Stellar RadiationStellar Radiation

Stellar RadiationStellar Radiation

Where do stars get their energy? Energy from stars can be understood

using Einstein’s famous equation E=mc2

The product of the nuclear reaction has less mass than the reactant.

The missing mass is converted to energy.

Where do stars get their energy? Energy from stars can be understood

using Einstein’s famous equation E=mc2

The product of the nuclear reaction has less mass than the reactant.

The missing mass is converted to energy.

Nuclear fusion in Stars (pg 496)

Nuclear fusion in Stars (pg 496)

What is the most important thing about a star?

What is the most important thing about a star?

MASS!The The massmass of a normal star almost of a normal star almost

completely determines itscompletely determines its LUMINOSITYLUMINOSITY and TEMPERATURETEMPERATURE!

Note: “normal” star means a star that’s fusing Hydrogen into Helium in its center (we say “hydrogen burning”).

The LUMINOSITY of a star is how much ENERGY it gives offper second:

The LUMINOSITY of a star is how much ENERGY it gives offper second:

The energy the Sun emits is generated by the fusion in its

core…

This light bulb has a luminosity of 60 Watts

What does luminosity have to do with mass?What does luminosity have to do with mass?

The mass of a star determines the pressure in its core:

PressurePressure

Gravity pulls outer layers in,

Gas Pressure pushes them out.

The core supports the weight of the whole star!

The more mass the star has, the higher the central pressure!

The core pressure determines the rate of

fusion…

The core pressure determines the rate of

fusion…

MASS PRESSURE &TEMPERATURE

RATE OF FUSION

…which in turn determines the star’s…which in turn determines the star’s

luminosity!

Luminosity is an intrinsic property… it doesn’t depend on distance!

Luminosity is an intrinsic property… it doesn’t depend on distance!

This light bulb has a luminosity of 60 Watts…

…no matter where it is, or where we view it from, it will always be a 60 Watt light bulb.

LuminosityLuminosity

The Luminosity of a star is the energy that it releases per second. Sun has a luminosity of 3.90x1026 W (often written as L): it emits 3.90x1026 joules per second in all directions.

The energy that arrives at the Earth is only a very small amount when compared will the total energy released by the Sun.

LuminosityLuminosity

Exercise

The Sun is a distance d=1.5 x 1011 m from the Earth. Estimate how much energy falls on a surface of 1m2 in a year.

d

L= 3.90x1026 W

Apparent brightnessApparent brightness When the light from the Sun reaches the Earth it

will be spread out over a sphere of radius d. The energy received per unit time per unit area is b, where:

When the light from the Sun reaches the Earth it will be spread out over a sphere of radius d. The energy received per unit time per unit area is b, where:

d

b is called the apparent brightness of the star

24 d

Lb

At a distance of d=1.5 x 1011 m, the energy is “distributed” along the surface of a sphere of radius 1.5 x 1011 m

d

The sphere’s surface area is given by:

A = 4πd2 = 4 π x (1.5 x 1011)2 =

=2.83 x 1023 m2

The energy that falls on a surface area of 1m2 on Earth per second will be equal to:

b = L/A = 3.90x1026 / 2.83 x 1023 =

= 1378.1 W/m2 or 1378.1 J/s m2 In a year there are: 365.25days x 24h/day x 60min/h x 60s/min = 3.16 x 107 s

So, the energy that falls in 1 m2 in 1 year will be:

1378.1 x 3.16 x 107 = 4.35 x 1010 joules

Black body radiationBlack body radiation A black body is a perfect emitter. A good model

for a black body is a filament light bulb: the light bulb emits in a very large region of the electromagnetic spectrum. i.e. ultra violet, visual, and infrared.

There is a clear relationship between the temperature of an object and the wavelength for which the emission is maximum. That relationship is known as Wien’s law:

A black body is a perfect emitter. A good model for a black body is a filament light bulb: the light bulb emits in a very large region of the electromagnetic spectrum. i.e. ultra violet, visual, and infrared.

There is a clear relationship between the temperature of an object and the wavelength for which the emission is maximum. That relationship is known as Wien’s law:

K m 2.9x10T

constantT3-

max

max

Star’s Color and Temperature

Star’s Color and Temperature

Black body radiation and Wien Law

Black body radiation and Wien Law

Wien Displacement lawWien Displacement law

By analysing a star’s spectrum, we can know in what wavelength the star emits more energy.The Sun emits more energy at λ=500 nm. According to Wien’s law, the temperature at the Sun’s surface is inversely proportional to the maximum wavelength.So:

By analysing a star’s spectrum, we can know in what wavelength the star emits more energy.The Sun emits more energy at λ=500 nm. According to Wien’s law, the temperature at the Sun’s surface is inversely proportional to the maximum wavelength.So:

K 5800500x10

2.9x10

2.9x10T

9-

-3

max

-3

Black body radiationBlack body radiation Apart from temperature, a radiation spectrum can

also give information about luminosity. The area under a black body radiation curve is equal

to the total energy emitted per second per unit of area of the black body.

The total power emitted by a black body is its luminosity.

According to the Stefan-Boltzmann law, a body of surface area A and absolute temperature T has a luminosity given by:

Apart from temperature, a radiation spectrum can also give information about luminosity.

The area under a black body radiation curve is equal to the total energy emitted per second per unit of area of the black body.

The total power emitted by a black body is its luminosity.

According to the Stefan-Boltzmann law, a body of surface area A and absolute temperature T has a luminosity given by:

4σATL where, σ = 5.67x10-8 W m-2 K-4

Why is this important?Why is this important?

The spectrum of stars is similar to the spectrum emitted by a black body.

We can therefore use Wien Law to find the temperature of a star from its spectrum.

If we know its temperature and its luminosity then its radius can be found from Stephan-Boltzmann law.

The spectrum of stars is similar to the spectrum emitted by a black body.

We can therefore use Wien Law to find the temperature of a star from its spectrum.

If we know its temperature and its luminosity then its radius can be found from Stephan-Boltzmann law.

Emission of LightEmission of Light Emission Spectra: The actual wavelengths of

light emitted by a source. These are dependent on transition states of the atom’s electrons. These can be seen with a spectroscope.

Here is Hydrogen’s Signature!

Here is Iron’s Signature!

Emission Spectra: The actual wavelengths of light emitted by a source. These are dependent on transition states of the atom’s electrons. These can be seen with a spectroscope.

Here is Hydrogen’s Signature!

Here is Iron’s Signature!

Absorption SpectraAbsorption Spectra When a Light source passes by a cool gas the

atomic signature of the cloud is revealed as specific wavelengths of light are absorbed.

When a Light source passes by a cool gas the atomic signature of the cloud is revealed as specific wavelengths of light are absorbed.

Absorption and Emission Spectra for Hydrogen

Absorption and Emission Spectra for Hydrogen

Real spectra are more complicated than this (remember emission and absorption lines?)

Real spectra are more complicated than this (remember emission and absorption lines?)

BlackbodySpectrum

Emission and Absorption

Lines

Stars can be arranged into categories based on the features in their spectra…

Stars can be arranged into categories based on the features in their spectra…

This is called “Spectral Classification”

1. by the “strength” (depth) of the absorption lines in their spectra

2. by their color as determined by their blackbody curve 3. by their temperature and luminosity

How do we categorize stars?A few options:

First attempts to classify stars used the strength of

their absorption lines…

First attempts to classify stars used the strength of

their absorption lines…

Williamina Fleming

They also used the strength of the Harvard “computers”!

Stars were labeled “A, B, C…”in order of increasing strength of Hydrogen lines.

OBAFGKM(LT)!

Later, these categories were reordered according to temperature/color…

Later, these categories were reordered according to temperature/color…

Annie Jump Cannon

OBAFGKM - MnemonicsOBAFGKM - Mnemonics

Only Boring Astronomers Find Gratification in Knowing Mnemonics!

O Be A Fine Girl/Guy Kiss Me

Eventually, the connection was made between the

observables and the theory.

Eventually, the connection was made between the

observables and the theory.

Observable:• Strength of Hydrogen Absorption Lines• Blackbody Curve (Color)

Theoretical:• Using observables to determine things we can’t measure: Temperature and Luminosity

Cecilia Payne

The Spectral SequenceThe Spectral SequenceClass Spectrum Color Temperature

O ionized and neutral helium, weakened hydrogen

bluish 31,000-49,000 K

B neutral helium, stronger hydrogen

blue-white 10,000-31,000 K

A strong hydrogen, ionized metals

white 7400-10,000 K

F weaker hydrogen, ionized metals

yellowish white 6000-7400 K

G still weaker hydrogen, ionized and neutral metals

yellowish 5300-6000 K

K weak hydrogen, neutral metals

orange 3900-5300 K

M little or no hydrogen, neutral metals, molecules

reddish 2200-3900 K

L no hydrogen, metallic hydrides, alkalai metals

red-infrared 1200-2200 K

T methane bands infrared under 1200 K

“If a picture is worth a 1000 words, a spectrum is

worth 1000 pictures.”

“If a picture is worth a 1000 words, a spectrum is

worth 1000 pictures.”

Spectra tell us about the physics of the star and how those physics affect the atoms in it

Spectra tell us about the physics of the star and how those physics affect the atoms in it

The Hertzsprung-Russell diagram

The Hertzsprung-Russell diagram

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This diagram shows a correlation between the luminosity of a star and its temperature.

The scale on the axes is not linear as the temperature varies from 3000 to 25000 K whereas the luminosity varies from 10-4 to 106, 10 orders of magnitude.

H-R diagramH-R diagram The stars are not randomly

distributed on the diagram. There are 3 features that emerge

from the H-R diagram: Most stars fall on a strip

extending diagonally across the diagram from top left to bottom right. This is called the MAIN SEQUENCE.

Some large stars, reddish in colour occupy the top right – these are red giants (large, cool stars).

The bottom left is a region of small stars known as white dwarfs (small and hot)

The stars are not randomly distributed on the diagram.

There are 3 features that emerge from the H-R diagram: Most stars fall on a strip

extending diagonally across the diagram from top left to bottom right. This is called the MAIN SEQUENCE.

Some large stars, reddish in colour occupy the top right – these are red giants (large, cool stars).

The bottom left is a region of small stars known as white dwarfs (small and hot)