Measuring the Stars

Parallax Revisited

Distance (Parsec)

Hipparcos satellite has measured parallax for about a million stars within ~200 pc

Proper Motion

Motion of stars perpendicular (transverse) to us

Usually measured in ''/year

Compare to Doppler Shift, which is motion toward or away (radial) from us

Real Space Motion

Pythagorean Theorem gives speed and direction

Luminosity

Luminosity

Intrinsic property of star

J/s = W

Distance independent

For a star: L = sT⁴(surface area) = sT⁴ (4pR²)

L µ T⁴ R²

Absolute measure

Brightness vs Luminosity

Brightness is what we measure from a star

Amount of energy striking an area (CCD chip or human eye) per unit time

J/(s m² ) = W/m²

Energy flux

What we measure depends on our distance from the star

Brightness = Apparent

Apparent brightness µ sT⁴ (4pR²) /d² =L/ d²

Brightness follows an inverse-square law

Brightness vs. Luminosity

Brightness is

What we measure on Earth

Distance dependent

Apparent

Luminosity

Intrinsic property

Distance independent

Absolute

Stellar Properties

Measuring radius, luminosity, and temperature

Magnitudes

Stars' brightnesses (W/m² ) are historically (Greek Hipparchus, 2^nd century BC) measured in magnitudes, m

Magnitude scale is logarithmic

1 magnitude unit change results in 2.5 X brightness change,

5 magnitude unit change, 100 X difference

Smaller magnitudes = larger brightnesses

More negative the number, the brighter the object

Apparent Magnitude Scale

m_sun = -26.8

Faintest object m=30, firefly seen from a distance equal to Earth's diameter

Absolute Magnitude

Absolute magnitude, M, is the apparent magnitude, m, that is measured exactly 10 pc from every object

M_sun= 4.85, m_sun= -26.8

In Fig. 17.6 Star A is closer to the observer and less luminous than Star B, but both appear to have the same brightness to the observer