EXERCISE-IV

Estimate qo using the LHb-sigma distance indicator at z~2

The LHb-sigma distance indicator for HII-like galaxies in the nearby universe is:

log LHb = log (sigma)5 - log (O/H) + 29.60

where LHb is in erg/s, sigma is in km/s, and (O/H) is the metallicity.

Assuming:

m = -2.5 log(FHb) - AHb + k

where FHb is in erg/s/cm2 and AHb is the extinction correction in magnitudes, and:

M = -2.5 log(LHb/(4pi (10pc)2)) + k

(i) Derive the expression for the distance modulus (m-M) as a function of FHb, sigma, (O/H), and AHb.

(Note: be careful with the units, e.g. "pc" has to be transformed to "cm").

The following table contains actual data for a sample of HII-like galaxies at z~2:

(ii) Calculate the distance modulus (m-M) for each galaxy.

The theoretical expression of the distance modulus, as a function of the cosmological parameters is (approximately):

m-M = 42.38 - 5 log(h) + 5 log(z) + 1.086z (1-qo)

You can assume h = 0.70.

(iii) Calculate qo for each galaxy. What is the average value of qo? What is the estimated error on this value? What is your conclusion?