Dots of light

What can we ask about a dot of light?

• How bright is it?
• Does it move?
• What colour is it?
• How small is the dot?

Apparent magnitude

• 'apparent' is used because this is how bright the star appears in the sky.
• 'magnitude' by itself usually means apparent magnitude.
• Stars of magnitude 1 are among the brightest.
• Stars of magnitude 6 are barely visible to the naked eye.
• Very bright objects can have negative magnitude.
• Objects can have fractional magnitudes, e.g. 1.75

The Winter Hexagon

Source: Jomegat Copyright - see source.

Rigel and Capella

• Both stars are magnitude 0.1.
• Are they two similar stars at the same distance?
• Or is one more luminous but further away?

Parallax

Source: Wikipedia CC-BY SA 3.0

Parallax and stars

Source: Wikipedia Public domain

Measuring parallax

1. View a star on a particular date.
2. Record its position - RA and declination.
3. Repeat 6 months later when Earth is at the other side of its orbit.
4. Record its position again.
5. Calculate the angle between the old and new positions - this is the parallax.

Degrees, arcminutes and arcseconds

• 1° is 60' or 60 arcminutes
• 1' is 60" or 60 arcseconds
• 1 mas is a milli-arcsecond or 0.001"
• The Moon is about 30' in diameter.
• Mars at opposition (when closest) is 25" in diameter.
• Betelgeuse is approx. 0.05" in diameter.

Parallax and distance

• 1 parsec (or pc) is defined to be a distance of parallax 1"
• 1 pc = 3.26 light years
• distance (in pc) = 1 / parallax (in arcseconds)
• distance (in ly) = 3.26 × distance (in pc)

Distance to Capella

• Capella has a parallax of 77.3 mas = 0.0773"
• So it's at a distance of 1/0.0773 = 12.9 pc
• Which is 12.9 × 3.26 = 42 ly

Distance to Rigel

• Rigel has a parallax of 3.78 mas = 0.00378"
• So it's at a distance of 1/0.00378 = 265 pc
• Which is 265 × 3.26 = 864 ly

Inverse square law

• A light source at double the distance is 2²=4 times dimmer.
• At triple the distance it's 3²=9 times dimmer.
• If the distance is x times larger, then it's x² times dimmer.

Inverse square law - diagram

Source: Borb CC-BY SA 2.5

You can understand the inverse square law by realising that light from a point source spreads out over larger areas.

Luminosity: Rigel vs Capella

• Rigel is 864/42 = 20.6 times further away than Capella.
• So Capella must be 20.6²=424 times dimmer than Rigel.
• This means that Rigel must be 424 times more luminous than Capella.
• Luminosity has a precise meaning.

Luminosity

• Luminosity is the rate at which an object emits energy as light
• For example, the luminosity of a 100 W light bulb is... 100 W
• The watt is a unit of power.
• Power is a rate of energy.
• Luminosity a property of the star itself, independent of distance

Absolute magnitude

• Absolute magnitude is another way to quantify the intrinsic brightness of a star.
• Absolute magnitude is the magnitude a star would have at a standard distance.
• The standard distance is 10 pc or 32.6 ly.
• Only a few stars are this close.

Examples

Colours of stars

Source: Mouser CC-BY SA 3.0

• Betelgeuse is tinged red. Rigel is blue-ish.
• Not very scientific...

Colour index

• Use a blue filter in the telescope, measure magnitude - call it B
• Use a filter in middle of visible spectrum, measure magnitude - call it V
• The difference B-V is called the colour index.
• If B is less than V, the star is brighter in the blue.
• So a blue star has a negative colour index.
• And a red star has a positive colour index.

Absolute magnitude and colour index

• We have the absolute magnitude for stars.
• And the B-V colour index for those stars
• How are they related?
• Let's plot them...

The Hertzsprung Russell Diagram

Source: Richard Powell CC-BY SA 2.5