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Stars aslkhasd (Magnitude (Magnitude Scale (A difference of 5 on the…
Stars aslkhasd
Magnitude
Apparent Magnitude, \(m\)
How bright a star appears from the Earth, taking no account of it's distance from us
Absolute Magnitude, \(M\)
How bright a star would appear to us, if it were at \(10\,Pc\) from us
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Luminosity, \(P\)
The total power output of a star, across all wavelengths of the electromagnetic spectrum, measured in \(W\)
Intensity, \(I\)
The total amount of energy, incident per second, per square meter on the Earth's surface, across all wavelengths of the electromagnetic spectrum, measured in \(Wm^{-2}\)
\[I=\frac{P}{4\pi\,d^{2}}\]
Where \(d\) is the distance of the star from us in metres
Magnitude Scale
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Key Values (Absolute Magnitude)
Sun: -26.7
Vega: 0
Limit of human eye: +6
Limit of binoculars: +10
Limit of most telescopes: +20
Limit of HST: +30
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Distances
1 Parsec, \(Pc\)
The distance that a star would have to be away to subtend an angle of parallax of one second of arc
Parallax
The apparent motion of a stationary nearby star, relative to more distant stationary stars, due to the Earth's motion around the Sun.
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\[\theta=\frac{R}{d}\]
Where \(R\) is the radius of the Earth's orbit around the Sun (\( 1Au\) ), \(d\) is the distance of the star from us and \(\theta\) is the angle of parallax in radians
1 Light Year, \(ly\)
The distance that a ray of light travels in one year in a vacuum
1 Astronomical Unit, \(Au\)
The average radius of the Earth's orbit around the Sun, over one year
Temperature
Black Body
A perfect absorber and perfect emitter of electromagnetic radiation. Will absorb all wavelengths incident onto it, and will emit all wavelengths of light
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Features of graph
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Falls slowly after peak, tending to zero at infinity
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The total area under a black body curve is the total power output of the star across all wavelengths (the luminosity)
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A black body is characterised by it's temperature. At higher temperatures the peak of the graph moves to lower wavelengths, the whole graph moves up, and the total power output (luminosity) of the star increases
A star behaves approximately as a black body, of temperature equal to the surface temperature of the star
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Spectra
Absorption Lines
Light of all wavelengths is produced in the core of a star. As the photons make their way to the outer atmosphere of the star, certain photons are absorbed by electrons existing in ions / atoms / molecules (in very cool stars), with excitation energies exactly equal to the energy of the photons
When these electrons de-excite, they do so by emitting the photons in a random direction, and possibly through multiple smaller energy jumps, leading to a lower (non-zero) overall intensity of light of that wavelength reaching the Earth
This appears as a darker band in the star's absorption spectrum, at that wavelength of light
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Balmer
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At low temperatures most electrons are in the n=1 level in hydrogen and so few electrons can be excited by a Balmer photon
As the temperature of the gas increases electrons gain more energy on average, and more frequently, from random collisions of hydrogen atoms transferring energy to the Balmer photons to excite them to the n=2 level. More Balmer photons can be absorbed in a given time, and so the intensity of the Balmer lines increases
Eventually a temperature is reached where the intensity of the Balmer lines starts to decrease again as the electrons, on average, start to exist in the n=3 and n=4 levels more often.
The intensity of the Balmer lines from a star can be used as a temperature gauge for the star, however other elements must also be used to accurately deduce the temperature of the star, as for each intensity of Balmer line there are two possible temperatures that could be causing it
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