Measuring the Stars

Chapter10 Measuring the Stars Giants, Dwarfs, and the Main Sequence Prepared by R. Erickson © 2017 Pearson Education, Inc. We have studied our Sun. Now what about all the other stars out there? A Problem . The nearest star, besides the Sun, is Proxima Centauri - 4.3 LY away! Q: How can we know what is actually happening out there? A: By studying a Star’s Light Recall that all we see are - Color Brightness Position 4 A Review: Light Tells us allot! <— Non-Rotation 5 Copyright © 2010 Pearson Education, Inc. Rotation —> Recall how a Star’s Rotation Rate is Detected through the Doppler Effect The Blackbody Spectrum of a Star From a star’s blackbody spectrum we can discover it’s - Distance Temperature Composition Mass Velocity Size Rotation rate The Solar System’s Neighborhood We have studied Earth and Moon, the solar system, and the Sun. Time to move away from our local environment into the depths of space. By analyzing the light from millions of distant stars, astronomers have learned a great deal about stellar properties - locations, masses, radii, densities, luminosities, ages and destinies. Stars tell us more about the fundamentals of astronomy than any other class of objects in the universe. We begin our study of stellar astronomy by reviewing the use of simple geometry in determining the distances to our neighbors. © 2017 Pearson Education, Inc. Parallax But First … The Parsec The parsec is the distance used in measuring distances between us and our local neighbors One parsec is approximately: = 3.3 light-years = 5.879 X 1012 miles or 5,879,000,000,000 miles = 3 X 1016 meters © 2017 Pearson Education, Inc. Distances to the nearest stars is measured Parallax using parallax - the apparent shift of an object The stars are so far away, stellar parallaxes are always very small Astronomers measure parallax in arc seconds rather than in degrees © 2017 Pearson Education, Inc. Stellar Neighbors The closest star to the Sun is called Proxima Centauri. part of a triple-star system known as the Alpha Centauri complex Proxima Centauri has the largest known stellar parallax, 0.77″ - It is 1 / 0.77 = 1.3 pc away - about 270,000 AU, or 4.3 light-years. This is a typical interstellar distance in the Milky Way Galaxy Analogy: Imagine Earth as a grain of sand orbiting a golfball-sized Sun - Earth’s orbital distance would then be 1 m from the golfball - The nearest star, also golfball-sized, is then 270 km away! - If the Sun is a golfball in LA then our neatest star is a golfball in Las Vegas! By the way: Jupiter is a small marble, Neptune is 50 m from the “Sun” The Kuiper belt and Oort cloud, trillions of tiny dust grains span to 100km Then nothing of consequence exists in the 270 km separating the Sun and the other star. © 2017 Pearson Education, Inc. Fewer than 100 stars lie within 5 pc of the Sun. Such is the void of interstellar space. © 2017 Pearson Education, Inc. Stellar Motion Barnard’s star, taken on the same day of the year but 22 years apart. Because Earth was at the same point in its orbit when the photographs were taken, the observed displacement is not the result of parallax. Instead, it indicates real space motion of Barnard’s star relative to the Sun. Motion is animated at https://en.wikipedia.org/wiki/Proper_motion Stellar Motion Proper Motion The radial component of motion of Alpha Centauri is measured using the Doppler shift of lines in it’s spectrum The transverse component is derived from the system’s proper motion (corrected for parallax) The true spatial velocity results from the combination of the two using the Pythagorean Theorem: Radial speed2 + Transverse speed2 = True speed2 © 2017 Pearson Education, Inc. Luminosity and Apparent Brightness Luminosity and Apparent Brightness Luminosity - the total amount of radiation leaving a star per unit time - is an intrinsic stellar property (internal to itself) It is sometimes referred to as the star’s absolute brightness When we observe a star, we see its apparent brightness - the amount of energy per unit area per unit time - striking the human eye or a CCD chip The solar constant, 1400 W/m2, is just the apparent brightness of the Sun Luminosity and Apparent Brightness As light moves away from a source it steadily dilutes while spreading over larger surface areas The amount of radiation received by a detector (or eye) is the source’s apparent brightness This varies inversely as the square of its distance from the source. Doubling the distance from a star makes it appear 22, or 4, times fainter. © 2017 Pearson Education, Inc. Luminosity and Apparent Brightness A star’s luminosity effects its apparent brightness. Doubling the luminosity doubles the energy crossing any spherical shell surrounding the star and hence doubles the apparent brightness. Ex: Two stars A and B of different luminosities can appear equally bright on Earth if the brighter star B is more distant than the fainter star A © 2017 Pearson Education, Inc. Reminder: ∝ is the symbol representing proportionality Luminosity and Apparent Brightness Determining a star’s luminosity is a twofold task. First, the astronomer must determine the star’s apparent brightness by measuring the amount of energy detected through a telescope in a given amount of time. Second, the star’s distance must be measured - by parallax for nearby stars - by other means for more distant stars (to be discussed later). The luminosity can then be found using the inverse-square law. The Magnitude Scale Instead of measuring apparent brightness in SI units (watts per square meter or W/m2) optical astronomers find it more convenient to work in terms of a construct called the magnitude scale - a system of ranking stars by their apparent brightness. This scale dates back to the second century b.c., when the Greek astronomer Hipparchus ranked the naked-eye stars into six groups. He categorized the brightest stars as first magnitude, labeled the next brightest stars as second magnitude, and so on, down to the faintest stars visible to the naked eye, which he classified as sixth magnitude. The range 1 (brightest) through 6 (faintest) spanned all the stars known to the ancients. We need to precisely define DIM and BRIGHT The Magnitude Scale A first-magnitude star is about 100 times brighter than a sixth-magnitude To compare intrinsic (absolute) properties of stars astronomers imagine looking at all stars from a standard distance of 10 pc (33 ly) A star’s absolute magnitude then is its apparent magnitude when viewed from a distance of 10 pc. Absolute magnitude is a measure of a star’s absolute brightness, or luminosity. The Sun has an absolute magnitude of 4.8 © 2017 Pearson Education, Inc. What does a star's Apparent Magnitude tell us? Not much! If a star is bright it could be: very close! very hot very large Or any combination of these! We Need Absolute Magnitude ! Lets establish reference distance that all stars can be measured by. Lets use a star’s magnitude as seen from 10 pc away! This is 33 ly We call such a magnitude the Absolute Magnitude of a star The Magnitude Scale Absolute magnitude is equivalent to luminosity Given that the Sun’s absolute magnitude is 4.8, we can construct a conversion chart relating these two quantities. An increase in brightness by a factor of 100 corresponds to a decrease in magnitude by 5 units © 2017 Pearson Education, Inc. Absolute Magnitude Also known as “Luminosity” How bright it REALLY is! A combination of size and temperature This tells us a LOT! – it’s an important intrinsic property of a star! But all we can see from Earth is APPARENT magnitude How do we determine a star's ABSOLUTE Magnitude? 1st: Measure it’s apparent Magnitude 2nd: Correct for the star’s distance Stellar Temperatures What’s the most meaningful property to assign to stars? Color !!! Color is Temperature Stellar Temperatures Because the basic shape of the blackbody curve is so well understood, astronomers can estimate a star’s temperature using as few as two measurements at selected wavelengths. This is accomplished by using telescope filters that block out all radiation except that within specific wavelength ranges © 2017 Pearson Education, Inc. © 2017 Pearson Education, Inc. Case Study: Stellar Temperatures of Orion The constellation Orion as it appears through a small telescope, the colors of the cool red star Betelgeuse (α) and the hot blue star Rigel (β) are clearly evident. Astronomers can determine a star’s surface temperature by measuring its apparent brightness (radiation intensity) at several frequencies, then matching the observations to the appropriate blackbody curve. In the case of the Sun, the theoretical curve that best fits the emission describes a 5800-K emitter. The same technique works for any star, regardless of its distance from © 2017Earth. Pearson Education, Inc. It’s hard to find the “peak” color Stellar Temperatures The spectra of the hottest stars show lines of helium and multiply ionized heavy elements. In the coolest stars helium lines are absent, but lines of neutral atoms and molecules are plentiful. At intermediate temperatures, hydrogen lines are strongest. Astronomers realized that stars could be more meaningfully classified according to surface temperature. In order of decreasing temperature these categories are O, B, A, F, G, K, M © 2017 Pearson Education, Inc. Stellar Temperatures The seven spectral types Stellar Temperatures © 2017 Pearson Education, Inc. “Pickering’s Harem” Discoveries by the “Computers” In 1897 Antonia Maury undertook the most detailed study of stellar spectra to that time, enabling Hertzsprung and Russell to, independently, develop what is now called the H–R diagram.

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