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Astrophysics for People Not in a Hurry

Douglas MacDougal

Updated: Mar 6, 2024


I was thumbing through Neil deGrasse Tyson’s Astrophysics for People in a Hurry. Nice, easy writing from an engaging popularizer. I wasn’t in any particular hurry, though, but if I were, there’s also the shorter version, the author’s Summary of Astrophysics for People in a Hurry. Maybe there’s a two-page version somewhere? But wait, what’s the rush? I am all for bringing science down to earth, but does the public really need to be whisked through the subject like hurried shoppers in a grocery store? Are we mistaking information for understanding? Let’s slow down – just a little – and look at what this astrophysics stuff is about, perhaps with some historical perspective, and figure out why people, even hurried, harried people, might be interested.


What is astrophysics?


If I had to define astrophysics in one sentence, I’d say: The study of selected wavelengths of the electromagnetic spectrum of the sun, stars, and nebulae to understand their physical nature.


In the words of A. S. Eddington, astrophysics in the early 20th century was “the study of the mechanical and physical conditions in the deep interior of the stars,” in order to “throw light on external phenomena accessible to observation.” The quote is from the beginning of Eddington’s classic The Internal Constitution of the Stars published in 1926. Going earlier, we see that astrophysics was an established discipline at the turn-of-the-century. Historian of astronomy Agnes Clerke described the state of research in the subject in her 1903 book, Problems in Astrophysics. Given the field was then young, the book is mostly a compendium of what we don’t know. It’s divided into problems in solar physics and problems in sidereal physics – the sun and the stars. The latter encompassed classification of stellar spectra, helium stars, hydrogen stars, stars with “fluted spectra,” carbon stars, variable stars, and various types of nebulae, among other things.


She distinguished this “new astronomy,” as she called it, from the art of calculating the motions of celestial bodies governed by the law of gravity. The latter, Newton’s triumph, is what she called “practical astronomy.” Wonderful as it is – “the most perfect of the sciences” – it tells us close to nothing about the constituent nature of the things it studies:

Gravity… is a force of the utmost generality in the way it affects matter. It takes no notice of distinctions of kind or quality. The substances acted upon may be hot or cold, dense or rare, elementary or compound; they may be of any imaginable chemical or mineralogical constitution; they may be in any state of aggregation; they may be organic or inorganic; no difference is perceptible; gravity is concerned solely with mass, and is measured strictly by movement; and from gravitational inquiries, accordingly, mass and movement can alone be learned [1].

In other words, mass and movement will never tell us what things are made of or how they work internally [2]. Yet if we can study the light from them – with (spoiler alert) a spectroscope – new windows open to investigation all sorts of qualitative properties.

There’s a sense of excitement about the wonderful possibilities of spectroscopy that comes through in early books. Samuel Pierpont Langley stated the situation simply in his 1888 book, The New Astronomy: “[T]he prime object of astronomy, until very lately indeed, has still been to say where any heavenly body is, and not what it is…But within a comparatively few years a new branch of astronomy has arisen, which studies sun, moon, and stars for what they are in themselves…” [3]


The century’s turn seemed like the dawn of a new era. The astronomer James Edward Keeler, (1857-1900) who undertook groundbreaking spectroscopic studies of the rotating rings of Saturn, wrote that “the light which reveals to us the existence of the heavenly bodies also bears the secret of their constitution and physical condition.” “The spectroscope placed new and hitherto undreamt-of powers in the hands of men. It is to the astrophysicist what the graduated circle and the telescope are to the astronomer.” [4] The spectroscope was the Promethean gift to man. The launch of a new journal is one sign of the birth of a new science. Keeler wrote those words in the publication he founded in 1895 with George Ellery Hale: it was (and still is) called the Astrophysical Journal, the premier publication on the subject in the world.


Since then, of course, astrophysics has grown through the decades into a monster subject encompassing virtually every aspect of astronomy that can be treated with physics – though traditionally still in the main focused on stars in all of their exotic variety, including exploding stars, neutron stars, magnetars, and things we probably haven’t yet discovered, and things in their environment such as nebulae and interstellar matter affected by their radiation. And now on the front page of The New York Times is a radio-wavelength picture of a black hole at the center of our own Milky Way galaxy, in Sagittarius A*, depicted above, the result of several years of combining and processing data from eleven radio telescopes around the world with the assistance of five million supercomputer simulations [5].

A Short Story of How Astrophysics Came to Be

To understand more what the science of astrophysics is and how it came to be, think first of the following key words: telescope + spectroscope, + photography. Around those words, and the work of some interesting people, arose a whole new science of the sky. The wavelength-by-wavelength analysis of light in the context of astronomy began early. One might pick any number of events to mark birth of astrophysics.

A good candidate might be the deployment of Langley’s 1881 bolometer. He used it to discover previously unknown infrared lines in the solar spectrum (discussed in my July, 2022 Sky & Telescope article, Charles Greeley Abbot and the Epic Hunt for the Solar Constant). Another might be the use after 1859 of the flame spectroscope by German scientists Gustav Kirchhoff and Robert Bunson to identify chemical elements by their emission spectra; they plainly foresaw the astronomical implications.

But it was with the experiments of Englishman William Huggins that it became clear that adding a spectroscope to the telescope and taking a picture of the resulting spectrum (utilizing the advantages of the new science of photography) yielded in their combination a new and vastly powerful tool. For the first time, astronomers could peer into the actual chemistry of stars and discover their chemical compositions. They could do this by comparing the photographed spectral lines they saw in stars and nebulae with the lines they could produce in the laboratory.

Stars could now be classified according to their spectra. Most stars seemed to have dark spectral lines (called absorption lines) at particular places in an otherwise continuous rainbow-like spectrum. Stars seemed to display various types of individual spectra, revealing different patterns of lines, yet maintained strong similarities among a handful of types – just as the large population of diverse people on Earth have relatively few discrete combinations of eye and hair colors. A few stars (including the Wolf-Rayet type) and many nebulae and planetary nebulae seemed to be dominated by bright spectral lines, called emission lines, evidence of energized atoms in gaseous environments.

To make sense of all these differences in stars, Annie J. Cannon and her team at Harvard led by Professor Pickering spent years poring over the spectra of thousands of stars on photographic plates. The parallel early 20th Century development of quantum physics and deepening understanding of the interaction between matter and radiation, began to fit together with what the stars were saying to Ms. Cannon in their subtle bar-coded language of the spectra. It ultimately became known (though earlier suspected) through Cecilia Payne Gaposhkin’s work in the 1920s that hydrogen was the main (but not sole) constituent of stars and that stellar temperatures were the chief causes of the differences of stellar spectra [6].

Spectral studies were not limited to stars. Spectroscopy made possible the analysis of solar, planetary, and even galactic rotation; the shifts in the wavelengths of spectral lines allowed the measurement of motion. Astronomers turned the spectroscope to “spiral nebulae” (now referred to as galaxies, but not then known to be extra-galactic), clusters of stars, and gaseous nebulae. As we discussed in our earlier blog, Vesto Slipher hung an enormous prism on the end of the 24-inch Lowell telescope in Arizona and noticed surprisingly high speeds in galaxies he surveyed spectroscopically. Edwin Hubble in the 1920’s built on this work, and by comparing red shifts with distances derived through other means (mainly Cepheid variable stars), he made the astounding discovery that distant galaxies were receding faster than nearby ones, and at a rate that was proportional to the distance.

What makes spectral lines?

This is a big subject and tremendously fascinating. It involves the key players in the revolution that dominated the early 20th century physics. It is indeed almost the whole subject of astrophysics! We’ll just barely touch on one aspect of it in the context of the simplest atom, hydrogen. Since the atom of hydrogen has one proton and one electron, it affords a simple model for understanding how Bohr’s quantum process works to create spectral lines. It is also appropriate to begin with hydrogen since it is the most abundant element in the universe and in stars (though this fact was not known at the time). Its spectral lines are strikingly evident in many stars, including the sun.

To begin to understand stars, we must understand atoms. Let’s contemplate that idea for a moment: to grasp the biggest things in the universe we must know the smallest.

In 1913 the great Danish physicist Niels Bohr (1885 – 1962) conceived of a simple model of the hydrogen atom (based in part upon the earlier-developed notion of the nuclear atom advanced in 1911 by Ernest Rutherford). He figured out that electrons can absorb photons in packets (quanta) of energy causing them to jump to a discrete higher energy level in the atom. Electrons in higher energy levels (above their ground state nearest the proton nucleus) can give up packets of energy by emitting photons. How they do it is what spectral lines are all about.

Bohr came up with two great principles or postulates that wonderfully explained spectral lines in relation to the above phenomena:

  • First, Bohr said that electrons in atoms are allowed only a discrete number of orbits (also called energy levels) – no in-between orbits allowed.

  • Second, Bohr announced that radiation in the form of a discrete quantum (photon) is emitted or absorbed when electrons jump from one orbit another. (Since they cannot exist between orbits, electrons must “jump” from one orbit to another.) The energy of this quantum of radiation is equal to the energy difference between orbits. When a photon of the just the right energy is absorbed by an electron, it jumps to a higher energy orbit, the energy difference between orbits exactly corresponding to the energy absorbed. This is called excitation. When an electron jumps back to a lower energy orbit, it emits a photon of an energy (frequency) exactly equal to the difference of the energy levels in the two orbits. This is called de-excitation or relaxation.

The gravity well is a useful analogy

A good way of understanding the Bohr energy level concept is to think of the analogy of a “gravity well.” A large mass, such as the Earth, can be thought of as a well of gravitational energy, and it takes work (energy to move a mass over a distance) to remove a mass from it. The initial effort at “liftoff” for example, where the distance to the Earth’s mass center is small, takes the greatest amount of work. As the spaceship moves farther and farther away, the amount of energy to overcome gravity to go the next kilometer, then the next, diminishes by the inverse square of the distance (though this kinetic energy to move it is not lost, but is accounted for (conserved) by an increase in the mass’s gravitational potential energy). At some distance, the additional energy to move the spaceship becomes negligible, and the spaceship is essentially deemed to be freed (escaped) from Earth’s gravity.

With the earth’s gravity in mind as a metaphor, let’s look at the little atom. The Bohr hydrogen atom with its positively charged nucleus (a proton) attracts the negatively charged electron. The attraction on the electron is the greatest in the ground state closest to the nucleus, at energy level n = 1. We can call this inner circle, n = 1, a state a zero-energy (corresponding to zero electron volts (eV)), where the electron is stable, relaxed, and “unexcited.” The amount of energy to jump to from n =1 to n = 2 in the hydrogen atom is 10.2 eV (electron volts). This measure, different for each atom, is sometimes called the excitation potential of an atom. After that takes less energy to bump it to the next higher energy level (think of them as concentric circles), and still less each rung higher. Thus, an electron beginning at n = 2 jumping to level 3 needs 1.89 eV; going from 3 to 4 takes only .66 eV; and hopping from 4 to 5 takes still less, .31 eV, etc., each level requiring less than the amount needed to reach the level just before. The diagram below, generated by my computer, shows the energy levels of the hydrogen atom from n = 2 to 9 (arbitrarily stopped at 9), the so-called "Balmer" series discussed below. The solitary proton is in the center. You can see the lines getting closer and closer as we look outward from the proton:


What happens when we keep adding energy, i.e., such that electrons get excited to states of even higher energy? As one goes farther out, as you can see, the differences between energy levels become still less and extremely small, where near the limit the electron is poised on the threshold of breaking loose from that awful proton’s nagging pull. Now, with the slightest addition of more energy, the electron will be freed from the nucleus and the hydrogen atom is said to be ionized. The ionization of the hydrogen atom, exciting the electron from the ground state till it’s out the door (from n = 1 to n = ∞ in the equation below) takes a high-energy photon of λ = 91.17636 nm or 13.6 eV. [7] That is, the sum of all the ever-diminishing increments of energy needed for escape eventually arrive at a limit, the magic ionization value of 13.6 eV for hydrogen. This measure, different for each atom, is sometimes called the ionization potential of an atom. At that point the electron is unbound and free. It’s the metaphorical equivalent to the energy needed for a rocket to achieve escape velocity, where it is no longer bound by the gravitational force of the earth. For the hydrogen atom, 13.6 eV is just the right amount of energy necessary to wrestle the electron free. Here in this graph I generated you can see that as the excitation energy become less, the wavelength becomes longer, most being in the infrared; the vertical dotted lines depict the range of the visible spectrum:

There is of course a caveat with these metaphors. With quantum theory, it became evident that the simple Bohr “solar system” model of the atom, – a sort of Newtonian-mechanical model – could not describe the actual, strange physical reality of the inside of the atom, the probability cloud that the electrons seem to inhabit. Nevertheless, the metaphors are useful for understanding and, amazingly, the calculations work!


Sirius Math

The best way to get a practical taste of this subject is to dive right in. Let’s look at the star Sirius. The bright, close, fast-moving first magnitude star Sirius (α Canis Majoris) was among the first stars discovered whose spectra to display strong and broad absorption lines of hydrogen, and for that reason stars of that type were put in the (then) lead-off spectral class A. The strongest absorption bands were at wavelengths λ656.3, λ486.1, and λ434.1 nanometers (billionths of a meter) (the lower numbers meaning shorter wavelengths and thus higher energies than the longer wavelengths). A portion of the Sirius spectrum is pictured below, with wavelengths in Ǻngstroms (ten times the nanometer). What order determined the placement of the black vertical bands?





In 1885 a Swiss schoolteacher of mathematics named Johann Jakob Balmer (1825-1898) had discovered that the wavelengths of the lines of hydrogen created in a laboratory here on earth, and earlier measured by the Swedish physicist Anders Jonas Ǻngström (1814-1874), seemed to display a kind of regular pattern. Balmer discovered that they obeyed a simple relationship below where R is a constant [8] and where n is any integer greater than 2. By making n = 3, 4, 5 … Balmer was able to recreate the wavelengths (1/λ or “wave numbers” as they are called) of the visible lines of hydrogen. These lines are now called the “Balmer series.”

We can use Balmer’s equation to show that the dark absorption lines discovered in the spectrum of Sirius can be explained by the presence of hydrogen in the star. Balmer came upon his equation by empirical methods; he was unaware of the existence of the Bohr orbital levels or atomic theory, which was still about 30 years in the future. But from our perspective, we can see that the problem implies that for each observed hydrogen absorption line in Sirius, hydrogen electrons have gained (absorbed) a discrete quantum or clump of energy from photons of that energy, and thus have jumped up (since we are talking about absorption lines in the star) from one lower energy level to a higher level. (The higher the energy of the photon quantum, the shorter is its wavelength.) The absorptions of photons in these places (corresponding to precise wavelengths (energies) of light) create the dark spaces (lines) in what would otherwise be a bright continuous spectrum of starlight. To see if we can find a match for spectrum of Sirius, we insert these values for n (3, 4 and 5) and solve for λ. If we do the math for n from 2 to 8, the equation will generate the following wavelengths in the chart below. We could keep working our way up (and outward from the nucleus) in absorbed photon energy by putting n = 6, 7, 8 … and the wavelengths would get shorter and shorter, out of the visible range of the spectrum, and into the ultraviolet, blocked too by earth’s atmosphere. Again, if the jump is from the lower energy level to a higher energy level, it creates an absorption line. If it is a jump back from higher to lower level, it creates an emission line [9].



You can see that the first three wavelengths correspond to the ones mentioned above found in spectrum of Sirius. These prominent lines are now called the hydrogen alpha, hydrogen beta and hydrogen gamma lines. Can you identify them in the spectrum graph of Sirius below, where the dips reveal absorptions? Can you also see how they match the dark bands in the spectrum of Sirius above?





Balmer began his series with level 2, because that worked empirically. Other investigators used the more general equation below with 1 as the starting level (Lyman series) (i.e., m = 1) ; with 3 as the starting level (Paschen series); with 4 as the starting level (Brackett series); and with 5 as the starting level (Pfund series), ,




where for absorption m is the “from level” and n, again, is the “to” level in the hydrogen atom; for emission it is the reverse. Here are the series’ wavelengths for hydrogen, run together in order (and somewhat overlapping) with my color coding. Most of the series are in the infrared:

 

NOTES [1] A. Clerke, Problems in Astrophysics, p.2 (London: Adam & Charles Black, 1903). [2] Of course, we can tell the densities of objects in space if they have companions revolving around or with them. [3] S. P. Langley, The New Astronomy, p. 3 (Boston: Ticknor & Co., 1888). [4] Quotes are from ibid, p. 3. [5] The reference is to the April 13, 2022, edition of The New York Times. [6] Incidentally, Dava Sobel’s excellent book, The Glass Universe tells the story of these intelligent and dedicated Harvard women. And Donovan Moore’s, What the Stars Are Made Of is about Cecilia Payne Gaposhkin’s life and discovery of the predominance of hydrogen in stars. [7] The Rydberg constant is the reciprocal of this ionization wavelength (i.e., the ionization wave number). At this point, at this far ultraviolet wavelength, the hydrogen electron has altogether escaped from the atom, and we say that the atom is ionized. The electron, now having been released from its quantum bondage to the atom, is free to have any energy. Any energy in excess of that needed to ionize the atom is conserved in the form of the electron’s kinetic energy, that is, in its energy of motion, with higher energies meaning higher electron velocities. The absorption spectrum becomes continuously dark past this point (into the ultraviolet), since photon absorptions by electrons (which increase their velocities) are not limited to select bands of wavelengths. [8] R is the Rydberg constant for hydrogen, 0.01096775524, expressed here in the standard SI units of nanometers (billionths of meters). The Rydberg constant can be derived from quantum theory of radiation, a topic for another day! [9] The Rydberg equation applies equally to emission spectra. Emission spectra, where bright lines instead of dark appear in the same precise places for the same types of electron transitions, are caused by electrons relaxing back to lower energy orbitals from higher energy orbitals, giving up their quanta of energy in the form of photons. The Rydberg equation for the hydrogen atom works for such emissions, with “to” and “from” roles reversed. Absorption and emission transitions occur from one excited state to other excited states by all the same rules.

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