What are the uncertainty values for my corrected magnitudes?

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SUMMARY

This discussion focuses on calculating the uncertainty values for corrected apparent magnitudes in astrophysics, specifically using the Colour Excess and extinction values. The Colour Excess is established at 0.36 with an uncertainty of 0.01. The ratios R_V for the SDSS r-band and g-band are 2.285 and 3.303, respectively. The calculated errors in the corrected g-band and r-band magnitudes are 0.033030 and 0.022850, respectively, derived from the formula ΔQ = R × √((Δa/b)² + (Δx/y)²).

PREREQUISITES
  • Understanding of Colour Excess in astrophysics
  • Familiarity with SDSS (Sloan Digital Sky Survey) data
  • Knowledge of apparent magnitudes and their uncertainties
  • Proficiency in applying error propagation formulas
NEXT STEPS
  • Study the application of Colour Excess in different astronomical contexts
  • Learn about the SDSS data release and its implications for astrophysical research
  • Explore advanced error propagation techniques in astrophysics
  • Investigate the impact of extinction on apparent magnitudes in various wavebands
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Astronomers, astrophysics students, and researchers involved in photometric measurements and error analysis in astronomical observations will benefit from this discussion.

Thomas Smith
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Homework Statement


I need to work out the errors of my corrected apparent magnitudes.

The Colour Excess is 0.36 with uncertainty = 0.01

The star was observed in two wavebands.
r-band = 2.285
g-band = 3.303

The 2.285 and 3.303 are the ratios R_V for the SDSS (Sloan digital sky servery) r and g bands.

The measured Apparent Magnitudes and Uncertainties.
g-band = 14.9228 uncertainty = 0.0003
r-band = 13.9178 uncertainty = 0.0002

The amount of extinction for g-band = 1.1890
The amount of extinction for r-band = 0.8226

g-band apparent magnitude extinction corrected = 13.7337
r-band apparent magnitude extinction corrected = 13.0952

Homework Equations



Colour Excess Uncertainty = a
Colour Excess = b
Measured Apparent Magnitude Uncertainty = x
Ratio of the band = y
##\Delta Q = 1.18908 × \sqrt{((a/b)^2 + (x/y)^2)}##[/B]

The Attempt at a Solution


Error in Corrected g band ##\Delta Q = 1.18908 × \sqrt{((Δ0.01/0.36)^2 + (Δ0.0003/3.303)^2)}## = 0.033030

Error in Corrected r band ##\Delta Q = 0.8226 × \sqrt{((Δ0.01/0.36)^2 + (Δ0.0002/2.285)^2)}## = 0.022850[/B]
 
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Thomas Smith said:

Homework Statement


I need to work out the errors of my corrected apparent magnitudes.

The Colour Excess is 0.36 with uncertainty = 0.01

The star was observed in two wavebands.
r-band = 2.285
g-band = 3.303

The 2.285 and 3.303 are the ratios R_V for the SDSS (Sloan digital sky servery) r and g bands.

The measured Apparent Magnitudes and Uncertainties.
g-band = 14.9228 uncertainty = 0.0003
r-band = 13.9178 uncertainty = 0.0002

The amount of extinction for g-band = 1.1890
The amount of extinction for r-band = 0.8226

g-band apparent magnitude extinction corrected = 13.7337
r-band apparent magnitude extinction corrected = 13.0952

Homework Equations



Colour Excess Uncertainty = a
Colour Excess = b
Measured Apparent Magnitude Uncertainty = x
Ratio of the band = y
##\Delta Q = 1.18908 × \sqrt{((a/b)^2 + (x/y)^2)}##[/B]

The Attempt at a Solution


Error in Corrected g band ##\Delta Q = 1.18908 × \sqrt{((Δ0.01/0.36)^2 + (Δ0.0003/3.303)^2)}## = 0.033030

Error in Corrected r band ##\Delta Q = 0.8226 × \sqrt{((Δ0.01/0.36)^2 + (Δ0.0002/2.285)^2)}## = 0.022850[/B]
I'm unsure about the brackets in the equation. Is this correct? ## \sqrt{((a/b)^2 + (x/y)^2)}##
Or should it be ## \sqrt{(a/b)^2 + (x/y)^2}##
 
Thomas Smith said:
I'm unsure about the brackets in the equation. Is this correct? ## \sqrt{((a/b)^2 + (x/y)^2)}##
Or should it be ## \sqrt{(a/b)^2 + (x/y)^2}##
I don't see a functional difference.