How are absorption lines in the Sun's photosphere different from absorption lines measured in an Earth laboratory?

(by Graeme Waddington, Oxford University, with permission)

The wavelengths and line profile shapes of photospheric absorption lines do not correspond with those observed in a terrestrial laboratory as a result of the following,

1) Gravitational Redshift

This wavelength shift is an inescapable consequence of the Principle of Equivalence. For a spectral line of wavelength 5500 Angstroms this effect gives rise to a shift of 11.6 milli-Angstroms (a Doppler shift of 0.63km/s).

2) Relative Motion of the Observer

As a result of the Earth's orbital motion about the Sun and the rotation of the observer about the Earth's axis the solar spectral lines are Doppler shifted relative to terrestrial standards. Both effects give rise to Doppler amplitudes of the order of 0.5km/s.

This effect has, in the past been overlooked, with one Eastern-block group "discovering" a diurnal shift in the Telluric O2 lines by comparing them with nearby photospheric lines (which were taken as wavelength standards) ! See I.Vince, Publ. Astron. Obs. Belgrade 26, p.167 (1978) for the expose.

For observations away from the centre of the solar disk there is also a contribution from the solar rotation.

3) Photospheric Oscillations The well-known solar 5-minute oscillation gives rise to an r.m.s. Doppler shift of the order of 0.05km/s in spatially averaged spectra obtained from the centre of the solar disk.

4) Convective Overshoot in the Photosphere

The overshooting of convective motions into the convectively stable photosphere - the well known solar granulation - gives rise to both wavelength shifts and asymmetric line profiles of spectral lines formed in the photosphere. In the case of spatially averaged observations the contribution from the bright, rising granules dominates over the contribution from the darker, sinking inter-granular regions (even though the downdrafts are faster than the upwellings).

For spatially resolved spectra one sees the typical "wiggly-line" structure as one traverses the length of the spectrometer slit - due to the alternating blue- and red- shifts which correlate with the brightness of the surrounding continuum. (see most astronomy textbooks for a photograph of a photospheric "wiggly-line").

When observed at the centre of the solar disk, spatially averaged lines formed at the base of the photosphere (around an optical depth of 0.1) have a Doppler blue shift of typically 0.3km/s; for lines whose core is formed at the top of the photosphere (optical depth around 0.00002) the observed Doppler blue shift is typically 0.05km/s. The cores of the Sodium D resonance lines are formed above the overshoot region and have a blue shift of around 0.005km/s (it being non-zero due to the Doppler shifted contributions to the line-wings that are formed lower down in the photosphere). The extent of the disk-centre blue shift is fairly linear with log(optical depth) throughout the photosphere.

It should be noted that, since the resulting line profiles are asymmetic, the actual size of the wavelength shift of any photospheric line depends on the part of the profile used in its determination; the above values refer to the wavelength derived from the bottom 20% of the line profile (i.e. the core) and were obtained by direct comparison with the same lines created at low pressure in the Oxford Spectroscopic Furnace (at the now defunct University Observatory) during the period 1977-79.

As one moves away from the centre of the solar disk the line of sight through the solar atmosphere ceases to be vertical and samples the horizontal motions in the granular flow in addition to the vertical ones. As a result the line wavelength shifts towards the red (or, more correctly, towards a zero shift) - the well-known "limb effect" of solar lines (or Evershed's "objectionable Earth" hypothesis!).

That the wavelengths of photospheric absorption lines, and their variation across the solar disk, are explicable in terms of the convective motions associated with the granulation is not new (St.John & Babcock 1924; Ap.J. 60, 32). In spite of this the literature continues to abound with exotic theoretical models purporting to explain these effects, often invoking quixotic hypotheses and flagrantly disregarding the dynamic state and inhomogeneous nature of the photosphere in the process.

Useful references:

J.M.Beckers, "Dynamics of the Solar Photosphere", 1981, in "The Sun as a Star", NASA SP-450, ed. S.Jordan, p.3-64.

D.Dravins, L.Lindegren & A.Nordlund, "Solar Granulation: Influence of Convection on Spectral line Asymmetries and Wavelength Shifts", 1981, Astronomy & Astrophysics, 96, p.345-364.

D.Dravins, "Photospheric Spectrum Line Asymmetries and Wavelength Shifts", 1982, Ann. Rev. Astron. Astrophys., 20, p.61-89.

R.J.Bray, R.E.Loughhead & C.J.Durrant, "The Solar Granulation", 2nd ed. CUP 1984

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Special Thanks to G. Waddington