Calculate the ratio of the fluxes of the Andromeda galaxy and NGC 5236 (M83).

Hints:

Calculate the semi-minor axes of both galaxies.

Calculate the solid angle each galaxy subtends on the sky.

M31 (Andromeda Galaxy)

Absolute Magnitude

The Major Axis in Minutes of Arc

The Ratio of the Minor Axis to the Major Axis

M83 ()

Absolute Magnitude

The Major Axis in Minutes of Arc

The Ratio of the Minor Axis to the Major Axis

Luminous Flux from a Celestial Source

Solid Angle Subtended by an Ellipse

Brightness Ratio of Two Extended Objects with Magnitudes (M) and Solid Angles ()

Luminous flux from a celestial source would be measured as:

where I is the intensity, θ is the zenith angle, and Ω is the solid angle subtended by the source. Consider the following example, in which the ratio of the flux densities of the two galaxies is calculated. To solve the problem, the following information must be given: the absolute magnitude of each galaxy and the solid angle that each subtends on the sky.

Calculating the extent of the semi-minor axes:

The solid angle subtended by an ellipse is:

For Andromeda:

For NGC 5236:

The ratio of the brightnesses of the two galaxies is:

So the flux ratio is:

Note that the ratios of the flux densities and magnitudes are not equivalent. In this case, the Andromeda galaxy is only about three times as bright as NGC 5236 but has about 26 times the flux density.