8.3 Line spectra: ions and spectral lines
For obvious reasons optical astronomy developed earlier than radio and X-ray astronomy, and astronomers are able to learn many things from analysis of optical emission. Just as in the radio band, optical pictures, i.e. the spatial distribution of emission, can be informative. Even when a source is not spatially resolved, astronomers can still deduce some information about what it might look like close-up. These ‘visualizations’ of what is happening in a particular source result from analysis of how the amount of light detected depends on time, or on wavelength, i.e. by looking at temporal or spectral properties of the emission.
Since hydrogen is the most abundant chemical element in the Universe, its spectral lines are particularly important in astrophysics. The Balmer series are the transitions in which the n = 2 energy level is the lower level. This series of lines appears in the optical wavelength region, and the H line (transitions between n = 2 and n = 3) is often the most prominent line in optical spectra. The highest energy transitions in the hydrogen line spectrum are those to and from the lowest energy level, i.e. transitions to and from n = 1. This series of lines is called the Lyman series, and the Ly line (transitions between n = 1 and n = 2) is prominent in ultraviolet spectra.
The Balmer limit, which occurs at 3646 Å corresponds to transitions between the n = 2 level of hydrogen and unbound states, i.e. this is the ionization transition from the n = 2 level. Similarly the Lyman limit at 912 Å corresponds to ionization from the ground state (n = 1). Consequently radiation with λ< 912 Å is known as ionizing radiation. Photons with energies just exceeding the Lyman limit are highly prone to absorption by neutral hydrogen gas: consequently the plane of our own Milky Way Galaxy is essentially opaque at wavelengths just short of the Lyman limit.
Generally astronomers label spectral lines using notation like CIV λλ1548, 1551, which concisely gives an enormous amount of information. Going through this piece by piece:
‘C’ indicates the chemical element, carbon in this example,
‘IV’ indicates the ionization state. ‘I’ indicates the neutral atom, with successive roman numerals indicating successive positively charged ions,
hence ‘IV’ indicates that three electrons have been removed. The CIV ion is C3+; the roman numeral is always one more than the number of positive charges. ‘λ’ indicates the following numerals give wavelength. In this case we have ‘λλ’, which means that the spectral line is a multiplet. In the case of a multiplet there are two or more ‘fine structure’ sublevels to one or both of the energy levels involved in the transition, so that there are multiple components to the spectral line, corresponding to the various possible energy differences between the initial and final states. This is illustrated in Figure 26. In our example, the line is a doublet, having two components. Triplets and higher multiplets are also possible.
‘1548, 1551’ gives the wavelength in Å of the two components of the doublet.
Spectral lines arise as a result of atomic transitions which are governed by quantum mechanical selection rules. Most common lines correspond to transitions which are permitted by the selection rules. For reasons which we will not explore here, it is also possible (with low probability) for transitions to occur which do not obey all of the selection rules. Such transitions are called forbidden or semiforbidden lines, depending on which of the selection rules are violated. Semiforbidden lines are also sometimes called intercombination lines. The astrophysically important point is that permitted transitions are, in general, much more likely than forbidden or semiforbidden transitions. This means that if an excited atom has a permitted transition that it can make to a lower level, it is not likely to make a non-permitted transition. Consequently the only forbidden and semiforbidden lines which are observed are those where no permitted transition is available. Furthermore, because non-permitted transitions have low probability of occurrence, an excited atom will remain in the excited state for a long time before the transition occurs. During this time, a collision with another atom, ion, or free electron may occur, and collisional de-excitation will result. Hence forbidden and semiforbidden lines are only observed from low-density regions, where collisions are relatively infrequent.
The notation used to indicate a forbidden line is a pair of square brackets around the chemical element and ionization state, e.g. [OII]. Similarly, a semiforbidden line is indicated by just the closing bracket, e.g. NIV].
List the permitted lines, the forbidden lines, and the semiforbidden lines present in optical and UV spectra of the Seyfert 1 galaxy NGC 5548. Refer to Peterson Figures 1.1 and 1.2.
The permitted lines are: Hδ, H, Hβ, H, HeI λ3587, CaK, HeII λ4686, HeI λ5876, NaD, Ly, NV λ1240, SiIV λλ1394, 1403, CIV λ1549, HeII λ1640, OI λ1304, CII λ1335.
The forbidden lines are: [NeV] λ3425, [OII] λ3727, [FeVII]λ3760, [NeIII] λ3869, [OIII] λ4363, [OIII] λ4959, [OIII] λ5007, [FeVII] λ6087, [NII] λ6583, [OI] λ6300, [NV] λ3346, [NIII] λ3968, [SII] λ4071, [CaV] λ5309, [FeVII] λ5721, [OI] λ6364, [FeX] λ6374, [SII] λλ6717, 6731.
The semiforbidden lines are: OIV] λ1402, OIII] λ1663, SiIII] λ1892, CIII] λ1909, NIV] λ1486, NIII] λ1750
The ionization of hydrogen from the ground state requires radiation of wavelength less than 912 Å. Calculate the frequency corresponding to this wavelength, and the equivalent photon energy. Give the energy in joules, in ergs and finally in electronvolts. Which of these three energy units is the most natural choice in this instance?
The wavelength and frequency are related by the wave equation: c = λ, where c is the speed of light and λ and are the wavelength and frequency respectively. Therefore, at wavelength 912 Å, the frequency iswhere we have been careful to use consistent units of length. Evaluating this we obtain = 3.29 × 1015 Hz.
The energy of the photon is given by Eph = h, so evaluating this with h = 6.626 × 10−34 J s, we obtain E ph = 6.626 × 10−34 × 3.29 × 1015 J, i.e. Eph = 2.18 × 10−18 J. If we instead use the cgs value for h: h = 6.626 × 10−27 erg s, we obtain Eph = 6.626 × 10−27 × 3.29 × 1015 erg, i.e. Eph = 2.18 × 10−11 erg. We could alternatively have arrived at this by multiplying the answer in joules by 107, since there are 107 erg per joule. To obtain the energy of the photon in electronvolts we need to remember that an electronvolt is the energy gained by accelerating an electron through a potential difference of 1 volt. Since the charge on the electron, e = 1.602 × 10−19 C, and 1 joule is liberated by accelerating a coulomb of charge through a potential difference of 1 volt, the energy in electronvolts is the energy in joules divided by the number of coulombs carried by a single electron. Hence
Eph = 2.18 × 10−18 J = (2.18 × 10−18)/(1.602 × 10−19) eV = 13.6 eV
The natural choice of units here is electronvolts, as the value of Eph is an easily visualised quantity in these units.
You may recognise this as the energy required to ionize hydrogen.
Activity 6: Quasar variability
Read Peterson Section 1.3.2.
Coherence arguments are to do with light travel time.
The chanting of the crowd at a football match is often incoherent: several versions of the same chant will be heard from different sections of the crowd, with perceptible time delay(s) compared to the leading chant. This occurs not because football crowds are a disorganised rabble, but because the time taken for sound to travel from one end of the stadium to the other causes an appreciable delay. In contrast, members of a choir inside a concert hall sing coherently. They have no difficulty in keeping in time, because the distance between the singers is small, so the sound travel time from one to another is imperceptibly small.
Keywords: variability, timescale