Cross Matching EUCLID and SKA using the Likelihood Ratio

Cross-matching SKA and EUCLID:The Likelihood Ratio

Kim McAlpine

Friday 02 August 2013

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


Cross-matching: A challenge? Low resolution radio data:

large positional offsets

Deeper data:Larger prob of random alignmentsMultiple counterparts

How to identify a ‘True’ counterpart


Likelihood RatioIdentifying CounterpartsLikelihood 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) = 12πσpos

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)




LR=f (r)q(m)

n(m)

Reli=LRi�

j LRj + (1− Q0)

f (r) = 12πσpos

exp( −r2

2σpos)







LR =f(r)q(m)

n(m)

Probability they are related




LR=f (r)q(m)

n(m)

Reli=LRi�

j LRj + (1− Q0)

f (r) = 12πσpos

exp( −r2

2σpos)







LR =f(r)q(m)

n(m)

Probability they are related

Probability they are unrelated




LR=f (r)q(m)

n(m)

Reli=LRi�

j LRj + (1− Q0)

f (r) = 12πσpos

exp( −r2

2σpos)







LR =f(r)q(m)

n(m)

Positional offset dependence




LR=f (r)q(m)

n(m)

Reli=LRi�

j LRj + (1− Q0)

f (r) = 12πσpos

exp( −r2

2σpos)







LR =f(r)q(m)

n(m)

Magnitude distribution of background

Magnitude distribution of counterparts


Positional Accuracy in Radio

Source

Noise

Source + Noise

= +


Positional Dependence f(r)3.3. LIKELIHOOD RATIO 50

Figure 3.3: Comparison between the errors in the radio source positions calculated using therelationships in Condon (1997) !Condon and the error estimates used in the LR analysis !Ivisonbased on the relationships in Ivison et al. (2007).

sections.

3.3.1 The radial dependence of the LR

The radial probability distribution, which represents the decreasing probability that a pair of

sources are related as their separation increases, f(r) is given by the Gaussian:

f(r) =1

2"!2pos

exp!!

r2

2!2pos

"(3.4)

where r is the o!set between the radio and infrared position and !pos is the combined positional

error of the radio and infrared sources.

Positional errors of radio sources can be ascribed to two independent sources of error,

calibration errors and noise-like errors (Condon et al., 1998). Calibration errors are independent

of source strength and are best estimated by a comparison with external, more accurate data.

In contrast, the noiselike contribution to positional errors is a function of the signal to noise

ratio of the detection and is thus the dominant contributor to the positional errors of sources

detected at low signal to noise. The noiselike positional errors of radio sources are usually

estimated from the models of Condon (1997) for the propagation of errors in 2-dimensional

Gaussian fits in the presence of Gaussian noise. The models give the noiselike contribution to

σ2pos = σ2

cal +

�0.6

FWHM

SNR

�2

f(r) =1

2πσposexp

−r2

2σpos


Magnitude Dependence

n(m) q(m)


Magnitude Dependence

3.3. LIKELIHOOD RATIO 54

Figure 3.4: Top: The distribution of real(m) and total(m). Middle: The magnitude dependenceof the of the LR P (m). Bottom: q(m) calculated by the LR in the cross-matching procedure.

Calculate excess sources: Total(m)

Subtract Background: real(m)

Calculate q(m)q(m) =

real(m)�m real(m)


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 areretained as reliable counterparts.

Q0 Fraction of True Counterparts

Multiple id’s

Ncont =�

Rel>0.8

(1− Rel)

Relj =LRj�

i LRi + (1−Q0)


Advantage of LR

Smith et al. 2011Identify sources with low reliabilites

Estimate how many missing id’s

Trade-off completeness vs contamination


LR: Depth & ResolutionVLA-survey:

100 microJyB-array6” 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


Cross-Matching at Lower Resolution

3.6. NEAR-INFRARED COUNTERPARTS TO RADIO SOURCES 63

Figure 3.7: The fraction of reliable counterparts detected at 6, 10 and 15 arcsec resolutionwhen matching against the VIDEO NIR catalogue restricted to detections with Ks < 22.6 andKs < 20.0. The greyscale bands represent the 1! Poisson error on the cross-matched fractions.

in !pos result in the expected decrease in the number of secure identifications.

A subsection of the radio data in this chapter has previously been matched to deep

K!band data using a LR procedure (Ciliegi et al., 2005). This matching was performed

over a 165 arcmin2 field observed by Iovino et al. (2005), the limiting magnitude used in the

matching procedure corresponds to the 50% completeness limit of Ks=23.9. Ciliegi et al.

(2005) find a total of 43 reliable K-band matches to the 65 radio sources located within this

subfield, corresponding to a completeness of " 66% which is significantly lower than the 88.7%

completeness achieved in this work. This improvement can be ascribed to the greater depth of

the VIDEO survey, which has factor of "12 greater integration time over the Iovino catalogue

with a telescope of similar aperture. Furthermore the q(m) distributions and LR in Ciliegi

et al. (2005) are derived from the VVDS optical catalogues from McCracken et al. (2003)

available over the whole 1 square degree radio field. As q(mopt) distributions are not precisely

equivalent to q(mNIR) it is likely that their use of the optical magnitude distribution in the

matching procedure contributes to an underestimate of the significance of some of the fainter

NIR matches.

3.6. NEAR-INFRARED COUNTERPARTS TO RADIO SOURCES 64

Figure 3.8: Close-in plot of the fraction of reliable counterparts detected for the faint radiosources (< 1 mJy) at 6,10 and 15 arcsec resolution when matching against the VIDEO NIRcatalogue 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 thePoisson 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 3.3

reveals a similar increasing trend in the number of contaminating sources with decreasing reso-

lution from 0.8% at 6 arcsec to 1.4 and 2.3% at the lower resolutions. However the completeness

of the cross-matched catalogue is nearly identical at all three resolutions, indicating that the

depth of the complementary near-infrared data is a more relevant limiting factor at these shal-

lower survey depths than radio survey resolution. This trend can be understood by examining

the middle plot in figure 3.4, which indicates that NIR counterparts with magnitudes lower than

Ks < 20.0 are assigned higher q(m)/n(m) fractions than fainter NIR matches. The intrinsic

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 deeper

NIR magnitudes the increasing density of faint sources dictates that resolution, or equivalently

positional accuracy, is increasingly relevant in determining the correct counterpart.

Figure 3.9 shows a plot of the fraction of reliably identified counterparts as a function

of Ks band magnitude. This demonstrates that deep near-infrared and/or optical data are

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%)


Cross-matching and magnitudesCross-Matching To Fainter Magnitudes

Most of the Cross-id’s arefaint

Cross-id’s are harder for faintsources.

Most of the Cross-id’s are faint

Cross-id’s are harder for faint sources


Cross Matching EUCLID and SKA using the Likelihood Ratio

Technology

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