Quasar Astrometric Redshifts with LSST
Christina M. Peters
LSST AGN Science Collaboration
Roadmap Development Meeting
3 January 2017
i-z
r-i
g-r
u-g
Redshift - Color Relation
0
1
2
3
Redshift
4
Quasar color as a function of redshift.
Redshift - Color Relation
5
SDSS colors
102
Number of Quasars
Photometric Redshift
4
3
101
2
1
00
1
2
3
4
Spectroscopic Redshift
5
100
Spectroscopic redshift vs. photometric
redshift using SDSS colors.
Differential Chromatic Refraction
• Light bends entering the
atmosphere, function of
wavelength and airmass.
(Kaczmarczik et al. 2009)
Differential Chromatic Refraction
Transmission / Flux
• Light bends entering the
3000
5000
z = 1.1
z = 1.4
z = 1.7
z = 2.0
7000
9000
3000
5000
Wavelength [Angstroms]
7000
9000
atmosphere, function of
wavelength and airmass.
• Effective wavelength of
the bandpass depends on
SED. (Schneider et al.
1983)
Differential Chromatic Refraction
• Light bends entering the
Offset (arcseconds)
0.05
0.00
−0.05
−0.10
u band
g band
0.00
−0.05
−0.10
0.01
0.00
−0.01
−0.02
r band
0.00
i band
−0.01
0.00
z band
−0.01
0.0
0.5
1.0
1.5
2.0
2.5
Redshift
3.0
3.5
4.0
4.5
atmosphere, function of
wavelength and airmass.
• Effective wavelength of
the bandpass depends on
SED. (Schneider et al.
1983)
• Emission lines in quasar
SED change the effective
wavelength as a function
of redshift.
Differential Chromatic Refraction
0.2
Parallel Offset [arcsecs]
0.1
• Light bends entering the
0.0
0.1
0.2
•
0.3
0.4
0.5
•
0.60.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
tan(Z)
•
atmosphere, function of
wavelength and airmass.
Effective wavelength of
the bandpass depends on
SED. (Schneider et al.
1983)
Emission lines in quasar
SED change the effective
wavelength as a function
of redshift.
Need observations at
multiple airmasses to
overcome astrometric
error.
g-band
u-band
agPar
auPar
Redshift - DCR Relation
Redshift
Astrometric offset as a function of redshift.
Astro-Photometric Redshifts
Spec. Redshift
Colors
Astrometry
• Photometric redshift
P(Redshift)
PDFs can have multiple
peaks or wide plateaus.
0
1
2
Redshift
3
4
Astro-Photometric Redshifts
Spec. Redshift
Colors
Astrometry
• Photometric redshift
P(Redshift)
PDFs can have multiple
peaks or wide plateaus.
• Incorporating
astrometric PDFs can
break degeneracies or
isolate the correct value.
0
1
2
Redshift
3
4
Can LSST detect the DCR effect?
• Fit the measured offsets
with a straight line.
Can LSST detect the DCR effect?
• Fit the measured offsets
with a straight line.
• Actually many fits, using
of MCMC walkers.
Bayes Factor
M1 = mx + 0.0 - a model quasar
M2 = 0.0x + b - a “star”
K=
eln LM1
P r(D|M1 )
= ln LM
2
P r(D|M2 )
e
More quasar: K > 1.
Very strongly favoring a quasar: K > 100.
(1)
Bayes Factor - Examples
• Redshift: 2.1
• Airmass Range: 1.0 to 2.5
• Astrometric Err.: 0.020 arcsec
• Number of Observations: 20
Bayes Factor - Examples
• Redshift: 2.1
• Airmass Range: 1.0 to 2.5
• Astrometric Err.: 0.100 arcsec
• Number of Observations: 20
Bayes Factor - Examples
• Redshift: 0.6
• Airmass Range: 1.0 to 2.5
• Astrometric Err.: 0.020 arcsec
• Number of Observations: 20
Bayes Factor - Examples
In general these increase the Bayes factor:
• Redshift: stronger emission lines in bandpass
• Airmass Range: wider range
• Astrometric Err.: smaller error
• Number of Observations: more observations
Operations Simulator
and Metric Analysis Framework
• OpSims: potential survey observing schedules.
• Give airmass and filter for every pointing on the sky.
• Produce maps of the sky that summarize a given
statistic.
• kraken 1042: the current baseline cadence.
Number of Observations at Every Position
u-band. 1 year. opsim: kraken_1042.
0
50
100
150
200 250
number of visits
300
350
400
Range of Airmasses of Observations
u-band. 1 year. opsim: kraken_1042.
0
0.2
0.4
0.6
0.8
1
Airmass Range
1.2
1.4
Bayes Factor for Every Position
u-band. error: 0.020, z: 2.1. 1 year. opsim: kraken_1042.
1
1e+01
Bayes Factor
1e+02
Bayes Factor for Every Position
u-band. error: 0.045, z: 2.1. 1 year. opsim: kraken_1042.
1
1e+01
Bayes Factor
1e+02
Bayes Factor for Every Position
u-band. error: 0.020, z: 0.6. 1 year. opsim: kraken_1042.
1
1e+01
Bayes Factor
1e+02
Summary
Astrometric Redshifts:
• Can break degeneracies in photozs.
• Improve accuracies of quasar redshifts.
Summary
Astrometric Redshifts:
• Can break degeneracies in photozs.
• Improve accuracies of quasar redshifts.
Developing a MAF:
• Can determine if DCR effect will be detectable based
on a given OpSim.
• Effected by number of observations, range of
airmasses, and astrometric errors.
Next Steps
• Combine the measured slopes and errors with colors
using machine learning regression algorithms to
estimate redshifts.
• How much will detection of DCR improve a redshifts?
• What redshift ranges will have the greatest benefit?
• What constraints on the cadence / airmass limits are
necessary to get a benefit?
• How can we make this more realistic?
• Baldwin Effect.
• Astrometric errors at the survey limit.