Chapter 5
The astronomer’s measurements
By : A E Roy and D
Clarce
From The Book “
Astronomy Principles and Practice”
5.1 Introduction
We
have now seen that one of the chief aims of the observational astronomer is to
measure the electromagnetic radiation which is arriving from space. The
measurements involve:
1.
the determination of the direction of arrival of the radiation (see section
5.2);
2.
the determination of the strength of the radiation, i.e. the brightness of the
source (see section 5.3);
3.
the determination of the radiation’s polarization qualities (see section 5.4).
All
three types of measurement must be investigated over the frequency range where
the energy can be detected by the suitably available detectors. They must also
be investigated for their dependence on time.
Let
us now consider the three types of measurement in a little more detail.
5.2 Direction of arrival of the
radiation
Measurements
of the direction of arrival of radiation are equivalent to determining the
positions of objects on the celestial sphere. In the case of the optical region
of the spectrum, the apparent size of each star is smaller than the
instrumental profile of even the best recording instrument. To all intents and
purposes, stars may, therefore, be treated as point sources and their positions
may be marked as points on the celestial sphere. For extended objects such as
nebulae and for radiation in the radio region, the energy from small parts of
the source can be recorded with a spatial resolution limited only by the
instrumental profile of the measuring instrument. Again the strength of the
radiation can be plotted on the celestial sphere for the positions where a
recording has been made.
In
order to plot the positions on the celestial sphere of the sources of radiation,
it is obvious that some coordinate system with reference points is needed. For
the system to be of real use, it must be independent of the observer’s position
on the Earth. The coordinate system used has axes known as right ascension (RA or α) and declination (Dec or δ). RA and Dec can be compared
to the coordinate system of longitude and latitude for expressing a particular
position on the Earth’s surface.
The
central part of figure 5.1 depicts the Earth and illustrates the reference
circles of the equator and the Greenwich meridian. The position of a
point on the Earth’s surface has been marked together with the longitude (λ W)
and latitude (φ N), angles which pinpoint this position.
The
outer sphere on figure 5.1 represents the celestial sphere on which the energy
source positions are recorded. The reference circle of the celestial equator corresponds to the projection of the Earth’s equator on to the celestial
sphere and the declination (δ*) of a star’s position is analogous to
the latitude angle of a point on the Earth’s surface. As the Earth is rotating
under the celestial sphere, the projection of the Greenwich meridian would
sweep round the sphere, passing through all the stars’ positions in turn. In
order to label the stars’ positions, therefore, some other meridian must be
chosen which is connected directly to the celestial sphere.
During the course of
the year, the Sun progresses eastwards round the celestial sphere along an apparent path known as the ecliptic.
Because the Earth’s axis of rotation is set at an angle to the perpendicular to
its orbital plane around the Sun, the ecliptic circle is set at the same angle
to the celestial equator. The points of intersection of the circles may be used as
reference points on the celestial equator; however,
it
is the intersection where the Sun crosses the equator from south to north which
is chosen as the reference point. This position which is fixed with respect to
the stellar background is known as the first
point of Aries, ϒ, or the vernal
equinox (see figure 5.1). The meridian through this point corresponds to RA
= 0 hr.
Any
stars which happen to be on the observer’s meridian (north–south line projected
on the celestial sphere) are related in position to the reference meridian on
the celestial sphere by time. Consequently, a star’s position in RA is normally
expressed in terms of hours, minutes and seconds of time rather than in
degrees, minutes and seconds of arc. By convention, values of RA increase in an
easterly direction round the celestial sphere. As a result, the sky acts as a
clock in that the passage of stars across the meridian occurs at later times
according to their RA values. A star’s position in declination is expressed in
degrees, minutes and seconds of arc and is positive or negative depending on
whether it is in the northern or southern celestial hemisphere.
For an observer at
the bottom of the Earth’s atmosphere, the problem of recording the energy source
positions in terms of RA and Dec is made difficult by the very existence of the
atmosphere. The direction of propagation of any radiation is affected, in
general, when it meets a medium where there is a change in the refractive
index. In particular, for astronomical observations made in the optical region of
the spectrum, the change of direction increases progressively as the radiation
penetrates deeper into the denser layers of the atmosphere. The curvature of a
beam of light from a star is depicted in figure 5.2. Lines illustrating the
true direction and the apparent direction of a given star are drawn in the
figure. The amount of refraction increases rapidly as the star’s position becomes closer to the observer’s horizon.
At
a true altitude of 1 degree, the amount of refraction is approximately a
quarter of a degree. There is, however, a simple method for estimating how much
a star’s position is disturbed by refraction and this can be applied to all
observations.
Because
of turbulence in the Earth’s atmosphere, the apparent direction of propagation
moves about by small amounts in a random fashion. Normal positional measurements
are, therefore, difficult to make as any image produced for positional
determination will be blurred. For the optical region of the spectrum, it is in
the first few hundred metres above the telescope aperture which give the
greatest contribution to the blurring. It is, therefore, impossible to record a
star as a point image but only as a blurred-out patch. For field imaging work
this may not be too serious; it should not be difficult to find the centre of
the blurred image as this would still retain circular symmetry. In the case of
positional measurements by eye (no longer made by professional astronomers),
the problem is more serious as the eye is trying to make an assessment of an
instantaneous image which is in constant motion.
In
the radio region, positional measurements can also be affected by refraction in
the ionosphere and in the lower atmosphere. The amount of refraction varies
considerably with the wavelength of the radiation which is observed. For the
refraction caused by the ionosphere, a typical value of the deviation for
radiation at a frequency of 60 MHz is 20 minutes of arc at 5◦ true altitude.
The refraction in the lower atmosphere is mainly due to water droplets and is
hence dependent on the weather. The measured effect is approximately twice the
amount which is apparent in the optical region. A typical value of the
deviation is 0·◦5 at a true altitude of 1◦ and the effect increases rapidly
with increasing altitude in the same way as in the case of the optical
radiation.
It
is obvious that all positional measurements can be improved by removing the
effects of refraction and of turbulence and this can now be done by setting up
equipment above the Earth’s atmosphere, in an orbiting satellite or on the
Moon’s surface.
5.3 Brightness
5.3.1 Factors affecting brightness
Not
all the radiation which is incident on the outer atmosphere of the Earth is
able to penetrate to a ground-based observer. The radiations of a large part of
the frequency spectrum are either absorbed or reflected back into space and are
consequently unavailable for measurement from the ground. The atmosphere is
said to possess a window in any
region of the spectrum which allows astronomical measurements.
Frequencies
higher than those of ultraviolet light are all absorbed by a layer of ozone in
the stratosphere which exists some 24 km above the Earth. Until the advent of
space research, x-rays and γ -rays had not been detected from astronomical
objects.
On
the other side of the frequency band corresponding to visible radiation, a
cut-off appears in the infrared. The absorption in this part of the spectrum is
caused by molecules, chiefly water vapour. This cut-off is not very sharp and
there are occasional windows in the infrared which are utilized for making observations.
The absorption remains practically complete until the millimetre-wave region,
where again a window appears. Over a broad part of the radio spectral range, the
ionosphere lets through the radiation and the measurement of this form of
energy belongs to the realm of the radio astronomer.
The
two main windows for observation are depicted in figure 5.3. It may be pointed
out that the boundaries are not as sharp as shown in this diagram. Comparison
of the spectral widths of the main windows with the whole of the
electromagnetic spectrum reveals the large range of frequencies which are
unavailable to the ground-based observer and the potential information that is
lost.
Above
the Earth’s atmosphere, however, the full range of the electromagnetic spectrum
is available. It has been one of the first tasks of the orbiting observatories
and will eventually be that of lunar-based telescopes to make surveys and
measurements of the sky in the spectral regions which had previously been
unavailable.
For
ground-based observations made through the transparent windows, corrections
still need to be applied to measurements of the strength of any incoming
radiation. This is particularly important for measurements made of optical
radiation. By the time a beam of light has penetrated the Earth’s atmosphere, a
large fraction of the energy has been lost, and stars appear to be less bright
than they would be if they were to be viewed above the Earth’s atmosphere.
If an observing site
is in an area where the air is pure and has little dust or smog content, most of
the lost energy in the optical region is scattered out of the beam by the atoms
and molecules in the air.
This type of scattering is known as Rayleigh scattering.
According to Lord Rayleigh’s theory, atoms and molecules
of any gas
should scatter light with an efficiency which is inversely proportional to the
fourth power of the wavelength (i.e. the scattering efficiency ∝ 1/λ4). Thus blue light, with a short wavelength, is
scattered more easily than red light, which has a longer wavelength. Rayleigh’s
law immediately gives the reason for the blueness of the daytime sky. During
the day, some light, with its broad spectral range, is incident on the
atmosphere. As it penetrates towards the ground, part of the energy is
scattered in all directions by the molecules in the air. It is this scattered
light which the observer sees as the sky. As the scattering process is
extremely efficient for the shorter wavelengths, the sky consequently appears
blue. When the Moon is observed in the daytime, a blue haze can be seen between
it and the observer. This haze is a result of the scattering of some light by
the molecules in the atmosphere along the path to the Moon’s direction.
Starlight, in
its path through the Earth’s atmosphere, is weakened by this same process of scattering.
As the scattering is wavelength dependent, so must be the weakening. The
apparent absorption of starlight, or its extinction,
is very much stronger in the blue part of the spectrum than in the red (see
figure 5.4). Thus the colours of the stars are distorted because of the passage
of their radiation through the Earth’s atmosphere. If colour measurements are
to be attempted, then allowances must be made for the wavelength-selective
extinction effects.
The amount of
extinction obviously depends on the total number of molecules that the light beam
encounters on its passage through the atmosphere, i.e. it depends on the light
path. Thus the amount of extinction depends on the altitude of any given star.
The light loss is at a minimum for any particular observing site when the star
is positioned at the zenith. Even at this optimum position, the total
transmission of visible light may only be typically 75%.
As a consequence
of the extinction being dependent on a star’s altitude, any star will show
changes in its apparent brightness during the course of a night as it rises,
comes to culmination and then sets. Great care must be exercised when
comparisons are made of the brightnesses of stars, especially when the stars
cover a wide range of altitudes.
Radio energy is
also absorbed on its passage through the layer of electrified particles known as
the ionosphere. Further absorption occurs in the lower atmosphere. The amount
of absorption is dependent on the particular frequency which is observed.
Ionospheric absorption depends on the physical conditions within the layers
and, as these are controlled to some extent by the activity on the Sun, the
amount of absorption at some frequencies can vary greatly. Refraction caused by
the ionosphere can also give rise to the diminution of radio signals. At low
altitudes, the ionosphere can spread the radiation in the same way as a
divergent lens, thus reducing the amount of energy which is collected by a
given radio telescope.
In the lower
atmosphere, the radio energy losses are caused by attenuation in rain clouds
and absorption by water vapour and oxygen and they are thus dependent on the
weather. However, lower atmosphere absorption effects are usually unimportant
at wavelengths greater than 100 mm.
Returning again
to the optical region, simple naked eye observations reveal that the light from
a star suffers rapid variations of apparent brightness. This twinkling effect
is known as intensity scintillation
and the departures of intensity from a mean level are known as scintillation noise. Scintillation is
caused by turbulence in the Earth’s atmosphere rather than by fluctuations in
the scattering and absorption; it is certainly not an inherent property of the
stars. Minute temperature differences in the turbulent eddies in the atmosphere
give rise to pockets of air with small differences in refractive index.
Different parts of the light beam from a star suffer random disturbances in
their direction of travel. For brief instances, some parts of the energy are
refracted beyond the edge of the telescope collecting area, causing a drop in
the total energy which is collected. There are other instances when extra
energy is refracted into the telescope aperture. Thus, the energy which is
collected shows rapid fluctuations in its strength. The magnitude of the effect
decreases as the telescope aperture increases, there being a better averaging
out of the effect over a larger aperture. Scintillation is very noticeable to
the naked eye as its collecting aperture is only a few millimetres in diameter.
Brightness
measurements are obtained by taking mean values through the scintillation noise
and they are, therefore, subject to uncertainties of a random nature. The magnitude
of these uncertainties depends on the strength of the scintillation noise,
which in turn depends on the quality of the observing site, on the telescope
system used and on the altitude of the star.
Scintillation is
also encountered in the radio region of the spectrum and is mainly caused by inhomogeneities
in the ionosphere. The fluctuations of signal strength which are observed are
less rapid than those recorded in the optical region.
Although
scintillation effects are detrimental to obtaining accurate measurements of a
source’s brightness, studies of the form of scintillation noise itself, in both
the optical and radio regions, are useful in gaining information about the
Earth’s atmosphere, upper winds and the ionosphere.
Although
allowances can be made successfully for the effects of atmospheric extinction,
it is obvious that absolute brightness measurements, brightness comparisons and
colour measurements could be made more easily, with less risk of large random
and systematic errors, above the Earth’s atmosphere. Again, such measurements
can be made by equipment on an orbiting platform or at a lunar observing
station.
5.3.2 The magnitude system
The energy
arriving from any astronomical body can, in principle, be measured absolutely.
The brightness of any point source can be determined in terms of the number of
watts which are collected by a telescope of a given size. For extended objects
similar measurements can be made of the surface brightness. These types of
measurement can be applied to any part of the electromagnetic spectrum.
However, in the
optical part of the spectrum, absolutely brightness measurements are rarely
made directly; they are usually obtained by comparison with a set of stars
which are chosen to act as standards. The first brightness comparisons were, of
course, made directly by eye. In the classification introduced by Hipparchus,
the visible stars were divided into six groups. The brightest stars were labelled
as being of first magnitude and the faintest which could just be detected by
eye were labeled as being of sixth magnitude. Stars with the brightnesses
between these limits were labelled as second, third, fourth or fifth magnitude,
depending on how bright the star appeared.
The advent of
the telescope allowed stars to be recorded with magnitudes greater than sixth; catalogues
of the eighteenth century record stars of seventh, eighth and ninth magnitude.
At the other end of the scale, photometers attached to telescopes revealed that
some stars were brighter than the first magnitude classification and so the
scale was extended to include zero and even negative magnitude stars. The range
of brightnesses amongst the stars revealed that it is necessary to subdivide
the unit of magnitude. The stars visible to the naked eye could have magnitudes
of −0·14, +2·83 or +5·86, say, while stars which can only be detected with the
use of a telescope could have magnitudes are of +6·76, +8·54 or even as faint
as +23.
A more complete
description of magnitude systems together with the underlying mathematical relationships
is reserved for Part 3.
5.4 Polarization
The presence of
any polarization in radiation can be detected by using special devices which
are sensitive to its orientation properties. They are placed in the train of
instrumentation between the telescope and the detector and rotated. If the
recorded signal varies as a device rotates, then the radiation is polarized to
some extent. The greater the variation of the signal, the stronger is the
amount of polarization in the beam.
In the case of
measurements in the optical region, the polarization-sensitive devices would be
the modern equivalents of the Nicol prism and retardation plates made of some
birefringent material. Brightness measurements are made after placing these
devices in the beam of light collected by the telescope. Although the Earth’s
atmosphere affects the brightness of any light beam, the polarization properties
are unaltered by the beam’s passage through the atmosphere; at least, any
disturbance is smaller than would be detected by current polarimetric
techniques. However, since polarization determinations result from brightness
measurements, the atmosphere will reduce their quality because of scintillation
and transparency fluctuations.
For the radio
region, the receiving antenna such as a dipole is itself inherently sensitive
to polarization. If the radio radiation is polarized, the strength of the
recorded signal depends on the orientation of the antenna in the beam. Simple
observation of TV receiving antenna on house roof tops demonstrates the
dipole’s orientational sensitivity. In some locations the dipole and the
guiding rods are in a horizontal plane. In other areas they are seen to be in a
vertical plane. This difference reflects the fact that the transmitting antenna
may radiate a TV signal with a horizontal polarization while another at a
different location may radiate with a vertical polarization, this helping to
prevent interference between the two signals. Obviously, to obtain the best
reception, the receiving antenna needs to be pointed in the direction of the
transmitter and its orientation set (horizontal or vertical) to match the
polarizational form of the signal.
Unlike the
optical region, the polarization characteristics of radio radiation are altered
significantly by passage through the Earth’s atmosphere or ionosphere. The
magnitude of the effects are very dependent on the frequency of the incoming
radiation. Perhaps the most important effect is that due to Faraday rotation:
as polarized radiation passes through the ionospheric layers, all the component
vibrational planes of the waves are rotated resulting in a rotation of the
angle describing the polarization. The total rotation depends on the physical
properties within the layers, the path length of the beam and the frequency of
the radiation. According to the frequency, the total rotation may be a few
degrees or a few full rotations. It can thus be a difficult task to determine
the original direction of vibration of any polarized radio radiation as it arrives
from above the Earth’s atmosphere.
As was the case
for positional and brightness measurements, the quality of polarization measurements
can be greatly improved if they are made above the Earth’s atmosphere, either
from an orbiting space laboratory or from the Moon’s surface. In addition,
orbiting satellites have been used to house radio transmitters and direct
measurements made on the Faraday rotation effect have beenused to explore the
properties of the ionosphere.
5.5 Time
If measurements
of the positions, brightnesses and polarization of astronomical sources are
repeated, the passage of time reveals that, in some cases, the position of the
source or some property of its radiation changes. These time variations of the
measured values are of great importance in determining many of the physical
properties of the radiating sources. It is, therefore, very necessary that the
times of all observations and measurements must be recorded. The accuracy to
which time must be recorded obviously depends on the type of observation which
is being attempted.
It would be out
of place here to enter into a philosophical discussion on the nature of time. However,
it might be said that some concept which is called time is necessary to enable
the physical and mechanical descriptions of any body in the Universe and its
interactions with other bodies to be related. One of the properties of any time
scale which would be appealing from certain philosophical standpoints is that
time should flow evenly. It is, therefore, the aim of any timekeeping system
that it should not show fluctuations in the rate at which the flow of time is
recorded. If fluctuations are present in any system, they can only be revealed
by comparison with clocks which are superior in accuracy and stability.
Timekeeping systems have changed their form as clocks of increased accuracy have
been developed; early clocks depended on the flow of sand or water through an
orifice, while the most modern clocks depend on processes which are generated
inside atoms.
About a century
ago, the rotation of the Earth was taken as a standard interval of time which could
be divided first into 24 parts to obtain the unit of an hour. Each hour was
then subdivided into a further 60 parts to obtain the minute, each minute
itself being subdivided into a further 60 parts to obtain the second. This
system of timekeeping is obtained directly from astronomical observation, and is
related to the interval between successive appearances of stars at particular
positions in the sky. For practical convenience, the north–south line, or
meridian, passing through the observatory is taken as a reference line and
appearances of stars on this meridian are noted against some laboratory
timekeeping device. As laboratory pendulum clocks improved in timekeeping
precision, it became apparent from the meridian transit observations that the
Earth suffered irregularities in the rate of its rotation. These irregularities
are more easily shown up nowadays by laboratory clocks which are superior in
precision to the now old-fashioned pendulum clock.
At best, a
pendulum clock is capable of accuracy of a few hundredths of a second per day.
A quartz crystal clock, which relies on a basic frequency provided by the
vibrations of the crystal in an electronic circuit, can give an accuracy better
than a millisecond per day, or of the order of one part in 108; and
this is usually more than sufficient for the majority of astronomical
observations. Even more accurate sources of frequency can be obtained from
atomic transitions. In particular, the clock which relies on the frequency
which can be generated by caesium atoms provides a source of time reference which
is accurate to one part in 1011. The caesium clock also provides the
link between an extremely accurate determination of time intervals and the
constants of nature which are used to describe the properties of atoms.
Armed with such
high-precision clocks, the irregularities in the rotational period of the Earth
can be studied. Some of the short-term variations are shown to be a result of
themovement of the observer’s meridian due to motion of the rotational pole
over the Earth’s surface. Other variations are seasonally dependent and
probably result in part from the constantly changing distribution of ice over
the Earth’s surface. Over the period of one year, a typical seasonal variation
of the rotational period may be of the order of two parts in 108.
Over and above
the minute changes, it is apparent that the Earth’s rotational speed is slowing
down progressively. The retardation, to a great extent, is produced by the
friction which is generated by the tidal movement of the oceans and seas and is
thus connected to the motion of the Moon. The effects of the retardation show
up well in the apparent motions of the bodies of the Solar System.
After the orbit
of a planet has been determined, its positions at future times may be
predicted. The methods employed make use of laws which assume that time is
flowing evenly. The predictions, or ephemeris positions, can later be checked
by observation as time goes by. If an observer uses the rotation of the Earth
to measure the passage of time between the time when the predictions are made and
the time of the observation, and unknowingly assumes the Earth’s rotational
period to be constant, it is found that the planets creep ahead of their
ephemeris positions at rates which are proportional to their mean motions. The
phenomenon is most pronounced in the case of the Moon.
Suppose that a
time interval elapses between the time the calculations are performed and the time
that the ephemeris positions are checked by observation. The time interval
measured by the rotation of the Earth might be counted as a certain number of
units. However, as the Earth’s rotation is continuously slowing down and the
length of the time unit is progressively increasing in comparison with the unit
of an evenly-flowing scale, the time interval corresponds to a larger number of
units on an evenly-flowing scale. Unknown to the observer who takes the unit of
time from the Earth’s rotation, the real time interval is actually longer than
he/she has measured it to be and the planets, therefore, progress further along
their orbits than is anticipated. Thus, the once unexplained ‘additional
motions’ of the planets and the Moon are now known to be caused by the fact
that the Earth’s rotational period slows down during the interval between the
times of prediction and of observation.
It is now
practice to relate astronomical predictions to a time scale which is flowing
evenly, at least to the accuracy of the best clocks available. This scale is
known as Dynamical Time (DT).
Postingan
