Astrophysics of Life : Stars

Wave Characteristics:

•

Wavelength

- Distance between successive wave peaks •

Period

– Time between passing wave peaks •

Frequency

– Number of wave peaks passing per unit time (1/Period) •

Wave Speed

– wavelength x frequency (follow a crest )

Light Speed is 3x10 8 m/s

2

Wavelength =

C O L O R

400nm 500nm 600nm 700nm Visible light ranges in wavelength from ~400 to ~700 nanometers.

3

Electromagnetic Spectrum

Microwav es, cooking communication heat sunburn detected by our eyes penetrate tissue most energetic 4

Blackbodies with different temperatures look like this: Hotter blackbodies are brighter and “bluer.” 5

Wien’s Law



“Hotter bodies radiate more strongly at shorter wavelengths (i.e. they’re bluer).”

 max

= 0.29 cm T (K)

We can measure a star’s temperature from its spectrum!

6

(Flux)

Wien math fun  max = 0.29 cm T (K) 7

Stefan’s Law



“Hotter blackbodies are brighter overall (at every wavelength).” F =



T

4 where: F = total radiative flux  = constant 8

Emission Line Spectra

Each element produces its own unique pattern of lines 9

Absorption Line Spectra

Spectrum of the Sun:

10

Luminosity and Apparent Brightness

Star B is more luminous, but they have the same brightness as seen from Earth.

Apparent Brightness and Inverse Square Law  Light appears fainter with increasing distance.

 If we increase our distance from the light source by 2, the light energy is spread out over four times the area. (area of sphere = 4  d 2 ) Flux = Luminosity 4  d 2 To know a star’s luminosity we must measure its apparent brightness (flux) and know its distance. Then, Luminosity = Flux *4  d 2

The

Magnitude

Scale 2 nd century BC, Hipparchus ranked all visible stars – brightest = magnitude 1 faintest = magnitude 6.

To our eyes, a change of one magnitude = a factor of 2.5 in flux.

Hence The magnitudes scale is logarithmic.

A change of 5 magnitudes means the flux 100 x greater!

Faintest Brightest

Apparent Magnitude -

star’s apparent brightness when seen from its actual distance

Absolute Magnitude

- apparent magnitude of a star as measured from a distance of 10 pc.

Sun’s

apparent magnitude

(if seen from a distance of 10 pc) is 4.8.

This is then the

absolute magnitude

of the Sun.

Enhanced color picture of the sky Notice the color differences among the stars

Starlight: Who Cares?

• •

We do!

Primary source of “life energy” on Earth

•

Many living things convert sunlight to energy

•

Most other living things eat them (or eat things that eat them, or …)

•

Also, heat/temperature

•

Living things want liquid phase (remember)

•

Need the right star/distance combination for this

•

Also, want STABLE temperatures for long time (i.e. millions, or better yet, BILLIONS of years)

Stellar Temperature : Color

• You don’t have to get the entire spectrum of a star to determine its temperature.

• Measure flux at blue (B) and yellow (“visual”=V) wavelengths.

• Get temperature by comparing B -V color to theoretical blackbody curve.

Stellar Temperature : Spectra

• 7 stars with same chemical composition •

Temperature

affects strength of absorption lines

Example

: Hydrogen lines are relatively weak in the hottest star because it is mostly ionized. Conversely, hotter temperatures are needed to excite and ionize Helium so these lines are strongest in the hottest star.

Spectral Classification: Before astronomers knew much about stars, they classified them based on the strength of observed absorption lines.

Classification by line strength started as A, B, C, D, …., but became: O, B, A, F, G, K, M, (L)

A temperature sequence!

Cannon’s system officially adopted in 1910.

Annie Jump Cannon

Spectral Classification “Oh Be A Fine Girl/Guy Kiss Me” “Oh Brother, Astronomers Frequently Give Killer Midterms”

Stellar Sizes

•Almost all stars are so small they appear only as a point of light in the largest telescopes •A small number are big and close enough to determine their sizes directly through geometry

Stellar Sizes

: Indirect measurement Stefan’s Law F =  T 4 Luminosity is the Flux multiplied by entire spherical surface Area of sphere A = 4  R 2 Luminosity = 4  R 2  T 4 -or L  R 2  T 4

Giants

- more than 10 solar radii

Dwarfs

less than 1 solar radii

Understanding Stefan’s Law: Radius L  R 2  T 4

Understanding Stefan’s Law: Temperature L  R 2  T 4

Hertzsprung-Russell (HR) Diagram HR diagrams plot stars as a function of their

Luminosity

&

Temperature

About 90% of all stars (including the Sun) lie on the Main Sequence.

…where stars reside during their core Hydrogen-burning phase.

From Stefan’s law…...

L = 4  R 2  T 4  More luminous stars at the same T

must

be bigger!

 Cooler stars at the same L

must

be bigger!

The HR Diagram: 100 Brightest Stars  Most of these luminous stars are somewhat rare – they lie beyond 5pc.

 We see almost no red dwarfs (even though they are very abundant in the universe) because they are too faint.

 Several non-Main Sequence stars are seen in the

Red Giant

region

Using The HR Diagram to Determine Distance: Spectroscopic “Parallax” Main Sequence Example: 1) Determine Temperature from color 2) Determine Luminosity based on Main Sequence position 3) Compare Luminosity with Flux (apparent brightness) 4) Use inverse square law to determine distance Flux = Luminosity 4  d 2

The HR Diagram: Luminosity & Spectroscopic Parallax What if the star doesn’t happen to lie on the Main Sequence - maybe it is a red giant or white dwarf??? We determine the star’s

Luminosity Class

based on its spectral line widths: These lines get broader when the stellar gas is at higher densities – indicating a smaller star.

A star

Supergiant

A star

Giant

A star

Dwarf (Main Sequence)

Wavelength 

The HR Diagram: Luminosity Class Bright Supergiants Supergiants Bright Giants Giants Sub-giants Main-Sequence (Dwarfs)

 We get distances to nearby planets from radar ranging.

 That sets the scale for the whole solar system (1 AU).

 Given 1 AU plus stellar parallax, we find distances to “nearby” stars.

The Distance Ladder  Use these nearby stars, with known Distances, Fluxes and Luminosities, to calibrate Luminosity classes in HR diagram.

 Then spectral class + Flux yields Luminosity + Distance for farther stars (Spectroscopic Parallax).

Stellar Masses: Visual Binary Stars •With Newton’s modifications to Kepler’s laws, the period and size of the orbits yield the sum of the masses, while the relative distance of each star from the center of mass yields the ratio of the masses. •The ratio and sum provide each mass individually.

Stellar Masses: Spectroscopic Binary Stars Many binaries are too far away to be resolved, but they can be discovered from periodic spectral line shifts.

In this example, only the yellow (brighter) star is visible…

Stellar Masses: Eclipsing Binary Stars How do we identify eclipsing binaries?

The system must be observed “edge on”.

Also tells us something about the stellar radii.

The HR Diagram: Stellar Masses Why is

mass

so important?

Together with the initial composition, mass defines the entire life cycle and all other properties of the star!

Luminosity, Radius, Surface Temperature, Lifetime, Evolutionary phases, end result….

Example: On the Main Sequence: Luminosity  Mass 3 Why?

• • • • • More mass means more gravity, more pressure on core, higher core temperatures, faster nuclear reaction rates, higher Luminosities!

How does Mass effect how long a star will live

Lifetime  Fuel available / How fast fuel is burned So for a star Lifetime  Mass / Luminosity Or, since Luminosity  Mass 3 For main sequence stars Lifetime  Mass / Mass 3 = 1 / Mass 2

How long a star lives is directly related to the mass!

Big stars live shorter lives, burn their fuel faster….