An atom or molecule may
become electronically excited, electrons transfer to higher energy levels, and
then later drop back to their normal, lower energy states, emitting this extra
energy as photons of light in the process. Molecules gain translational,
rotational, vibrational or electronic energy, depending on how much energy they
first absorb. They must emit this quantised amount of energy again. Different
elements and have different energy levels, this is why we can associate certain
wavelengths with the physical behaviour of a particular atom. Even small
molecules cannot withstand the high temperatures of stars, their spectra are
only visible for cool stars. An absorption spectrum is apparent when wavelengths
of light are missing against the continuous background of emitted light. These
missing wavelengths have firstly been emitted from atoms in the inner layers of
the star, but then absorbed by different chemicals in the outer layers. Thus we
can identify the elements in the outer layers of a star. The Balmer series
refers to the emission spectrum of hydrogen, specifically for high energy level
electrons dropping back to the second energy level (n=2). Light emitted falls in
the visible region of the electromagnetic spectrum, and the intensity of this
light is an indication of a star’s surface temperature. The Balmer series is due
to atoms being excited by kinetic collisions. The electrons of cool atoms occupy
their ground state (n=1), as there are few collisions to excite the electrons.
The hotter the atoms, the more energetic the collisions; more electrons are
excited to even higher levels (n=3, 4,.etc). These electrons now absorb
wavelengths beyond the Balmer series. The most intense Balmer emission spectra
are from stars with intermediate surface temperatures at around 10 000K. Most
electrons can absorb and re-emit wavelengths of the visible spectrum at this
temperature. The light from stars travels very great distances, taking a long
time, to reach Earth. Unsurprisingly, it can be affected by the time it reaches
us. Of course, our nearest star is the Sun, and our nearest ‘neighbour’ is the
moon. However, ‘near’ in space is nowhere near close enough to actually measure
by hand. The first logical estimates used simple trigonometry in a method called
parallax. This is where a distant object will appear at a different spot when
viewed from a different angle.
Simply, the position of a star is measured
relative to the background, at the two times when the apparent distance between
these viewing positions is as great as possible. As the Earth rotates around the
Sun, with a radius of 1 astronomical unit (1AU = 1.496 x 1011 m), the greatest
possible angle between two different views of a star is achieved at six month
intervals, when the distance between these two times is 2AU: The further away
the object, the smaller the parallax angle would be, as: Distance (d) = 1AU Tan
(r) Distance (d) in parsec (pc) = _____________1_____________ Parallax angle (r)
in arc-seconds Measuring parallax in this way is called annual parallax. It is
suitable for objects up to about a distance of 100pc from us. Earth based
instruments are less reliable as the parallax angle being measured gets smaller,
greater measurements have been made by Earth orbiting telescopes such as 1989 ESA Hipparcus which avoid atmospheric limitations. We can only estimate the
distances of more distant objects such as supernovae. One method is called
spectroscopic parallax, where we can make the assumption that all stars are
equally bright (although we know of course that they are not), and so the
brighter a star the closer it is. The apparent magnitude (m) of a star is
related to its intensity (I); its is an observational logarithmic scale. The
absolute magnitude is a comparative scale based on the assumption that all
objects are at a distance (d) of 10 pc. The two measurements are related: d =
10pc x 10 (m – M) / 5 The distance of an object is related to its intensity
(using the inverse square law): I = L 4pD2 For objects further away than 10
megaparsecs, astronomers have made use of more unusual objects as reference
points in the sky. Cepheid variable stars have luminosity which varies
periodically. They vary in brightness as their surface temperature rises and
falls. The absolute magnitude is directly proportional to the period, and using
the above formula the distance of these stars can be calculated. These stars are
present in distant galaxies, we can deduce how far away these are. Some
supernovae behave in the same way. We know that stars and galaxies are moving
away from us, because the spectra lines from some are shown to have been
shifted. This is the Doppler effect, where the spectrum lines are displaced,
because their wavelengths have been changed. The change in wavelength is related
to the velocity: Df = Dl = v f l c
