Cross Matching EUCLID and SKA using the Likelihood Ratio

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AIMS Seminar by Dr Kim McAlpine, July 2013

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Cross Matching EUCLID and SKA using the Likelihood Ratio

  1. 1. Cross-matching SKA and EUCLID: The Likelihood Ratio Kim McAlpine Friday 02 August 2013
  2. 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. 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. 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. 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. 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. 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. 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. 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. 10. Positional Accuracy in Radio Source Noise Source + Noise =+ Friday 02 August 2013
  11. 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. 12. Magnitude Dependence n(m) q(m) Friday 02 August 2013
  13. 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. 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. 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. 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. 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. 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

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