity relationship of the Cepheid variables, had discovered a “Standard Candle” of the universe...the reference stars which can be used to estimate the distance to all galaxies in which they can be detected. • Unfortunately, Cepheid variables are visible only to a distance of about 60 Mpc...other methods have to be used for greater distances.

  4. EXAMPLE PROBLEM: A Cepheid variable star with the same period as delta-Cephei is detected in a distant galaxy. Its apparent brightness is 22 magnitudes less than delta-Cephei. How far away is the star and galaxy? (show solution in NB) Given: Unknown: Equation:

  5. EXAMPLE PROBLEM: A Cepheid variable star with the same period as delta-Cephei is detected in a distant galaxy. Its apparent brightness is 22 magnitudes less than delta-Cephei. How far away is the star and galaxy? (show solution in NB) Given: Unknown: Equation:

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