Hubble law The purpose of the project is to measure Hubble expansion from a set of measured redshifts and distances of galaxies. A data set of redshifts, distance moduli are available for this data set from this file. The first column gives the measured velocities (v=cz, where c is the speed of light and z is the redshift). The second column given the distance modulus. Assume that the velocity measurement is infinitely accurate where as the distance moldulus errors follow a Gaussian distribution with standard deviation of 0.5. Estimate the real distances and their errors. which distribution the errors follow? Estimate H0 from the data using the maximum likelihood mehtod and the minmum chi-squared method and discuss the differences. Obviously your model here should be Hubble's law, i.e., v=H0d. Think carefully about how to include the errors. Estimate directly from your error on H0. Create a Monte Carlo realization of the data. Namely, choose a specific H0 value and produce distance moduli accroding to the following steps: use v=H0 d then transform d to distance modulus and finally, create a realization of the erros in the distance modulus. Estimate H0 from the mock (simulated) catalogue. Estimate the errors on your H0 estimate from the simulated data. Follow two routes. A: Through the maximum likelihood estimation. B: From producing a large number of simulated sets. Estimate the excess error on H0 (contributed by the peculiar velocities). Discuss how important it is to include the peculiar velocities in your model.
Hubble law
The purpose of the project is to measure Hubble expansion from a set of measured redshifts and distances of galaxies. A data set of redshifts, distance moduli are available for this data set from this file. The first column gives the measured velocities (v=cz, where c is the speed of light and z is the redshift). The second column given the distance modulus. Assume that the velocity measurement is infinitely accurate where as the distance moldulus errors follow a Gaussian distribution with standard deviation of 0.5. Estimate the real distances and their errors. which distribution the errors follow? Estimate H0 from the data using the maximum likelihood mehtod and the minmum chi-squared method and discuss the differences. Obviously your model here should be Hubble's law, i.e., v=H0d. Think carefully about how to include the errors. Estimate directly from your error on H0. Create a Monte Carlo realization of the data. Namely, choose a specific H0 value and produce distance moduli accroding to the following steps: use v=H0 d then transform d to distance modulus and finally, create a realization of the erros in the distance modulus. Estimate H0 from the mock (simulated) catalogue. Estimate the errors on your H0 estimate from the simulated data. Follow two routes. A: Through the maximum likelihood estimation. B: From producing a large number of simulated sets. Estimate the excess error on H0 (contributed by the peculiar velocities). Discuss how important it is to include the peculiar velocities in your model.