AIMS Seminar by Dr Kim McAlpine, July 2013

1. Cross-matching SKA and EUCLID:
The Likelihood Ratio
Kim McAlpine
Friday 02 August 2013

2. Euclid complements SKA
Multi-wavelength data provides:
Photo-z’s:
Galaxy properties via SED-fitting:
Classification of AGN/SF
Cosmology
Evolution
Galaxy evolution
Environments
AGN Evolution
AGN/SF connection
Friday 02 August 2013

3. Cross-matching: A challenge?
Low resolution radio data:
large positional offsets
Deeper data:
Larger prob of random alignments
Multiple counterparts
How to identify a ‘True’
counterpart
Friday 02 August 2013

4. Likelihood RatioIdentifying Counterparts
Likelihood ratio technique
(e.g. Sutherland & Saunders 1992, Smith et al. 2011)
LR=
f (r)q(m)
n(m)
Reli =
LRi
j LRj + (1 − Q0)
f (r) = 1
2πσpos
exp
( −r2
2σpos
)
Radial probability density
- errors in VLA and VIDEO positions
n(m) Probability density of possible counterparts
ie. VIDEO K-band number counts
q(m) Probability density of true counterparts
Likelihood ratio technique
(e.g. Sutherland and Saunders 1992, Smith et al. 2011)
LR =
f(r)q(m)
n(m)
Friday 02 August 2013

5. Likelihood RatioIdentifying Counterparts
Likelihood ratio technique
(e.g. Sutherland Saunders 1992, Smith et al. 2011)
LR=
f (r)q(m)
n(m)
Reli =
LRi
j LRj + (1 − Q0)
f (r) = 1
2πσpos
exp
( −r2
2σpos
)
Radial probability density
- errors in VLA and VIDEO positions
n(m) Probability density of possible counterparts
ie. VIDEO K-band number counts
q(m) Probability density of true counterparts
Likelihood ratio technique
(e.g. Sutherland and Saunders 1992, Smith et al. 2011)
LR =
f(r)q(m)
n(m)
Friday 02 August 2013

6. Likelihood RatioIdentifying Counterparts
Likelihood ratio technique
(e.g. Sutherland Saunders 1992, Smith et al. 2011)
LR=
f (r)q(m)
n(m)
Reli =
LRi
j LRj + (1 − Q0)
f (r) = 1
2πσpos
exp
( −r2
2σpos
)
Radial probability density
- errors in VLA and VIDEO positions
n(m) Probability density of possible counterparts
ie. VIDEO K-band number counts
q(m) Probability density of true counterparts
Likelihood ratio technique
(e.g. Sutherland and Saunders 1992, Smith et al. 2011)
LR =
f(r)q(m)
n(m)
Probability they are
related
Friday 02 August 2013

7. Likelihood RatioIdentifying Counterparts
Likelihood ratio technique
(e.g. Sutherland Saunders 1992, Smith et al. 2011)
LR=
f (r)q(m)
n(m)
Reli =
LRi
j LRj + (1 − Q0)
f (r) = 1
2πσpos
exp
( −r2
2σpos
)
Radial probability density
- errors in VLA and VIDEO positions
n(m) Probability density of possible counterparts
ie. VIDEO K-band number counts
q(m) Probability density of true counterparts
Likelihood ratio technique
(e.g. Sutherland and Saunders 1992, Smith et al. 2011)
LR =
f(r)q(m)
n(m)
Probability they are
related
Probability they are
unrelated
Friday 02 August 2013

8. Likelihood RatioIdentifying Counterparts
Likelihood ratio technique
(e.g. Sutherland Saunders 1992, Smith et al. 2011)
LR=
f (r)q(m)
n(m)
Reli =
LRi
j LRj + (1 − Q0)
f (r) = 1
2πσpos
exp
( −r2
2σpos
)
Radial probability density
- errors in VLA and VIDEO positions
n(m) Probability density of possible counterparts
ie. VIDEO K-band number counts
q(m) Probability density of true counterparts
Likelihood ratio technique
(e.g. Sutherland and Saunders 1992, Smith et al. 2011)
LR =
f(r)q(m)
n(m)
Positional offset
dependence
Friday 02 August 2013

9. Likelihood RatioIdentifying Counterparts
Likelihood ratio technique
(e.g. Sutherland Saunders 1992, Smith et al. 2011)
LR=
f (r)q(m)
n(m)
Reli =
LRi
j LRj + (1 − Q0)
f (r) = 1
2πσpos
exp
( −r2
2σpos
)
Radial probability density
- errors in VLA and VIDEO positions
n(m) Probability density of possible counterparts
ie. VIDEO K-band number counts
q(m) Probability density of true counterparts
Likelihood ratio technique
(e.g. Sutherland and Saunders 1992, Smith et al. 2011)
LR =
f(r)q(m)
n(m)
Magnitude distribution
of background
Magnitude distribution
of counterparts
Friday 02 August 2013

10. Positional Accuracy in Radio
Source
Noise
Source + Noise
=+
Friday 02 August 2013

11. Positional Dependence f(r)
3.3. LIKELIHOOD RATIO
Figure 3.3: Comparison between the errors in the radio source positions calculat
relationships in Condon (1997) σCondon and the error estimates used in the LR an
based on the relationships in Ivison et al. (2007).
sections.
σ2
pos = σ2
cal +
0.6
FWHM
SNR
2
f(r) =
1
2πσpos
exp
−r2
2σpos
Friday 02 August 2013

12. Magnitude Dependence
n(m) q(m)
Friday 02 August 2013

13. Magnitude Dependence
Calculate excess sources:
Total(m)
Subtract Background:
real(m)
Calculate q(m)
q(m) =
real(m)
m real(m)
Friday 02 August 2013

14. Reliability 3.4. RELIABILITY OF COUNTERPARTS 59
Figure 3.6: Likelihood ratios and reliabilities for the VLA-VIDEO cross-matched dataset.
Reliability is not linearly related to likelihood ratio and only sources with reliabilities 0.8 are
Q0 Fraction of True
Counterparts
Multiple id’s
Ncont =
Rel0.8
(1 − Rel)
Relj =
LRj
i LRi + (1 − Q0)
Friday 02 August 2013

15. Advantage of LR
Smith et al. 2011
Identify sources with low reliabilites
Estimate how many missing id’s
Trade-off completeness vs contamination
Friday 02 August 2013

16. LR: Depth Resolution
VLA-survey:
100 microJy
B-array
6” resolution
1 sq degree
VIDEO survey:
Z,Y,J,H,Ks photometry
limits, 25.,24.6,26.5,24.0,23.5
Positional Accuracy
σ2
pos = σ2
cal +
0.6FWHM
SNR
2
FWHM σpos
VLA- B 6” 0.72
EMU 10” 1.2
WODAN 15” 1.8
Simulate lower-res EMU/WODAN
Friday 02 August 2013

17. Cross-Matching at Lower Resolution
6. NEAR-INFRARED COUNTERPARTS TO RADIO SOURCES 63
ure 3.7: The fraction of reliable counterparts detected at 6, 10 and 15 arcsec resolution
n matching against the VIDEO NIR catalogue restricted to detections with Ks 22.6 and
3.6. NEAR-INFRARED COUNTERPARTS TO RADIO SOURCES 6
Figure 3.8: Close-in plot of the fraction of reliable counterparts detected for the faint rad
sources ( 1 mJy) at 6,10 and 15 arcsec resolution when matching against the VIDEO NI
catalogue restricted to detections with Ks 22.6. The greyscale filled bands represent the 1
variation between the 100 simulated low resolution radio catalogues and do not include th
Poisson errors.
3.6.2 Counterparts as a function of near-infrared magnitude
In the case of matching against the VIDEO catalogue limited to the depth of the VHS, table 3
reveals a similar increasing trend in the number of contaminating sources with decreasing res
lution from 0.8% at 6 arcsec to 1.4 and 2.3% at the lower resolutions. However the completene
of the cross-matched catalogue is nearly identical at all three resolutions, indicating that th
depth of the complementary near-infrared data is a more relevant limiting factor at these sha
lower survey depths than radio survey resolution. This trend can be understood by examinin
the middle plot in figure 3.4, which indicates that NIR counterparts with magnitudes lower tha
Ks 20.0 are assigned higher q(m)/n(m) fractions than fainter NIR matches. The intrins
rarity of brighter NIR sources thus increases the significance of these bright NIR matches allow
ing us to partially overcome the limitation of poorer positional accuracy. In contrast at deep
NIR magnitudes the increasing density of faint sources dictates that resolution, or equivalent
3-5% loss at low res ()
Worst for faint sources
Very few mis-ids:
95, 90% same id
Low cont (0.7, 1.4, 2.3%)
Friday 02 August 2013

18. Cross-matching and magnitudes
Cross-Matching To Fainter Magnitudes
Most of the Cross-id’s are
faint
Cross-id’s are harder for faint
sources.
Most of the Cross-id’s are
faint
Cross-id’s are harder for
faint sources
Friday 02 August 2013