ASTR Fall Semester Joel E. Tohline, Alumni Professor Office: 247 Nicholson Hall [Slides from Lecture05]

Gustav’s Effect on this Course Fall Holiday has been cancelled, which means our class will meet on Thursday, 9 October. (This makes up for one class day lost to Gustav last week.) We will hold an additional makeup class on Saturday, 20 September! (This will account for the second class day lost to Gustav last week.) Date of Exam #1 has been changed to Tuesday, 23 September!

Chapter 17: The Nature of Stars

Individual Stars… Location in Space –Coordinate (angular) position on the sky –Distance from Earth Motion through Space –Motion across the sky (“proper” motion) –Motion toward/away from us (radial velocity) Intrinsic properties –Brightness (luminosity/magnitude) –Color (surface temperature) –Mass –Age

Astronomers’ Magnitude System Ancient, Greek astronomers made catalogues of all the (visible) stars in the sky –Name –Position on the sky (angular coordinates) –Any observed motion? –Brightness on the sky (hereafter, apparent brightness)  The Greeks defined a “magnitude” system to quantify the (apparent) brightness of each star.

Astronomers’ Magnitude System The brightest stars were labeled “1 st magnitude” stars Successively fainter stars were catalogued as 2 nd magnitude, 3 rd magnitude, etc. Faintest stars (visible to the “naked eye”) were catalogued by Greek astronomers as 6 th magnitude stars. Astronomers continue to use this “magnitude” system, extending it to much fainter objects (that are visible through telescopes but were not bright enough to be seen by Greek astronomers). The Sun can also be put on this “magnitude” system.

Apparent magnitudes (m)

Stars of different brightness

Catalog of Stars Data drawn from two textbook appendices: Appendix 4 = “The Nearest Stars” Appendix 5 = “The Visually Brightest Stars”

Apparent brightness due to… Each star’s intrinsic brightness Each star’s distance from us A star of a given intrinsic brightness will appear to get fainter and fainter if you move it farther and farther away from us

Concept of Apparent Brightness 10 stars that are identical in every respect (all having, for example, the same intrinsic brightness) will appear to have different brightness in the night sky if they are all at different distances from us. Apparent brightness varies as the “inverse square” of the distance. –Move a star twice as far away, it becomes 4 times fainter –Move a star 3 times farther away, it becomes 9 times fainter –Move a star 10 times farther away, it becomes 100 times fainter –Move a star to half its original distance, it becomes 4 times brighter –Move a star to 1/10 th its original distance, it becomes 100 times brighter

Apparent Brightness varies with Distance

Determining Intrinsic Brightness Measure apparent magnitude, “m”. Measure distance to star using stellar parallax. “Move” star to a standard distance from us (10 parsecs) and adjust its magnitude accordingly  absolute magnitude, “M”. –The absolute magnitude of each star in our catalog tells us “how bright the star would appear to be if it was 10 parsecs away from us.” –“M” is therefore a measure of each star’s intrinsic brightness

Intrinsic Brightness Distribution of Stars in our Galaxy

Catalog of Stars Data drawn from two textbook appendices: Appendix 4 = “The Nearest Stars” Appendix 5 = “The Visually Brightest Stars”

Individual Stars… Location in Space –Coordinate (angular) position on the sky –Distance from Earth Motion through Space –Motion across the sky (“proper” motion) –Motion toward/away from us (radial velocity) Intrinsic properties –Brightness (luminosity/magnitude) –Color (surface temperature) –Mass –Age

Continuous Spectra from Hot Dense Gases ( or Solids ) Kirchhoff’s 1 st Law: Hot dense gas produces a continuous spectrum ( a complete rainbow of colors ) A plot of light intensity versus wavelength always has the same general appearance (blackbody function): –Very little light at very short wavelengths –Very little light at very long wavelengths –Intensity of light peaks at some intermediate wavelength But the color that marks the brightest intensity varies with gas temperature: –Hot objects are “bluer” –Cold objects are “redder”

Continuous Spectra from Hot Dense Gases ( or Solids ) Kirchhoff’s 1 st Law: Hot dense gas produces a continuous spectrum ( a complete rainbow of colors ) A plot of light intensity versus wavelength always has the same general appearance (blackbody function): –Very little light at very short wavelengths –Very little light at very long wavelengths –Intensity of light peaks at some intermediate wavelength But the color that marks the brightest intensity varies with gas temperature: –Hot objects are “bluer” –Cold objects are “redder”

The Sun’s Continuous Spectrum (Textbook Figure 5-12)

Continuous Spectra from Hot Dense Gases ( or Solids ) Kirchhoff’s 1 st Law: Hot dense gas produces a continuous spectrum ( a complete rainbow of colors ) A plot of light intensity versus wavelength always has the same general appearance (blackbody function): –Very little light at very short wavelengths –Very little light at very long wavelengths –Intensity of light peaks at some intermediate wavelength But the color that marks the brightest intensity varies with gas temperature: –Hot objects are “bluer” –Cold objects are “redder”

Color-Temperature Relationship

Wien’s Law for Blackbody Spectra As the textbook points out (§5-4), there is a mathematical equation that shows precisely how the wavelength (color) of maximum intensity varies with gas temperature.

Color Filters: U, B, V

Individual Stars… Location in Space –Coordinate (angular) position on the sky –Distance from Earth Motion through Space –Motion across the sky (“proper” motion) –Motion toward/away from us (radial velocity) Intrinsic properties –Brightness (luminosity/magnitude) –Color (surface temperature) –Mass –Age

Intrinsic Brightness vs. Color

Hertzsprung-Russell (H-R) diagram

Individual Stars… Location in Space –Coordinate (angular) position on the sky –Distance from Earth Motion through Space –Motion across the sky (“proper” motion) –Motion toward/away from us (radial velocity) Intrinsic properties –Brightness (luminosity/magnitude) –Color (surface temperature) –Mass –Age

Measuring Stellar Masses Astronomers determine the mass of a star by examining how strong the gravitational field is around that star. (Isaac Newton’s law of universal gravitation; §4-7) By studying the motion of planets around our Sun, astronomers have determined that the Sun has a mass of 2 x kilograms. We cannot measure the mass of individual, isolated stars. We have an opportunity to measure the mass of a star if it resides in a binary star system. –Fortunately, most stars are in binary systems! –The Sun is unusual in this respect because it does not have a companion star about which it orbits.

Measuring Stellar Masses

Intrinsic Brightness vs. Stellar Mass