Observing Stars (a Level Physics/astrophysics)

Our view of the sky at night is possible because of the emission and reflection of light. ‘Light’ is the better-known term for the electromagnetic spectrum, which includes waves in the visible, ultra-violet, infra-red, microwave, radio, X-ray and gamma-ray regions. The scale of the spectrum is so large that no region is distinct, several overlap each other.

Each of these regions in the electromagnetic spectrum represent transverse waves, travelling as electrical and magnetic fields which interact perpendicularly to each other, with different ranges of wavelength. The magnetic field oscillates vertically and the electric field horizontally, and each field induces the other.

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By the end of the nineteenth century, Maxwell gave a realistic value for c, the speed of light:

c = __1__ = 3 x 108 ms-1

O(mo eo)

The relationship between the speed of all electromagnetic radiation, wavelength (l) and frequency (f) is shown to be c = l f.

Because the Universe is so vast, interstellar distances are so great that light emitted can take upwards of millions of years to reach us. Such large distances are often measured in light-years’; one light-year (ly) is the distance travelled by a wave of light in a year. Because of the massive speed of light and distances, the light arriving at us would have left the object many years ago, so that looking at a far away star is much like looking back in time.

Scientific observation of the stars is difficult because of the distorting effect of the Earth’s atmosphere. One problem is atmospheric refraction-where light is bent. Turbulent air currents cause varying refractive indices, as there is no uniform air density. This causes an effect called scintillation, where stars appear to twinkle. The effect on regions of the electromagnetic spectrum other than the visible part, such as the absorption of certain frequencies by atmospheric chemicals, and the reflection of waves by charged molecules in the ionosphere, means that some spectral data is simply invisible to us on Earth.

The Earth receives electromagnetic radiation of all wavelengths from all directions in space, but most of the electromagnetic spectrum is blocked out by the atmosphere well above the Earth’s surface, where our eyes and instruments are mostly based. However, wavelengths from only two regions of the electromagnetic spectrum are able to penetrate the atmosphere. These two spectral windows in the atmosphere through which we can observe the Universe are called the optical window-which allows the visible wavelength region through; and the radio window-which includes the wavelength region from about 1 mm to 30 m. The telescopes used by astronomers on the ground are therefore classed as optical and radio telescopes. Optical telescopes work by either reflecting or refracting light, using lenses or curved mirrors to focus the light from a subject to form an image.

Radio telescopes consist of a parabolic reflector and receiver on which the waves are focused. The gathering and resolving power depend on the diameter of the antenna. Radio observations are unaffected by the weather or time of day, and because of the larger wavelength of radio waves, dust in space and atmospheric convection currents are not a problem. Radio astronomy is used in the chemical analysis of elements (by emission and absorption spectra); to detect the motion of bodies due to the Doppler effect; and in investigation into the early Universe and the Big Bang. We can analyse radio waves from the centres of galaxies, including our own.

Despite the radio window, there are still wavelengths that do not penetrate the atmosphere. Some radio waves are reflected from the ionosphere, part of the thermosphere, where streams of charged particles from the sun ionise gas molecules: this is photo-ionisation. Ultra-violet radiation, X-rays and gamma-rays are also absorbed at this layer.

Absorption of the electromagnetic spectrum at various altitudes above Earth occurs to varying degrees. Much infra-red radiation does not reach ground level because of absorption in the upper atmosphere by water, and some carbon dioxide and oxygen molecules that lie between the ground and about 15 km of altitude (the troposphere). Ozone (tri-oxygen) and di-oxygen in the stratosphere absorbs much of the ultra-violet radiation (hence the ozone layer’ at about 30km). A side effect of the ozone layer is that molecules re-radiate the energy in a few wavelengths of the green, red, and infrared regions, causing airglow’.

It is because of the limitations of Earth’s atmosphere, that astronomers learnt the benefits of observing from beyond it. Placing telescopes and instruments of mountain tops-to avoid clouds, bad weather and turbulence-or using balloons or aircraft, are useful, but satellites are far more so. All electromagnetic radiation can be detected, unaffected by absorption, reflection or refraction, dust, atmospheric haze, airglow, weather, light pollution or the time of day.

The Hubble Space Telescope is probably the most famous astronomical satellite in orbit around Earth. Photographs taken by it have far improved detail than an Earth-based telescope. We have greater knowledge of elements and compounds present thanks to emission and absorption spectroscopy. The 1983 NASA Infra-Red Astronomical Satellite (IRAS) has been successful in infra-red observations across the sky, detecting nuclear and chemical reactions by spectrometry, and hot clusters where stars are born. The 1989 NASA Cosmic Background Explorer (COBE) satellite undertook a detailed study of background radiation: the echo’ of the Big Bang. Low frequency microwaves present today are the result of the red-shift over a long time of the original, high-energy electromagnetic radiation from the time of the birth of the Universe. The future of satellite observations lies with X-ray and gamma-ray astronomy. X-ray images show where high-energy events occur, such as nuclear processes and matter entering a black hole. Gamma-rays are emitted from only the hottest and most violent bodies, and although difficult to detect, telescopes are used to map the Universe.

Most observations surround the light from stars. There are billions of them in the Universe; we classify stars by their various characteristics. The properties of stars can be determined by the application of principles explained below.

All stars visible to us must have surface temperatures high enough to emit light which we can see from so far away. Some appear brighter than others. The difficulty is in determining weather a star is very hot and bright, or not as bright but just much closer to us. We know that very hot things appear red hot’ or even white hot’, that the temperature of an object relates to the colour of light it radiates. The electromagnetic radiation emitted by any object (whatever its temperature) is known as thermal radiation. Hot objects such as stars emit high energy, high frequency radiation. At about 1000oc, thermal radiation falls in the visible region of the electromagnetic spectrum.

To find out the temperature of a star, measurements need to be relative rather than absolute, as there is no possible way of measuring a star’s surface temperature physically! No object can perfectly emit (or absorb) light in practice, but it is useful to imagine such a body to make comparisons with: a black body’. A black body is a perfect absorber of light; it follows therefore that it is also a perfect emitter of light. A perfect absorber would appear totally black; a perfect emitter would emit all radiation, including visible light, and would appear bright white. We know that a black body therefore emits a broad range of the electromagnetic spectrum. The most intense emission will peak at a particular wavelength. The hotter the body, the shorter the peak wavelength, but the higher the peak. Wein’s displacement law states that the peak wavelength, lmax , is inversely proportional to absolute (actual) temperature of an object. We assume that a star behaves as a black body. The relationship is shown below:

lmax T = 2.898 x 10-3 m K

Hence, we can relate the colour of a star to estimate its temperature, depending on where in the electromagnetic spectrum lmax lies. Astronomical objects have peak wavelengths ranging from radio to X-rays, i.e. surface temperatures from absolute zero to 107 K.

It is apparent that the hotter an object is, the more intense the emission of radiation is. Luminosity (L) is the total power emitted by a body. The Stefan-Boltzmann law states that the total energy radiated per unit time by a black body is proportional to the fourth power of its absolute temperature’; it also depends on the surface area (A):

L = s A T4

Stefan’s constant (s) = 5.67 x 10-8 W m-2 K-4

The amount of power received per unit area is flux (equal to power / area). Light emitted from an object spreads out in all directions, the further away it gets the less intense it becomes according to the inverse square law:

L = d-2

E.g., As Saturn is ten times the distance from the Sun as Earth, the intensity of radiation is receives is 1/100 th of that for Earth.

The light reaching Earth from the sun can be analysed using a technique called spectroscopy. It is used to identify the chemical composition of stars (which is mostly hydrogen and helium), and their surface temperature. Once these are known, stars can be classified accurately.

An emission spectrum is the spectrum of wavelengths of light emitted from atoms or molecules. They do this when they lose energy, which corresponds to a specific frequency of the electromagnetic spectrum. 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

The Doppler shift can occur when something is moving towards or away from us, however receding galaxies is evidence that our Universe is expanding (their light is shifted towards the red / longer wavelength part of the spectrum). It can also be used to determine the distance of an object from us. Hubble made the important finding that the further away a galaxy is, the greater its velocity. Also, all galaxies are generally moving apart from each other, including ours. Hubble’s law depends on the Hubble constant (Ho), but there is no accurate value for this, due to the inaccurate estimates for distances by other methods.

v = Ho x d

It is speculated that Ho lies between 40 and 100 km s-1 Mpc-1

The Doppler effect is also used to measure how fast stars and galaxies are rotating, and the orbital period of binary stars. A pair of binary stars each orbit a common centre of mass, as they are attracted by each other’s gravity. The stars usually have different masses, and will have different orbits (the radius of which is inversely proportional to the mass). When the stars are close to each other, it is difficult to distinguish between them, except by their different spectra (these are spectroscopic binary stars). Each is identified to be receding or approaching as they rotate, by Doppler shifting.

We can find the combined mass of the two stars (M), based on Kepler’s third law of planetary motion:

M = 4p2r3

GT2

G = Universal gravitational constant = 6.67 x 10-11 N m2 kg-2

The mass of each star can be calculated, as they are known to be in ratio of the distance to the centre of mass.

We can see that there is so much to be discovered about the sky, over the years physicists have somewhat overcome the problem of sheer distance across the Universe. We have catalogued data about many stars, and crucially we can compare other stars to ones we already know about. We can learn how stars evolve from our observations, however we can only view a tiny part of history. Star populations are mapped on the Hertzsprung-Russell diagram, basically a graph of luminosity against surface temperature:

From it we can examine the life sequences of a star, deduce a star’s absolute magnitude, and then their spectral class according to their surface temperature and other properties. We can identify what stage in its life a star it. This is discussed further in How Stars Form’.

Bibliography: Astrophysics’, Nigel Ingham ; Physics Passcards’, Graham Booth, Letts

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