Isochrone fitting gives a globular cluster an age of

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Astrophysics & Cosmology · Uncertainty in measurement

Stars from the Inside, Ch Stellar evolution: from the Hayashi track to the iron core, and the ages of clusters

Problem

Isochrone fitting gives a globular cluster an age of 12 Gyr12\ \mathrm{Gyr}. Three inputs carry uncertainties. The distance is known to 5%5\%. The reddening is known to δE(B−V)=0.02 mag\delta E(B-V) = 0.02\ \mathrm{mag}; dust that reddens a star by E(B−V)E(B-V) also dims it in VV by about 3.1 E(B−V)3.1\,E(B-V) magnitudes. The metallicity is known to 0.150.15 dex in [Fe/H][\mathrm{Fe/H}], and model isochrones give an age sensitivity of about 0.30.3 in ln⁡t\ln t per dex at fixed turn-off luminosity. ((a)) Using δln⁡t≈−0.92 δ(m−M)\delta\ln t \approx -0.92\,\delta(m-M), find the size of δln⁡t\delta\ln t from the distance error. An error in the dimming shifts every star's inferred absolute magnitude just as a distance-modulus error does; find the size of δln⁡t\delta\ln t from the reddening error. ((b)) Find the size of δln⁡t\delta\ln t from the metallicity error. ((c)) Treating the three errors as independent and adding them in quadrature, find the total fractional age error and the age uncertainty in Gyr. Which term dominates?

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