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PHY2083Lecture 1 - Summary:
1 AU = 1.49 x 1011 m = mean Earth-Sun distance1 pc = 206265 AU ~ 3.26 lydistance (pc) = 1 / parallax (arcsecs)
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PHY2083ASTRONOMY
Lecture 2 - Magnitudes and photon fluxes
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Flux and luminosityThe “brightness” of a star is measured in terms of the flux received from it.
Flux: amount of energy received per unit time per unit area i.e., Watts / m2
Flux depends on intrinsic luminosity (energy / time) and distance
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Flux and luminosityImagine a star of luminosity L surrounded by a huge spherical shell of radius d (see fig.) Assuming that no light is absorbed during its journey out to the shell, the flux is given by:
F = L / (4πd2)
radius of a sphere
F ∝ 1 / d2inverse square law
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Flux and luminosityKey point:
Luminosity does NOT depend on distance, but flux does.
If a star appears faint, is it because it is really (i.e. intrinsically) faint, or because it is very far away [or both] ?
N.B. For stars at the same distance, the ratio of their fluxes = ratio of their luminosities
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Flux and luminosityKey point:
Luminosity does NOT depend on distance, but flux does.
F ∝ 1 / d2
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Example:The luminosity of the sun is 3.839 x 1026 W.
Calculate the flux received at Earth.
Solution:
Earth is 1 AU from the Sun = 1.49 x 1011m
F = L / (4πr2) = 1365 W / m2
This value of the solar flux is known as the “solar irradiance” or “solar constant”
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The magnitude systemIn theory: measure the brightness of astronomical objects in an absolute way by measuring the energy emitted in a specific wavelength region.
In practice: difficult due to absorption by atmosphere, instrument calibration etc.
Solution: perform relative measurements with respect to standard stars which have been calibrated in an absolute way
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The magnitude system• The Greek astronomer Hipparchus catalogued 850 stars that he saw, and invented a numerical scale corresponding to how bright each star was.
• He divided the stars into 6 groups or “magnitudes” with m = 1 being the brightest stars, and m = 6 being those that were faintest
Larger (positive) magnitudes => fainter objects
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The magnitude system
Stars brighter than 1st magnitude were assigned negative magnitudes.
Larger (positive) magnitudes => fainter objects
It was thought the response of the human eye was logarithmic (and not linear) => quantify the scale so that a difference of 1 magnitude => constant ratio in brightness.
Pogson’s Law (1895): 5 magnitudes = factor of 100 in brightness
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Blackboard derivations + notes
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The magnitude equation
m = −2.5 log f + C
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Apparent and absolute magnitudes
The magnitudes of standard stars are corrected for absorption by the Earth’s atmosphere. The magnitude of any object determined by comparison is therefore a measure of its flux at Earth. This is called the APPARENT MAGNITUDE (m)
In order to make comparisons more meaningful, define a measure of intrinsic brightness, which is a function of its distance and apparent magnitude.
The ABSOLUTE MAGNITUDE (M) is the magnitude a star would have if it were located at a distance of 10pc
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Example:
The apparent magnitude of the Sun is -26.83. Calculate its absolute magnitude. Calculate the flux received from the Sun if it were at 10pc
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Solution:The apparent magnitude of the Sun is -26.83. i) Calculate its absolute magnitude. ii) Calculate the flux received from the Sun if it were at 10pc
i) Msun = msun - 5 lg (d) + 5 d = 1 AU = 4.848 x 10-6 pc => Msun = -26.83 - 5 lg (4.848 x 10-6) + 5 => Msun = +4.74
ii) F = L / 4πr2 c.f. previous example at 1 AU now 10 pc = 2.063 x 106 AUInverse square law => flux will be 1 / (2.063 x 106)2 times lower => Flux at 10pc = 3.21 x 10-10 W / m2
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Filter systems
Magnitudes should be quoted for a specific wavelength range since real detectors are not sensitive to the entire EM spectrum, and the Earth’s atmosphere transmits radiation only over certain wavelength regions.
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Johnson UBV filter system
In practice, magnitudes are quoted for well-defined wavelength regions using filters e.g.
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Vega: magnitude 0 by definition
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What can we do with light from stars / galaxies?
I. We can take images e.g in different filters. Stars emit different amounts of energy at different wavelengths
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What can we do with light from stars / galaxies?
II. We can take disperse the light and measure the amount of flux as a function of wavelength i.e. obtain a spectrum of the object
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If the spectrum can be approximated by a blackbody, then we can estimate its temperature
absorption lines
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emission lines
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Recall basic atomic physics:
Emission lines: arise from energy state transitions of electrons in gas atoms / ions / molecules. Excited electrons decay back down to equilibrium level, releasing photons of a characteristic energy.
Absorption lines: Produced by a continuous source with cooler gas in front. The cooler gas preferentially absorbs at characteristic wavelengths, causing dark lines.
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We can use spectra to
i) estimate the composition of the star
ii) estimate the physical conditions (e.g. Teff)
iii) measure its radial velocity (i.e. the velocity in the line-of-sight to the observer) using the Doppler shift of spectral lines:
∆λ / λ = vradial / c where ∆λ = λ - λ0
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Astronomical measurements summary:
• Astrometry (Position, sky-plane velocity)
• Photometry (Brightness of objects)
• Spectroscopy (Flux as a function of wavelength)
• Spectroscopy (Doppler shift gives radial velocity)
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Optical Telescopes
© G. Bertini
Galileo Galilei
“The Starry Messenger”
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28-inch Refractor
Greenwich Observatory
London
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2.5-m Isaac
Newton Telescope
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4x8.2m
Very Large Telescope
Paranal, Chile
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Sensitivity
Photons/secnλ =NλD2
16 d2
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Sensitivity
Photons/secnλ =LλD2
16 d2
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nλ =AλCD2Lλ
64πR2h∆2
photons/sec
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20-m Giant Magellan Telescope
(~2021?)
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Thirty-Metre Telescope
(~2020)
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42-m European Extremely Large Telescope
(2021?)