Astronomy 115 – Section 4 Week 11 Adam Fries • SF State • [email protected] Important Notes • Finish CH. 6 • HW #3 is due next week. Hw Questions? Trick Question: Which star is closest/furthest from us? Recall: Distance to local stars from parallax angle Distance to local stars from parallax angle • Definition: The parallax angle p is equal to Sun-Earth distance (1 AU) divided by the distance from the Sun to the star, d. 1 AU • p = d • where p is in units of arcseconds (00) • and d is the distance in units of parsecs (pc) • 1 pc = 3:26 light years Example: the distance to the brightest star in Canus Minor, Procyon, is 3:5 pc, what is the parallax angle? 1 AU p = = 0:2900 3:5 pc We can’t get distances just by looking at stars, but we can say something about how bright they appear! • Astronomers categorize the apparent brightness of a star with a unitless number called an apparent magnitude • The ancient greek astronomer, Hipparchus, was the first to classify stars according to brightness. • The brightest stars he could see were of 1st magnitude... • . while the faintest stars he could see were of 6th magnitude. • Modern astronomers now define Hipparchus’ 1st magnitude stars as being exactly 100 times brighter than Hipparchus’ 6th magnitude. • This corresponds to a magnitude difference of 5 between the brightest and faintest stars we can see with our eyes. • In this system, 6th magnitude stars are about 2:512 times fainter than 5th magnitude stars. • Likewise, 6th magnitude stars are about (2:512 × 2:512) = 6:310 times fainter than 4th magnitude stars. Quiz: How many times brighter is a 1st magnitude star compared to a 4th magnitude star? Quiz: How many times brighter is a 1st magnitude star compared to a 4th magnitude star? Answer: the magnitude difference is 4 − 1 = 3 (faint minus bright). Therefore, the 1st mag star is (2:512 × 2:512 × 2:512) = 15:85 or (2:512)3 times brighter than the 4th mag star. This means you’d need about 16 4th mag stars to produce the same amount of light as one 1st mag star. • The magnitude system extends to negative numbers for very bright objects. • This scale uses the star Vega in the constellation Lyra as a reference to determine all other magnitudes. • Vega is assigned an apparent magnitude of 0. • Stars or objects that appear brighter than Vega are assigned negative magnitudes. • . that appear fainter than Vega are assigned positive magnitudes. A Quick note on Star names: • Only the brightest stars have been given names, i.e. Sirius • Bayer System: uses greek alphabet and the constellation the star is in. Categorizes stars according to apparent brightness. • Flamsteed System: does not consider the brightness of a star, only position on Celestial Sphere. Assigns a number to the star name based on RA. Example: Bayer System • The brightest star in Orion is Rigel. • Rigel’s Bayer designation is α Orionis • Betelgeuse is the second brightest star in Orion • Betelgeuse’s Bayer designation is β Orionis Example: Flamsteed System • Rigel’s Flamsteed designation is 19 Orionis • Betelgeuse’s Flamsteed designation is 58 Orionis From our perspective on Earth, about how many times brighter is the brightest star in the sky, Sirius, compared to Betelguese? From our prespective on Earth, about how many times brighter is the brightest star in the sky, Sirius, compared to Betelguese? mB − mS = 0:45 − −1:44 = 1:94 ' 2 So Sirius is about 2:5121:94 ' 2:5122 = 6:310 times brighter than Betelegeuse. Apparent magnitudes depend on distance between the observer and the star: Inverse Square Law of astronomy Specifically, apparent brightness decreases inversely with the square of the distance between the star and the observer: 1 b / d2 For example: Let’s compare the apparent brightness of two identical Suns, the second Sun twice as far from us (2 AU). Then the second Sun will appear 2 2 b2AU d1AU 1 = 2 = = 1=4 b1AU d2AU 2 as bright as the Sun that’s 1 AU from us. • Astronomers also define an absolute magnitude, M, of a star • The apparent magnitude doesn’t imply anything about the star’s distance from us. • The absolute magnitude is the brightness a star would have a distance of 10 pc away from Earth. Example: the apparent magnitude of the Sun is −26:74 Place the Sun 10 pc away and its apparent magnitude is 4:83 = absolute magnitude Comparing absolute magnitudes tells us which stars are intrinsically brighter. Example: the absolute magnitude of Betelgeuse is M = −5:14. The absolute magnitude of Sirius is M = 1:42. Therefore, Betelgeuse is an intrinsically brighter star, even though its apparent brightness is fainter. The absolute magnitude of a star depends on the star’s power output (energy emitted per second), its luminosity. Luminosity is an intrinsic property of a star that is independent of how far away it is from an observer. The smaller (or more negative) a star’s absolute magnitude, the greater the star’s luminosity. • The observed brightness (not magnitude) of a star is related to the star’s luminosity by the following: • total light emitted per second Brightness = Area of sphere of radius d Luminosity = 4πd2 • stellar luminosities are usually measured relative to the Sun’s luminosity, L . For every 1 million Sun-like stars, there exists 1 star whose luminosity is 100; 000 L Recall: A star’s visible color can reveal it’s surface temperature • Star’s look visibly different: red, orange, yellow, white, and blue-white • Stars behave nearly like blackbodies - have peaks at particular wavelength - provides a unique surface temperature • observe the spectrum of a star, and find its peak - Wein’s law: T / 1/λmax Stars were first classified by the appearance of their spectra • . before stars, atoms, or radiation were well understood • astronomers looked at the dark bands (absorption lines) in their spectra (somewhat arbitrarily) • The original classification depended on the prominence of particular spectral lines associated with hydrogen during the 1800s. Recall: • The spectral lines (absorption lines) in a star’s spectral are due to atoms and molecules in the stars’ atmosphere which absorb parts of the contiunous spectra and disrupt the smooth blackbody curve. • Different elements create different patterns of absorption lines and act as a fingerprint for astronomers. Depending on the observed prominence of these spectral lines, stars were labeled as A for having strongest lines, B for weaker, and so on. all the way up through P • But hotter and cooler stars produce weak hydrogen spectral lines • For extremely hot stars, electrons in the atmosphere are stripped off the hydrogen from very energetic photons and so therefore produce no spectral lines. • For very cool stars, the photons have too little energy and are not absorbed by the electrons attached to the hydrogen in the atmosphere. • The strongest hydrogen absorption lines are produced by stars in between these temperatures. The Harvard Computers The Harvard Computers • Early 1900s, William Pickering and Williamina Fleming, and later Annie Jump Cannon and colleagues. • . designed the spectral classification we use today based on surface temperatures and kept only 7 spectral types. • The complete sequence of spectral types of stars from hottest to coolest: O, B, A, F, G, K, M • Oh Be A Fine Girl (Guy) Kiss Me • Astronomers divide the main spectral types into subtypes: e.g. B0 (hottest B) to B9 (coolest B) • For example, the Sun is a G2 star • Additionally, blue stars are hottest, red stars are coolest • The hottest stars have surface temperatures of 30,000 K to 50,000 K (these are the O-type stars) • The coolest stars have surface temperatures of 2500 K to 3000 K (these are the M-type stars) • Mintaka; O-type; blue-violet; 33,000 K • Rigel; B-type; blue-white; 12,000 K • Sirius; A-type; white; 9,900 K • Procyon; F-type; yellow-white; 7,700 K • Sun; G-type; yellow; 5800 K • Aldebaran; K-type; orange; 3,900 K • Betelguese; M-type; red-orange; 3,500 K Quiz: Which is hotter, a G0 star or an G9 star? • Leads us to the H-R diagram. • Around 1911, Ejnar Hertzsprung and Norris Russell were looking for patterns in the properties of stars • Noticed a correlation between Surface Temperature and Luminosity (or Absolute Magnitude) of stars • Plotted Luminosity versus Surface Temperature using Annie Jump Cannons classifications scheme • Find that many stars lie on a middle band in the plot, cannot fully explain this at the time • the middle band is called the Main Sequence • over 91% of all stars surrounding the Solar System fall on the main sequence • the vast majority of stars on the main sequence are the M and K stars • O and A stars are quite few in number Aside from the main sequence, there are other groups of stars • However, there exists some ambiguity with this plot. • there are stars that can have the same surface temperature, but different luminosities! • how do we tell them apart? • . a luminosity class system was developedby W.W. Morgan and P.C. Keenan of the Yerkes Observatory • by studying the absorption lines of the spectra in greater detail. • they observed effects (change in width) on the spectral lines from variations in pressure and density in the star’s atmosphere • these effects depended on whether the star is a white dwarf, main sequence, giant, or supergiant Morgan-Keenan Luminosity Classes • Ia and Ib – supergiants • II, III, IV – giants of various luminosity • V – main sequence • white dwarfs don’t get a luminosity class • the Sun is a G2 V star Spectral Type and Luminosity Class ) 2nd distance measuring tool • observe apparent magnitude and spectrum • determine spectral class (OBAFGKM) from spectrum • determine luminosity class from spectrum (MS, giant, supergiant) and thus find the luminosity • distance is related to luminosity (absolute magnitude) from the apparent magnitude b / L=d2 SOURCES Astronomical images courtesy of http://apod.nasa.gov/ http://www.nature.com/ http://www.stellarium.org/ http://www.skyandtelescope.com http://www.earthsky.org.