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Analyzing Light

Flux and magnitude

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Magnitude System
Practice Problems

Astronomers measure the brightness of celestial objects using two related systems: flux and magnitude.

Flux

  • Flux (F) is the amount of energy received from an object per unit area per unit time.

  • It’s measured in units such as watts per square meter (W/m²).

  • Flux decreases with distance following the inverse square law.

  • Flux ∝ 1 / distance²

Apparent Magnitude (mm)

  • The apparent magnitude is a logarithmic measure of how bright an object appears from Earth.

  • A difference of 5 magnitudes corresponds to a factor of 100 in brightness

  • m₁ - m₂ = -2.5 × log₁₀(F₁ / F₂)

  • Smaller magnitudes mean brighter objects (e.g., the Sun has m= -26.7).

Absolute Magnitude (MM)

  • The absolute magnitude is the apparent magnitude an object would have if it were placed at a standard distance of 10 parsecs.

  • It allows comparison of intrinsic brightness between objects.

  • Relationship between apparent and absolute magnitude:
    m - M = 5 × log₁₀(d) - 5, where distance d is in parsecs.

Color and Color Magnitude

  • Color in astronomy is defined as the difference in magnitudes measured in two different filters (e.g., blue and visual).

  • For example:
    Color = B - V, where B is the blue magnitude and V is the visual (green-yellow) magnitude.

  • This color index reflects the temperature and spectral characteristics of a star:

    • Bluer stars (hotter) have smaller or negative color indices.

    • Redder stars (cooler) have larger color indices.

  • Color–Magnitude Diagram (CMD) plots absolute magnitude versus color, analogous to the Hertzsprung–Russell diagram. It’s a powerful tool for studying stellar evolution and star clusters.

 Self-Evaluating Questions

Try answering these questions after completing the reading. If you find any difficult to answer, revisit the textbook to reinforce your understanding.

  • a. The dimmer star is closer to us
    b. The dimmer star is farther away
    c. The stars are at the same distance
    d. The dimmer star is hotter

  • a. Closer
    b. Farther
    c. Exactly 10 parsecs
    d. Cannot be determined

  • a. A magnitude 1 star is 10 times fainter than a magnitude 6 star
    b. A smaller magnitude number means a dimmer star
    c. A star with m = 2 is brighter than a star with m = 5
    d. The magnitude scale is linear

  • a. B–V = –1.0, so the star is blue and hot
    b. B–V = +1.0, so the star is red and cool
    c. B–V = 0.0, so the star is white
    d. B–V = –1.0, so the star is red and cool

  • a. Cool, dim stars
    b. Hot, bright stars
    c. Cool, bright stars
    d. Hot, dim stars

    1. b. The dimmer star is farther away

    2. b. Farther

    3. c. A star with m = 2 is brighter than a star with m = 5

    4. a. B–V = –1.0, so the star is blue and hot

    5. b. Hot, bright stars