Lecture 18 Stellar Distance: Luminosity Heliocentric Parallax Brightness; apparent magnitudes Luminosity Mar 1, 2006 Astro 100 Lecture 18 1 Stars and the Universe The significance of stars 80-90% visible matter in universe is now in stars. Almost all of visible matter in universe was once in a star. Stability, energy output of stars responsible for life. We will be looking at stars to answer the following questions about the Sun: Is the Sun similar to the other stars? How did the Sun form and what is its fate? Might other stars be suitable abodes for life? Mar 1, 2006 Astro 100 Lecture 18 2
The Program Some of the least Sun-like stars out there will allow exploration of some pretty mind-bending physics: The compact remnants of stars: white dwarfs, neutron stars, and black holes Cataclysmic explosions and the origin of the elements So first let s see what we can find out about the basic properties of other stars: Position (distance) Luminosity Temperature (Radius) Mass Mar 1, 2006 Astro 100 Lecture 18 3 Distance Scale change between the solar system and other star systems is one of largest in science: nearest star (other than our Sun): Proxima Centauri 300,000 AU most distant human artifact: Voyager I 99 AU round trip light travel time now 28 hrs: launched summer 1977 reached edge of solar wind ( termination shock ) Dec 2004 may reach interstellar space ( heliopause ) in 2015 enough power to continue transmissions until 2020 (~150 AU) http://voyager.jpl.nasa.gov/ Mar 1, 2006 Astro 100 Lecture 18 4
Heliocentric Parallax Recall Tycho Brahe (1600) argued that the Earth couldn't move around sun, since then the nearby stars would appear to change position with respect to more distant ones. In fact, they do! This is the basis for the only direct method of measuring the distance to extra-solar system objects. In one year, as the Earth changes position relative to sun by 1 AU, any nearby star changes from its mean position by an angle called heliocentric parallax p. For small angles p: heliocentric parallax p = constant/distance p is the same as the maximum angle the Earth gets from the Sun as seen from the star Applet: http://www.astro.washington.edu/labs/parallax/solar.html Mar 1, 2006 Astro 100 Lecture 18 5 Distance Units Parsec. For convenience, astronomers define the distance at which p is one arcsec to be the "parsec" ("pc"). From trigonometry 1 pc = 206,265 AU = 3.18x10 13 km So that if parallax p is in arcsec and distance d is in pc: p(arcsec) = 1 / d(pc) d(pc) = 1 / p(arcsec) Light-Year. There is another commonly used distance unit, the light-year (ly) 1 ly = (speed of light) x (one year) = 3 10 5 km/sec 3.16 10 7 sec = 9.5 10 12 km 1 pc = 3.26 ly Mar 1, 2006 Astro 100 Lecture 18 6
Measured Distances Example, for the star Proxima Centauri: p = 0.772 arcsec d = 1.3 pc = 4.2 ly This very tiny motion is the largest parallax! Ground-based. Even with a lot of care, can only measure p > 0.05 arcsec, so d < 20 pc. This covers about 2000 stars (eg, Appendix table 9). Map of solar neighborhood (http://www.anzwers.org/free/universe/12lys.html) Hipparchos Satellite. Has now measured parallaxes down to 0.01 arcsec, which will gives us reliable distances out to 100 pc, expanding the number of nearby stars by 100x. Mar 1, 2006 Astro 100 Lecture 18 7 Apparent Brightness and Luminosity Recall, Apparent Brightness = Luminosity / (4 π Distance 2 ) We can measure apparent brightness (astronomers jargon: "flux") from a star at the Earth (using a photometer). If we know distance (above), can now calculate its luminosity. These are unimaginably small (brightness) and large (luminosity) numbers, so Astronomers have another set of units: Mar 1, 2006 Astro 100 Lecture 18 8
Brightness Units Magnitude: a measurement of relative intensity where a ratio of 10 gives a difference in magnitude of 2.5 (called a "logarithmic" scale). Greek origin, based on human eye. m(star 1) - m(star 2) = -2.5 log 10 (brt(star 1) / brt(star 2)) or brt(star 1) / brt(star 2) = 10 -(m(star 1) - m(star 2))/2.5 Apparent magnitude: magnitudes "relative to the brightness of Vega" (α Lyrae, one of the stars in the Summer Triangle). So for apparent magnitude, star 2 in the formula is Vega. This means Vega s apparent magnitude is 0 Apparent magnitude is usually written (lower case) "m". Some Examples Mar 1, 2006 Astro 100 Lecture 18 9 Luminosity Units Solar luminosities" "L sun " L sun = 3.9x10 26 W L(Vega)/L sun = b(vega)/b sun (d(vega)/d sun ) 2 = 10-11 (5.5x10 6 ) 2 = 52 Bottom Line: By combining brightnesses and distances from parallax of nearby stars, find stellar luminosities have huge range: L(star) = 10-5 -10 6 L sun This means a star can have a large brightness (low magnitude) if it is close, or if it is intrinsically luminous Mar 1, 2006 Astro 100 Lecture 18 10
Voyager Interstellar Progress Mar 1, 2006 Astro 100 Lecture 18 11 Heliocentric Parallax Mar 1, 2006 Astro 100 Lecture 18 12
Luminosity of Some Stars m brtness parallax dist Lum (mag) b(vega) (arcsec) (pc) (Lsun) Sun -27.5 10 27.5/2.5 =10 11 5x10-6 1 Proxima Cen 10.7 5.3 10-5 0.775 1.3 6x10-5 α Cen 0.1 0.91 0.775 1.3 1 Vega (α Lyr) 0.0 1.00 0.038 26.5 52 Betelgeuse (α Ori) 0.5 0.63 0.011 95 20,000 Mar 1, 2006 Astro 100 Lecture 18 13