Galaxy fluxes
<Text-field style="Heading 1" layout="Heading 1">Problem</Text-field> 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.
<Text-field style="Heading 1" layout="Heading 1">Data</Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= M31 (Andromeda Galaxy) Absolute Magnitude 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 The Major Axis in Minutes of Arc LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYuLUkjbWlHRiQ2JVEkQWFnRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEqJmNvbG9uZXE7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSSNtbkdGJDYkUSYxOTAuNUYnRjktRjY2LVEifkYnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZXLUY2Ni1RIjpGJ0Y5RjtGPkZARkJGREZGRkhGSkZNLUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHRlcvJSZkZXB0aEdGW28vJSpsaW5lYnJlYWtHUShuZXdsaW5lRidGU0Zmbi1GZ242JkZpbkZcb0Zeby9GYW9RJWF1dG9GJy1GLDYjUSFGJy8lK2V4ZWN1dGFibGVHRj1GOQ== The Ratio of the Minor Axis to the Major Axis 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 M83 (LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JlEpTkdDfjUyMzZGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==) Absolute Magnitude 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 The Major Axis in Minutes of Arc 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 The Ratio of the Minor Axis to the Major Axis 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=
<Text-field style="Heading 1" layout="Heading 1">Useful Equations</Text-field> Luminous Flux from a Celestial Source 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 Solid Angle Subtended by an Ellipse 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Brightness Ratio of Two Extended Objects with Magnitudes (M) and Solid Angles (LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEnJiM5Mzc7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lK2V4ZWN1dGFibGVHRjFGMg==) 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 1" layout="Heading 1">Solution</Text-field> Luminous flux from a celestial source would be measured as: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic= 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where I is the intensity, \316\270 is the zenith angle, and \316\251 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: 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 JCImZzQnISIk 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 JCImIls2ISIk The solid angle subtended by an ellipse is: 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic= For Andromeda: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVEnJiM5Mzc7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2Ji1GIzYlLUYsNiVRImFGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHRjFGMkYyLyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnLUkjbW9HRiQ2LVEiPUYnRjIvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0Znbi1GLDYlUSZldmFsZkYnRj1GPy1GNjYkLUYjNictSSZtZnJhY0dGJDYoLUYsNiVRI1BpRidGL0YyLUYjNictSSNtbkdGJDYkUSI0RidGMkY9RkEvJTBmb250X3N0eWxlX25hbWVHUSgyRH5NYXRoRidGPy8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGZXAvJSliZXZlbGxlZEdGMS1GSjYtUScmc2RvdDtGJ0YyRk1GT0ZRRlNGVUZXRlkvRmZuUSYwLjBlbUYnL0ZpbkZecS1GNjYkLUYjNictRmJvNigtRiw2JVEkQWFnRidGPUY/LUYjNiUtRmpvNiRRIjJGJ0YyRj1GP0ZgcEZjcEZmcEZocEZqcC1GYm82KC1GLDYlUSRCYWdGJ0Y9Rj9GaXFGYHBGY3BGZnBGaHBGQUYyRjJGQUYyRjJGQUYy LyZJJk9tZWdhRzYiNiNJImFHRiUkIitjTz0hRyMhIic= For NGC 5236: 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 LyZJJk9tZWdhRzYiNiMiJU9fJCIrN0guM0ghIik= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic= The ratio of the brightnesses of the two galaxies is: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= 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 JCIrUFlFIypIISIq LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic= So the flux ratio is: 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 JCIrMGM9O1EhIzY= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiRRIjFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2Jy1GLzYkUS4wLjAzODE2MTg1NjA1RidGMi8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EoMkR+TWF0aEYnL0YzUSdpdGFsaWNGJy8lLmxpbmV0aGlja25lc3NHRjEvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGSS8lKWJldmVsbGVkR0Y/Rj1GMg== JCIrP3dUP0UhIik= 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.
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=