Derive surface brightness formula

Thread starter Zapped17
Start date May 31, 2024
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Brightness Derivation Surface

In summary, the surface brightness formula is derived from the relationship between the total flux received from an astronomical object and its angular size on the sky. It quantifies how much light is emitted per unit area of the object's surface, typically expressed in magnitudes per square arcsecond. The formula incorporates the object's total luminosity, distance, and area, allowing astronomers to compare the brightness of different celestial objects regardless of their distance from Earth. This derivation is crucial for understanding the intrinsic properties of galaxies and other astrophysical phenomena.

May 31, 2024

Zapped17

Homework Statement: How to derive derive formula for surface brightness that converts mag/arcsec^2 to L⊙/pc^2?

Relevant Equations: S(mag/arcsec^2) = M⊙ + 21.572 -2.5 log_{10} S(L⊙/pc^2)

Derive formula for surface brightness
The formula in question we wanna derive is:
S(mag/arcsec^2) = M⊙ + 21.572 -2.5 log_{10} S(L⊙/pc^2).
Best regards.

FAQ: Derive surface brightness formula

What is surface brightness?

Surface brightness is a measure of the brightness of an astronomical object per unit area. It is typically expressed in magnitudes per square arcsecond or in flux units like watts per square meter. Surface brightness allows astronomers to compare the brightness of objects regardless of their distance from Earth.

How is surface brightness calculated?

Surface brightness is calculated by dividing the total brightness of an object (usually measured in magnitudes or flux) by the area over which that brightness is spread. The formula can be expressed as: Surface Brightness = Total Magnitude + 2.5 * log10(Area), where the area is typically measured in square arcseconds.

What factors affect surface brightness?

Several factors affect surface brightness, including the total luminosity of the object, its distance from the observer, and the distribution of its light. For extended objects, surface brightness can also vary depending on the object's shape and structure, as well as any intervening material that may obscure or scatter light.

Why is surface brightness important in astronomy?

Surface brightness is crucial for understanding the characteristics of astronomical objects, especially for galaxies and nebulae. It helps astronomers determine the physical properties of these objects, such as their size, structure, and distance, and allows for comparisons between different objects or populations of objects.

What is the relationship between surface brightness and distance?

The relationship between surface brightness and distance is such that an object's surface brightness remains constant regardless of distance, while its total brightness decreases with increasing distance. This means that while an object may appear dimmer from farther away, its surface brightness (the brightness per unit area) does not change, making it a useful metric for comparing objects at different distances.