The Universe Is Expanding — Question 5

Question 5

Cosmological time dilation stretches a transient light curve

A transient at z=.80 rises for 12 days in its rest frame and emits photons of rest-frame wavelength 400 nm. Neglect peculiar motion.

1. Find the observed rise time and wavelength.

2. If one pulse emitted N photons of energy E each over rest-frame duration t, find the observed energy-arrival rate factor due solely to redshift and time dilation, excluding geometric dilution.

Question 5 - Solution

Cosmological time dilation stretches a transient light curve

(a) Method and calculation

$$\boxed{t_o=(1+z)t_e=1.8(12)=21.6\ {\mathrm{d}}}.$$$$\boxed{\lambda_o=1.8(400)=720\ {\mathrm{nm}}}.$$

(b) Interpretation and further calculation

$$E_o=E_e/(1+z),\quad t_o=(1+z)t_e.$$$$\boxed{\frac{NE_o/t_o}{NE_e/t_e}=(1+z)^{-2}=.308642}.$$

Physical check

Each photon loses an energy factor and their arrival rate gains a separate time factor; luminosity distance incorporates these effects.