Stellar Luminosity • Apparent brightness (flux) is a measure of how bright a star appears on Earth • Luminosity is a measure of how much energy per second (W) a star emits • The apparent brightness of an object declines with distance (inverse square) Luminosity Apparent brightness (flux) = 2 4π × (distance) • If we measure apparent brightness (energy/sec/m2) and we know distance, we can get the luminosity of the star • For Sun, apparent brightness = 1370 W/m2 and d = 150 million km = 1.5 × 1011 m L = 4π(1370 W/m2 )(1.5 × 1011 m)2 = 3.9 × 1026 W Two identical stars, one 5 light years from Earth, and a second 50 light years from Earth are discovered. How much fainter does the farther star appear to be? A square root of 10 B 10 C 100 D 1,000 E the farther star does not appear fainter, since it is identical Distance and Parallax • It is relatively easy to measure apparent brightness of a star • Distance is much harder to measure • For nearby stars (d ≤ 3000 ly) we can use the technique of parallax • You can quickly understand parallax by putting your finger in front of your face, then alternate closing your two eyes - note how your finger appears to move relative to the more distant objects in the room (Image at right) Distance and Parallax • As the Earth orbits the Sun, relatively nearby stars appear to move relative to more distant stars Interactive Figure 15.3 • Because even the nearest stars are so distant, there is a simple relationship between distance and apparent angle a star moves 1 d (in parsecs) = p (in arcseconds) • 1 parsec ≈ 3.26 light years Which of the following stars is closest to us? A Procyon (parallax angle = 0.29") B Ross 780 (parallax angle = 0.21") C Regulus (parallax angle = 0.04") D Sirius (parallax angle = 0.38") On Earth, the parallax angle for the star Procyon is 0.29 arcseconds. If you were to measure Procyon’s parallax angle from Venus, what would the parallax angle be? (Note: Earth’s orbital radius is larger than Venus’s orbital radius A more than 0.29 arcseconds B 0.29 arcseconds C less than 0.29 arcseconds D zero arcseconds (no parallax) The star Gamma Gemini has an apparent magnitude=1.9 and Epsilon Gemini has an apparent magnitude=2.9 How do the observed fluxes of the two stars compare? A FGamma Gem = 0.1 FEpsilon Gem B FGamma Gem = 0.4 FEpsilon Gem C FGamma Gem = 2.5 FEpsilon Gem D FGamma Gem = 10 FEpsilon Gem The brightest star in the constellation Taurus (which is named Aldebaran) has twice the flux of the 2nd- brightest star in that constellation (Elnath). How do the magnitudes of the two stars compare? A Aldebaran is 0.3 magnitudes brighter B Aldebaran is 0.75 magnitudes brighter C Aldebaran is 1.0 magnitude brighter D Aldebaran is 2.5 magnitudes brighter In 1843, the massive star Eta Carinae flared remarkably, increasing in magnitude to m = −1 (becoming the 2nd-brightest star in the entire sky) before fading away again to 8th mag. How much did its luminosity change then? 9 A • By a factor of 10 4.5 B • By a factor of 10 C • By a factor of 4×103 D • By a factor of 2×104 Stellar Luminosities • Stellar luminosities vary from 0.0001 L¤–1,000,000 L¤, ten orders of magnitude • Note that most of the stars in this image are at the same distance, so their relative apparent brightness is the same as their relative luminosities • Note that there are many more faint stars than bright stars, suggesting that less luminous stars are far more common.