Magnitude Scale - Apparent Magnitude

• It is related to our perception.

• It is a logarithmic scale:

  • A change of 5 in magnitude

  • corresponds to a change of a factor of 100 in apparent brightness. 

• It is inverted:

  • Larger magnitudes are dimmer.

• The original magnitude scale was defined so that

  • the brightest stars in the night sky have magnitude 1,

  • whereas the faintest stars visible to the naked eye have magnitude 6.

• Now, an increase of 1 in apparent magnitude corresponds to a decrease in apparent brightness by a factor of approximately 2.5.

Therefore

• Observe apparent brightness (e.g in magnitude scale)

• Know / Measure the distance

• Calculate Luminosity = Total Energy

Spectral Classification

• Colors   ➤  Classification

• But we need spectral lines for more detailed classification

• Differences in star's spectra means differences in Temperature; not in composition

• But stars show "similar behaviors" at certain temperatures. 

  • Example: T > 25 000 K

  • Strong absorbtion lines: He (singly ionized), O,N (multiply ionized)

  • Because these can only occur in hot stars (large temperatures  ➤  ionization)

  • However, weak H absorbtion lines: because not much H left  ➤  mostly ionized

Classification

• Spectral lines: mainly H line intensity (the early order)

➤  A, B, C ... (strongest to weakest)

• Then, they used surface temperature, Teff  (order is shuffled)

➤  O, B, A, F, G, K, M (dropped the others)

• These are called spectral classes or spectral types

  • Then each class subdivided into 10 parts designated by 0-9 (hotter to cooler)

H–R Diagram of Well-Known Stars

Plotted here are the data for some stars mentioned earlier in the text.

• The Sun:

  • luminosity : 1 solar unit.

  • temperature : 5800 K (read off the bottom scale); that of a G-type star.

• B-type star Rigel (at top left)

  • temperature : 11,000 K

  • luminosity more than 10,000 times that of the Sun.

• M-type star Proxima Centauri (bottom right)

  • temperature : 3000 K

  • luminosity less than 1/10,000 that of the Sun. 

H–R Diagram of Nearby Stars

Most stars have properties within the long, thin, shaded region of the H–R diagram known as the main sequence (MS)

• These are the 80 closest stars to us

• The points plotted here are for stars lying within about 5 pc of the Sun.

• Each dashed diagonal line corresponds to a constant stellar radius, so that stellar size can be indicated on the same diagram as stellar luminosity and temperature. 

• The most stars are in the main sequence.

• White dwarf region: they are hot but not very luminous, as they are quite small.

H–R Diagram of Brightest Stars

An H–R diagram for the 100 brightest stars in the sky is biased in favor of the most luminous stars

• They appear toward the upper left

• We can see them more easily than we can the faintest stars. 

• These stars are all more luminous than the Sun.

• Two new categories appear here: the red giants and the blue giants.

• The brightest stars in the sky appear bright because of their enormous luminosities, not their proximity.

In summary

• T (temperature) - increases - right to left

• L (Luminosity) - increases - bottom to top

• R (radius) - increases - bottom-left to top-right

• M (mass) - increases - along MS bottom-right to top-left

H-R Diagram for 20 000 stars

• The main sequence is clear

• The red giant region is clear

• About 90% of stars lie on the main sequence

• 9% are red giants

• 1% are white dwarfs.

Spectroscopic Parallax

A measurement of the apparent brightness of a light source combined with some knowledge of its intrinsic properties can yield an estimate of the source's distance.

• Since most of the stars are in MS and they show L & T correlation, MS can tell us about average properties of most stars

  • Get the spectrum

  • Find the temperature (T)

  • Use H-R and find corresponding luminosity (L)

  • Use L to calculate the flux (F)

  • Flux then can be related to distance (d) since it is 1 / d2