hw5 - q depends on Ω m Ω q and the w for the dark energy...

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Ph 444 Problem Set 6 Due: Friday, November 12, 2010 1. (Ryden problem 7.5) The surface brightness Σ of an astronomical object is de±ned as its observed ²ux divided by its observed angular area; thus, Σ f/ ( δθ ) 2 . For a class of objects that are both standard candles and standard yardsticks, what is Σ as a function of redshift? Would observing the surface brightness of this class of objects be a useful way of determining the value of the deceleration parameter q 0 ? Why or why not? 2. This problem explores the number of type Ia supernova would need to be observed at z = 0 . 5 to determine the dark energy equation of state parameter w to 1% accuracy. At this redshift, it is a reasonable approximation to adopt Ryden equation (7.45) d L c H 0 z b 1 + 1 q 0 2 z B . This leads to Ryden equation (7.52) for relation between the distance modulus of a supernova, m M , and redshift. Assume that we know Ω m, 0 = 0 . 3 and Ω q, 0 = 0 . 7 precisely. Using how
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Unformatted text preview: q depends on Ω m, , Ω q, , and the w for the dark energy, determine how m − M depends on w and z . If w is constant, then its value is determined by measuring distance moduli for one set of supernovae at small z (where the q dependence is negligible) and another set at, say, z = 0 . 5. Explain why we need supernovae at both small and large z . The distance modulus to an individual type Ia supernova can be measured with an accuracy of ± . 15 mag. How many supernovae must be measured, equally divided between small z and z = 0 . 5, to determine w for the dark energy to ± . 01? Assume that there are no systematic errors, so that the uncertainty in the average distance modulus of a group of supernovae is determined only by the number of supernovae contributing to the average. 3. Ryden problem 8.1 4. Ryden problem 8.3...
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