PH507
Astrophysics
Professor Michael Smith
THE MULTIWAVELENGTH UNIVERSE AND EXOPLANETS
School of Physical Sciences Convenor Prof. Michael Smith
Taught in Term 2
Teaching Provision:
Prerequisites:
1
PH507
ECTS Credits 7.5
Kent Credits 15 at Level I
30 lectures + 4 workshops + 2 class tests
PH300, PH301, PH304
Aims: To provide a basic but rigorous grounding in observational,
computational and theoretical aspects of astrophysics to build
on the descriptive course in Part I, and to consider evidence for
the existence of exoplanets in other Solar Systems.
Learning Outcomes:
1. An understanding of the fundamentals of making astronomical
observations across the whole electromagnetic spectrum,
including discussion of photometry and spectroscopy, and the
physics of the astrophysical radiation mechanisms.
2. An understanding of the motions of objects in extrasolar
systems and the basic techniques required to solve the 2-body
problem to measure their properties.
3. An understanding of observational characteristics of stars,
and how their physical structures are derived from observation
and using simple physical models.
4. To be able to discuss coherently the origin and evolution of
Solar Systems and be able to evaluate claims for evidence of
Solar Systems other than our own.
SYLLABUS:
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Part 1: measurements
Part 2: radiation
Part 3: dynamics
Part 4: star and planet formation
Part 5: telescopes/instruments
Part 6: stars and stellar structure
Assessment Methods:Examination 70%, Homework 10%, 1st class test 10%, 2nd cla
7 assignments.
Class Test 1: end of week 6.
Class Test 2: end of week 12
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Astrophysics
Professor Michael Smith
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Recommended Texts:
Carroll & Ostlie, An Introduction to Modern Astrophysics,
Addison-Wesley, second edition if possible
THESE LECTURE NOTES, posted at the end of each week on my
webpage
[Note: Changes may occur to the syllabus during the year]
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Convenor: Prof. Michael Smith:
101 Ingram, x7654, m.d.smith@kent.ac.uk
Office hours: 10-12am Wed ??
Bad weather
Numbers, names
Locations, times of lectures: SPS110
Lecturers: Drs Price & Miao
PART 1: Measurement
LECTURE 1: DISTANCE
Distance: Distance is an easy concept to understand: it is just a
length in some units such as in feet, km, light years, parsecs etc. It
has been excrutiatingly difficult to measure astronomical
distances until this century.
Unfortunately most stars are so far away that it is impossible to
directly measure the distance using the classic technique of
triangulation.
Trignometric parallax: based on triangulation – need three
parameters to fully define any triangle e.g. two angles and one
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Astrophysics
Professor Michael Smith
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baseline.
To triangulate to even the closest stars we would need to use a very
large baseline. In fact we do have a long baseline, because every 6
months the earth is on opposite sides of the sun. So we can use as a
baseline the major axis of the earth's orbit around the sun.
BASELINE: 2 x earth-sun distance = 2 Astronomical Units (AU)
(The average distance from the earth to the sun is called the
Astronomical Unit.)
Note: size of earth:
6,000 km
Sun
700,000 km
1 AU 150,000,000 km (1.49 x 1011 m)
360 degree = 2  radians
57 degrees = 1 radian
Therefore solar disk subtends an angle of 2 x 700,000/150,000,000
radians = 0.01 radians i.e. about half a degree
angular size:
The parallactic displacement of a star on the sky as a result of the
Earth’s orbital motion permits us to determine the distance from the
Sun to the star by the method of trigonometric (heliocentric)
parallax. We define the trigonometric parallax of the star as the
angle p subtended, as seen from the star, by the Earth’s orbit of
radius 1 AU. If the star is at rest with respect to the Sun, the
parallax is half the maximum apparent annual angular
displacement of the star as seen from the Earth.
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Astrophysics
Professor Michael Smith
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Astrophysics
Professor Michael Smith
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Astrophysics
Professor Michael Smith
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1 radian is defined as:
1 radian =
360
 57.3 degrees = 206265 arc seconds, approximately. There are
2
2 rad in a circle (360˚), so that 1 radian equals 57˚17´44.81” (206,
264.81”).
Independent distance unit is the light year:
c  t ( year )  9.47 1015 m
The light year is not used much by professional astronomers, who
work instead with the unit of similar size called the parsec, where
1 parsec = 1 pc = 206265 AU = 3.086 x 1016 m = 3.26 light years.
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Astrophysics
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 The measurement and interpretation of stellar parallaxes are a
branch of astrometry, and the work is exacting and timeconsuming. Consider that the nearest star, Proxima/Alpha
Centauri (Rigil Kent), at a distance of 1.29 pc, has a parallax of
only 0.772”; all other stars have smaller parallaxes.
Formula:
1AU
tan p 
d
or
1
d 
AU
p
where p is in radians
for small angles.
To convert to arcseconds:
2.063 105
d 
AU
p ''
or
d 
1
pc .
p"
Defines the parsec – parallax second abbreviation!
Technique:
The ground-based trigonometric parallax of a star is determined by
photographing a given star field from a number (about 20) of selected points in
the Earth’s orbit.
The comparison stars selected are distant background stars of nearly the same
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Astrophysics
Professor Michael Smith
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apparent brightness as the star whose parallax is being measured.
Corrections are made for atmospheric refraction and dispersion and for
detectable motions of the background stars; any motion of the star relative to
the Sun is then extracted. What remains is the smaller annual parallactic
motion; it is recognised because it cycles annually.
Because a seeing resolution of 0.25” is considered exceptional (more
typical it is 1”), it may seem strange that a stellar position can be
determined to ±0.01” in one measurement; this accuracy is possible
because we are determining the centre of the fuzzy stellar image.
Astrometry: Technological advances (including the Hubble Space
Telescope) have improved parallax accuracy to 0.001” within a few
years. Before 1990, fewer than 10,000 stellar parallaxes had been
measured (and only 500 known well), but there are about 10 12 stars
in our Galaxy.
Space observations made by the European Space Agency with the
Hipparcos mission (1989-1993) accurately determined the parallaxes
of many more stars. Though a poor orbit limited its usefulness,
Hipparcos was expected to achieve a precision of about 0.002”. It
actually achieved 0.001” for 118,000 stars. The method of
trigonometric parallax is important because it is our only direct
distance technique for stars.
In 2011 – 2013, Gaia will be set into orbit with a Soyuz rocket.
Limiting magnitude V=16 ; 100 million stars, over a 5-yr mission lifetime
(and SIM Space Interferometric Mission from the US –pointed
deep, to V=20). It will be able to measure parallaxes of 10 microarcseconds. It consists of a rotating frame holding three
telescopes. Some aims:
…….Accurate distances even to the Galactic centre, 8000 parsecs
away.
……..Photometry: accurate magnitudes.
……..Planet quest
……..Reference frame from distant quasars (3C273 is 800 Mpc
away)
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Astrophysics
Professor Michael Smith
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Parallax remains limited to nearby objects.
In the meantime, to go further, we construct the COSMIC
LADDER.
If we can estimate the luminosity of a star from other properties,
they can be used as STANDARD CANDLES.
Example: Sirius A (Class A1, V= -1.44) has an observed parallax of
0.3792 arcsec.. Distance? 2.64 parsecs.
2 LUMINOSITY.
We can actually only measure the radiant flux of a flame
and need to make a few assumptions to find the true
luminosity. Luminosity depends on the distance and
extinction (as well as relativistic effects).
The measured flux f is in units of W/m2 , the flow of
energy per unit area. The radiated power L, ignoring
extinction, is given by an inverse square law:
f 
d2 
L
4d 2
L
4f
’
showing that a standard candle can yield the distance.
The Stellar Magnitude Scale
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Astrophysics
Professor Michael Smith
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The first stellar brightness scale - the magnitude scale - was
defined by Hipparchus of Nicea and refined by Ptolemy
almost 2000 years ago. In this qualitative scheme, nakedeye stars fall into six categories: the brightest are of first
magnitude, and the faintest of sixth magnitude. Note that the
brighter the star, the smaller the value of the magnitude. (Sun:
(minus) -26.72 (1st); Sirius -1.46; Deneb 1.25, 21st)
In 1856, N. R. Pogson verified William Herschel’s finding
that a first-magnitude star is 100 times brighter than a sixthmagnitude star and the scale was quantified. Because an
interval of five magnitudes corresponds to a factor of 100 in
brightness, a one-magnitude difference corresponds to a
factor of 1001/5 = 2.512.
This definition reflects the operation of human vision,
which converts equal ratios of actual intensity to equal
intervals of perceived intensity. In other words, the eye is a
logarithmic detector).
The magnitude scale has been extended to positive
magnitudes larger than +6.0 to include faint stars (the 5-m
telescope on Mount Palomar can reach to magnitude +23.5)
and to negative magnitudes for very bright objects (the star
Sirius is magnitude -1.4). The limiting magnitude of the
Hubble Space Telescope is about +30.
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Astrophysics
Professor Michael Smith
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Astronomers find it convenient to work with logarithms to
base 10 rather than with exponents in making the
conversions from brightness ratios to magnitudes and vice
versa.
Consider two stars of magnitude m and n with respective
apparent brightnesses (fluxes) lm and ln. The ratio of their
fluxes fn / fm corresponds to the magnitude difference m n. Because a one-magnitude difference means a brightness
ratio of 1001/5= 2.51189, (m - n) magnitudes refer to a ratio
of (1001/5)m-n = 100(m-n)/5, or
fn / fm = 100(m-n)/5
Taking the log10 of both sides (because log xa = a log x and
log 10a = a log 10 = a),
log (fn / fm) = [(m - n)/5] log 100 = 0.4(m - n)
or
m - n = 2.5 log (fn / fm)
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Astrophysics
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This last equation defines the apparent magnitude; note
that m > n when fn > fm, that is: brighter objects have
numerically smaller magnitudes.
Also note that when the brightnesses are those observed at
the Earth, physically they are fluxes. Apparent magnitude
is the astronomically peculiar way of talking about fluxes.
Here are a few worked examples:
(a) The apparent magnitude of the variable star RR Lyrae
ranges from 7.1 to 7.8 - a magnitude amplitude of 0.7. To
find the relative increase in brightness from minimum to
maximum, we use
log (fmax / fmin) = 0.4 x 0.7 = 0.28
so that
fmax / fmin = 100.28 = 1.91
This star is almost twice as bright at maximum light than at
minimum.
(b) A binary system consists of two stars a and b, with a
brightness ratio of 2; however, we see them unresolved as a
point of magnitude +5.0. We would like to find the
magnitude of each star. The magnitude difference is
mb - ma = 2.5 log (fa / fb) = 2.5 log 2 = 0.75
Since we are dealing with brightness ratios, it is not right to
put ma + mb = +5.0. The sum of the luminosities (fa + fb)
corresponds to a fifth-magnitude star. Compare this to a
100-fold brighter star, of magnitude 0.0 and luminosity l0:
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Astrophysics
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ma+ b - m0 = 2.5 log [l0 / (fa + fb)]
or
5.0 - 0.0 = 2.5 log 100 = 5.
But
fa = 2 fb, so that fb = (fa + fb)/3.
Therefore
(mb - m0) = 2.5 log (f0 / fb) = 2.5 log 300 = 2.5 x 2.477 =
6.19.
The magnitude of the fainter star is 6.19, and from our
earlier result on the magnitude difference, that of the
brighter star is 5.44.
What units are used in astronomical photometry?
The well-known magnitude scale of course, which has been
calibrated using standard stars which (hopefully) do not vary
in brightness.
But how does the astronomical magnitude scale relate to
other photometric units? Here we assume V magnitudes,
unless otherwise noted, which are at least approximately
convertible to lumes, candelas, and lux'es.
**************************************************************
1 mv=0 star outside Earth's atmosphere = 2.54 10-6 lux
= 2.54 10-10 phot
Luminance: ( 1 nit =1 candela per square metre)
1 mv= 0 star per square degree outside Earth's atmosphere
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Astrophysics
Professor Michael Smith
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= 0.84 10-2 nit
= 8.4 10-7 stilb
1 mv = 0 star per square degree inside clear unit airmass
= 0.69 10-2 nit
= 6.9 10-7 stilb
One star, Mv=0 outside Earth's atmosphere = 2.451029 cd
3 Attenuation in the earth’s atmosphere
Light incident on the Earth's atmosphere from an
extraterrestrial source is diminished by passage through the
Earth's atmosphere.
Thus, sources will always appear less bright below the
Earth's atmosphere than above it.
1 clear unit airmass transmits 82% in the visual, i.e. it
dims 0.2 magnitudes).
to a good approximation from
The path length that light from a celestial object takes
through Earth’s atmosphere relative to the length at the
zenith. Airmass is 1 at the zenith and roughly 2 at an
altitude of 60°. It can be calculated to a good
approximation from the formula
A = 1.0 / [ cos(Z) + 0.50572 A = 1.0 / [ cos(Z) + 0.50572 x
(96.07995 - Z)-1.6364] x (96.07995 - Z)-1.6364]
Note that a unit airmass at Mauna Kea (with a mean
barometric pressure of 605 millibars) is equivalent to 0.60
airmass at sea level.
From a practical standpoint, you can see that, for example:
At
z=60 degrees you look through 2 airmasses
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Astrophysics
Professor Michael Smith
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(obtainable from plane parallel approximation).
At
z=71 degrees you look through 3 airmass.
At limit of z=90degrees you look through 38 airmasses.
Atmospheric extinction at optical wavelengths is due
primarily to two phenomena:
1 Absorption:
◦ On UV side primary absorption is ozone O3
On IR side water vapor, CO2.
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Astrophysics
Professor Michael Smith
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Atmospheric extinction across the electromagnetic spectrum. Figure from
Observational Astronomy by Lena, Lebrun and Mignard.
As may be seen, most EM radiation is blocked by the
Earth, and only a few atmospheric windows allow certain
wavelengths through:
▪ Optical
▪ Various near and mid-infrared ranges
▪ Millimeter and radio wavelengths
◦ As may be seen, increasing elevations open up new
atmospheric windows:
▪
On high mountains and Antarctic plateau (where
atmosphere is compressed -- equivalent to higher altitude at
warmer latitudes): More mid- and far- infrared wavelengths
accessible.
2 Scattering:
Two mechanisms depending on size of scatterer:
Molecular scattering: scattering radius a << wavelength
▪
Mainly Rayleigh scattering (elastic -- energies of
scattered photons preserved), which has a scattering
cross-section as function of wavelength.
Aerosol scattering: scattering radius a >~ /10 wavelength
▪ Mie scattering is light scattered by "large" [relative to
wavelength of light] spheres), and the strict theory
accounts for Maxwells equations in the context of all
kinds of reflections (external and internal) and surface
waves on the scatterer, polarization, etc. Full theory
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Astrophysics
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requires computer.
The sky seems more/deeper blue when you look at greater
angles from the Sun because that is mostly Rayleigh
scattering, while close to the Sun the sky appears "whiter"
because this is primarily Mie scattering.
▪ Aerosols highly variable from night to night.
▪ air pollution
▪ dust = "haze"
▪ volcanic ash (can be horrible)
▪
dust storms
Apparent magnitude is an irradiance or illuminance, i.e.
incident flux per unit area, from all directions. Of course a star
is a point light source, and the incident light is only from
one direction.
Apparent magnitude per square degree is a radiance,
luminance, intensity, or "specific intensity". This is sometimes
also called "surface brightness".
Still another unit for intensity is magnitudes per square
arcsec, which is the magnitude at which each square arcsec of
an extended light source shines.
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Astrophysics
Professor Michael Smith
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Only visual magnitudes can be converted to
photometric units. U, B, R or I magnitudes
are not easily convertible to luxes, lumens
and friends, because of the different
wavelengths intervals used. The conversion
factors would be strongly dependent on e.g.
the temperature of the blackbody radiation
or, more generally, the spectral
distribution of the radiation. The
conversion factors between V magnitudes and
photometric units are only slightly
dependent on the spectral distribution of
the radiation.
Here we're not interested in the photometric response of
some detector with a well-known passband (e.g. the human
eye, or some astronomical photometer). Instead we want to
know the strength of the radiation in absolute units: watts
etc. Thus we have:
Radiance, intensity or specific intensity:
W m-2 ster-1 [Å-1]
SI unit
-2
-1
-1
-1
erg cm s ster [Å ]
CGS unit
-2
-1
-1
-1
photons cm s ster [Å ] Photon flux, CGS units
Irradiance/emittance, or flux:
W m-2 [Å-1]
SI unit
-1
erg cm-2 s-1 [Å ]
CGS unit
-1
photons cm-2 s-1 ster-1 [Å ] Photon flux, CGS units
Note the [A-1] within brackets. Fluxes and
intensities can be total (summed over all
wavelengths) or monochromatic ("per Angstrom
Å" or "per nanometer").
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Astrophysics
Professor Michael Smith
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In Radio/Infrared Astronomy, the unit Jansky is often used
as a measure of irradiance at a specific wavelength, and is
the radio astronomer's equivalence to stellar magnitudes.
The Jansky is defined as: 1 Jansky = 10-26 W m-2 Hz-1
4. Absolute magnitude represents a total flux.
Absolute Magnitude and Distance Modulus
So far we have dealt with stars as we see them, that is, their
fluxes or apparent magnitudes, but we want to know the
luminosity of a star. A very luminous star will appear dim
if it is far enough away, and a low-luminosity star may look
bright if it is close enough.
Our Sun is a case in point: if it were at the distance of the
closest star (Alpha Centauri), the Sun would appear slightly
fainter to us than Alpha Centauri does. Hence, distance
links fluxes and luminosities. (Sun’s apparent magnitude is
–26.83)
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Astrophysics
Professor Michael Smith
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The solar irradiance is the amount of incoming solar
radiation per unit area, measured on the outer surface of
the Earth's atmosphere, in a plane perpendicular to the
rays. The solar constant includes all types of solar radiation,
not just the visible light. It is measured by satellite to be
roughly 1366 watts per square meter,[
The luminosity of a star relates to its absolute magnitude,
which is the magnitude that would be observed if the star
were placed at a distance of 10 pc from the Sun, in the
absence of interstellar extinction.
By convention, absolute magnitude is capitalised (M) and
apparent magnitude is written lowercase (m). The inversesquare law of radiative flux links the flux f of a star at a
distance d to the flux, F, it would have if it were at a
distance d = 10 pc:
F / f = (d / D)2 = (d / 10) 2.
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Astrophysics
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If M corresponds to F and m corresponds to the flux f, then
m - M = 2.5 log (F / f ) = 2.5 log (d/10)2 = 5 log (d / 10)
Expanding this expression, we have useful alternative
forms. Since
m1 – m2 = 5 log d1 - 5 log d2
defining the absolute magnitude m2 = M at d2 = 10
pc, so m1 = m and d2 = d ,
m - M = 5 log d - 5
M = m + 5 - 5 log d
In terms of the parallax,
M = m + 5 + 5 log p”
Here d is in parsecs and p” is the parallax angle in arc
seconds.
The quantity m - M is called the distance modulus, for it is
directly related to the star’s distance. In many applications,
we refer only to the distance moduli of different objects
rather than converting back to distances in parsecs or lightyears.
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Astrophysics
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EXAMPLE:
Luminosity – Absolute magnitude?
22
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Astrophysics
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Absolute magnitudes for stars generally range from -10 to
+17. The absolute magnitude for galaxies can be much
lower (brighter). For example, the giant elliptical galaxy M87
has an absolute magnitude of –22. Many stars visible to the
naked eye have an absolute magnitude which is capable of
casting shadows from a distance of 10 parsecs; Rigel (-7.0),
Deneb (-7.2), Naos (-6.0), and Betelgeuse (-5.6).
Magnitudes at Different Wavelengths
The kind of magnitude that we measure depends on how
the light is filtered anywhere along the path of the detector
and on the response function of the detector itself. So the
problem comes down to how to define standard magnitude
systems.
Magnitude Systems
Detectors of electromagnetic radiation (such as the
photographic plate, the photoelectric photometer, and the
human eye) are sensitive only over given wavelength
bands. So a given measurement samples but part of the
radiation arriving from a star.
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Astrophysics
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Multiwavelength Astronomy: Four images of the Sun, made
using (a) visible light, (b) ultraviolet light, (c) X rays, and (d)
radio waves. By studying the similarities and differences among
these views of the same object, important clues to its structure and
composition can be found.
Photographic magnitude
Because the flux of starlight varies with wavelength, the
magnitude of a star depends upon the wavelength at which
we observe. Originally, photographic plates were sensitive
only to blue light, and the term photographic magnitude
(mpg) still refers to magnitudes centred around 420 nm (in
the blue region of the spectrum).
Visual magnitude
Similarly, because the human eye is most sensitive to green
and yellow, visual magnitude (mv) or the photographic
equivalent photo visual magnitude (mpv) pertains to the
wave-length region around 540 nm.
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Astrophysics
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Filters
Today we can measure magnitudes in the infrared, as well
as in the ultraviolet, by using filters in conjunction with the
wide spectral sensitivity of photoelectric photometers.
In general, a photometric system requires a detector, filters,
and a calibration (in energy units). The properties of the
filters are typified by their effective wavelength, 0, and
bandpass, ∆ which is defined as the full width at half
maximum (FWHM) in the transmission profile.
The three main filter types are wide (∆≈ 100 nm),
intermediate (∆≈ 10 nm), and narrow (∆≈1 nm). There
is a trade-off for the bandwidth choice: a smaller ∆
provides more spectral information but admits less flux into
the detector, resulting in longer integration times. For a
given range of the spectrum, the design of the filters makes
the greatest difference in photometric magnitude systems.
A commonly used wide-band magnitude system is the UBV
system: a combination of ultraviolet (U), blue (B), and
visual (V) magnitudes, developed by H. L. Johnson. These
three bands are centred at 365, 440, and 550 nm; each
wavelength band is roughly 100 nm wide. In this system,
apparent magnitudes are denoted by U, B or V and the
corresponding absolute magnitudes are sub-scripted: MU,
MB or MV.
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Astrophysics
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To be useful in measuring fluxes, the photometric system
must be calibrated in energy units for each of its
bandpasses. This calibration turns out to be the hardest
part of the job. In general, it relies first on a set of standard
stars that define the magnitudes, for a particular filter set
and detector; that is, these stars define the standard
magnitudes for the photometric system to the precision with
which they can be measured.
Infrared Windows
The UBV system has been extended into the red and
infrared (in part because of the development of new
detectors, such as CCDs, sensitive to this region of the
spectrum). The extensions are not as well standardised as
that for the Johnson UBV system, but they tend to include R
and I in the far red and J, H, K, L, and M in the
infrared.
As well as measuring the properties of individual stars at
different wavelengths, observing at loner wavelengths,
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particularly in the infrared, allows us to probe through
clouds of small solid dust particles, as seen below
A visible-light (left) vs. 2MASS infrared-light (right) view of the
central regions of the Milky Way galaxy graphically
illustrating the ability of infrared light to penetrate the
obscuring dust. The field-of-view is 10x10 degrees
Infrared passbands
absorption):
J Band: 1.3 microns
H Band: 1.6 microns
K band: 2.2 microns
L band 3.4 microns
M band 5 microns
N band 10.2 microns
Q band 21 microns
which
allow
transmission
(low
Bolometric magnitudes can be converted to total radiant
energy flux: One star of Mbol = 0 radiates 2.97 1028 Watts.
System is defined by Vega at 7.76 parsecs from the Sun
with an apparent magnitude defined as zero.
With Lbol = 50.1 Lsolar and Mbol = 0.58.
Sun: mbol = -26.8
Full moon: -12.6
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Astrophysics
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Venus: -4.4
Sirius: -1.55
Brightest quasar: 12.8
For Vega: mb = mv = 0.
mk = +0.02
Sun: Mb = 5.48, Mv = 4.83, Mk = 3.28
Colour Index:
B-V, J-H, H-K are differences in magnitude….flux ratios.
But cooler, redder objects possess higher values. It is
independent of the star’s distance.
Extinction
Interstellar Medium modifies the radiation. Dust particles
with size of order of the wavelength of the radiation.
Blue radiation is strongly scattered compared to red: blue
reflection nebulae and reddened stars. Hence a colour
excess is produced.
Colour Excess:
E(B-V) = B-V - (B-V)o
measures the reddening.
Modified distance modulus:
m() = M() + 5 log d – 5 + A()
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where A () is the extinction due to both scattering and
absorption, along the entire line of sight. It is strongly
wavelength dependent. The optical depth is given by
I
exp(  ) 
.
Io
Therefore A() = 1.086 

The optical depth is

where N is the total column density of dust (m-2) between
the
star
and
the
observer
and
is
the
scattering/absorption cross-section (m2).
ISM empirical Law related extinction to reddening:
Av / E(B-V) = 3.2 + - 0.2
OK, so an objects emission is modified/attenuated by the
interstellar medium and the atmosphere. But these effects
can be estimated.
END OF WEEK 1