Subject: converting pipeline mags to AB mags

From: David Hogg

Submitted: Tue, 13 Aug 2002 18:02:35 -0400

Message number: 845 (previous: 844, next: 846 up: Index)

Conversion from SDSS natural 2.5m "pipeline" magnitudes to an AB system
-----------------------------------------------------------------------
  David W. Hogg (NYU)
  2002 August 13

Summary: to get from the 2.5m natural magnitudes output by the SDSS
pipelines--denoted, eg, r(2.5m)--to our best guess at a "true" AB
system--denoted, eg, r(AB,2.5m)--use the following transformations:

  u(AB,2.5m) = u(2.5m) - 0.042
  g(AB,2.5m) = g(2.5m) + 0.036
  r(AB,2.5m) = r(2.5m) + 0.015
  i(AB,2.5m) = i(2.5m) + 0.013
  z(AB,2.5m) = z(2.5m) - 0.002

where the uncertainties in these corrections are probably at the
few-percent level at least, but also positively covariant.  Note that
current DR1 (u-g) colors are off the AB system by about 8 percent.

-----
Details:

The following from Smith, Tucker et al, 2002, AJ, 123, 2121

  Here is the (nearly) AB photometry for BD+17 in the USNO system
  (denoted by, eg, "r'")

  BD+17
  r': 9.350 +/- 0.001
  (u'-g'): 0.920 +/- 0.001
  (g'-r'): 0.290 +/- 0.001
  (r'-i'): 0.100 +/- 0.001
  (i'-z'): 0.020 +/- 0.001

From the above I compute that BD+17 has, in the USNO system:

  u' = 9.350+0.290+0.920 = 10.560
  g' = 9.350+0.290       =  9.640
  r' = 9.350             =  9.350
  i' = 9.350-0.100       =  9.250
  z' = 9.350-0.100-0.020 =  9.230

The following from http://www-sdss.fnal.gov:8000/edoc/jeg_photometric_eq.html

  Here is how to convert USNO magnitudes (denoted by, eg, "r'") into
  the natural 2.5m magnitudes output by the SDSS survey pipelines
  (denoted by, eg, "r(2.5m)").

  To convert from u'g'r'i'z' to 2.5m ugriz:
    u(2.5m) = u' - b25(u)*( (u'-g')-(u'-g')_zp ) + zpOffset25(u)
    g(2.5m) = g' - b25(g)*( (g'-r')-(g'-r')_zp ) + zpOffset25(g)
    r(2.5m) = r' - b25(r)*( (r'-i')-(r'-i')_zp ) + zpOffset25(r)
    i(2.5m) = i' - b25(i)*( (r'-i')-(r'-i')_zp ) + zpOffset25(i)
    z(2.5m) = z' - b25(z)*( (i'-z')-(i'-z')_zp ) + zpOffset25(z)
  where
    b25(u) =  0.000
    b25(g) = -0.060
    b25(r) = -0.035
    b25(i) = -0.041
    b25(z) =  0.030
    (u'-g')_zp = 1.39
    (g'-r')_zp = 0.53
    (r'-i')_zp = 0.21
    (i'-z')_zp = 0.09
    zpOffset25(u) = 0.000
    zpOffset25(g) = 0.000
    zpOffset25(r) = 0.000
    zpOffset25(i) = 0.000
    zpOffset25(z) = 0.000

Plugging in, I get, for BD+17, the SDSS pipeline magnitudes:

  u(2.5m) = 10.560 - 0.000*( 0.920 - 1.390 ) + 0.000 = 10.560
  g(2.5m) =  9.640 + 0.060*( 0.290 - 0.530 ) + 0.000 =  9.626
  r(2.5m) =  9.350 + 0.035*( 0.100 - 0.210 ) + 0.000 =  9.346
  i(2.5m) =  9.250 + 0.041*( 0.100 - 0.210 ) + 0.000 =  9.245
  z(2.5m) =  9.230 - 0.030*( 0.020 - 0.090 ) + 0.000 =  9.232

  These are the magnitudes BD+17 WOULD BE GIVEN BY THE SDSS PIPELINES
  if it could be observed by the 2.5m without saturating the detector.

Daniel Eisenstein computes, for BD+17, plus 2.5m sensitivities, plus
  1.2 atmospheres of typical extinction:

  u(AB,2.5m) = 10.518
  g(AB,2.5m) =  9.662
  r(AB,2.5m) =  9.361
  i(AB,2.5m) =  9.258
  z(AB,2.5m) =  9.230

  I.e., our best bet to estimate "true" AB magnitudes is to take the
  SDSS pipeline outputs and make the following adjustments:

  u(AB,2.5m) = u(2.5m) - 0.042 +/- 0.050
  g(AB,2.5m) = g(2.5m) + 0.036 +/- 0.030
  r(AB,2.5m) = r(2.5m) + 0.015 +/- 0.030
  i(AB,2.5m) = i(2.5m) + 0.013 +/- 0.030
  z(AB,2.5m) = z(2.5m) - 0.002 +/- 0.030

  where the uncertainties are optimistic, educated guesses about the
  quality of the spectrophotometry.  On the other hand, if the
  spectrophotometry errors are correlated over wavelengths, there will
  be positive covariances among neighboring bandpasses, and maybe
  overall.  This means that although the u- and g-band adjustments are
  only about one sigma individually, the (u-g) adjustment might be
  many sigma.

  Douglas Tucker points out that there is a definite contribution to
  the uncertainties in the AB offsets from the uncertainties in the
  correct values of the "b" coefficients:
    (0.000 +/- 0.003)
    (0.060 +/- 0.001)
    (0.035 +/- 0.003)
    (0.041 +/- 0.001)
    (0.030 +/- 0.005)
  but this is sub-dominant at present

Please email me with comments or questions.
--
David W. Hogg        *  assistant professor
Center for Cosmology and Particle Physics
Department of Physics, New York University
4 Washington Pl, New York, NY 10003
212-992-8781 (tel)   *  212-995-4016 (fax)
david.hogg@nyu.edu   *  http://physics.nyu.edu/hogg/

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