Astronomical Spectroscopy and Photometry

ASTRONOMICAL SPECTROSCOPY AND PHOTOMETRY

The spectrum of the radiation

When a beam of light passes through a prism or some other dispersion device, it is resolved into the various component wavelengths, forming a coloured band, known as spectrum of the source of light.
The spectrum of light provides a lot of information as to the chemical composition of the source and its physical state (temperature, density and ionization degree). Many types or spectra exist in nature: the continuous spectrum, the emission spectrum, and the absorption spectrum.
A continuous spectrum contains all the wavelengths of the radiation, at least those that fall in a given interval, without interruptions. Such spectrum is emitted by solid and liquid compressed gases at high temperatures.
An emission spectrum is a spectrum in which only certain lines (or wavelengths) are present. Such kind of spectrum is emitted by hot and rarefied gases, and the lines that can be observed are characteristic of the chemical elements that compose the gas.
An absorption spectrum is a continuous spectrum in which some wavelengths are missing. These are called absorption lines. It is produced when the light of a continuous source travels through a colder gas, that absorbs some of the wavelengths, according to the elements it contains.

A particular type of continuous spectrum is that emitted by the black body.
A black body is a hypothetical body that, when cold, absorbs the radiation of any wavelength, and therefore appears completely dark, but, when hot, emits a radiation with all the wavelengths. So, it is a hypothetical perfect emitter and absorber.
A black body emits a spectrum the "shape" of which, that is the intensity of the radiation at the various wavelengths, is fixed and depends only on the temperature of the body. The point of maximum intensity of the radiation corresponds to a wavelength that is inversely proportional to the temperature.

Astronomical photometry

Astronomical photometry is the measure of the light emitted by a celestial source. A number of optical, photographic and electronic procedures are used in order to measure the luminous flux (that is the energy that hits a detector per unit time). The ancient astronomers had already subdivided the stars into classes, according to their apparent brightness, but on the basis of their observations carried out by naked eye. With the invention of the astronomical instruments, the photographic films and, later, of the photoelectric and electronic detectors, quantitative measures were obtained.

Astronomical photometry is based on the concept of magnitude, which is the measure of the intensity of the light emitted by a star. It got its name from the Latin word meaning "bigness", because in ancient times it was thought that the brightest stars were also the biggest. For the same reason, the ancient astronomers had divided the stars in 6 classes of size: the stars of the first magnitude were the brightest, those of the sixth magnitude the weakest.
The scale of magnitude used today uses the same terminology, so the number indicating the magnitude increases as the brightness decreases. The magnitude of the brighter celestial bodies (like the Sun, Venus or Jupiter), is indicated by a negative number.
The magnitude scale is not linear, but geometrical: two stars, whose luminous intensity ratio is 100 differ by 5 magnitudes; they differ by one magnitude when their luminosity ratio is 2,512. Only stars up to the sixth magnitude can be observed with the bare eye, while objects with a much smaller intensity, that is a bigger magnitude, up to over 23, can be observed with a telescope.
These considerations refer to the luminous energy that reaches the Earth, that is to its apparent magnitude: if two identical stars have different distances from us, the nearest appears to be the brightest. With equal intrinsic luminosity, the apparent magnitude of an object is inversely proportional to the squared distance of the same object. In order to set a real luminosity scale, independent of the distance, we ideally set all the stars at the same distance, that is 10 parsec (32.6 light years), and we call absolute magnitude of these stars the apparent magnitude that they would have at that distance. For example, the Sun has an apparent magnitude of -26.5, due to its closeness, but if it were placed at a distance of 10 parsec, it would appear to us as a star of magnitude 4.8, which, in fact, is its absolute magnitude. The absolute magnitude of a star (indicated as M), and the apparent magnitude (indicated as m) are connected to its distance d by the relation

M = m - 5 Log (D/10)

where D is expressed in parsec.

Besides, the magnitude depends on the instrument used for the measurement: a star emits at all wavelengths, even though more intensely in some spectral bands and less in others. Instead, the detectors have only a given interval of sensitivity: some are sensitive to red light, some to blue light, some others to infrared, etc... Often, in astrophysics, we refer to the magnitude of a star in a given spectral band, rather than to the total. In order to measure the magnitude of a star in a band, you need a detector and filters able to block any radiation outside that interval of wavelengths.

Astronomical spectroscopy

The development of spectroscopy, that is of the study of the spectrum of the luminous beams, began in the 19th century, when the first spectroscope was built. The spectroscope is an instrument that allows to separate the various components of a beam of light, that is the different wavelengths. If we add to it a device that measures the intensity of the light at the various wavelengths, the instrument is called spectrometer.
Each chemical element absorbs and emits particular frequencies, that is particular lines. Their spectra can be studied in the laboratory under different temperature, density and pressure conditions. By studying the light emitted by various chemical substances, and by analysing the light coming from the Sun and some stars, the astronomers of the last century were able to discover their chemical composition.
A fundamental discovery was that the stellar spectra can be divided into groups, called spectral types, on the basis of some similarities, like the colour or the presence of certain spectral lines. In particular, scientists became aware that the type and the aspect of the spectral lines changed as the colour of the star changed.

The spectrum of a star shows absorption lines. Hypothetically, the continuous part of this spectrum can be approximated with that of a black body with a temperature equal to that of the surface of the star, even though a star is not a perfect emitter and does not have a well defined physical surface. In astrophysics, a star is characterized by a "colour" and a "superficial temperature", according to the shape of its spectrum: you compare the spectrum of the star to that of a black body, and you assign to the star the temperature of the black body with the nearest spectrum. The colour is determined by the region of the spectrum in which the intensity of the light is maximum; stars have superficial temperatures measuring thousands of degrees, and many emit the maximum power in the optical region of the spectrum. The Sun emits in the yellow region of the optical band at the maximum of intensity, therefore its superficial temperature was set at 5,780 degrees Kelvin.

As already said, each chemical element emits and absorbs certain wavelengths. A chemical element, if present in the outer layers of a star, produces an absorption line, that is it absorbs that wavelength from the light that comes from the star, leaving a dark line in its spectrum.
Only the young and massive stars have a superficial temperature high enough to ionize the surrounding gas (ten thousand degrees). Such gas, hot and rarefied, absorbs the energy coming from the star, and re-emits it in form of spectral lines; for this reason, overlaid to the stellar spectrum with its absorption lines, these stars have also an emission line spectrum, that of the rarefied gas.

Some spectral lines are very important in astrophysics. Among these, the lines of hydrogen, in particular that called H alpha, with a wavelength of 6,563 Angstrom. Other important lines are those of sodium, ionized calcium, etc...

The spectral types are the following:

Class O : they have superficial temperatures exceeding 30 thousand degrees, that can even ionize helium. Therefore, they show in their spectra the lines of ionized helium. These are relatively rare stars.
Class B : their superficial temperature ranges between 15 thousand and 25 thousand degrees. They are more common than the class O, but still quite rare.
Class A : these are stars with a temperature ranging between 8 and 12 thousand degrees approximately, and are very numerous. The lines of hydrogen dominate their spectra. Sirius, Vega and Altair belong to this spectral type.
Class F : these are stars with temperatures ranging between 6 and 8 thousand degrees; the lines of ionized calcium dominate their spectrum. The Polar Star belongs to this spectral type.
Class G : this is the class that comprises the Sun, and the stars with a superficial temperature of 4-6 thousand degrees, characterized by the lines of metals and of ionized calcium in their spectra.
Class K : these have temperatures ranging between 3,500 and 5,000 degrees and a spectrum characterized by the lines of metals and neutral calcium.
Class M : this is the class that comprises for example Betelgeuse and Antares. They have superficial temperatures of 2-3 thousand degrees and are characterized by the lines titanium oxide.
Class S : they have the same temperatures as class M, but they have the lines of the zirconium oxide in their spectrum. They are very rare.
Classes R and N : they also have the same temperatures as the class M stars, but their spectrum is dominated by Carbon, and they are therefore called carbon stars. These are quite rare stars.

Each of these spectral types is in turn divided in subclasses, marked with numbers, from 0 to 9 (for example the Sun is a star of the G5 spectral type).
For the same superficial temperature and therefore colour, the stars can have a different luminosity. The astronomers have therefore introduced some luminosity classes in order to classify them. For example, two stars with equal superficial temperature but different luminosity, must have a different irradiating surface and different volume, because the luminosity of a star is proportional to its surface. In fact, the luminosity is the energy emitted in one second by the entire surface of the star; under equal conditions of temperature, the amount of energy emitted per time and surface unit is the same, therefore a different luminosity is due to a different extension of the irradiating surface.
So, the stars are divided in supergiant, giant and dwarf. They differ not only as far as the size is concerned, but also for their density: the giant and supergiant stars are very rarefied and "expanded", while the dwarf stars are dense, small and compact. The white dwarfs somewhat constitute an extension of this scale, being the smaller and more compact stars.
It must be pointed out that there is not necessarily a relation between the size and the mass of a star: the mass of Antares is only 20 times larger than that of the Sun, while its diameter is 480 times longer, and there are white dwarfs with a mass equal to that of the Sun, and a diameter that is only 1/200 that of the Sun.

The HR diagram

Once a sufficient number of stars had been classified, some astronomers thought of gathering all the existing data in order to discover possible relations between the quantities that characterize them. Two astronomers, Hertzprung from Denmark and Russell, American, independently elaborated a diagram in which the absolute luminosity and the superficial temperature of the stars are shown. It is called HR diagram and it is of fundamental importance for the study of stellar evolution. According to the position of a star in the diagram, one can deduce many of its physical characteristics and its evolution state.

The HR diagram and the various types of stars

In the HR diagram the luminosity or absolute magnitude of the star is reported on the ordinate axis, with increasing values, while the temperature is reported on the abscissae axis, with decreasing values. It was discovered that the stars are not distributed randomly in this diagram, but the majority are gathered along a band that crosses the plane diagonally, from the high temperature and luminosity to the lower.
Such band is called main sequence and is characterized by the fact that the brightness and temperature of the stars decrease regularly from the top to the bottom. The luminosity of the stars of the main sequence depends on their mass, therefore it is also a mass sequence, that decrease downwards. The sequence is composed of dwarf stars and blue giants; the latter can be found in the top-left part of the HR diagram.
Other stars are concentrated in the top-right part of the diagram, that is the region of high luminosity and low temperature; this is the region of the red giants. The outer layers of these stars are very expanded and therefore, although they are not very hot, they have a very large irradiating surface and a high luminosity.
Other stars are gathered in the bottom-left region, at high temperature and low luminosity: these are the white dwarfs, very small stars, hot and compact. They emit large quantities of energy per surface unit, being very hot like the white stars of the main sequence, but, seeing as they are very small, the irradiating surface and therefore the total luminosity, is low.

The region on the right of the diagram, at temperatures lower than 2,000 degrees approximately, is that of the so-called pre-sequence stars, that is those with a central temperature that is not high enough to allow the fusion of hydrogen to create helium. They are placed approximately along a vertical line on the right, and when their core heats up and the nuclear fusion starts, they shift towards the main sequence, each one occupying a point corresponding to its mass.
Finally, there are stars that occupy a region called horizontal branch, a horizontal band that corresponds to absolute magnitudes of approximately 0.5. These are stars with a small mass, that burn helium in the nucleus; it is a subsequent phase to the main sequence.

It can be noted that the probability for a star to occupy a region of the diagram is proportional to the duration of the corresponding phase. The stars in the sequence are those that burn hydrogen in their nucleus, transforming it into helium. Since hydrogen is a very abundant element in the stars, this phase is very long and therefore it is more likely to observe a star in this region of the diagram. The other phases of evolution, that correspond to the region of the red giants, or the horizontal branch, are a lot quicker, and therefore it is less likely to find stars here.

Gliese 623b, one of the smaller stars in our Galaxy. Its distance from us is 25 light years, in the Hercules constellation; it is the smallest component of a binary system. It is 10 times less massive than the Sun and 60 thousand times less bright. If its distance from us were that of the Sun, it would appear only 8 times brighter than the full moon. (HST)

The methods of investigation of astronomical spectroscopy and photometry are applied not only to the stars, but also to stellar clusters and to galaxies; one can define the colours of a galaxy, or its spectrum, just like one would do for a single star, considering the result of the superimposition of the emissions of the various stars that compose the galaxy.

Image of the NGC 300 galaxy in different spectral bands:
from top to bottom, in the radio continuum,
in the radio at the wavelength of 21 cm, in the far infrared,
in the Halpha line, in the optical band and in the X band.