A How do I determine the surface magnitude of a galaxy from a SED?

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To determine the surface magnitude of a galaxy from its spectral energy distribution (SED), one can use the BlackBodyNorm1D model in Python's synphot library to generate flux data. By calculating the area of a circular aperture in square arcseconds, the surface brightness can be derived by dividing the flux by this area. The resulting surface brightness is expressed in FLAM per square arcsecond. Adjusting the aperture diameter allows for accurate measurements based on the source's angular size. This method effectively provides the surface brightness needed for further analysis of the galaxy's characteristics.
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Let's say I have a galaxy SED like this:

[CODE lang="python" title="SEDgen"]from synphot import SourceSpectrum
from synphot.models import BlackBodyNorm1D
sp = SourceSpectrum(BlackBodyNorm1D, temperature=6170.4796)

wave = sp.waveset
flux = sp(wave) #Photlam
flux_flam = flux.to(u.erg / u.s / u.angstrom/u.cm**2,equivalencies=u.spectral_density(wave))


plt.plot(wave, flux_flam)
plt.xlim(1000, 30000)
plt.xlabel('Wavelength (Angstrom)')
plt.ylabel('Flux [FLAM]')[/CODE]

How do I get surface brightness from this?
 
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Python:
import numpy as np

# Assuming a circular aperture with a diameter in arcseconds
aperture_diameter_arcsec = 1.0  # Example: 1 arcsecond diameter aperture

# Calculate the area of the circular aperture in square arcseconds
aperture_area_arcsec2 = np.pi * (aperture_diameter_arcsec / 2)**2

# Calculate the surface brightness in FLAM per square arcsecond
surface_brightness_flam_arcsec2 = flux_flame / aperture_area_arcsec2

# Plot the surface brightness
plt.plot(wave, surface_brightness_flam_arcsec2)
plt.xlim(1000, 30000)
plt.xlabel('Wavelength (Angstrom)')
plt.ylabel('Surface Brightness [FLAM/arcsec^2]')
Replace the aperture_diameter_arcsec variable with the appropriate angular size of your source. This will give you the surface brightness inFLAM per square arcsecond.
 
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