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Home , Balmer series, Henry Draper catalogue

Astronomy 218 Classifying A wide variety of Stars We have built a fine catalog of nearby and apparently bright stars, but how do we make rhyme or reason? Luminosity Temp. Radius Mass B 0.025 4.7 0.007 0.98 Proxima Cen 0.0017 0.52 0.15 0.12 Barnard’s Star 0.0045 0.56 0.2 0.16 α Cen B 0.5 0.91 0.87 0.91 Sun 1 1 1 1 α Cen A 1.52 1 1.22 1.1 Sirius A 23 2.1 1.9 2.12 55 1.6 2.8 2.14 Arcturus 160 0.78 21 1.1(?) 63,000 1.9 70 17 Betelgeuse 120,000 0.55 >900 18 Stellar Overload With billions of stars in the sky visible to a large enough telescope, it can be hard to find a pattern in the details of the myriad of individual stars. Stellar Taxonomy If we wish to proceed from observations of a large number of individual stars to a general understanding of how stars function, we need a classification system. Taxonomy is the science of classification. Originating in biology as a system for classifying organisms, a taxonomy, or taxonomic scheme, is a system of hierarchical classification. The root includes all characteristics common to the entire set. From this root, a successive divisions branch from common types, with each sub-type adding a unique characteristic to the set of characteristics inherited from the overlying type. The use of taxonomy is a fundamental contribution of science to other areas of human thought. Designing a Scheme In order to classify stars, quantifiable measures are needed on which to base sub-types. From the demonstrated relationship between mass and lifetime, mass would seem a likely basis for stellar classification. However, the difficulty in measuring mass (for non-binary stars) make it unsuitable for observational classification. The observed mass-radius relation, R ∝ M 0.8, would make radius a desirable measure, but it is also difficult to measure in general. Likewise, the observed mass-luminosity relation, L ∝ M 4, makes luminosity a useful surrogate, but measuring L depends on measuring distance. Stellar Temperature The simplest characteristic of a star to measure, regardless of the distance, is the temperature. Whether via Wien’s law or color indices, temperatures can be measured at the limit of detectability. By combining the Stefan-Boltzmann law,

2 4 L = 4πR σSB T with the mass-radius (R ∝ M 0.8 ) and mass-luminosity (L ∝ M 4) relations yields a relation between mass and temperature M 2.4 ∝ T 4 or T ∝ M 0.6 While this relation is only valid for “normal” stars, like the mass-radius and mass-luminosity relations, for such stars T is a useful surrogate for M. Stellar Spectra Stellar spectra are not simply blackbody curves, they contain a number of spectral lines. These reveal to us much more than simply the temperature but the atomic composition and surface gravity as well. Classify ≠ Understand Unfortunately, the need for a stellar classification scheme arose before Wien derived his displacement law in 1893 or Planck explained the blackbody in 1901. In 1890, Edward Pickering, assisted by , published the Draper Catalogue of Stellar Spectra, with spectra of 10,000 stars. They established a stellar classification scheme based on the strength of the Balmer lines. The Draper Catalogue scheme, also called the Harvard classification system, assigned the letters A-N (but not J) in order of decreasing strength of these lines, plus O for stars whose spectra showed weak Balmer lines but other strong lines, P for planetary nebulae. Stars that did not fit into A-P were labelled Q. Balmer Series

Hα Hβ Hγ Hδ Balmer Limit The series of optical spectral lines from carry the name of Johann Balmer (1825-1898) who in 1885 showed that these obeyed the relation

for m > 2 (1854-1919) generalized Balmer’s result in 1888, the -1 Where RH= (91.16 nm) Lyman & Paschen The nature of the formula the Rydberg created in 1888 suggested the existence of additional series of lines.

-1 RH= (91.16 nm)

Between 1906 and 1914, Theodore Lyman (1874-1954) measured the series of n = 1, the .

In 1908, Friedrich Paschen (1865-1947) observed the n = 3 series, which lie in the infrared.

The n=4 series is named for Frederick Brackett, the n=5 series for August Pfund and n=6 for Curtis Humphreys. Bohr’s Model Bohr’s 1913 quantum model for the provided a physical basis for the empirical relations of Balmer and Rydberg. An with L = nℏ has energy An atomic transition from the n2 orbital to the n1 orbital emits a with = (91.16 nm)-1 Beyond Bohr’s Atom While wildly successful for mono-electron atoms, hydrogen or nearly fully ionized heavier atoms, Bohr’s model fails for multi-electron atoms. Modern QM replaces orbitals with probability distributions. are fermions, with half-integer spin, obeying the Pauli exclusion principle. Bohr’s quantum number becomes the principle quantum number, but additional quantum numbers for orbital angular momentum and spin. Removing Redundancy The Harvard College team continued their cataloging of stellar spectra, expanding their efforts to the southern Hemisphere in 1890. A catalog of bright stars in the Southern Hemisphere was published in 1901 by Pickering and , using a revised stellar classification scheme developed by Cannon and . This scheme removed redundant letters from the old Harvard scheme and placed O and B before A, leaving O, B, A, F, G, K, & M plus P and Q. With improved spectra, Cannon was able to sub-divide each type into 10 subtypes, 0-9. The fruit of this effort was the Henry Draper Catalogue, with 225,300 stars, published from 1918-1924. Star are still frequently referred to by their Draper Catalogue number, for example, Betelgeuse is HD 39801. Mnemonics The absence of alphabetic order in the Harvard Classification scheme has engendered a cottage industry in mnemonic devices. O Oh Overseas Only Oh B Be Broadcast Beer Boy, A A A And F Fine Flash Fine Final's G Girl/Guy /Gorilla/GodzillaGoat Grass Gonna K Kiss Kills Keep Kill M Me Mothra, My Me, R Right Rodan Rattled Really N Now! Named Nerves Need to S Smack! Successor Sane Study Temperature Scale There are seven general categories of stellar spectra, with very different patterns of lines. It wasn’t realized that the ordering O B A F G K M represented a temperature scale until 1921. Work by Meghnad Saha showed how the populations of atomic levels varied with temperature. Making Balmer Lines Creating a Balmer absorption line requires an atom to be in the n=2 excited state. In a cold gas, all of the electrons are in the n=1 ground state. Thus cold atoms can absorb Lyman , but not Balmer. One way to place an electron in an excited state is photo- excitation, where absorption of Lα photons moves electrons from n = 1→2. Another excitation process is collisional excitation, where a collision with a free electron or another atom leaves the atom in an excited state, X + ½ m �2 → X* + ½ m �′2, with the initial � larger than the final �′. Collisional de-excitation, X*+ ½ m �2 → X + ½ m �′2, is also a possibility, with the final �′ larger than the initial �. Ionization If sufficiently energetic, atomic transitions can excite an electron to energies above n∞. This removes an electron, ionizing the atom.

E∞ − E1 is called the Ionization Potential. + 2 Photoionization, X + hν→X + ½ me� , 2 requires hν > E∞ − En + ½ me� . For Hydrogen in the ground state hν > 13.6 eV. 2 + 2 2 Collisional ionization, X + ½ m� → X + ½ m�′ + ½ me�′′ , requires a similar energy exchange from the colliding atom or electron.

+ 2 The reverse process, X + ½ me� → X + hν is called recombination. Collisional Competition In local thermodynamic equilibrium (LTE), the relative populations obey the Boltzmann equation. density of states Since E1 − E2 <0, n2 < n1 LTE also determines the ionization states of an atom. The populations obey the Saha Equation. Ionization Potential partition function

For Balmer lines, E1 − E2 = 10.2 eV, E1 − E∞ = 13.6 eV. The population n2 increases with temperature until 10,000 K, where ionization begins to reduce neutral hydrogen population. Stellar Lines This competition between excitation and ionization affects all species according to their ionization potential (IP). Molecules having the smallest IP and the largest. Additional Types Beyond the OBAFGKM stellar types, a number of specialized types have been added. The include ✴ W/WR for H-deficient or H-poor Wolf-Rayet stars, with subtypes WN & WC, depending on the dominance of carbon or nitrogen lines. ✴ C for carbon-rich stars, with C-R and C-N replacing the older R and N types. ✴ S for stars that show strong zirconium oxide lines. ✴ D for dwarfs, with a range of sub-types including DA, DB, DO, DQ, DZ, depending on whether the outer layers are rich in hydrogen, helium or heavier species. Brown Dwarves A very important extension of the classification system are classes L and T. Class L indicates a photospheric temperature between 1300-2000 K. Low temperatures allow species with low IP, for example alkali metals, and low dissociation energies, like metal hydride molecules, to survive. Class T indicates a photosphere with strong methane spectral features (temperature 700?-1300 K). Class Y show a strong ammonia(?) feature (T < 700? -250 K). One key point is that Class L & T objects are not stars, because they are not powered by nuclear fusion. The term Brown Dwarf was coined for these relatively rare objects, n ~ 0.01 pc-3, 10% of M stars. Spectral Linewidths Even among stars of the same type, there are visible differences in the spectral lines. Some of these differences result from differences in composition. A key difference is the linewidth, which was observed to be much wider in main sequence stars than in giants and supergiants. This allows observations to distinguish giants and supergiants from main-sequence stars. This is very important in cases where the distance and therefore luminosity can not be measured. Luminosity Classes The Yerkes spectral classification system, introduced in 1943, added a second dimension to the existing temperature-based types. The width of spectral lines defines luminosity classes. Luminosity classes range from 0, for mass-losing hypergiants, and I for supergiants to V for main sequence stars and VI for subdwarfs.

Measurement of stellar type and luminosity class allows a good estimate of the luminosity and distance. Next Time Stellar Atmospheres.