Introduction to Cosmology Example Exam Question: Answer

Lecture 13: Cosmological constant part 1

Briefly describe the mechanism and the observational properties of Type Ia supernovae. [2]
Mechanism: a white dwarf in a close binary accretes enough matter from its companion star to exceed the Chandrasekhar limit and collapse under gravity. This collapse initiates a runaway carbon fusion reaction which destroys the white dwarf. [1]
Properties: diagnostic is absence of hydrogen lines in spectra (this makes it a Type I) together with presence of a silicon line (makes it a Type Ia). Lightcurve of Type Ia shows fast rise and initial steep decline, then slow exponential fall over several months, powered by radioactive decay (of 56Ni via 56Co to 56Fe, but you don't need that for one mark). All SNe Ia have very similar peak absolute magnitudes of –19 to –20. [1]
You wish to investigate the variation of H with cosmic epoch out to redshifts of the order of 1. Why do you choose to use Type Ia supernovae as your distance indicators? [3]
To study the variation of H, you need an indicator which can reach redshift of order 0.5 to 1 (needed to see any significant variation), is common enough for a reasonable sample to be amassed in a few years' work, and (this is the key) has essentially no age or metallicity related systematic errors (age-related systematics would fake the deviation from linearity that you are looking for; metallicity-related systematics are likely to do the same, since you expect a systematic increase in metallicity over time). [1]
The extreme brightness of SNe Ia makes them visible out to redshifts of about 1, which is good enough for the purpose. Although there is some variation in peak brightness, it is correlated with the rate of initial decline, and can therefore be calibrated out: this makes the relative distances precise enough to spot small effects. The rate of 1 per large galaxy per century seems low, but there are a lot of galaxies out there and you don't care which ones you measure. (This is the difference between cosmology and astrophysics: in astrophysics, where you probably want to measure the distance of a specific galaxy, SNe Ia are too rare for your purposes.) [1]
Because the precursor object is well-defined – 1.4 solar masses of degenerate carbon, with a bit of oxygen – we expect age-related systematics to be minimal. There may be metallicity effects, but because SNe Ia occur in all types of galaxies, we can study these in the local universe by looking at SNe Ia in host galaxies of different metallicity. [1]

(2005 Q4.)

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