The Distance Modulus. Absolute Magnitude. Chapter 9. Family of the Stars

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Foundations of Astronomy 13e Seeds Phys1403 Introductory Astronomy Instructor: Dr. Goderya Chapter 9 Family of the Stars Cengage Learning 016 Topics for Today s Class 1.

Diameters of Stars a) Luminosity Radius and Temperature b) H-R Diagram c) Luminosity Classes Recall from Chapter section.

1 Foundations of Astronomy 13e Seeds Phys1403 Introductory Astronomy Instructor: Dr. Goderya Chapter 9 Family of the Stars Cengage Learning 016 Topics for Today s Class 1. Recap: Intrinsic Brightness a) Apparent Magnitude b) Brightness, Luminosity and Distance c) Absolute Magnitude and Distance Modulus. Diameters of Stars a) Luminosity Radius and Temperature b) H-R Diagram c) Luminosity Classes Recall from Chapter section.1: Definitions Apparent Magnitude (m v ): Brightness of the star irrespective of its distance from us Apparent magnitude versus intensity (flux) m = apparent magnitude I = intensity A = Star A B = Star B Intensity versus apparent magnitude I B ma mb.5log I A I A m (.51) B m A I B Absolute Magnitude To characterize a star s intrinsic brightness or Luminosity (L), define Absolute Magnitude (M V ) at visual wavelength: Absolute Magnitude = Magnitude that a star would have if it were at a distance of 10 pc (Parallax p = 0.1 arc seconds). If M is measured at visual wavelength then we say absolute visual magnitude M V Hot stars emit more radiation at other wavelengths than at visual so astronomers account for it and define absolute bolometric magnitude M The Distance Modulus If we know a star s absolute magnitude, we can infer its distance by comparing absolute and apparent magnitudes: Distance Modulus = m V M V = log 10 (d [pc]) Distance in units of parsec Equivalent: d = 10 (m V M V + 5)/5 pc 1

Distance Modulus Demo http://astro.unl.edu/classaction/animations/stell arprops/stellarmag.

distances to Stars There are other methods we can find distance to Stars. We will study them in later chapters.

proportional to the square of the distance (d): F ~ L d Factors affecting Luminosity L ~ T 4 T Star A Star B Earth Both stars may appear equally bright, although

2 Distance Modulus Demo arprops/stellarmag.html Example of Betelgeuse and Rigel Magnitude-Distance Formula m V M V = log 10 (d [pc]) Equivalent: d = 10 (m V M V + 5)/5 pc A second method to find distances to Stars There are other methods we can find distance to Stars. We will study them in later chapters. Flux, Luminosity and Distance More quantitatively: The flux received from the light is proportional to its intrinsic brightness or luminosity (L) and inversely proportional to the square of the distance (d): F ~ L d Factors affecting Luminosity L ~ T 4 T Star A Star B Earth Both stars may appear equally bright, although star A is intrinsically much brighter than star B. Stefan s Boltzmann Law from Chapter 7 Flowvella.com Factors affecting Luminosity Combining Quantitatively: L = 4 R T 4 L ~ R Surface area of the star Surface flux due to a blackbody spectrum The Heart of Astrophysics Astronomynote.com

3 Luminosity, Temperature and Radius in Solar Units Example Suppose a star is 10 times the sun s radius but only half as hot. How luminous would it be? L star / L sun = 4 R star T star 4 / 4 R sun T sun 4 L star / L sun = (R star / R sun )(T star4 /T sun4 ) Example Suppose a star is 40 times the luminosity of the sun and twice as hot. How big is the star? Cengage Learning 016 Sorting and Graphing is Common in Astronomy Organizing the Family of Stars: The Hertzsprung-Russell Diagram We know: Stars have different temperatures, different luminosities, and different sizes. To bring some order into that zoo of different types of stars: organize them in a diagram of Fig. 9-6, p. 178 Absolute mag. or Luminosity versus Temperature (or spectral type) Luminosity Hertzsprung-Russell Diagram Temperature Spectral type: O B A F G K M 3

The Hertzsprung-Russell Diagram Fig. 9-8, p.

Luminosity but hotter than Sun The Radii of Stars in the H-R Diagram Observations with interferometers can resolve the size and

The examples shown here are flattened by rapid rotation, but most stars rotate slower and are more nearly spherical.

The Relative Sizes of Stars in the HR Diagram An H R diagram showing the luminosity and temperature of many well-known stars.

The dashed lines are lines of constant radius; star sizes on this diagram are not to scale.

4 The Hertzsprung-Russell Diagram Fig. 9-8, p. 179 The Hertzsprung-Russell Diagram Same temperature, but much brighter than MS stars Must be much larger Giant Stars Same Luminosity but hotter than Sun The Radii of Stars in the H-R Diagram Observations with interferometers can resolve the size and shape of some nearby stars. The stars of the upper main sequence are indeed larger than the Sun, as predicted by the H R diagram. The examples shown here are flattened by rapid rotation, but most stars rotate slower and are more nearly spherical. On the scale of this diagram, the supergiant Betelgeuse would have a diameter of about 7 meters ( 3 feet ). The Relative Sizes of Stars in the HR Diagram An H R diagram showing the luminosity and temperature of many well-known stars. Individual stars that orbit each other are designated A and B, for example Spica A and Spica B. The dashed lines are lines of constant radius; star sizes on this diagram are not to scale. To visualize the size of the largest stars, imagine that the Sun is the size of a tennis ball. Then, the largest supergiants would be the size of a sports stadium and white dwarfs the size of grains of sand. Masses of Stars in the H-R Diagram The more massive a star is, the brighter it is High-mass stars have much shorter lives than low-mass stars L = M 3.5 4

Comparison of Spectral Lines These model spectra show how the widths of spectral lines reveal a star s luminosity class.

Certain spectral lines are more sensitive to this effect than others; Careful inspection of a star s spectrum can determine its

Luminosity Class See Figure 9-1 Ia Bright Supergiants Ib Supergiants II Bright Giants III Giants IV Subgiants V Main-Sequence Stars

5 Comparison of Spectral Lines These model spectra show how the widths of spectral lines reveal a star s luminosity class. Supergiants have very narrow spectral lines, and main-sequence stars have broad lines. Certain spectral lines are more sensitive to this effect than others; Careful inspection of a star s spectrum can determine its luminosity classification. Luminosity Class See Figure 9-1 Ia Bright Supergiants Ib Supergiants II Bright Giants III Giants IV Subgiants V Main-Sequence Stars Our Sun: G star on the Main Sequence: GV Example Luminosity Classes Luminosity Classes and H-R Diagram Our Sun: G star on the Main Sequence: GV Polaris: G star with Supergiant luminosity: GIb Ia Bright Supergiants Ia Ib II III IV V Ib Supergiants II Bright Giants III Giants IV Subgiants V Main-Sequence Stars 5

Acknowledgment The slides in this lecture is for Tarleton: PHYS1411/PHYS1403 class use only Images and text material have been borrowed from various

6 Acknowledgment The slides in this lecture is for Tarleton: PHYS1411/PHYS1403 class use only Images and text material have been borrowed from various sources with appropriate citations in the slides, including PowerPoint slides from Seeds/Backman text that has been adopted for class. Cengage Learning 016 6

Chapter 9. Stars. The Hertzsprung-Russell Diagram. Topics for Today s Class. Phys1411 Introductory Astronomy Instructor: Dr.

Chapter 9. Stars. The Hertzsprung-Russell Diagram. Topics for Today s Class. Phys1411 Introductory Astronomy Instructor: Dr. Foundations of Astronomy 13e Seeds Phys1411 Introductory Astronomy Instructor: Dr. Goderya Chapter 9 Stars Cengage Learning 2016 Topics for Today s Class HR Diagram Variable Stars Intrinsic Variables Cepheids