What determines Luminosity? What determines Luminosity? • Stephan’s law: Power radiated Stephan’s law: Power radiated

depends on Temp to the 4depends on Temp to the 4thth power! power!

• L (Luminosity) depends on L (Luminosity) depends on Area of Star x tempArea of Star x temp44

• hot stars can be MUCH hot stars can be MUCH brighter than larger cooler brighter than larger cooler stars. stars.

• Temp is easily measured from Temp is easily measured from the peak wavelength of the the peak wavelength of the spectrum (Wein’s law) spectrum (Wein’s law)

Temp, Luminosity, Size: Temp, Luminosity, Size: • For Example, Deneb has For Example, Deneb has

a luminosity of 170,000 a luminosity of 170,000 times the luminosity of times the luminosity of the sun. Its spectral the sun. Its spectral type is A2, which means type is A2, which means its temp is about 10,000 its temp is about 10,000 Kelvin (compared with Kelvin (compared with suns temp is 5800 suns temp is 5800 kelvin). kelvin).

• This Makes the Area of This Makes the Area of Deneb about 40000 x Deneb about 40000 x the area of the sun, so the area of the sun, so its radius and diameter its radius and diameter are about 200x the are about 200x the diameter of the sun.l diameter of the sun.l

http://www.daviddarling.info/images/Deneb_2.jpg

Masses of StarsMasses of Stars

• MassMass is the single most important is the single most important property of any star. It determines: property of any star. It determines:

• TemperatureTemperature• Luminoisty (at each stage of life)Luminoisty (at each stage of life)• LifetimeLifetime• How it will “die”How it will “die”

Direct measure of Mass from Direct measure of Mass from Binary StarsBinary Stars

• Optical doubles—just in the same Optical doubles—just in the same area of the sky. Not orbiting! area of the sky. Not orbiting!

• Visual binariesVisual binaries• a binary which is spatially a binary which is spatially

resolved, i.e. two stars are seen resolved, i.e. two stars are seen ((e.g.e.g. SiriusSirius))

Binary StarsBinary Stars• Spectroscopic binariesSpectroscopic binaries

• only one star is seen; the existence only one star is seen; the existence of the second star is inferred from of the second star is inferred from the Doppler shift of lines.the Doppler shift of lines.

Binary StarsBinary Stars• Eclipsing binariesEclipsing binaries

• a binary whose orbital plane lies a binary whose orbital plane lies along our line of sight, thus causing along our line of sight, thus causing “dips” in the light curve.“dips” in the light curve.

Binary StarsBinary Stars

• The stars orbit each other via The stars orbit each other via gravity.gravity.

• Newton’s version of Kepler’s Third Newton’s version of Kepler’s Third Law:Law:

PP2 2 = 4 = 42 2 aa33 / G (m / G (m11 + m + m22))• If you can measure the orbital period If you can measure the orbital period

of the binary (of the binary (PP) and the distance ) and the distance between the stars (between the stars (aa), then you can ), then you can calculate the sum of the masses of calculate the sum of the masses of both stars (both stars (mm11 + m + m22).).

Here are the Stars of Orion.

Whis the most Luminious? The Largest? Which isn’t a star at all? Check out: http://www.youtube.com/watch?v=mcJ35f57O8Q for a video comparing sizes!

Betelguese: 1000 x the diameter of the sun. Temp =

3000K (burr!)

Rigel: 70,000x Lsun

Temp = 10,000Kelvin.

The Orion Nebula—a star forming region!

The Hertzsprung-Russell The Hertzsprung-Russell DiagramDiagram

MV

Spectral type

bright

fainthot 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

HOT COOL

BRIGHT

FAINT

The Main Sequence (MS)The Main Sequence (MS)

90% of all stars lie on the main sequence!

Stellar LuminosityStellar Luminosity• Review: The luminosity of a star depends on Review: The luminosity of a star depends on

2 things:2 things:• surface temperaturesurface temperature• surface area (radius squared)surface area (radius squared)

• L = constant x (TL = constant x (T44 x R x R22)) The largest stars are in the upper right The largest stars are in the upper right

corner of the H-R Diagram.corner of the H-R Diagram. Note that Absolute Magnitude is a measure Note that Absolute Magnitude is a measure

of the Luminosity of the Starof the Luminosity of the Star Apparent visual Magnitude is a measure of Apparent visual Magnitude is a measure of

the Apparent Brightness (or Intensity) of the Apparent Brightness (or Intensity) of the starlight reaching the observer. the starlight reaching the observer.

Regions of the H-R DiagramRegions of the H-R Diagram

Stellar Luminosity Classes Stellar Luminosity Classes

Stellar Masses on the H-R Stellar Masses on the H-R DiagramDiagram

Mass-Luminosity Mass-Luminosity RelationRelation

L m3.5

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 RelationMass–Luminosity Relation• All main sequence stars fuse H into He in their All main sequence stars fuse H into He in their

cores.cores.• Luminosity depends directly on mass because:Luminosity depends directly on mass because:

• more mass means more weight from the star’s outer layersmore mass means more weight from the star’s outer layers• nuclear fusion rates must be higher in order to maintain nuclear fusion rates must be higher in order to maintain

gravitational equilibriumgravitational equilibrium

Lifetime on the Main Lifetime on the Main SequenceSequence

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 M3.5

How long before it is used up? Time =Amount/(rate it is being used)

M/L = M/M3.5 = M-2.5

Lifetime on the Main SequenceLifetime on the Main Sequence

• O & B Dwarfs burn fuel like a O & B Dwarfs burn fuel like a Hummer!Hummer!

• M Dwarfs burn fuel like a Prius! M Dwarfs burn fuel like a Prius! • Our Sun will last 10Our Sun will last 101010 years on the years on the

Main Sequence. Let Main Sequence. Let = (Lifetime of Sun)/(Lifetime = (Lifetime of Sun)/(Lifetime

of Star)of Star)• MS Lifetime MS Lifetime = 10 = 1010 10 yrs / Myrs / M2.52.5

Lifetime on the Main Lifetime on the Main SequenceSequence

So for example:

B2 dwarf (10 M) lasts 3.2 x 107 yr

F0 dwarf (2 M) lasts 1.8 x 109 yr

M0 dwarf (.5 M) lasts 5.6 x 1010 yr

But the Universe is 1.37 x 1010 yr old!

Every M dwarf that was ever created is still on the main sequence!!

Another Rung on the distance Another Rung on the distance ladder: Cepheid Variablesladder: Cepheid Variables

Henrietta Leavitt(1868-1921)

She studied the light curves of variable stars inthe Magellenic clouds.

Assumption: all stars are at theSame distance

Cepheid VariablesCepheid Variables

The brightness of the stars varied in a regular pattern.

Cepheid Variables as Cepheid Variables as Distance Distance IndicatorsIndicators

prototype: Cephei

F - G Bright Giants (II) whose pulsation periods (1-100 days) get longer with brightness (MV = -2 to -6)

Cepheid VariablesCepheid Variables

The Instability StripThe 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!