EUHOU Teacher Training - April 2012 What is a Standard Candle? Alexander L. Rudolph Professeur Invité, UPMC Professor of Physics and Astronomy California State Polytechnic University, Pomona EUHOU Teacher Training - April 2012

Stellar Luminosity Apparent brightness 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) If we measure apparent brightness (energy/sec/m2) and we know distance, we can get the luminosity of the star For Sun, apparent brightness = 1400 W/m2 and d = 150 million km = 1.5 × 1011 m

EUHOU Teacher Training - April 2012 Brightness Quiz I Two identical 50 W bulbs are placed at different distances from you. Which one appears brighter? The closer one The further one They appear the same brightness There is not enough information to tell EUHOU Teacher Training - April 2012

EUHOU Teacher Training - April 2012 Brightness Quiz II A 50 W and a 100 W bulb are placed the same distance from you. Which one appears brighter? The 50 W bulb The 100 W bulb They appear the same brightness There is not enough information to tell EUHOU Teacher Training - April 2012

EUHOU Teacher Training - April 2012 Brightness Quiz III A 50 W and a 100 W bulb are placed at different distances from you. If the 100 W bulb is closer, which one appears brighter? The 50 W bulb The 100 W bulb They appear the same brightness There is not enough information to tell EUHOU Teacher Training - April 2012

EUHOU Teacher Training - April 2012 Brightness Quiz IV A 50 W and a 100 W bulb are placed at different distances from you. If the 50 W bulb is closer, which one appears brighter? The 50 W bulb The 100 W bulb They appear the same brightness There is not enough information to tell EUHOU Teacher Training - April 2012

EUHOU Teacher Training - April 2012 Brightness Quiz V 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? square root of 10 10 100 1,000 the farther star does not appear fainter, since it is identical EUHOU Teacher Training - April 2012

The Distance Ladder Radar ranging (few AU) Parallax (AU few  1000 light years) Main sequence fitting (100s  10s of thousands of light years) Cepheid variable stars (100s of thousands  100s of millions of light years) Distant standards (Tully-Fisher, White Dwarf supernovae; 10s of millions to 10+ billion light years)

EUHOU Teacher Training - April 2012 Distance and Parallax As the Earth orbits the Sun, relatively nearby stars appear to move relative to more distant stars Because even the nearest stars are so distant, there is a simple relationship between distance and apparent angle a star moves 1 parsec ≈ 3.26 light years EUHOU Teacher Training - April 2012

EUHOU Teacher Training - April 2012 Standard Candles We can use this equation to find the distances to objects in the universe using the concept of a standard candle Thus, if we know an object’s luminosity, and measure its apparent brightness, we can find its distance EUHOU Teacher Training - April 2012

Standard Candles - Examples Cepheid variable stars (Inter. Fig. II) Very bright stars which vary in luminosity in a regular way A relation exists between variation period and the star’s luminosity Calibrated using nearby Cepheids of known distance White Dwarf (Type I) supernovae All WD Sne cross the Chandrasekhar limit and explode in the same way; hence all have similar luminosities Calibrated in nearby galaxies of known distance EUHOU Teacher Training - April 2012

Galactic Distances Quiz Cepheid variable stars are located in two different galaxies, A and B. Both stars have the same average apparent brightness. The star in galaxy A has a bright-dim-bright period of 10 days, while the one in galaxy B has a bright-dim-bright period of 30 days. Which of the two galaxies is at a greater distance from us? Galaxy A Galaxy B They are located at the same distance. There is insufficient information to tell.