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PHY2083
Lecture 1 - Summary:
1 AU = 1.49 x 1011 m = mean Earth-Sun distance
1 pc = 206265 AU ~ 3.26 ly
distance (pc) = 1 / parallax (arcsecs)
PHY2083
ASTRONOMY
Lecture 2 - Magnitudes and photon fluxes
Flux and luminosity
The “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
Flux and luminosity
Imagine 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
inverse square law
F∝1/
d2
Flux and luminosity
Key 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
Flux and luminosity
Key point:
Luminosity does NOT depend on distance, but flux does.
F ∝ 1 / d2
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”
The magnitude system
In 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
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
The magnitude system
Larger (positive) magnitudes => fainter objects
Stars brighter than 1st magnitude were assigned
negative magnitudes.
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
Blackboard derivations + notes
The magnitude equation
m = −2.5 log f + C
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
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
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 AU
Inverse square law => flux will be 1 / (2.063 x 106)2 times
lower => Flux at 10pc = 3.21 x 10-10 W / m2
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.
In practice, magnitudes are quoted for well-defined
wavelength regions using filters e.g.
Johnson UBV filter system
Vega: magnitude 0 by definition
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
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
If the spectrum can be approximated by a
blackbody, then we can estimate its temperature
absorption lines
emission lines
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.
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
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)
Optical Telescopes
Galileo Galilei
“The Starry
Messenger”
© G. Bertini
28-inch Refractor
Greenwich
Observatory
London
2.5-m
Isaac
Newton
Telescope
4x8.2m
Very Large Telescope
Paranal, Chile
Sensitivity
Nλ D 2
Photons/sec
nλ =
2
16 d
Sensitivity
Lλ D 2
Photons/sec
nλ =
2
16 d
Aλ CD2 Lλ
photons/sec
nλ =
2
2
64πRh ∆
20-m Giant
Magellan Telescope
(~2021?)
Thirty-Metre Telescope
(~2020)
42-m European Extremely Large Telescope
(2021?)