Lecture 16 - Measuring the Stars

Lecture 16 - Measuring the Stars - Measuring the Stars...

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Unformatted text preview: Measuring the Stars ASTRONOMY 3 Lesson 16 1 A new born cluster of stars (NGC 3603) as observed with the ESO Very Large Telescope in the near-infrared. The cluster houses several 1,000s of stars with masses down to 0.1, and up to 100 times the mass of the Sun. See http://www.eso.org/outreach/press-rel/pr-1999/ pr-16-99.html NATURE of the Universe Astronomy - Measuring the Stars Review of Lesson 15: Review of Lesson 15 Conduction, convection, and radiation are the 3 ways to transport heat (energy). The Sun has a core, a radiative zone and a convective zone. The Sun's structure can be studied by helioseismology, and the principle of hydrostatic equilibrium. The Sun produces energy with the proton-proton chain in its core. 4 hydrogen nuclei (protons) fuse to 1 helium nucleus (2 protons, 2 neutrons). 2 positrons, 2 neutrinos and 2 gamma-ray photons are emitted. 2 NATURE of the Universe Astronomy - Measuring the Stars Questions from Lesson 15 Think about (questions from Lesson 15): Are all stars like the Sun? How old do stars get? 3 NATURE of the Universe Astronomy - Measuring the Stars Today's Topics Distances to nearby stars (Ch. 10.1) Luminosity and apparent brightness (Ch. 10.2) Temperature (Ch. 10.3) Sizes and masses (Ch. 10.4, 10.6) The Hertzsprung-Russell diagram (10.5) Summary & Homework & Announcements see also Lab 6 on "Stars & the H-R diagram" 4 NATURE of the Universe Astronomy - Measuring the Stars Distances The parallax p enables us to measure the distance to nearby stars. 5 NATURE of the Universe Astronomy - Measuring the Stars Distances Stars closer to the Sun show a larger parallax than stars at larger distances. distance (in lightyears) = 3.3 / parallax (in arcseconds) Proxima Centauri (a member of the alpha Centauri triple system) has a parallax of 0.772 arcsec. This corresponds to a distance of 4.22 lightyears. 6 NATURE of the Universe Astronomy - Measuring the Stars Stars within 12.5 lightyears of the Sun. Distances 7 The solar neighbourhood - stars within 12.5 lightyears of the Sun. Note that there are many more red (M-type) and orange (K-type) stars than there are yellow (G-type) and white (Atype) stars. - see http://www.atlasoftheuniverse.com/ NATURE of the Universe Astronomy - Measuring the Stars Distances Southern Cross Alpha Centauri The triple star system Alpha Centauri is the closest neighbor to the Sun. 8 Image of a region of the southern Milky Way by Humayun Qureshi NATURE of the Universe Luminosity and apparent brightness Astronomy - Measuring the Stars The apparent brightness (or the energy received from a star) is inversely proportional to the square of its distance (see also Lab 6). If two stars are identical, but at different distances, the star closer to us appears brighter than the more distant star. star This is similar to traffic lights seen along a street. The light closer to us appears brighter. 9 NATURE of the Universe Luminosity and apparent brightness Astronomy - Measuring the Stars The luminosity (or absolute brightness) of a star is a measure of its total energy output. Apparent brightness is how bright a star appears on Earth. It depends on the absolute brightness of the stars and its distance. The apparent brightness is proportional to the luminosity and inversely proportional to the square of the distance. Two stars with the same apparent brightness could either be two stars with the same luminosity at the same distance or a closer, fainter star and a brighter more distant star 10 NATURE of the Universe Luminosity and apparent brightness Astronomy - Measuring the Stars About 2,150 years ago, the Greek astronomer Hipparchus ranked stars according to their brightness into 6 magnitude classes. The brightest stars were assigned apparent magnitude 1, the faintest stars visible to the eye apparent magnitude 6. A range of 1 magnitude corresponds to a factor of 2.5 in brightness. A range of 5 magnitudes corresponds to a factor 100 in brightness. Astronomers still use the magnitude scale today, and have extended it include brighter objects like the Moon or the Sun (-26.7mag), and the faintest stars visible by large telescopes (+30mag). The absolute magnitude is the magnitude a star would have at a distance of 33 lightyears. 11 NATURE of the Universe Luminosity and apparent brightness Astronomy - Measuring the Stars mag mag mag Sirius is the brightest star in the sky. The two brightest stars in the constellation of Orion are Rigel and Betelgeuse. mag mag mag Note that Betelgeuse is much redder than, e.g., Rigel or Sirius! 12 NATURE of the Universe Astronomy - Measuring the Stars Temperature intensity [W / (m2 m)] wavelength [m] Wien's law: the wavelength of the peak emission is inversely proportional to the temperature. Stefan's law: the energy output per area scales with the 4th power of the temperature. 13 NATURE of the Universe Astronomy - Measuring the Stars Temperature In the 1880s, astronomers at Harvard sorted stellar spectra according to the strength of the hydrogen lines, and assigned 22 types lettered A to W. In 1898, Annie Jump Cannon realized that 7 spectral types ordered by temperature are sufficient to classify spectra of stars. The final spectral sequence in order of decreasing temperature is O B A F G K M L O B A F G K M L The "geeky" mnemonic devised by astronomers to remember the spectral sequence is Oh Be A Fine Girl/Guy, Kiss My Lips 14 NATURE of the Universe Astronomy - Measuring the Stars surface temperature Temperature 40,000 K 30,000 K 14,000 K 9,200 K 8,200 K 7,200 K 6,400 K 6,000 K 5,600 K 5,200 K 4,300 K 3,800 K 3,200 K L 15 Note that the hydrogen lines (H, H, ...) are strongest for A-type stars, and weaker in the hotter B- and O-types stars (as most hydrogen atoms get ionized) and the cooler stars of spectral type F, G, ... (as less and less photons have sufficient energy). Note also that cooler stars tend to have more complex spectra, as molecules start to appear in their atmospheres. NATURE of the Universe Astronomy - Measuring the Stars Temperature spectral temperature (K) class O B A F G K M L 30,000-50,000 10,000-30,000 7,200-10,000 6,000-7,200 5,200-6,000 3,900-5,200 2,500-3,900 1,600-2,500 color electric blue blue white yellow-white examples Mintaka Rigel Sirius, Vega Canopus yellow Sun, Centauri orange orange-red red Aldebaran Betelgeuse Kelu 1 16 NATURE of the Universe Astronomy - Measuring the Stars Betelgeuse (M2) Temperature Sirius (A1) Aldebaran (K5) Mintaka (O9) Rigel (B8) Spectral types of some of the brightest stars in the winter constellations of Canis Major, Orion and Taurus 17 Photograph by Jerry Lodriguss - see http://www.astropix.com/HTML/SHOW_DIG/015.HTM NATURE of the Universe Astronomy - Measuring the Stars Can we measure the diameter of stars? Size and Mass Viewed from the distance of Centauri, the Sun's diameter corresponds to 0.0072 arcsec. Large optical interferometric telescopes can resolve these scales. Proxima Centauri has about 1/10 the diameter of the Sun, and is only slightly larger than Jupiter. Jupiter Centauri A is slightly larger than the Sun, Centauri B is slightly smaller than the Sun. 18 NATURE of the Universe Astronomy - Measuring the Stars Size and Mass Compared to the Sun, some stars are "giants" or even "supergiants". Betelgeuse has 650 times the diameter of the Sun. It was first resolved in 1921 by A. Michelson and F. Pease after converting the 2.5m (100 inch) telescope on Mount Wilson into a 7 meter interferometer. 19 NATURE of the Universe Astronomy - Measuring the Stars Size and Mass Most stars are either too distant or too small (or both) to measure their diameter directly. For these stars, the diameter can be computed from the luminosity and the temperature using Stefan's law. The luminosity of proportional to the square of the diameter and the fourth power of the temperature: luminosity diameter2 * temperature4 (see also Lab 6 on "Stars & the H-R diagram") 20 NATURE of the Universe Astronomy - Measuring the Stars Size and Mass Stars have a wide range of sizes from less than 1/10 the diameter of the Sun to more than 600 times the diameter of the Sun. 0.15 21 NATURE of the Universe Astronomy - Measuring the Stars Size and Mass Many stars come in pair. We call these pairs binary stars. The masses of binary stars can be measured using Newton's laws. The brighter component of this system has just 0.085 times the mass of the Sun. The fainter component has only 0.065 times the mass of the Sun - not enough mass to start hydrogen fusion in its core. We call such objects brown dwarfs. 22 See http://www.spacetelescope.org/news/html/heic0410.html for more details. NATURE of the Universe Astronomy - Measuring the Stars Size and Mass Stellar masses range from 0.08 to 100 times the mass of the Sun. The Sun is a rather typical star, as stars with very high masses are rare. 23 NATURE of the Universe Astronomy - Measuring the Stars Size and Mass How luminous are the brightest and the faintest stars? Stars of spectral type O have up to 10 times the diameter of the Sun, and up to 10 times its surface temperature. Hence the luminosity of stars of spectral type O is up to 102 * 104 = 106 = 1,000,000 times the luminosity of the Sun. The coolest, and lowest mass stars have only 1/10 of the diameter of the Sun and 1/3 of the Sun's temperature. Their luminosity is (1/10)2 * (1/3)4 = 1/8,100 or 0.012% the luminosity of the Sun. 24 The numbers quoted above corresponds to main sequence stars. When we talk about white dwarfs and supernova, we will see that there are even more extreme stars. NATURE of the Universe Astronomy - Measuring the Stars How long do stars live? Size and Mass The life-span of the Sun is about 10 billion years. The mass of stars of spectral type O is up to 100 times the mass of the Sun. Since O-type stars have 1 million times the luminosity of the Sun, yet only 100 times the mass of the Sun, their use up their hydrogen much fast. Hence life-spans of O-type stars are much shorter: lifetime = mass (M ) / luminosity (L ) * 10 billion years 102 / 106 * 1010 years = 106 years, i.e. O-type stars live as short as 1 million years The coolest, and lowest mass stars have 1/10 of the mass of the Sun and 0.0001 times the luminosity. Their lifetimes are 10-1 / 10-4 * 1010 years = 10 trillion years, i.e. 1,000 times the life-span of the Sun. 25 NATURE of the Universe Astronomy - Measuring the Stars H-R diagram Around 1910, Ejnar Hertzsprung and Henry N. Russell created diagrams depicting a star's spectral type versus its luminosity. This type of diagram is now called Hertzsprung-Russell diagram (or H-R diagram). In the H-R diagram, the Sun is located a spectral-type G2 (temperature 5,780 K) and at luminosity L = 1. 26 NATURE of the Universe Astronomy - Measuring the Stars H-R diagram consists of stars producing energy by hydrogen fusion in their core. Stars located far below the main-sequence are much less luminous, and are called white dwarfs. Stars located far above the main-sequence are much more luminous, and are called giants and supergiants. 27 Many nearby stars are located along one curve. We call this curve the main sequence. It NATURE of the Universe Astronomy - Measuring the Stars H-R diagram The main sequence corresponds to a sequence of stellar masses. Low mass stars have low luminosity and low surface temperature. High mass stars have a high luminosity and a high surface temperature. sequence The numbers correspond to masses in units of the mass of the Sun. 28 NATURE of the Universe Astronomy - Measuring the Stars H-R diagram This H-R diagram depicts 22,000 stars in the solar neighborhood with measured parallax (distance). 90% of the stars are on the main sequence, 9% are giants, and 1% are white dwarfs. 29 NATURE of the Universe Astronomy - Measuring the Stars Summary Summary: Measuring the Stars The distance to nearby stars can be computed by measuring the parallax. The apparent brightness of a star scales inversely with the square of its distance. The absolute luminosity of a star scales with the 2nd power of its diameter and the 4th power of its surface temperature. 30 NATURE of the Universe Astronomy - Measuring the Stars Summary Summary: Measuring the Stars The spectral types O B A F G K M L corresponds to a sequence of decreasing surface temperature. The life-span of massive and hot O-type stars is as short a 1 million years. Very cool and low-mass L-type stars can live for up to 10 trillion years The H-R diagram is a plot of the luminosity of a star against its surface temperature. Most stars in the solar neighborhood lie on the main-sequence. The mass of a star determines where is falls on the main sequence. 31 NATURE of the Universe Astronomy - Measuring the Stars Homework Homework Reading assignment: Chapter 11 Homework 5 is online. Due date is Mo, Nov 13 at 12:00 pm (noon) Think about: How was the Sun born? Where do stars form? 32 NATURE of the Universe Astronomy - Measuring the Stars Announcements Wed, Nov 8, 2:30 - 4:00 pm, in Math Sciences Building Planetarium (8th floor) and Telescopes (9th floor) - see http://www.astro.ucla.edu/planetarium/events_mercury06.shtml (this is also an opportunity for you to earn your "telescope viewing" extra credits) Mid-term Exam 2 is on Wed, Nov 15, at 12:00 pm in class. Reviews Review of Homework 4: Wed, Nov 8 Review of Homework 5: Mon, Nov 13 33 ...
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This note was uploaded on 10/13/2008 for the course ASTR 3 taught by Professor Hauser during the Fall '07 term at UCLA.

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Lecture 16 - Measuring the Stars - Measuring the Stars...

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