I have a catalog I am experimenting with that has some spectroscopic red shift data available (in the range from 0.5-1) as well as total Ks (K -short band) flux data available, how would I go about obtaining distance measures from Earth in parsecs or some other conventional units. Mainly I would need to know the method/formula for converting these values. Thanks!
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For 0 < z < 20 we can neglect the radiation density in respect of the densities of matter and dark energy.
$$\Omega_{R_0}=0$$
We also assume flat universe.
$$\Omega_{K_0}=0$$
Then, the proper distance "d" can be calculated from de redshift "z" with:
$$\boxed{d=\frac{c}{H_0} \int_0^z \dfrac{dx}{\sqrt{\Omega_{M_0}(1+x)^3+\Omega_{\Lambda_0}}}}$$
The best values that we have for the parameters, come from Planck Collaboration 2015:
$$H_0=67.74 \ (km/s)/Mpc$$
$$\Omega_{M_0}=0.3089$$
$$\Omega_{\Lambda_0}=0.6911$$
$$c=299792.458 \ km/s$$
For each value of z the integral can be easily calculated using numerical methods
Albert
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