ABSOLUTE  RADIAL  VELOCITIES

Although radial velocities are normally determined through spectroscopy, the accuracies in space astrometry now permit their determination also from purely geometric measurements.  The differences between astrometric and spectroscopic radial velocities can disentangle which effects (other than stellar motion) affect the wavelength positions of spectral lines.

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  Effects of stellar granulation are seen in photospheric line asymmetries and wavelength shifts.  These originate from correlated velocity and brightness patterns: rising (blueshifted) elements are hot (bright), and a convective blueshift results from a larger contribution of such blueshifted photons than of redshifted ones from the sinking and cooler (darker) gas.  For the Sun, the effect is typically 300 m/s.  High-excitation (and ionized) lines form predominantly in the hottest elements and show a more pronounced blueshift.  Strong lines (formed above the granulation layers) show smaller shifts.

  Differential wavelength shifts exist between lines inside individual stellar spectra, and between binary or cluster stars sharing the same system velocity.  However, accurate absolute lineshifts (i.e. displacements of the line wavelengths from their laboratory values, corrected for the relative object-Earth motion) were until recently measured only for the Sun.  The solar motion is known from planetary system dynamics and does not depend on spectroscopic data.  Thus, absolute solar lineshifts can be interpreted as originating from gravitational redshift, convective blueshift, and other atmospheric phenomena.

  Radial velocities in astronomy are normally determined through spectroscopy, applying the Doppler principle.  However, they can also be determined from purely geometric (astrometric) measurements, e.g. from the secular change of a star's proper motion.  Although such a possibility was realized already a long time ago, the required accuracies (except for a few special cases) were not available before the advent of Hipparcos and space astrometry.

  A comprehensive observing program, aiming at both precise and accurate wavelength shift determinations in a wide variety of stars has been carried out with the radial-velocity instrument ELODIE at Haute-Provence Observatory, the instrument with which the first "normal" exoplanet (that around 51 Pegasi) was discovered.

  One aim of this program is to search for signatures of differential lineshift between various classes of spectral lines; between stars of different spectral type; between stars of different metallicity; and between stars of different rotational velocity.

  Absolute lineshifts, i.e. the apparent radial velocities of different spectral lines, has the potential of becoming a novel diagnostic tool for stellar atmospheres, beyond the established ones of line-strength, -width, -shape, and asymmetry.  This example shows a situation when different hydrodynamic models predict essentially the same line profiles and the same line asymmetries; they can be segregated only because the lineshifts are different.

Figure: The same spectral line in different stars. Fe I profiles and bisectors from four different hydrodynamic stellar models are plotted on the same absolute scale.  Top to bottom, left to right, these represent Procyon (F5 IV-V), Beta Hyi (G2 IV), Alpha Cen A (G2 V), and Alpha Cen B (K1 V).  Convective blueshift increases with increasing temperature, and also with increasing luminosity.  Observed solar values fall between those of Alpha Cen A and Alpha Cen B.

D. Dravins & Å. Nordlund: Stellar granulation. V. Synthetic spectral lines in disk-integrated starlight, A&A 228, 203, 1990; and D. Dravins: High Resolution Spectroscopy of Stellar Velocity Signatures, in M.H.Ulrich, ed.: High Resolution Spectroscopy with the Very Large Telescope, ESO, p. 55, 1992.

Figure: Different Fe I lines in the same star.  Bisectors for lines in integrated sunlight (left) and Procyon (right), were averaged and divided according to line strength.  The relative-velocity (wavelength) scale is absolute except for a zero-point offset.  The velocity span between strong and weak lines is much greater in Procyon (800 m/s) than in the Sun (400 m/s).

Carlos Allende Prieto, Martin Asplund, Ramón García López, David Lambert & Åke Nordlund: R 200,000 Spectroscopic Observations of Procyon. The Surface Convection and Radial Velocity; Poster presented at the 11th Cambridge Workshop on Cool Stars, Stellar Systems and the Sun, Tenerife, Oct.1999.  Corresponding model calculations are in D.Dravins & Å.Nordlund: Stellar Granulation.V. Synthetic spectral lines in disk-integrated starlight, A&A 228, 203, 1990.

  For light emitted from the solar photosphere, the gravitational redshift is 636 m/s.  For giants, the value decreases to below 100 m/s, while for white dwarfs it may reach 30 km/s.  Thus, (unless corrected for) different gravitational redshifts among various stars may mimic, e.g., an apparent velocity dispersion inside star clusters.

  The gravitational redshifts in the Hertzsprung-Russell diagram change by three orders of magnitude between white dwarfs (some 30 km/s) and supergiants (some 30 m/s).  For the Sun, the shift is 636.1 m/s for light escaping from the solar photosphere to infinity, and 633 m/s for light intercepted at the Earth: the Earth's location inside the solar gravitational potential blueshifts stellar photons by 3 m/s.

  Accuracy levels of meters per second require the fundamental concept of "radial velocity" to be precisely defined, in particular with respect to relativistic velocity effects and measurements made inside gravitational fields.  A resolution for the stringent definition of "radial-velocity measure", applicable to accurate spectroscopic measurements, was prepared for the IAU XXIV:th General Assembly, Manchester (August 2000).

Figures: Effects due to relativity and gravity, influencing the wavelength displacements of stellar spectral lines.  The formula is for the weak-field post-Newtonian approximation, neglecting higher-order terms of order 1/c³.

L.Lindegren, D.Dravins & S.Madsen: Exactly what is Stellar ‘Radial Velocity’?, in Precise Stellar Radial Velocities, IAU coll.170, eds. J.B.Hearnshaw & C.D.Scarfe, ASPC 185, 73, 1999.

  An atomic species commonly used for accurate lineshift studies is iron.  It has high atomic mass (minimizing the thermal broadening of the stellar lines), its hyperfine and isotope splitting has few complications from atomic and isotope structure, and it has a rich and well-studied spectrum.

  Recently, accurate laboratory wavelengths have become available also for several other species, significantly enhancing the number of stellar lines accessible for lineshift study.  Efforts to improve such atomic data for astrophysics are being made by several groups, e.g., the Atomic astrophysics group at Lund University.

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