astrophysics of life : stars. 2 wave characteristics: wavelength - distance between successive wave...

Astrophysics of Life :Astrophysics of Life :

StarsStars

2

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 3x108 m/s

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

400nm 500nm 600nm 700nm

Wavelength = COLOR

4

Electromagnetic SpectrumElectromagnetic Spectrum

communication

heat

detected by our eyes

sunburnmost

energetic

penetrate tissue

Microwaves,

cooking

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Blackbodies with different temperatures look like this:

Hotter blackbodies are brighter and “bluer.”

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Wien’s LawWien’s Law “Hotter bodies radiate more

strongly at shorter wavelengths (i.e. they’re bluer).”

max = 0.29 cmT (K)

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

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(Flux)

max = 0.29 cmT (K)

Wien math fun

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Stefan’s LawStefan’s Law “Hotter blackbodies are brighter

overall (at every wavelength).”

where: F = total radiative flux

= constant

F = T4

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Emission Line Spectra

Each element produces its own unique pattern of lines

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Absorption Line Spectra

Spectrum of the SunSpectrum of the Sun:

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 = 4d2)

Luminosity4d2Flux =

To know a star’s luminosity we must measure its apparent brightness (flux) and know its distance. Then,

Luminosity = Flux *4d2

The Magnitude Scale

2nd 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.

The magnitudes scale is logarithmic.

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

Hence

BrightestBrightest

FaintestFaintest

Apparent Magnitude Apparent Magnitude -- star’s apparent brightness when seen from its actual distance

Absolute MagnitudeAbsolute 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 skyNotice 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.

Annie Jump Cannon

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.

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 = T4

Luminosity is the Flux multiplied by entire spherical surface

Area of sphere A = 4R2

Giants - more than 10 solar radii

Dwarfs - less than 1 solar radii

L R2 T4

Luminosity = 4R2 T4

-or-

Understanding Stefan’s Law: Radius

L R2 T4

Understanding Stefan’s Law: Temperature

L R2 T4

Hertzsprung-Russell (HR) Diagram

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

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

HR diagrams plot stars as a function of their

Luminosity & Temperature

L = 4R2 T4

From Stefan’s law…...

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

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

Example:

Luminosity4d2Flux =

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 starSupergiant

A starGiant

A star Dwarf (Main Sequence)

Wavelength

The HR Diagram: Luminosity & Spectroscopic Parallax

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.

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).

The Distance Ladder

•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: Visual Binary Stars

Stellar Masses: Spectroscopic Binary Stars

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

Many binaries are too far away to be resolved, but they can be discovered from periodic spectral line shifts.

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 Mass3

Why?

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

Lifetime Fuel available / How fast fuel is burned

Lifetime Mass / Mass3 = 1 / Mass2

Lifetime Mass / Luminosity

So for a star

Or, since Luminosity Mass3 For main sequence stars

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

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

How does Mass effect how long a star will liveHow does Mass effect how long a star will live