Astronomical Techniques Lecture 4 Magnitude Systems

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Astronomical Techniques Lecture 4Magnitude
Systems
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Brief History

• Hipparchus (129 BC)
• 1st magnitude brightest stars
• 2nd magnitude next brightest stars
• 6th magnitude faintest (naked eye) stars
• Refined by Ptolemey (140 AD)
• Telescope invented by Galileo (1610) led to
  discovery of fainter stars (7th, 8th mag)

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Pogson (Visual) System

• Pogson quantified magnitude system in 1856
• Observed that1st mag star roughly 100 times
  brighter than 6th mag
• Defined 5 magnitude difference to correspond
  exactly to brightness ratio of 1001
• 1 mag difference corresponds to fifth root of
  100, roughly a factor of 2.512 (Pogson ratio)
• Pogson magnitudes are logarithmic. Human
  perception is not quite logarithmic, so some
  stars became brighter than 1st magnitude

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Some Definitions

• Flux received from source of luminosity L at
  distance d decreases as square of distance F
  L/4pd2
• Magnitude is logarithmic m m0 2.5 log10 F
• Magnitude difference corresponds to ratio of
  fluxes m1 m2 2.5 log10 (F1/ F2)

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Visible Magnitude Scale

• Sun has mag 26.7
• Brightest star (Sirius) has mag 1.5
• Deepest HST image reaches 30
• 1022 range in brightness

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Photographic Magnitudes

• Early photographic emulsions were more
  blue-sensitive than human eye
• Stars with same visual magnitude (mV) may have
  different photographic magnitude (mP), or vice
  versa
• Different emulsions and human observers have
  different colour sensitivity
• Need better-defined magnitude systems

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Spectral Response

• Sensitivity of a detector, or detector plus
  filter combination, as a function of wavelength ?
  may be written S(?)
• Measured flux of source with flux distribution
  F(?)

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Spectral Response

• A bolometric detector is equally sensitive to all
  wavelengths, S(?) ? 1
• Other detectors /filters have an equivalent
  wavelength ?0 given by

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Magnitudes vs Flux

• Note that only optical and near-IR astronomers
  use magnitudes
• Astronomers at other wavelengths use flux units,
  particularly Janskys (Jy)
• 1 Jy 10-23 erg sec-1 cm-2 Hz-1
• Rest of lecture applies only to optical/near-IR
  astronomy

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Colour Index

• Colour index is just the magnitude difference
  between two filters BV ? mB mV 2.5 log10
  (FB/ FV)
• It is normally written with the bluer filter
  first, in which case the smaller the colour
  index, the bluer the object

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Johnson System (UBVRI)

• UBVRI filters defined using photoelectricdetector
  s with equivalent wavelengths of 365, 440, 550,
  640 and 790 nm
• Zero-points defined by Alpha Lyr (Vega) has
  V0.03 and all colour indices zero

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Spectrum of Vega
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Related Systems

• Kron-Cousins UBVRI for use with CCDs
• UBVRI system extended into the near-infrared with
  JHK filters
• J 1.25 microns
• H 1.65 microns
• K 2.22 microns
• K band light is a good tracer of mass in evolved
  stars

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AB Magnitudes

• Defined such that, when monochromatic flux f is
  measured in erg sec-1 cm-2 Hz-1 mAB 2.5
  log(f) 48.60 The value of the constant is
  selected so that mAB V for a flat-spectrum
  source
• In this system, an object with constant flux per
  unit frequency interval has zero colour

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SDSS Filters

• The Sloan Digital Sky Survey (SDSS) filter
  system is denoted ugriz
• Filters designed to avoid strong sky lines and to
  estimate photometric redshifts
• Based on AB system, although u magnitudes are
  about 0.04 mag off uAB uSDSS 0.04 mag

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SDSS Filter Response
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Specialist Systems

• So far we have discussed general purpose
  broadband (10 ? wide) systems
• Specialized filters
• Stromgren ubvy sensitive to stellar
  metallicities, narrower (0.25 ?) than
  JohnsonUseful for estimating globular cluster
  ages
• Narrow Band, eg H?, OII, OIII searching for
  specified ions

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Standard Stars

• Wavelength sensitivity varies from detector to
  detector
• Thus all systems are defined by a set of standard
  stars, whose magnitudes are defined by the system

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Photometric Redshifts

• Given observations of a source through many
  filters, we effectively have a low-resolution
  spectrum
• Can use multi-colour photometry to estimate
  redshift for a galaxy photometric redshift
• The COMBO-17 uses 17 filters to achieve
  moderately accurate redshifts without spectra

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Absolute vs Apparent Mags

• So far, all magnitudes have been apparent, ie. as
  observed
• The absolute (intrinsic) magnitude is defined to
  be equal to the apparent magnitude for a source
  at a distance of 10pc
• Sun has absolute mag MV 4.85
• A typical galaxy has MV ? ?20