Stellar Radiation

 Where do stars get their energy?  Energy from stars can be understood using Einstein’s famous equation E=mc 2  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=mc 2  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)

What is the most important thing about a star? MASS! The mass of a normal star almost completely determines its LUMINOSITYTEMPERATURE The mass of a normal star almost completely determines its LUMINOSITY and TEMPERATURE!  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 off per 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? The mass of a star determines the pressure in its core: Pressure 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… MASS PRESSURE & TEMPERATURE RATE OF FUSION …which in turn determines the star’s luminosity!

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.

Luminosity The Luminosity of a star is the energy that it releases per second. Sun has a luminosity of 3.90x10 26 W (often written as L  ): it emits 3.90x10 26 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.

Luminosity Exercise The Sun is a distance d=1.5 x m from the Earth. Estimate how much energy falls on a surface of 1m 2 in a year. d L  = 3.90x10 26 W

Apparent 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: d b is called the apparent brightness of the star

At a distance of d=1.5 x m, the energy is “distributed” along the surface of a sphere of radius 1.5 x m d The sphere’s surface area is given by: A = 4πd 2 = 4 π x (1.5 x ) 2 = =2.83 x m 2 The energy that falls on a surface area of 1m 2 on Earth per second will be equal to: b = L  /A = 3.90x10 26 / 2.83 x = = W/m 2 or J/s m2 In a year there are: days x 24h/day x 60min/h x 60s/min = 3.16 x 10 7 s So, the energy that falls in 1 m 2 in 1 year will be: x 3.16 x 10 7 = 4.35 x joules

Black 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:

Star’s Color and Temperature

Black body radiation and Wien Law

Wien 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:

Black 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: where, σ = 5.67x10- 8 W m -2 K -4

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 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 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.

Absorption and Emission Spectra for Hydrogen

Real spectra are more complicated than this (remember emission and absorption lines?) Blackbody Spectrum Emission and Absorption Lines

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… 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… Annie Jump Cannon

OBAFGKM - 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. 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 Sequence ClassSpectrumColorTemperature O ionized and neutral helium, weakened hydrogen bluish31,000-49,000 K B neutral helium, stronger hydrogen blue-white10,000-31,000 K A strong hydrogen, ionized metals white ,000 K F weaker hydrogen, ionized metals yellowish white K G still weaker hydrogen, ionized and neutral metals yellowish K K weak hydrogen, neutral metals orange K M little or no hydrogen, neutral metals, molecules reddish K L no hydrogen, metallic hydrides, alkalai metals red-infrared K T methane bands infraredunder 1200 K

“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

The Hertzsprung-Russell diagram You are here 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 K whereas the luminosity varies from to 10 6, 10 orders of magnitude.

H-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)