Cepheid Variables: Measuring the distance of Galaxies Dr Lisa Jardine-Wright Cavendish Laboratory, University of Cambridge

Measuring Distances How do we measure the distances of galaxies outside our own Milky Way? We use objects called standard candles within each of the galaxies –Can be thought of as bright beacons which act as reference points. For example, Cepheid variable stars Supernovae

Cepheid Variable Stars Cepheids are special stars because they blink, what’s more they blink at a rate that is precisely related to their brightness. –If we can measure the rate that they are blinking then we can infer how bright they are. –Then we compare how bright they look to us and how bright they are as calculated from their blink rate. –Distance

Why Do Cepheids Pulse? A cepheid is a young star which is burning brightly. –He 2+ is more opaque and won’t let the radiation escape, so the radiation heats the gas within the star Heating increases the pressure of the gas and this pressure pushes layers of the star outwards, increasing it’s size and luminosity As it expands it cools and becomes transparent again.

Practical: Cepheid Variables Using some real light curves for Cepheid Variables we will measure the distances to the 4 galaxies to which they belong. 0 0

Measuring the Distance First of all we measure the light curve for the cepheids in our distant galaxy to calculate the period of its pulses. The period of our distant Cepheid is then compared it to observations of Cepheids in the local Universe to calculate its luminosity Time in days Apparent Brightness in Magnitudes

Data Table Star Average Period (days) Apparent Luminosity (m) Absolute Luminosity (M) Distance (parsecs) Example HV 837 HV 1967 HV 843 HV 2063

Calibration Line

Data Table Star Average Period (days) Apparent Luminosity (m) Absolute Luminosity (M) Distance (parsecs) Example HV 837 HV 1967 HV 843 HV 2063

Final Step: Distance We now know the real luminosity, L of the Cepheid and we know the flux, F of light that we measured from Earth → distance. –Light energy from the Cepheid is emitted in all directions. –Flux is the amount of energy that crosses a square metre at a given distance, d. d

Derivation of Distance Modulus A magnitude is defined as so that magnitude = 0 corresponds to a flux F 0 Comparing to stars D and E Absolute magnitude is what the apparent magnitude of the same star at 10 parsecs

Derivation of Distance Modulus Combining these equations (where distance d is in parsecs)