B3 - cepheids as standard candles

standard candle

an astronomical object with a known luminosity used to measure the distance to far-off objects

cepheids

class of stars that have period change in luminosity due to radial pulsation, and the period depends on the stellar luminosity

the period-luminosity (PL) relation is:

M_{I} = - 1.3 - 3.5 \log_{10} P

where, $M_{I}$ is the absolute magnitude for the $I$ band (centred at $800$ nm), and $P$ is the variability period in days

typically, $P = 2 - 60$ days
measuring the period is relatively easy using photometry
the absolute magnitude, which is harder to measure, can be calculated
using the distance-modulus, $d$ can be found