■ Atmospheric transmission as a function of wave-length.The curve shows the fraction of transmission at each wavelength. Note the good transmission in the radio and visible parts of the spectrum.Also note a few narrow ranges, or "windows" of relatively good transmission in the infrared. [IRAM]

some narrow windows in the infrared. A window is simply a wavelength range in which the atmosphere is at least partially transparent.

Until relatively recently, astronomers could only gather information in the visible part of the spectrum, because of the lack of equipment. Much of the development of astronomy was biased by this handicap. In the middle of the 20th century, the radio part of the spectrum was opened for astronomical observations (taking advantage of equipment developed for radar in WW II). Even more recently, other parts of the spectrum have become available to us, due in part to observatories orbiting the Earth. Observing in various parts of the spectrum will be discussed throughout this book.

2.3 I Colors of stars

2.3.1 Quantifying color

When we look at a star, we would like to know how much energy it gives off at various wavelengths. We sometimes refer to a graph, or some equivalent representation, showing intensity as a function of wavelength (or frequency) as a spectrum. It is not really proper to talk about the energy given off at a particular wavelength. If we can specify a wavelength to an arbitrary number of decimal places then even a small wavelength range has an infinite number of wavelengths. If there was even a little energy "at" each wavelength, then there would be an infinite amount of energy.

Instead, we talk about the energy given off over some wavelength (or frequency) range. For example, we define the intensity function 1(A) such that 1(A) dA is the energy/unit time/unit surface area given off by an object in the wavelength range A to A + dA. Similarly, I(v) dv is the energy/ unit time/unit surface area given off by an object in the frequency range v to v + dv.

Star cluster H and Chi Persei. (We will talk more about clusters of stars in Chapter 13.) Notice the wide range of star colors. [NOAO/AURA/NSF]

Star cluster H and Chi Persei. (We will talk more about clusters of stars in Chapter 13.) Notice the wide range of star colors. [NOAO/AURA/NSF]

When we make a plot of 1(A) vs. A for a star we find that the graph varies smoothly over most wavelengths. There are some wavelength ranges at which there is a sharp increase or decrease in 1(A) over a very narrow wavelength range. These sharp increases and decreases are called spectral lines and will be discussed in the next chapter. In this chapter, we will be concerned with the smooth or continuous part of the spectrum. This is also called the continuum.

When we look at stars we see that they have different colors. Stars with different colors have different continuous spectra. In Fig. 2.4, we look at a cluster of stars, and note a wide range of colors. If we took a continuous spectrum of various colored stars, we would find that stars that appear blue have continuous spectra that peak in the (shorter wavelength) blue. The color of a star depends on its temperature. We know that as we heat an object, first it glows in the red, then turns yellow/green, and then it turns blue as it becomes even hotter.

We can therefore measure the temperature of a star by measuring its continuum. In fact, it is not necessary to measure the whole spectrum in detail. We can measure the amounts of radiation received in certain wavelength ranges. These ranges are defined by filters that let a given wavelength range pass through. By comparing the intensity of radiation received in various filters, we can come up with a quantitative way of determining the color of a star and therefore its temperature.

2.3.2 Blackbodies

We can understand the relationship between color and temperature by considering objects called blackbodies. A blackbody is a theoretical idea that closely approximates many real objects in thermodynamic equilibrium. (We say that an object is in thermodynamic equilibrium with its surroundings when energy is freely interchanged and a steady state is reached in which there is no net energy flow. That is, energy flows in and out at the same rate.) A blackbody is an object that absorbs all of the radiation that strikes it.

A blackbody can also emit radiation. In fact, if a blackbody is to maintain a constant temperature, it must radiate energy at the same rate that it absorbs energy. If it radiates less energy than it absorbs, it will heat up. If it radiates more energy than it absorbs, then it will cool. However, this does not mean that the spectrum of emitted radiation must match the spectrum of absorbed radiation. Only the total energies must balance. The spectrum of emitted radiation is determined by the temperature of the blackbody. As the temperature changes, the spectrum changes. The black-body will adjust its temperature so that its emitted spectrum contains just enough energy to balance the absorbed energy. When the temperature t« —

Frequency (1015 Hz)

Blackbody spectra. Note the shift of the peak wavelength to higher frequency (shorter wavelength) at higher temperature. Note also that, at any frequency, a hotter blackbody gives off more radiation than a cooler one. (a) Intensity as a function of frequency. Notice the big change in intensity with only a factor of three change in temperature. For this reason, we often find it useful to make a plot such as the set of curves in (b), which show the log of the intensity as a function of the log of the frequency.

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