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Radial Velocity and Proper Motion Barbieri Chapter 9 Kathy Geise Stellar or Annual Parallax • The apparent motion of a nearby star is a small ellipse in the sky relative to background stars over the period of a year. • The parsec is the distance for which the annual parallax is one arcsecond. • The reciprocal of the parallax is the distance in parsec. http://en.wikipedia.org/wiki/Parallax Two Components of Velocity Over time, star X moves to position X’ as seen from the heliocenter S along velocity vector, V. The velocity vector has components vr in the radial direction and vt in the transverse direction. Proper Motion, μ • • • The linear drift in this graph is from proper motion. The elliptical motion is from the annual parallax. http://csep10.phys.utk.edu/astr162/lect/motion/pr oper.html A slow, angular change to equitorial coordinates due to a star’s transverse velocity relative to the viewer (Carroll and Ostlie) or heliocenter (Barbieri) Units of arcseconds per year. Tangential velocity vt is related to proper motion, μ, as follows: μ = π/4.740 *vt (arcsec/yr) where π is annual parallax in arcsec and vt in km/s. Barnard’s star The Sky 6 • Second closest to Sol after Alpha Centauri • 6.0 light years away • Constellation Ophiuchus • Dim red dwarf (m. 9.55) • Old star, possibly 11-12 by • Approaching Sol • Largest known proper motion of all stars (10.3”) • http://www.solstation.com/stars /barnards.htm Radial Velocity • Radial velocity is the component of the velocity toward or away from the observer. • Radial velocity is measured through the Doppler effect. • When the velocities measure less than 0.01c, we can use prerelativistic formulae: – Vr = c*(λobserver – λs)/ λsource – z=Δλ/λ=Vr/c • Z>0 red-shifted; radial velocity positive • Z<0 blue-shifted; radial velocity negative http://www.mhhe.com/physsci/astronomy/arny/i nstructor/graphics/ch12/1211.html Astrometric Velocities • “Precise astrometry permits accurate determination of stellar radial velocity from purely geometric measurements without using spectroscopy nor employing the Doppler principal.” • Changes in parallax and proper motion over time reveal radial velocity. • Possible only with precise measurements. • Hipparcos satellite data in combination with older stellar data. • Changing angular separation of stars sharing the same space velocity as in a moving cluster measured by Hipparcos. • http://www.astro.lu.se/~dainis/HTML/HIPPARCOS.html • View a Java animation of Bernard’s Star proper motion on the Hipparcos website: – The Hipparcos and Tycho Catalogues: Nearby Stars Hipparcos animations Animation of intermediate astrometry data of Hipparcos star. http://www.rssd.esa.int/Hipparcos/TOUR/intastrom.html Motion of the Pleiades over 120,000 years. This is an 8x6 degree field. http://www.rssd.esa.int/hipparc os/Pleiades_distance.html Relativistic Considerations • The whole velocity vector is affected by relativity, not just the radial component. Relativity predicts a transverse Doppler effect. • General relativity is important for high accuracy, for example, spacecraft moving within the solar system. • High velocity stars, like Barnard’s • Expanding gaseous envelopes of exploding supernovas • High red-shifted, very distant galaxies • Light emitted from atoms in a gravitational field, for example the surface of a star, may be red-shifted. The Sky 6 Snake Nebula Cover photo APOD Snake Nebula http://antwrp.gsfc.nasa.gov/apod/ap050521.html