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The Cosmic Distance Scale. Convergent point method. Convergent point method. Main-sequence fitting. This shows the HR diagram for the solar neighbourhood from the Hipparcos satellite. Variable stars: Cepheids. Cepheids: P-L relations. Type Ia Supernovae. Type Ia Supernovae.
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Main-sequence fitting This shows the HR diagram for the solar neighbourhood from the Hipparcos satellite
Type Ia Supernovae Accurate standard candles, luminosity depends on the physics of core collapse in stars and therefore is mostly independent of the host galaxy properties.
Cluster gravitational lenses imply large amounts of dark matter
Rotation curves: Explanations MOdified Newtonian Dynamics (MOND) (Milgrom 1983) F = m (a/a0) a Where (x) = 1 if x>>1 and (x) = x if x<<1 So for low acceleration F = ma2/a0 = GMm/r2 M(r) = v4 / (a0G) a0 ~ 10-10 ms-2 Using Newton F = ma = GMm/r2 a = v2/r M(r) = v2 r / G Implies dark matter
Clowe et al. 2006 • Stellar masses • Integrate I-band light, apply M/LI = 2 (range 0.5 to 3 for typical galaxies in solar units) • Plasma masses • Integrate X-ray luminosity, apply M/LX from 3D model using hydrostatic equilibrium, T~6 keV (sub-cluster) and 14 keV (main) • Weak lensing masses
Weak gravitational lensing Method is statistical; see intrinsic aspect ratios shown below; expect signal of 0.02-0.10 Figures by B. Jain
Weak lensing by cluster Cluster z~0.3; mean background galaxies at z~1 for Clowe et al. 2006 Away from mass Around cluster Figures by B. Jain
Conclusion • Lensing mass map peaks around stars as expected for dark matter