What determines Luminosity? Stephans law: Power radiated depends on Temp to the 4 th power! Stephans law: Power radiated depends on Temp to the 4 th power! L (Luminosity) depends on Area of Star x temp 4 L (Luminosity) depends on Area of Star x temp 4 hot stars can be MUCH brighter than larger cooler stars. hot stars can be MUCH brighter than larger cooler stars. Temp is easily measured from the peak wavelength of the spectrum (Weins law) Temp is easily measured from the peak wavelength of the spectrum (Weins law)

Temp, Luminosity, Size: For Example, Deneb has a luminosity of 170,000 times the luminosity of the sun. Its spectral type is A2, which means its temp is about 10,000 Kelvin (compared with suns temp is 5800 kelvin). For Example, Deneb has a luminosity of 170,000 times the luminosity of the sun. Its spectral type is A2, which means its temp is about 10,000 Kelvin (compared with suns temp is 5800 kelvin). This Makes the Area of Deneb about x the area of the sun, so its radius and diameter are about 200x the diameter of the sun.l This Makes the Area of Deneb about x the area of the sun, so its radius and diameter are about 200x the diameter of the sun.l

Masses of Stars Mass is the single most important property of any star. It determines: Mass is the single most important property of any star. It determines: Temperature Temperature Luminoisty (at each stage of life) Luminoisty (at each stage of life) Lifetime Lifetime How it will die How it will die

Direct measure of Mass from Binary Stars Optical doublesjust in the same area of the sky. Not orbiting! Optical doublesjust in the same area of the sky. Not orbiting! Visual binaries Visual binaries a binary which is spatially resolved, i.e. two stars are seen (e.g. Sirius) a binary which is spatially resolved, i.e. two stars are seen (e.g. Sirius)

Binary Stars Spectroscopic binaries Spectroscopic binaries only one star is seen; the existence of the second star is inferred from the Doppler shift of lines. only one star is seen; the existence of the second star is inferred from the Doppler shift of lines.

Binary Stars Eclipsing binaries Eclipsing binaries a binary whose orbital plane lies along our line of sight, thus causing dips in the light curve. a binary whose orbital plane lies along our line of sight, thus causing dips in the light curve.

Binary Stars The stars orbit each other via gravity. The stars orbit each other via gravity. Newtons version of Keplers Third Law: Newtons version of Keplers Third Law: P 2 = 4 2 a 3 / G (m 1 + m 2 ) If you can measure the orbital period of the binary (P) and the distance between the stars (a), then you can calculate the sum of the masses of both stars (m 1 + m 2 ). If you can measure the orbital period of the binary (P) and the distance between the stars (a), then you can calculate the sum of the masses of both stars (m 1 + m 2 ).

Here are the Stars of Orion. Whis the most Luminious? The Largest? Which isnt a star at all? Check out: for a video comparing sizes! Betelguese: 1000 x the diameter of the sun. Temp = 3000K (burr!) Rigel: 70,000x L sun Temp = 10,000Kelvin. The Orion Nebulaa star forming region!

The Hertzsprung-Russell Diagram MVMV Spectral type bright faint hot cool A very useful diagram for understanding stars We plot two major properties of stars: Temperature (x) vs. Luminosity (y) Spectral Type (x) vs. Absolute Magnitude (y) Stars tend to group into certain areas

HOTCOOL BRIGHT FAINT

The Main Sequence (MS) 90% of all stars lie on the main sequence!

Stellar Luminosity Review: The luminosity of a star depends on 2 things: Review: The luminosity of a star depends on 2 things: surface temperature surface temperature surface area (radius squared) surface area (radius squared) L = constant x (T 4 x R 2 ) L = constant x (T 4 x R 2 ) The largest stars are in the upper right corner of the H- R Diagram. The largest stars are in the upper right corner of the H- R Diagram. Note that Absolute Magnitude is a measure of the Luminosity of the Star Note that Absolute Magnitude is a measure of the Luminosity of the Star Apparent visual Magnitude is a measure of the Apparent Brightness (or Intensity) of the starlight reaching the observer. Apparent visual Magnitude is a measure of the Apparent Brightness (or Intensity) of the starlight reaching the observer.

Regions of the H-R Diagram

Stellar Luminosity Classes

Stellar Masses on the H-R Diagram

Mass-Luminosity Relation L m 3.5 for main sequence stars only We use binary stars to measure directly the masses of stars of every type. This leads to the: As one moves to the upper-left of the main sequence: stars become more massive stars become more luminous stars become fewer in number

Mass–Luminosity Relation All main sequence stars fuse H into He in their cores. All main sequence stars fuse H into He in their cores. Luminosity depends directly on mass because: Luminosity depends directly on mass because: more mass means more weight from the stars outer layers more mass means more weight from the stars outer layers nuclear fusion rates must be higher in order to maintain gravitational equilibrium nuclear fusion rates must be higher in order to maintain gravitational equilibrium

Lifetime on the Main Sequence How long will it be before MS stars run out of fuel? i.e. Hydrogen? How much fuel is there? M How fast is it consumed? L M 3.5 How long before it is used up? Time = Amount/(rate it is being used) M/L = M/M 3.5 = M -2.5

Lifetime on the Main Sequence O & B Dwarfs burn fuel like a Hummer! O & B Dwarfs burn fuel like a Hummer! M Dwarfs burn fuel like a Prius! M Dwarfs burn fuel like a Prius! Our Sun will last years on the Main Sequence. Let Our Sun will last years on the Main Sequence. Let = (Lifetime of Sun)/(Lifetime of Star) = (Lifetime of Sun)/(Lifetime of Star) MS Lifetime = yrs / M 2.5 MS Lifetime = yrs / M 2.5

Lifetime on the Main Sequence So for example: B2 dwarf (10 M ) lasts 3.2 x 10 7 yr F0 dwarf (2 M ) lasts1.8 x 10 9 yr M0 dwarf (.5 M ) lasts5.6 x yr But the Universe is 1.37 x yr old! Every M dwarf that was ever created is still on the main sequence!!

Another Rung on the distance ladder: Cepheid Variables Henrietta Leavitt ( ) She studied the light curves of variable stars in the Magellenic clouds. Assumption: all stars are at the Same distance

Cepheid Variables The brightness of the stars varied in a regular pattern.

Cepheid Variables as Distance Indicators prototype: Cephei F - G Bright Giants (II) whose pulsation periods (1-100 days) get longer with brightness (M V = -2 to -6)

Cepheid Variables

The Instability Strip There appears to be an almost vertical region on the H-R Diagram where all stars within it (except on the Main Sequence) are variable. They pulsate due to partial ionization!