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10/17/2012 Stellar Distances and Magnitudes Lecture 6 Obese Bears Acquire Fish Greedily, Killing Many Luscious Trout 1 10/17/2012 *** A HUGE UNIVERSE *** ENORMOUS DISTANCES *** VERY LOW MEAN DENSITIES *** ALMOST AN EMPTY UNIVERSE *** 10 TO THE MINUS 31 GM/CUBIC CM CARL SAGAN PLANET WALK ALPHA CENTAURI SEPTEMBER 28, 2012 2 10/17/2012 Speed of Light • Light travels at fixed speed – c – 186,000 miles/second, or 3x108 meters/second • We see the Sun as it was 8.3 minutes ago! – Nearest star: 4.3 years ago! – Andromeda galaxy: 2.2 million years ago! – LEARN THE HISTORY OF THE UNIVERSE REAL JUMINOSITY • The spectral type (class) of a star gives us temperature information, but we don’t know its luminosity. • To get the luminosity, we must know the distance! • Remember the inverse square law! 3 10/17/2012 Stellar Distances • How do we measure distances to stars? • Astronomers use the parallax method to measure distances to nearby stars. • The method is similar to that used by surveyors. Surveyor’s method A baseline distance Object B Observing the object from points A and B, we can compute the distance to it from angles and , and the baseline. 4 10/17/2012 Stellar Parallax Earth Now p 1 AU d Sun 6 Months Later p = parallax (angle) d = distance A nearby star will change position on the sky relative to distant (background) stars. Photo taken now Photo taken 6 months later 5 10/17/2012 How do we get distances? • We have a very NARROW triangle on the sky. p 1 AU s d s p d d s p Finding distances • Parallax is measured in arcseconds. 206265 AU p 1 d parsecs (pc) p d For example: p = 0.2” => d = 5 pc. 6 10/17/2012 Notes on parallax: • As stars get further away, their parallax becomes smaller. • Parallax can not be measured to better than ~0.02” from the ground (d < 50 pc). – Interferometry is improving on this for selected applications • Cen has the largest parallax (~0.8”) • 1 pc = 3.26 ly (light-years) • 1 pc = 206265 au Current status • The Hipparcos Satellite (1989 – 1993) – Astrometry mission, produced two catalogs • Hipparcos catalog: ~120,000 stars – Measured parallaxes to better than 0.002” => d < 500 pc • Tycho catalog: ~ 1,100,000 stars – Measured parallaxes and proper motions to ~ 0.025” (40 pc) • Tycho 2 catalog: 2,500,000 stars – Update version of Tycho catalog – Reprocessed raw Tycho data & used 144 other catalogs to obtain proper motions – Proper motions to 0.0025”/yr 7 10/17/2012 Statistical Parallax • The Sun and Solar System are moving at 20 km/sec towards the Hercules constellation. – 4.1 AU/year! Importance of Parallax Distances • Parallaxes are the key to knowing distances in the universe. • Nearby stars are the stepping stone to measuring distance to everything else in the universe. • We can now compute the luminosity of stars! 8 10/17/2012 L, f and d • The luminosity, brightness (flux) and distance are related by the inverse square law: f L 4 d 2 Knowing the the brightness and the distance, we can compute L. Cen The closest stars Prox Sun Star Proxima Centauri Centauri A Centauri B Barnard’s Star Wolf 359 Lalande 21185 Sirius A Sirius B Parallax Dist. Luminosity Visual (“) (pc) (Lsun=1) mag 0.763 1.31 5x10-5 11.1 0.741 1.35 1.45 -0.1 0.741 1.35 0.4 0.6 -4 0.522 1.81 4x10 9.5 -5 0.426 2.35 2x10 13.5 -3 0.397 2.52 5x10 7.5 0.377 2.65 23 -1.5 -3 0.377 2.65 2x10 8.3 9 10/17/2012 Comparing stars • If all stars were at the same distance, it would be easy to compare their properties. • But we can - Find stellar distance - Use inverse square law to find what it’s brightness would be at a standard distance. Absolute Magnitude • mv - apparent magnitude – How bright a star appears in the sky. • Mv - absolute magnitude – Brightness if the star were at 10 pc – This is an intrinsic property of the star! • To get Mv we must know the distance to the star. 10 10/17/2012 Relating Apparent (mv) and Absolute (Mv) Magnitude • Suppose a star has mv = 7.0 and is located 100 pc away. • It is 10 times the standard distance. • Thus, it would be 100 times brighter to us at the standard distance. • Or 5 magnitudes brighter • => Mv = 2.0 Example magnitudes Sun: Full Moon: Sirius: Canopus: Arcturus: Deneb: mV -26.8 -12.6 -1.47 -0.72 -0.06 1.26 MV 4.77 (32) 1.4 -3.1 -0.3 -6.9 11 10/17/2012 The Distance Modulus Equation • The relation between mv and Mv is written in equation form as: mv - Mv = - 5 + 5 log10( d ) where d is in parsecs. • mv - Mv is called the distance modulus. 12 10/17/2012 Examples • Deneb: mv = 1.26 and is 490 pc away. mv - Mv = - 5 + 5 log10( d ) 1.26 - Mv = - 5 + 5 log10( 490 ) = -8.5 => Mv = -7.2 • Sun: mv = -26.8, d = 1 AU -26.8 - Mv = - 5 + 5 log10( 1/206265 ) => Mv = 4.8 Bolometric Magnitude • The absolute bolometric magnitude is the brightness at ALL wavelengths. • Usually represented by M. • Mv is the absolute visual magnitude. 13 10/17/2012 Magnitude Summary • mv = Apparent Magnitude – apparent visual brightness of a star on the sky. • Mv = Absolute Magnitude – visual brightness the star would have if it were at 10 pc. • M = Bolometric Magnitude – total brightness (all wavelengths) of a star if it were at 10 pc. Luminosity vs. Color of Stars • In 1911, Ejnar Hertzsprung investigated the relationship between luminosity and colors of stars in within clusters. • In 1913, Henry Norris Russell did a similar study of nearby stars. • Both found that the color (temperature, spectral type) was related to the luminosity. 14 10/17/2012 106 Schematic Hertzsprung-Russell Diagram -10 104 -5 102 0 Giants 1 5 10-2 Absolute Magnitude Luminosity (Lsun) Supergiants 10 White Dwarfs 10-4 15 O B A F G K M Spectral Class Notes on H-R Diagram • There are different regions – main sequence, giant, supergiant, etc. • Most stars lie along the main-sequence. • For a given spectral class (e.g. K), there can be more than one luminosity. – i.e. main-sequence, giant or supergiant • On the main sequence, there are many more K and M stars than O and B stars. 15 10/17/2012 106 Luminosity Classes brightest supergiants Ia supergiants 104 Luminosity (Lsun) bright giants 102 Ib II III giants IV sub-giants 1 Main-sequence V 10-2 B A F G K Spectral Class M Hipparcos H-R Diagram Hertzsprung-Russell (M_V, B-V) diagram for the 16631 single stars from the Hipparcos Catalogue with relative distance precision better than 10% and sigma_(B-V) less than or equal to 0.025 mag. Colours indicate number of stars in a cell of 0.01 mag in (B-V) and 0.05 mag in V magnitude (M_V). Note that this sample is biased towards more luminous stars. From: http://astro.estec.esa.nl/Hipparcos/vis_stat.html 16