Intrinsic Brightness and Absolute Magnitude

1
Intrinsic Brightness and Absolute Magnitude

• brightness b and magnitude m depend on distance
  d to star
• can we find a distance-independent way to
  classify them?
• if the star were at a distance of 10 pc, then
  its magnitude m is its absolute magnitude M
• analogously, the intrinsic brightness of a
  star the brightness the star would show if at
  10 pc is called the luminosity L
• a star at d (b, m) or at 10 pc (L, M)

Some rules for logarithms

• a great way to reduce the breadth of numbers
• turns multiplication to addition, powers to
  multiplication
• recall that, for example, 102 100 ? log10100
  2
• log (ab) log a log b log(a/b) log a -
  log b
• log(ab) b log a base 10 log ?
  log

2
Recall brightness/apparent magnitude relation

• Now take base-10 log of both sides flipping R
  for L gives

• This is exact!! The 2.5 is NOT a rounded-off
  2.512!!

3
Move on to absolute magnitude/luminosity
If d 10 pc, then b L. So we say, since power
1/d2 . . .

• consider one star at distance is 10 pc then its
  magnitude m1 is absolute magnitude M and its
  brightness b1 is luminosity L
• at distance d its magnitude is m2 and its
  brightness is b2

• final version of the relation

4
Example 1 A star with apparent magnitude -3.5 is
at d 4 pc a) Find M b) How much brighter is
the star at 4 pc than at 10 pc?
Example 2 Two identical stars appear so that one
is 100 times brighter than the other a) Find
the difference in their apparent magnitudes b)
Find the ratio of their distances
5
Typical stars are pretty dim little fellas
So it turns out that most of the stars we see
are not only bright (duh!) but also are luminous
too!!
6
Fig.16.06
Three kinds of rainbows
Ordinary blackbody spectrum
Dark-line (absorption) spectrum
Bright-line (emission) spectrum
7
Fig.16.08
The Bohr model of hydrogen
Drawing ridiculously not to scale, but lowest
energy orbit IS smallest
Drawing quite accurately to scale its about 10
eV from 1 to 2, and 13.6 eV from 1 all the way up
to ?
8
Fig.16.09

• the electron in hydrogen can ONLYabsorb (n gets
  bigger) or emit (n gets smaller) photons of
  precisely quantized energy (color) and no other
• The QUANTUM idea
• note that the electrons energy levels are
  quantized too, along with the photon transition
  energies
• all atoms work this way, but with more electrons
  running around, the possibilities get messy but
  one can identify elements by these spectral lines
• atoms must be cool enough

9
In October comes the Series

• Lyman series (ends on n 1) all UV and so not
  visible!!
• black white photo of H atoms Balmer series
  (ends on n 2)

Balmer a
Balmer b
series limit

• Paschen series (ends on n 3) all IR and so
  not visible!!!
• Brackett series (ends on n 4) ditto!!

10
Fig.16.11
Color is related to surface temperature by BB idea
Cooler stars show more Balmer, hotter more Lyman,
hotter still little H spectra at all since H is
more completely ionized
Hottest Coolest
11
Fig.16.15

• Abundances of elements in a star ? note the
  logarithmic scale!!
• Note anamalously high iron content
• Details of the absorption spectrum indicate
  relative abundances of elements

12
Some spectra, in good old-fashioned bw
B0V
He lines strong hot star H lines weak
B5V
H lines strong hot star He lines strong
G0V
Ca and Fe lines strong cooler star
K0V
Ca and Fe lines strong molecular lines too!!
cool star