Homework: Parallax Given p in arcseconds (”), use d=1/p to calculate the distance which will be in units “parsecs” By definition, d=1pc if p=1”, so convert d to A.U. by using trigonometry To calculate p for star with d given in lightyears, use d=1/p but convert ly to pc. Remember: 1 degree = 3600” Note: p is half the angle the star moves in half a year

Our Stellar Neighborhood

Scale Model If the Sun = a golf ball, then –Earth = a grain of sand –The Earth orbits the Sun at a distance of one meter –Proxima Centauri lies 270 kilometers (170 miles) away –Barnard’s Star lies 370 kilometers (230 miles) away –Less than 100 stars lie within 1000 kilometers (600 miles) The Universe is almost empty! Hipparcos satellite measured distances to nearly 1 million stars in the range of 330 ly almost all of the stars in our Galaxy are more distant

Reminder: Three Things Light Tells Us Temperature –from black body spectrum Chemical composition –from spectral lines Radial velocity –from Doppler shift

Luminosity and Brightness Luminosity L is the total power (energy per unit time) radiated by the star, actual brightness of star, cf. 100 W lightbulb Apparent brightness B is how bright it appears from Earth –Determined by the amount of light per unit area reaching Earth –B  L / d 2 Just by looking, we cannot tell if a star is close and dim or far away and bright

Brightness: simplified 100 W light bulb will look 9 times dimmer from 3m away than from 1m away. A 25W light bulb will look four times dimmer than a 100W light bulb if at the same distance! If they appear equally bright, we can conclude that the 100W lightbulb is twice as far away!

Same with stars… Sirius (white) will look 9 times dimmer from 3 lightyears away than from 1 lightyear away. Vega (also white) is as bright as Sirius, but appears to be 9 times dimmer. Vega must be three times farther away (Sirius 9 ly, Vega 27 ly)

Distance Determination Method is (L)Understand how bright an object is (L) appears (B)Observe how bright an object appears (B) Calculate how far the object is away: B  L / d 2 So L/B  d 2 or d  √L/B

Homework: Luminosity and Distance Distance and brightness can be used to find the luminosity: L  d 2 B So luminosity and brightness can be used to find Distance of two stars 1 and 2: d 2 1 / d 2 2 = L 1 / L 2 ( since B 1 = B 2 ) i.e. d 1 = (L 1 / L 2 ) 1/2 d 2

The Magnitude Scale A measure of the apparent brightness Logarithmic scale Notation: 1 m.4 (smaller  brighter) Originally six groupings –1 st magnitude the brightest –6 th magnitude is 100x dimmer So a difference of 5mag is a difference of brightness of 100 Factor 2.512=100 1/5 for each mag.

Absolute Magnitude The absolute magnitude is the apparent magnitude a star would have at a distance of 10 pc. Notation example: 2 M.8 It is a measure of a star’s actual or intrinsic brightness called luminosity Example: Sirius: 1 M.4, Sun 4 M.8 –Sirius is intrinsically brighter than the Sun

Finding the absolute Magnitude To figure out absolute magnitude, we need to know the distance to the star Then do the following Gedankenexperiment: –In your mind, put the star from its actual position to a position 10 pc away –If a star is actually closer than 10pc, its absolute magnitude will be a bigger number, i.e. it is intrinsically dimmer than it appears –If a star is farther than 10pc, its absolute magnitude will be a smaller number, i.e. it is intrinsically brighter than it appears

Measuring the Sizes of Stars Direct measurement is possible for a few dozen relatively close, large stars –Angular size of the disk and known distance can be used to deduce diameter

Indirect Measurement of Sizes Distance and brightness can be used to find the luminosity: L  d 2 B (1) The laws of black body radiation also tell us that amount of energy given off depends on star size and temperature: L  R 2  T 4 (2) We can compare two values of absolute luminosity L to get the size

Sizes of Stars Dwarfs –Comparable in size, or smaller than, the Sun Giants –Up to 100 times the size of the Sun Supergiants –Up to 1000 times the size of the Sun Note: Temperature changes!

Classification of the Stars: Temperature Class TemperatureColorExamples O30,000 Kblue B20,000 KbluishRigel A10,000 KwhiteVega, Sirius F8,000 KwhiteCanopus G6,000 KyellowSun,  Centauri K4,000 KorangeArcturus M3,000 KredBetelgeuse Mnemotechnique : Oh, Be A Fine Girl/Guy, Kiss Me

The Key Tool to understanding Stars: the Hertzsprung-Russell diagram Hertzsprung-Russell diagram is luminosity vs. spectral type (or temperature) To obtain a HR diagram: –get the luminosity. This is your y-coordinate. –Then take the spectral type as your x-coordinate, e.g. K5 for Aldebaran. First letter is the spectral type: K (one of OBAFGKM), the arab number (5) is like a second digit to the spectral type, so K0 is very close to G, K9 is very close to M.

Constructing a HR-Diagram Example: Aldebaran, spectral type K5III, luminosity = 160 times that of the Sun O B A F G K M Type … … L Aldebaran Sun (G2V) 160

The Hertzprung- Russell Diagram A plot of absolute luminosity (vertical scale) against spectral type or temperature (horizontal scale) Most stars (90%) lie in a band known as the Main Sequence

Hertzsprung-Russell diagrams … of the closest stars…of the brightest stars