Docstoc

Photometry

Document Sample
Photometry Powered By Docstoc
					Photometry
                                 Measuring Energy
• Photometry measures the             • Spectroscopy measures energy
  energy from a source using a          over a wide range of
  narrow range of wavelengths.          wavelengths.
   – Visual wavelengths from             – Visual spectrum
      400-700 nm                         – UV, IR spectra
   – Narrower slice of                   – Full EM spectra
      wavelengths
                                      • Spectroscopy requires
• Photometry uses filters to select     instruments to get at each
  wavelengths.                          wavelength separately.
                                         – Interferometer
                         Luminosity of Stars
• Luminosity measures how much energy is produced.
   – Absolute brightness L

• Relative luminosity is usually based on the Sun.
• Astronomers measure luminosity relative to the Sun.
   – LSun = 1 L
   – LSirius = 23 L

• Stars range from 0.0001 L to 1,000,000 L .
                                        Magnitude
                             • The observed brightness is
                               related to the energy received.

m  n  2.5 log( En / Em )   • The magnitude scale was
                               originally 6 classes.
                                – Effectively logarithmic
For 1 unit of magnitude:
                             • The magnitude (m) was made
 En
     101 2.5  2.512          formal in 1856.
 Em                             – Lower numbers brighter
                                – 6m at the limit of human
                                   vision
                         Brightness Magnified
• Images from a telescope must
                                      fe                    fo
  fit within the pupil.             P D                 M
   – Brightness proportional to       fo                    fe
       the aperture squared
   – Ratio of observed to natural
                                    R
                                         Ltelescope
                                                      
                                                        D M 2  1
• No increase for extended                 Leye           P2
  objects from magnification.
   – Eg. M31(> moon)
   – Light on more rods
   – Exclusion of other light
                     Point Source Magnified
• Point sources are smaller than
  one pixel (or rod).
   – No increase in image size         D2
                                     G 2
      from magnification               P
• The ratio of brightness increase
  is the light grasp G.              G  2 10 4 (m 2 ) D 2
   – Pupil size 7 mm

• The limiting magnitude comes       mm in  16 .8  5 log10 D
  from the aperture.
   – CCD 5 to 10 magnitudes                                in meters
      better
                                          8” aperture is 13.3m
                             Apparent Magnitude
• The observed magnitude             • Some bright stars (app. mag.):
  depends on the distance to the        – Sun                  -26.7
  source.                               – Sirius               -1.4
   – Measured as apparent               – Alpha Centauri       -0.3
      magnitude.
                                        – Capella              0.1
                                        – Rigel                0.1
• The scale is calibrated by stars
  within 2° of the north celestial      – Betelgeuse           0.5
  pole.                                 – Aldebaran            0.9

                                     • These are all brighter than first
                                       magnitude (m = 1.0)
                            Distance Correction
                                    • Brightness falls off as the
                d     2

                 100 
M  m  2.5 log      
                                      square of the distance d.
                     
                                    • Absolute magnitude M
M  m  5  5 log d                   recalculates the brightness as if
                                      the object was 10 pc away.
                                       – 1 pc = 3 x 1016 m = 3.26 ly

M  m  5  5 log d  AD
                                    • The absolute magnitude can be
AD = 0.002 m/pc in galactic plane     corrected for interstellar
                                      absorption AD.
                             Absolute Magnitude
• Distance is important to           • Some bright stars (abs. mag.):
  determine actual brightness.          – Sun                  4.8
                                        – Sirius               1.4
                                        – Alpha Centauri       4.1
• Example: 2 identical stars            – Capella              0.4
  A is 7 pc, B is 70 pc from Earth      – Rigel                -7.1
  The apparent brightness of B is       – Betelgeuse           -5.6
  1/100 that of A                       – Aldebaran            -0.3
  The magnitude of B is 5 larger.
                                     • These are quite different than
                                       their apparent magnitudes.
                                                   Imaging
• Photographic images used the     • CCDs can directly integrate the
  width of an image to determine     photoelectrons to get the
  intensity.                         intensity.
   – Calibrate with known stars       – Sum pixels covered by
   – Fit to curve                        image
                                      – Subtract intensity of nearby
      D  A  B log 10 I                 dark sky

                                   • Data is corrected for reddening
                                     due to magnitude and zenith
                                     angle.
                                             Solar Facts
• Radius:
   – R = 7  105 km = 109 RE        • Composition:
                                        – Mostly H and He
• Mass :
   – M = 2  1030 kg                • Temperature:
   – M = 333,000 ME                    – Surface is 5,770 K
                                        – Core is 15,600,000 K
• Density:
   – r = 1.4 g/cm3                  • Power:
   – (water is 1.0 g/cm3, Earth is      – 4  1026 W
     5.6 g/cm3)
                                       Hydrogen Ionization

ep = p2/2m                                 • Particle equilibrium in a star is
                                             dominated by ionized hydrogen.

  n=3                                      • Equilibrium is a balance of
  n=2                                        chemical potentials.

                                                                         g H n nQp 
   n=1                                         H n   mH n c  kT ln 
                                                                2                   
                                                                         nH 
                                                                               n   
                                                                       g p nQp 
                                                p   m p c  kT ln 
                                                            2
                                                                       n 
                                                                                
              H n    e     p                                p 
                                                                      g e nQe 
                                               e  me c  kT ln 
                                                             2
                                                                      n      
                                                                      e 
                                Saha Equation

                             • The masses in H are related.
mHn c2  mpc2  mec2  e n
                                – Small amount en for
                                  degeneracy

g (H n )  gn ge g p  4n2   • Protons and electrons each have
                               half spin, gs = 2.
                                – H has multiple states.


n ( H n ) g n e n           • The concentration relation is the
              e     kT
                               Saha equation.
 ne n p    nQe
                                – Absorption lines
                                         Spectral Types
• The types of spectra were originally                      •
  classified only by hydrogen              • Type   Temperature
  absorption, labeled A, B, C, …, P.           O      35,000 K
                                               B      20,000 K
• Understanding other elements’                A      10,000 K
  lines allowed the spectra to be
  ordered by temperature.                      F       7,000 K
                                               G       6,000 K
• O, B, A, F, G, K, M                          K       4,000 K
• Oh, Be A Fine Guy/Girl, Kiss Me              M       3,000 K
• Our Brother Andy Found Green
  Killer Martians.
                                   Spectral Classes
• Some bright stars (class):
   – Sun                  G2
   – Sirius               A1       • Detailed measurements of
   – Alpha Centauri       G2         spectra permit detailed classes.
   – Capella              G8
   – Rigel                B8
   – Betelgeuse           M1       • Each type is split into 10 classes
   – Aldebaran            K5         from 0 (hot) to 9 (cool).


• Temperature and luminosity are
  not the same thing.
                                                   Filters
• Filters are used to select a restricted bandwidth.
   – Wide: Dl ~ 100 nm
   – Intermediate: Dl ~ 10 nm
   – Narrow: Dl < 1 nm

• A standard set of optical filters dates to the 1950’s
   – U (ultraviolet – violet): lp = 365 nm, Dl = 70 nm
   – B (photographic): lp = 440 nm, Dl = 100 nm
   – V (visual): lp = 550 nm, Dl = 90 nm
                                                 Filter Sets
• Other filter sets are based on a   • CCDs have are good in IR, so
  specific telescope.                  filter sets have moved into IR as
   – HST: 336, 439, 450, 555,          well.
      675, 814 nm                       – U, B, V, R, I, Z, J, H, K, L,
   – SDSS: 358, 490, 626, 767,              M.
      907 nm                            – Example M : lp = 4750 nm,
                                            Dl = 460 nm
• The standard intermediate filter
  set is by Strömgren.
   – u, b, v, y, b
   – bw: lp =486 nm, Dl=15 nm
                                          Color Index
• The Planck formula at relates the
  intensity to the temperature.                        2c 2 h
   – Approximate for T < 104 K
                                      Wl (l , T )               e  hc / lkT
                                                         l5
• Two magnitude measurements at                  hc   hc
  different temperatures can          TB V              0.65 10 4 K
                                                lB k lV k
  determine the temperature.
   – Standard with B and V filters                             TB V 
                                      B  V  2.5 log 10 exp        
   – Good from 4,000 to 10,000 K                                T 
                                               7090 K
                                      T
                                           ( B  V )  0.71
                                    Stellar Relations
• The luminosity of a star should   • Some bright stars:
  be related to the temperature.       – Sun        G2     4.8
   – Blackbody formula                 – Sirius     A1     1.4
   – Depends on radius                 – Alpha Centauri G2 4.1
                                       – Capella G8        0.4
        L  4R 2T 4                  – Rigel      B8     -7.1
                                       – Betelgeuse M1     -5.6
                                       – Aldebaran K5      -0.3
                         Luminosity vs. Temperature

                 -20
                 -15
                                        • Most stars show a relationship
                 -10                      between temperature and
Abs. Magnitude




                  -5                      luminosity.
                  0            Sun         – Absolute magnitude can
                  5                          replace luminosity.
                 10                        – Spectral type/class can
                 15                          replace temperature.
                 20
                       O B A F G K M
                        Spectral Type
       Hertzsprung-Russell Diagram
• The chart of the stars’
  luminosity vs. temperature is
  called the Hertzsprung-Russell
  diagram.

• This is the H-R diagram for
  hundreds of nearby stars.
   – Temperature decreases to
     the right
                                                   Main Sequence

                 -20
                                                  • Most stars are on a line called
                 -15                                the main sequence.
                 -10
Abs. Magnitude




                  -5
                           Sirius                 • The size is related to
                  0                                 temperature and luminosity:
                  5                     1 solar      – hot = large radius
                 10                     radius       – medium = medium radius
                 15                                  – cool = small radius
                 20
                       O B A F G K M
                        Spectral Type
                                    Balmer Jump
• The color indexes can be
  measured for other pairs of
  filters.

• The U-B measurement brackets
  the Balmer line at 364 nm.
   – Opaque at shorter
      wavelength

• This creates a discontinuity in
  energy measurement.
   – Greatest at type A
   – Drop off for B and G
                                         Michael Richmond, RIT
                Photometric Comparison
• Stellar classification is aided by different response curves.
                       Bolometric Magnitude
                                      • Bolometric magnitude measures
 BC  mbol  V                          the total energy emitted at all
 BC  M bol  M V                       wavelengths.
                                         – Modeled from blackbody
                                         – Standard filter V
                                         – Zero for main sequence
                
L  3 10 28 W 10 0.4 M bol
                                            stars at 6500 K


                      
  2.5 10 8 W m 2 10 0.4 mbol
                                      • Luminosity is directly related to
                                        absolute bolometric magnitude.
                                         – Flux to apparent bolometric
                                           magnitude

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:4
posted:8/31/2011
language:English
pages:25