Stellar Spectra and the Secrets of Starlight

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In 1842 when Comte (the father of Sociology) penned the words quoted above it really did seem that detailed knowledge of the stars was "forever denied to us". By that time astronomers were beginning to get an inkling of just how vast the distances between stars and how utterly unlikely it would (will?) be to visit a star. But the science of spectroscopy was just beginning and, before the middle of the next century, spectroscopy was yielding up many of the secrets of the stars. In fact one of the things we can say with a great deal of confidence (in most cases) is the temperature of a star.

Spectral Lines and Spectral Line Intensity Profiles

The following shows a spectrum from the star Vega. The prominent dark lines are due to hydrogen gas in the atmosphere of the star. These are called absorption lines.

Figure 6.14 A low resolution spectrum of the star Vega showing prominently the Balmer lines of hydrogen.

In the past this was the most common way of displaying spectra - they were usually produced photographically. With the advent of electronic detectors, however, it is much more common to look at the spectrum "graphically". Since the light detectors (usually CCD's) record light levels digitally it is easy to turn an image like the one seen above into a graph that relates intensity to wavelength. This provides one with a very useful tool called a spectral-line intensity profile or just line profile. The following illustrates this idea: 

	This is a spectrum of the star bluish-white star HD 21619. To an experienced eye the dark bands are Hydrogen absorption lines and, despite what Auguste Comte may have thought, we know that the temperature of this star is about 9000 K. The top figure shows the photographic form of the spectrum while the bottom is a line intensity trace. The units for wavelength are Angstroms.
Figure 6.15 Photo and trace versions of a stellar spectrum

Temperature, Composition and Cosmic Fingerprinting!

Perhaps the most basic things that a spectrum tells us are:

• the temperature of the object
• the composition of the object

These two ideas are inter-linked, however. For example, we now know that a star is mostly hydrogen gas. The spectra of stars such as Vega are dominated by the Balmer lines of the hydrogen spectrum. A cooler star, however, has a much different spectrum in which it might be very difficult to detect hydrogen at all! The following spectra are from a star of surface temperature about 9000 K (Balmer lines dominate the spectrum) and a star with a temperature of about 3200 K. The latter spectrum is a complex pattern of lines caused by many elements and simple molecules - even though most of its atmosphere is hydrogen!

Figure 6.16 When a star has a temperature of around 10 000 K its spectrum is dominated by hydrogen lines (Wavelength is measured in Angstrom units; 1 Angstrom = 0.1 nm)
Figure 6.17 Cool stars (T < 4000 K) have very complex spectra with many lines.

Even though the atmosphere of a star is mostly hydrogen the small traces of the other elements all contribute to producing the spectrum for the star. Figure 6.18 shows how various atoms and molecules contribute to the formation of spectral lines as a function of temperature.

Figure 6.18 How temperature affects the strength of spectral lines.

Recall that it is how electrons are distributed in the energy levels of an atom that will determine what kind of photons will be emitted. If you look at Figure 6.18 you will notice that the H curve (Hydrogen) peaks at around 10 000 K but quickly tails off on either side of this temperature. This happens because at very high temperatures the hydrogen is almost completely ionized and hence has lost its electron and its ability to absorb (or emit) photons. At lower temperatures the hydrogen is not excited - it does not have enough electrons in excited states to contribute significantly to the formation of spectral lines. Other atoms exhibit a similar behaviour.

Example 6.6 Star "X" has a spectrum with very weak hydrogen lines, strong ionized calcium (CaII) lines and iron (FeI) and ionized iron (FeII) lines. Star "Y" has very weak hydrogen lines, faint lines due to ionized silicon (SiIV) and stron lines due to helium (HeI) and ionized helium (HeII). Estimate the temperature of each star.

Solution: Figure 6.18 is the key here! The graph shows the line strength for various species of atoms and their ions. Star "X" could easily be our own sun given the description. At 5800 K you would have a spectrum dominated by iron and calcium. Star "Y" must be very hot to have HeII lines so it is likely > 30 000 K.

The temperature sensitivity of spectral line strength provides us with a very precise thermometer! The applet BalmerThermometer (shown in Figure 6.19) illustrates this.

Figure 6.19 Applet Balmer Thermometer illustrates the dependence of line depth on temperature.

It's actually a bit more complicated than this but by looking a specific combinations of spectral lines and their strengths astronomers are able to determine very precise star temperatures (typically to within a few degrees!)

Also, implicit in all of this is the ability to determine the composition of stars by noting the "elemental signatures" of the spectral lines. So, again Comte seems dead wrong, not only can we know the temperatures but we can also know what stars are made of!

Ever since astronomers began looking at the spectra of stars they had a "hunch" that there was an underlying "pattern" or classification system that would point to deeper, underlying principles governing how stars work. Finding a classification system was a daunting challenge however because the essential physics of atoms and light that you learned about earlier had yet to be discovered. The first successful classification system and its link to the physics of stars was provided by two astronomers early in the last century.

Annie Jump-Cannon lead a team of female astronomers who were given a very "un-glamorous" job of finishing the Henry Draper Catalogue of stars. It was during this work (1896 - 1900) that the problem of classifying stars according to their spectra lead Cannon to propose the spectral classification system still used today. This is commonly called the Harvard Classification System and is summarized in Table 6.4. The first successful explanation of why the classification system worked and what it told us about the nature of the stars had to wait until about 1925 in the doctoral work of one of the great astronomers of the 20th century, Cecilia Payne. British born, Payne completed here PhD under Harlow Shapley at Harvard. In her work she demonstrated that the sun and other stars were composed mostly of Hydrogen. This was surprising because the spectrum of a star like the sun has virtually no Hydrogen spectral lines but does have numerous iron lines! Figure 6.18 helps explain this "mystery" and this work was initiated by Payne. Class Temperature Apparent color Hydrogen lines Other noted spectral features O ≥ 30,000 K blue Weak ionized helium lines B 10,000–30,000 K blue white Medium neutral helium A 7,500–10,000 K white to blue white Strong ionized calcium (weak) F 6,000–7,500 K white Medium ionized calcium (weak) G 5,200–6,000 K yellowish white Weak ionized calcium (medium) K 3,700–5,200 K yellow orange Very weak ionized calcium (strong) M ≤ 3,700 K orange red Very weak Titanium oxide lines Table 6.4 The Harvard Classification System Figure 6.22 provides an applet (SpectralType) that illustrates this for you.
	Figure 6.20 Annie Jump-Cannon inspecting a spectral plate at the Harvard Observatory.
	Figure 6.21 Cecilia Payne was the first astronomer to apply the science of quantum mechanics to the atmospheres of stars.

Figure 6.22 SpectralType allows you to explore how the appearance of a stellar spectrum is related to the temperature of a star.

Example 6.7 Sort the following 3 spectra from highest temperature star to lowest and attempt to identify the spectral type in each case. Explain how you did this.

Mystery Star #1	Mystery Star #2	Mystery Star #3

Solution: The first thing to note is that the hydrogen lines are very weak in two of the stars (2&3). This means they are either very hot or very cool. Next, star 2 has a very complex spectrum with lots of lines but two very conspicuous lines at the blue end - this makes it easy to recognize as a K star! Star 1 has very prominent hydorgen lines so it is likely an early F-star or an A-star. Star 3 has very weak lines but if you look carefully you can see helium lines - this guy is hot! So, the order from hottest to coolest is: 3 -- 1 -- 2

Pop Quiz!

The Doppler Effect

Absent mindedly you step into a busy intersection without looking. A blaring car horn warns you back and as the car speeds by you can't help but hear the rising and then dropping pitch of the horn. You have just heard a classic example of the Doppler effect.

• Wavelength is affected by motion. If a wave source moves toward you the frequency (pitch) of the wave goes up. If the wave source moves away from you the frequency drops. When the wave frequency rises the wavelength becomes smaller or bluer: blue shift. When the wave frequency drops the wavelength becomes bigger or redder: red shift. Figure 6.23 illustrates this.

Figure 6.23 Diagram showing Doppler effect. Waves are "compressed" in the direction of motion resulting in a shortened wavelength (or blue-shift).

The applet Doppler which is provided as Figure 6.24 gives you an interactive illustration of the Doppler Effect.. Experiment with how the wavecrests varying as you change the velocity of the waves source. If you click the "show ruler" option you can measure the distance between wavecrests and thereby measure the Doppler shift.

Figure 6.24 Doppler is an interactive applet illustrating the Doppler effect.

Example 6.8 Use the applet Doppler in Figure 6.24 to anser this. Leave the velocity set at zero (its default value). Press "go" and after a few seconds press"pause" to freeze the motion. Use the ruler to mesure the distance between wave crests. What is the wavelength of the source (note that the ruile is in units of micro-meters or 10^-6 m)? What part of the spectrum is this in?

Solution: The wavecrests appear 2 ruler units apart so the wavelength of the source is 2 micro-metres of 2 x 10 ^-6 m = 2000 nm. This is an infrared source.

But Officer I Was Only Going ...

The excuse usually doesn't work.  The traffic cop is using the physics of the Doppler Effect every time she aims a radar gun at an unsuspecting motorist.  Astronomers routinely using the Doppler effect to measure the approach or recession of moving objects.  The amount by which a spectral line is shifted is in simple proportion to how fast the object is moving with respect to light.  So, if you are traveling at 10% the speed of light (VERY FAST!) the spectrum coming from you will be shifted by 10%.  Let's assume that you are moving away from me.  The light from you will be red shifted by 10%.  A hydrogen line normally at 650 nm will now be seen at 650 + 65 = 715 nm.
We can express this as a simple formula:

Example 6.9 When you compare the spectrum of sodium from a faint star with the spectrum from sodium gas produced in your lab on earth you find that the green absorption line normally seen at 589 nm is now at 570 nm.  What can you conclude about the motion of this object?

Solution:  First, notice that the wavelength has gotten shorter (blue-shifted).  The object is moving toward you.  Next, use the doppler shift formula and determine "delta lambda":

This means that you are going 0.032c (a little over 3% the speed of light)  or v = 0.032(300 000) = 9677 km/s!

Link to a Case Study using the Dopper Effect to measure the motion of two galaxies...

How We Use Doppler Shifts to Understand Spectral Lines

Any motion in an absorbing or emitting atom will give itself away through the Doppler Effect. Because of this we can detect and measure:

• rotation
• atmospheric turbulence
• orbital motion (we will consider this in a future lecture)

Detecting Rotation

Imagine watching a whirling star. Part of the star will rotate toward you (blue shift) while the other edge (limb) will rotate away from you (red shift).  Since the light that we see has all the light from all the various parts of the star mixed together, the net result is a blended and broadened line. We call this effect rotational line broadening. The applet RotationalBroadening in Figure6.25 illustrates the effect that different rotation rates would have on spectral lines.

Figure 6.25 Rotational Broadening allows you to adjust the rotational speed of a star and observe the effect it would have on a stellar line profile.

Detecting Turbulence

The chaotic tumbling motion in the atmosphere of some stars also "smears out" spectral lines. Figure 6.26 illustrates this.

 

Figure 6.26 Diagram depicting the broadening effect due to atmospheric turbulence in stars.

 Although both rotation and turbulence broaden spectral lines, they do so in slightly different ways that can be "disentangled" through careful analysis of the shapes of the spectral lines. Usually both effects are present and combine to broaden spectral lines

The Effect of Pressure on Spectral Lines

In addition to the Doppler Effect, spectral lines can also be effected by the pressure of a gas. In general pressure is a measure the frequency and vigor of collisions between atoms in a gas. The higher the pressure of a gas the broader the resulting absorption or emission line. This is referred to as pressure broadening.

Figure 6.27 Illustation of the differences in appearance of line profiles for a supergiant star (upper half) and dwarf star.

Case Study - Comparison of Rotation and Pressure Broadening Effects in Marakb and Deneb

Figure 6.28 Applet PressureBroaden allows you to experiment with the effect of stellar photospheric pressure on the width of the red Hydrogen alha line in a stellar spectrum.

Practice

1. An astronomer measures a hydrogen spectrum and discovers that a line normally at 656 nm is now at 659 nm.  What can you tell about the motion of the gas producing this?
2. Supposing one side of a star is approaching you (because its rotating) at 20 km/s and the other side is receding at 20 km/s.  What effect will this have on a spectral line whose wavelength is 500 nm as measured in your lab?

To understand what stellar spectra are and what they tell us about the stars

Chp 7.3

9.3