Elementi di Astronomia e Astrofisica
per il Corso di Ingegneria
Aerospaziale
VI settimana
L'Atmosfera terrestre
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1
The terrestrial atmosphere - 1
This chapter is devoted to the examination of the influence of the Earth’s
atmosphere on the apparent coordinates of the stars and on the shape of their
images; the discussion will be limited essentially to the visual band. The
discussion of the effects of the atmosphere on photometry and spectrophotometry
are deferred to a later chapter.
The figure gives a
schematic representation
of the vertical structure of
the atmosphere; the visual
band is mostly affected by
what happens in the
troposphere, namely in
the first 15 km or so of
height, where some 90%
of the total mass of the
atmosphere is contained.
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2
The terrestrial atmosphere -2
Na Layer
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The terrestrial atmosphere - 3
The temperature profile in the troposphere is actually more complicated than
shown in the Figure. The height of the tropopause (a layer of almost constant
temperature) from the ground ranges from 8 km at high latitudes to 18 km
above the equator; it is also highest in summer and lowest in winter. The
average temperature gradient is approximately –6 C/km, but often, above a
critical layer situated in the first few km, the temperature gradient is
inverted, with beneficial effects on astronomical observations, thanks to the
intrinsic stability of all layers with temperature inversion (such as the
stratosphere and the thermosphere), essentially because convection cannot
develop. This is the case for instance of the Observatory of the Roque de los
Muchachos (Canary Islands, height 2400 m a.s.l.), where the inversion layer is
usually few hundred meters below the telescopes at the top of the mountain.
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Chemical composition and structure
The chemical composition of the troposphere is mostly molecular Nitrogen N2
and molecular Oxygen O2 (approximately 3:4 and 1:4 respectively), with traces
of the noble gas Argon and of water vapor (the water vapor concentration may
be as high as 3% at the equator, and decreases toward the poles).
Above the tropopause, at higher heights in the stratosphere, the temperature
raises considerably thanks to the solar UV absorption by the Ozone (O3)
molecule with the process:
UV photon + O3 = O2+O+heat.
The mesosphere ranges from 50 to 80 km; in this region, concentrations of O3
and H2O vapor are negligible, hence the temperature is lower than in the
stratosphere. The chemical composition of the air becomes strongly heightdependent, with heavier gases stratified in the lower layers. In this region,
meteors and spacecraft entering the atmosphere start to warm up.
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The ozone O3
O3 is a molecule
containing 3 O atoms.
It is blue in color and
has a strong odor.
Normal molecular O2,
has 2 oxygen atoms
and is colorless and
odorless. Ozone is
much less common
than normal oxygen.
Out of each 10 million
air molecules, about 2
million are normal
oxygen, but only 3 are
ozone.
Most atmospheric ozone is concentrated in a layer in the stratosphere, about 1530 kilometers above the Earth's surface. Even this small amount of ozone plays
a key role in the atmosphere, absorbing the UVB portion of the radiation from
the sun, preventing it from reaching the planet's surface.
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Water vapor nomenclature - 1
Water vapor is water in the gaseous phase.
The actual amount is the concentration of water vapor in the air, the relative
concentration is the ratio between the actual amount to the amount that would
saturate the air. Air is said to be saturated when it contains the maximum
possible amount of water vapor without bringing on condensation. At that point,
the rate at which water molecules enter the air by evaporation exactly balances
the rate at which they leave by condensation.
The partial pressure of a given sample of moist air that is attributable to the
water vapor is called the vapor pressure. The vapor pressure necessary to
saturate the air is the saturation vapor pressure. Its value depends only on the
temperature of the air. (The Clausius-Clapeyron equation gives the saturation
vapor pressure over a flat surface of pure water as a function of temperature.)
Saturation vapor pressure increases rapidly with temperature: the value at 32°C
is about double the value at 21°C. The saturation vapor pressure over a curved
surface, such as a cloud droplet, is greater than that over a flat surface, and the
saturation vapor pressure over pure water is greater than that over water with a
dissolved solute.
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Water vapor nomenclature - 2
Relative humidity is the ratio of the actual vapor pressure to the saturation vapor
pressure at the air temperature, expressed as a percentage. Because of the
temperature dependence of the saturation vapor pressure, for a given value of
relative humidity, warm air has more water vapor than cooler air. The dew point
temperature is the temperature the air would have if it were cooled, at constant
pressure and water vapor content, until saturation (or condensation) occurred. The
difference between the actual temperature and the dew point is called the dew
point depression.
The wet-bulb temperature is the temperature an air parcel would have if it were
cooled to saturation at constant pressure by evaporating water into the parcel. (The
term comes from the operation of a psychrometer, a widely used instrument for
measuring humidity, in which a pair of thermometers, one of which has a wetted
piece of cotton on the bulb, is ventilated. The difference between the temperatures
of the two thermometers is a measure of the humidity.) The wet-bulb temperature
is the lowest air temperature that can be achieved by evaporation. At saturation, the
wet-bulb, dew point, and air temperatures are all equal; otherwise the dew point
temperature is less than the wet-bulb temperature, which is less than the air
temperature.
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Water Vapor Mixing ratio
Specific humidity is the ratio of the mass of water
vapor in a sample to the total mass, including both
the dry air and the water vapor. The mixing ratio is
the ratio of the mass of water vapor to the mass of
only the dry air in the sample. As ratios of masses,
both specific humidity and mixing ratio are
dimensionless numbers. However, because
atmospheric concentrations of water vapor tend to
be at most only a few percent of the amount of air
(and usually much lower), they are both often
expressed in units of grams of water vapor per
kilogram of (moist or dry) air. Absolute humidity
is the same as the water vapor density, defined as
the mass of water vapor divided by the volume of
associated moist air and generally expressed in
grams per cubic meter. The term is not much in use
now.
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Water reservoir
Water vapor is constantly
cycling
through
the
atmosphere,
evaporating
from
the
surface,
condensing to form clouds
blown by the winds, and
subsequently returning to
the Earth as precipitation.
Heat from the Sun is used to
evaporate water, and this
heat is put into the air when
the water condenses into
clouds and precipitates. This
evaporation - condensation
Water vapor is the most abundant of the greenhouse gases
cycle is an important
in the atmosphere and the most important in establishing
mechanism for transferring
the Earth's climate. Greenhouse gases allow much of the
Sun's shortwave radiation to pass through them but absorb heat energy from the Earth's
surface to its atmosphere
the infrared radiation emitted by the Earth's surface.
Without water vapor and other greenhouse gases in the air, and in moving heat around
surface air temperatures would be well below freezing.
the Earth.
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Aerospace devices
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A multitude of systems
exist for observing water
vapor on a global scale and
at high altitudes,
supplementing the
instruments on the ground,
that measure in special sites
and at ground level. Each
has different characteristics
and advantages. To date,
most large-scale water
vapor climatological studies
have relied on analysis of
radiosonde data, which
have good resolution in the
lower troposphere in
populated regions but are of
limited value at high
altitude and are lacking
over remote oceanic
regions.
11
The Water Vapor content in 1992
NASA Water Vapor Project (NVAP) Total Column Water Vapor 1992
The mean distribution of precipitable water, or total atmospheric water vapor above
the Earth's surface, for 1992. This depiction includes data from both satellite and
radiosonde observations.
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Cloud effects on Earth Radiation
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The outer layers
Following the smooth decrease in the mesosphere, the temperature raises
again in the thermosphere, because the solar UV and X-rays, and the
energetic electrons from the magnetosphere can partly ionize the very thin
gases of the thermosphere.
The weakly ionized region which conducts electricity, and reflects radio
frequencies below about 30 MHz is called ionosphere; it is divided into the
regions D (60-90 km), E (90-140 km), and F (140-1000 km), based on
features in the electron density profile.
Finally, above 1000 km, the gas composition is dominated by atomic
Hydrogen escaping the Earth’s gravity, which is seen by satellites as a bright
geocorona in the resonance line Ly- at  = 1216 Å.
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Refraction Index
As is well known, the light propagates in a straight line in any medium of
constant refraction index n, with a phase velocity v given by
v  c / n  1/( )1/ 2
where  is the dielectric constant and  the magnetic permeability of the
medium. All these quantities are wavelength dependent. The group velocity u
is instead:
u  v  dv / d
At the separation surface between two media of different refraction index (say
vacuum/air), the ray changes direction, so that the observer immersed in the
second medium sees the light coming from an apparent direction different from
the ‘true’ one (see Figure):
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The atmospheric refraction - 1
Suppose that the atmosphere can be treated as a succession of parallel planes
(hypothesis of plane-parallel stratification), by virtue of its small vertical
extension with respect to the Earth’s radius. According to Snell’s laws, when the
ray coming from the region of index of refraction n0 encounters the separation
surface with a medium of refraction index n1> n0, part of the energy will be
reflected to the left, on the same hemi-space with the same angle r0 with respect
to the normal. This part will not be considered here, it only implies a dimming of
the source. The remaining fraction will be refracted, in the same plane as the
incident ray, to an angle r1 < r0. Indeed, in a clear atmosphere without clouds, no
sharp air-vacuum separation surface exists, the refraction index gradually
increases from 1 to a final value nf near the ground, with typical scale lengths
much greater than the wavelength of light (as already said, we limit our
considerations to the visual band), so that the continuously varying direction can
be considered as a series of finite steps in the plane passing through the vertical
and the direction to the star.
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The atmospheric refraction - 2
By following each refraction in cascade we have:
n0 sin r0  n1 sin r1
ni sin ri  n11 sin ri 1
n f 1 sin rf 1  n f sin rf
where ni+1> ni, and ri+1< ri. By equating each term:
n0 sin r0  n f sin rf
Therefore: in a plane-parallel atmosphere the total angular deviation only
depends on the refraction index close to the ground, independent of the
exact law with which it varies along the path.
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The atmospheric refraction - 3
The net effect is as shown in
the figure: the star is seen in
direction z’ smaller than the
true direction z, namely
closer to the local Zenith, by
an amount R which is the
atmospheric refraction:
z’ = z – R
By virtue of
n0 sin r0  n f sin rf
and for small R’s (in practice, if z < 45°):
n f sin z '  sin z  sin( z ' R)  sin z 'cos R  cos z 'sin R  sin z ' R cos z '
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The atmospheric refraction - 4
and finally:
R  (n f  1) tan z '
In the visual band, for average values of temperature and pressure (T = 273 K,
P = 760 mm Hg), nf  1.00029, so that in round numbers
R(15°)  16”,
R(45°)  60”
Already for Zenith distances as small as 20°, the refraction is larger than the
annual aberration, and of any of the effects discussed in previous chapters that
alter the apparent direction of a star.
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The atmospheric refraction - 5
For zenith distances larger than 45°, the path of the ray inside the atmosphere
is so long that the curvature of the Earth cannot be ignored, and the
mathematical treatment becomes more intricate, even restricting it to
successive refraction in the same plane with n decreasing outwards with
continuity.
nf
R  a  n f sin z ' 
1
dn
n d 2  n 2  a 2  n f 2 sin 2 z '
After several mathematical steps:


l
l
3
R  A tan z ' B tan z '  (n f  1) (1  ) tan z ' tan z '
a
a


3
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Effect of the refraction on the coordinates
The main effect of refraction is to move
the star closer to the Zenith in the
vertical plane, thus raising its elevation h
but leaving essentially unchanged its
azimuth A.
XX’ = R = h
PXX’ = PXZ = q
ZX = z, ZX’ = z’
PX = 90-
XU = 
HA cos   ( '  ) cos   R sin q

   '   R cos q
cos  cos q  sin  cos h  cos  sin h cos A
sin A sin h  cos HA sin q  sin HA cos q sin 
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For
an
object
in
meridian, the refraction
is all in declination, and
in particular this is true
for the Sun at true noon.
21
Approximate formulae for refraction
For Zenith distance not greater than approximately 45°, after several passages
we finally get:

sec2  sin HA
  (n f  1) cos HA  tan  tan 


  (n  1) tan   tan  cos HA
f

cos HA  tan  tan 
by means of which formulae we can derive the true (or the apparent,
according to the sign) topocentric positions. Obviously no such correction
is necessary for a telescope in outer Space.
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The chromatism of the refraction
The refraction index n depends from the wavelength, diminishing from the blue
to the red, and the same will be true for the refraction angle R: the image on the
ground of the star is therefore a succession of monochromatic points aligned
along the vertical circle; the blue ray will be below the red one, and thus the blue
star will appear to the eye above the red one
The atmosphere behaves therefore like a
prism producing a short spectrum in the
vertical plane, whose length increases with
the zenith distance, reaching several arc
seconds at low elevations. The relationships
n() can be expressed by the so-called
Cauchy’s formula:
 0.00566 0.000047 
n( )  0.00028 1 


2
4




( in micrometers), corresponding to a variation
of about 2% over the visible range, namely to
about 1”.2 at 45°.
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Density - temperature relationship
Once we have fixed , the refraction index n depends from the density 
according to Gladstone-Dale’s law:
n 1  k 
and with the hypothesis of a perfect gas of pressure P, temperature T and
molecular weight  :

n 1  k '
P
T
P
(where R is now the gas universal constant)
RT
n  1 P T0

n0  1 P0 T
P
n  1  78.7  10
T
6
R  60".4
( P / 760)
tan z
(T / 273)
(P in mm Hg, T in K)
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Vertical gradients of temperature
Calling H the height over the ground, we have:
1
P

dn  k '  dP  dT 
T
T

dn
P  T dP dT 
 1 dP P dT 
 k '
 2

k
'



2 
dH
T  P dH dH 
 T dH T dH 
The variation of pressure with the height is equal to the weight of the air in the
elementary volume having unitary base and height dH, dP   g  dH
so that:
dn
P  g
dT 
 k ' 2 


dq
T  R  dH 
where the constant g/R equals approximately 3.4 K/km, and is called adiabatic
lapse.
Hence the conclusion that the variations of the refraction index depend from the
vertical gradients of the temperature. A practical consequence is that all effort must
be made to control and minimize those gradients over the accessible volume of the
telescope enclosure.
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Turbulence, Scintillation, Seeing
The Earth's atmosphere is turbulent and variations in the index of refraction
cause the plane wavefront from distant objects to be distorted. This distortion
introduces amplitude variations, positional shifts and image degradation.
This causes two astronomical effects:
•scintillation, which is amplitude variations, which typically varies over scales
of few cm: generally very small for large aperture telescopes
•seeing: positional changes and image quality changes. The effect of seeing
depends on aperture size: for small apertures, one sees a diffraction pattern
moving around, while for large apertures, one sees a set of diffraction patterns
(speckles) moving around on scale of ~1 arcsec.
These observations imply:
• wavefronts are flat on scales of small apertures
• instantaneous slopes vary by ~ 1 arcsec.
The typical time scales are few milliseconds and up.
The effect of seeing can be derived from theories of atmospheric turbulence,
worked out originally by Kolmogorov, Tatarski, Fried.
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Structure function
The structure of the refraction index n in a turbulent field can be described
statistically by a structure function:
Dn ( x)   n(r  x)  n(r ) 
2
where x is separation of points, r is position. Kolmogorov turbulence gives:
1
Dn ( x)  Cn 2 x 2
3
where Cn is the refractive index structure constant. From this, one can derive
the phase structure function at the telescope aperture:
x5/ 2
D  6.88
r0
r0  0.185
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6/ 5
cos
3/ 5
z   C0 dh 
2
where the coherence length r0 (also
known as the Fried parameter) is:
3/ 5
where z is zenith angle,  is wavelength.
Using optics theory, one can convert D
into an image shape.
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The Fried parameter
Notice that r0 increases with 6/5 = 1. 2.
Physically, the image size d from seeing is (roughly) inversely proportional to r0
d   / r0
as compared with the image size from a diffraction-limited telescope of aperture D:
d /D
Seeing dominates when r0 < D ; a larger r0 means better seeing. Seeing is more
important than diffraction at shorter wavelengths, diffraction more important at
longer wavelengths; effect of diffraction and seeing cross over in the IR (at  5
microns for 4m); the crossover falls at a shorter wavelength for smaller telescope
or better seeing. Fried’s parameter r0 varies from site to site and also in time. At
most sites, there seems to be three regimes called:
surface layer (wind-surface interactions and manmade seeing),
planetary boundary layer ( influenced by diurnal heating),
free atmosphere (10 km is tropopause: high wind shears)
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An example of Cn
2
A typical site
has
r0  10 cm
at 5000Å ,
namely a
seeing of 1".
On rare
occasions, in
the best
sites, the
seeing can
be as low as
0".3.
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The isoplanatic angle
We also have to consider the coherence of the same turbulence pattern over the
sky: coherence angle call the isoplanatic angle:
  0.314r0 / H
where H is the average distance of the seeing layer:
For r0  10 cm, H = 5000 m ,   1.3 arcsec.
In the infrared r0  70 cm, H = 5000 m ,   9 arcsec.
Note however, that the ``isoplanatic patch for image motion" (not wavefront)
is  0.3D/H. For D = 4m, H = 5000 m, kin  50 arcsec.
Another useful parameter is the correlation time 0, which is
approximately the dimension of the typical air bubble divided by the velocity
of the wind. As r0, also 0 increases with 6/5.
-
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The seeing
Bubbles of air having slightly different temperatures, and therefore slightly
different refractive indexes, are carried by the wind across the aperture of the
telescope.
The Fried parameter r0 can be used to simplify the description of a very complex
rapidly varying medium, namely the typical size of the bubble. Values vary from
few centimeters (a poor site) to some 30 cm (a very good site).
r0 can be understood also as the effective diameter of the diffraction limited
telescope in that site (with respect to the angular resolution).
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Representation of the seeing
There are two main
components of the seeing:
•one coming from high
altitudes (choice of site)
•one due to ground layers (it
can be actively controlled by
shape of dome and proper
thermalisation of structure)
• The spectral power of the air
turbulence is appreciable over
a large interval of frequencies ,
say 1 to 1000 Hz, with a 1/f
distribution.
The angles are exaggerated, actually AdOpt correction can be made over small fields
of view. Another useful parameter is the maximum angle over which fluctuations are
coherent (isoplanatic angle). Both Fried’s parameter and isoplanatic angle improve
with increasing wavelength, the correction is better in the IR than in the Visible.
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A first remedy: Speckle
Interferometry
• a very large number of short duration
exposures are taken with very long focal
length (say 100m) and narrow bandwidth
(say 1 nm); in each exposure the seeing is
frozen, each speckle represents the
diffraction figure of the aperture
• Fourier Transforms allow the reconstruction
of the true image;
• The technique works well for simple
structures (e.g. double or multiple stars,
disks).
Obtained with
the Asiago 1.8 cm
telescope
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A better remedy: Adaptive Optics
The fairly complex techniques that are nowadays implemented on the
largest telescopes to contrast the seeing are known collectively as
Adaptive Optics devices.
• A suitable reference wavefront is also necessary. Suitably bright stars are
rare.
•An artificial laser star is a possible solution.
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The artificial laser star
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Before and after AdOpt
If one ‘freezes’ the image with short exposure times (say less than 0.01
sec) and a narrow filter, the seeing image breaks up in large number of
‘speckles’, each having dimension of the order of the diffraction figure of
the telescope.
The number of speckles is of the order of :
(seeing diameter/diffraction figure)2
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The Galactic Center with the Keck
AdOpt
Without AdOpt
With AdOpt
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Quality of the image -1
The quality of an image can be described in many different ways. The overall
shape of the distribution of light from a point source is specified by the point
spread function (PSF). Diffraction gives a basic limit to the quality of the PSF,
but any aberrations or image motion add to structure/broadening of the PSF.
Another way of describing the quality of an image is to specify it's modulation
transfer function (MTF). The MTF and PSF are a Fourier transform pair.
Turbulence theory gives:
MTF  e
3.44( v / a )5/ 3
where  is the spatial frequency. Note that a Gaussian goes as  2, so this MTF is
close to a Gaussian. The shape of seeing-limited images is roughly Gaussian in
core but has more extended wings. This is relevant because the seeing is often
described by fitting a Gaussian to a stellar profile.
A potentially better empirical fitting

( x  p2 ) 2  y  p3  
I  p1  1 


2
5
function is a Moffat function:
p
p
4
5


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 p6
38
Quality of the image -2
Probably the most common way of describing the seeing is by specifying the fullwidth-half-maximum (FWHM) of the image, which may be estimated either by
direct inspection or by fitting a function (usually a Gaussian); note the
correspondence of FWHM to  of a Gaussian: FWHM = 2.355 .
The FWHM doesn't fully specify a PSF, and one should always consider how
applicable the quantity is.
Another way of characterizing the PSF is by giving the encircled energy as a
function of radius, or at some specified radius.
A final way of characterizing the image quality, more commonly used in adaptive
optics applications, is the Strehl ratio SR. The Strehl ratio is the ratio between the
peak amplitude of the PSF and the peak amplitude expected in the presence of
diffraction only. In practice, in the visible it is already very good reaching SR =
0.1 .
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The EE of the Rosetta WAC
The WAC is in space, so
there is no seeing to worry
about, only the vibrations of
the spacecraft or thermal
distortions of the jitter of the
attitude.
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Effects of the atmosphere at radiofrequencies - 1
The ionosphere will introduce a
delay on the arrival time of the
wave, given by:
40.3
 T  2  N e ds
c I
seconds, being I the path along the
line of sight and Ne the electron
density (cm-3). This density will
vary with the night and day cycle,
with the season and also with the
solar cycle.
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Effects of the atmosphere at radiofrequencies -2
The tropospheric delay can be resolved in two components, a dry one and a wet
one. The dry component amounts to about 7 ns at the Zenith, and varies with
the ‘modified cosec z’ we have discussed for the optical observations:
t  7(cos z 
0.0014
) ns
0.0445  cot z
The wet component depends on the amount of water vapour, and amounts
to about 10% of the dry one, but it varies rapidly and in unpredictable way.
Finally, two other mediums affect the propagation of the radio
waves, namely the solar corona and the ionized interstellar medium.
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Extinction and spontaneous
emission by the atmosphere
In addition to chaotic refraction effects, the atmosphere absorbs a fraction
of the incident light, both in the continuum and inside atomic and molecular
lines and bands.
Furthermore, the atmosphere spontaneously emits in particular atomic and
molecular bands (this is in addition to scattering of artificial lights, see
later).
The molecular oxygen O2 in particular is so effective at blocking radiation
around 6800A and 7600A that Fraunhofer could detect by eye two dark
absorption bands in the far red of the solar spectrum, bands he called
respectively B and A (he examined the spectra from red to blue, the current
astronomical practice is from blue to red).
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Extinction
Let us consider the absorption due to a thin layer of atmosphere at height
between h and h+dh in the usual simple model of a plane-parallel atmosphere.
The light beam from the star makes an angle z with the Zenith, so that the
traversed path is dh/cosz = seczdh.
If I(h) is the intensity at the top of the layer, at the exit it will be reduced by
the quantity:
dI    I  (h)k (h)sec zdh
In total, if I() is the intensity outside the atmosphere, at the elevation h0 of
the Observatory the intensity will be reduced to:

I  (h0 )  I  ()e
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
 sec z k ( h )dh
h0
 I  ()e   (  )sec z
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Optical Depth
where we have introduced the a-dimensional quantity  called optical depth :

d   k (h)  dh
    k (h)  dh
h0
The variable k (dimensionally, cm-1) represents the absorption per unit
length of the atmosphere at that wavelength.
Astronomers use a particular measure of the apparent intensity, namely the
magnitude, defined by m = m0 -2.5logI (see in a later lecture), so that:
mground  moutside  2.5D ()  sec z
D is called the optical density of the atmosphere, while the variable X(z) = secz
is called air-mass. The minimum value of the airmass is 1 at the Zenith, and 2 at
z = 60° (the limit of validity of the present approximate discussion).
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The Bouguer line
Suppose we start observing the star at its upper transit, and then keep observing it
while its Hour Angle (and therefore also its Zenith distance) increases: we would
notice a linear increase of its magnitude in agreement with the previous equation,
namely a straight line with slope 2.5D in a graph (m, secz).
It is common practice to plot the m-axis pointing down. This straight line is known
as Bouguer line, from the name of the XVIII century French astronomer who
introduced it.
The extrapolation of this line to X = 0 (a mathematical absurdity) gives the socalled loss of magnitude at the Zenith, or else the magnitude outside atmosphere.
According to the formulae of the first lectures we have:
sec z 
1
 X ( z)
sin  sin   cos  cos  cos HA
where  is the latitude of the site,  and HA the coordinates of the star.
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The least continuous extinction
The Table shows the continuous extinction of the atmosphere above Mauna
Kea, whose elevation above sea level (4300 m) is higher than that of most
observatories so that the transparency of the sky is at its best, in the extended
visible region.
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Wavelength (nm)
Extinction
(mag / air mass)
Wavelength (nm)
Extinction
(mag / air mass)
310
1.37
500
0.13
320
0.82
550
0.12
340
0.51
600
0.11
360
0.37
650
0.11
380
0.30
700
0.10
400
0.25
800
0.07
450
0.17
900
0.05
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Figures of the extinction from the visible to the
near IR
The figure on the left gives the optical depth, the one on the right the transmission
(one is the reverse of the other). In the violet region, the transparency quickly
goes to zero, essentially because of the ozone O3 molecular absorption; at the
other end of the spectrum the transparency is reasonably good until about 2.4
micrometers, when the H2O and CO2 molecules heavily absorb the light.
The astronomical photometric wide bands (U,B,V, R, I, J, H, …) are indicated.
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Spontaneous and artificial emissions
To complete these considerations about the influence of the atmosphere on the
photometry (and also on the spectroscopy) of the celestial bodies, we must add
that the atmosphere contributes radiation, by spontaneous emission and by
scattering of natural and artificial lights. If the Observatory is close to populated
areas, bright emission lines of Mercury and Sodium from street lamps are
observed: Hg at  4046.6, 4358.3, 5461.0, 5769.5, 5790.7; Na at 5683.5,
5890/96 (the yellow D-doublet), 6154.6; Ne at 6506, and so on.
Natural lines come from the atomic Oxygen in forbidden transitions (designated
with [OI]) at  5577.4, 6300 and 6367, and especially from the molecular
radical OH who provides a wealth of spectral lines and bands filling the near-IR
region above 6800A. The OH comes from the dissociation of the water vapor
molecule under the action of the solar UV radiation.
Therefore, the atmosphere is a diffuse source of radiation, whose intensity
strongly depends on the Observatory site; to set an indicative value in the visual
band, a luminosity equivalent to one star of 20th mag per square arcsec at the
Zenith can be assumed.
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The visible spectrum of the night sky
The night sky is calibrated (see ordinate) in surface brightness, given as mag/(arcsec)2.
Mt. Boyun is in Korea.
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The Near-IR sky emission - 2
A very
detailed
section of
the nearIR night
sky OHemission
obtained
at ESO
Paranal
with
UVES.
http://www.eso.org/observing/dfo/quality/UVES/uvessky/sky_8600U_1.html
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A second limit of the terrestrial atmosphere:
the artificial lights
The full
Moon has
difficulties in
competing
with the
spectrum of
artificial
lights.
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The situation in Italy
1998
2025
If the extrapolation is correct, in 2025 no Italian will be able to
see the Milky Way
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Planetary light
pollution
From a paper by Cinzano, Falchi e Elvidge (2001)
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