1. Towards cosmology with a million supernovae: The BEAMS method Renée Hlozek Phys. Rev. D 75 103508 In collaboration with Bruce Bassett Martin Kunz

2. Lightcurve Fitting SN Ia SN Ibc SDSS ugriz lightcurve template fits (SDSS SN Survey use g,r,i for convenience)

3. Light curve fitting   2 Goodness of fit

4. Spectroscopic confirmation Si II line 6150 Å rest frame rest frame SALT spectrum (Bassett, Chen, van der Heyden, Vaisanen)

5. So what is the problem? 2006/7 - 2 SNe Ia/night 2006/7 - 2 SNe Ia/night 2010 - 30 SNe/night (SKYMAPPER) 2010 - 30 SNe/night (SKYMAPPER) 2014 - 500 SNe/night (LSST) 2014 - 500 SNe/night (LSST) Obtaining spectra for all the SN Ia detections will be impossible – we will be spectroscopically starved. Obtaining spectra for all the SN Ia detections will be impossible – we will be spectroscopically starved.

6. What is special about LSST? 8.4 m mirror 8.4 m mirror 10 degree 2 FOV 10 degree 2 FOV ( >25x the throughput of Subaru) Drift scans of the sky every 3 nights in survey mode, plus deep ‘searching mode’ Drift scans of the sky every 3 nights in survey mode, plus deep ‘searching mode’ Expected to yield ~250 000 SN Ia per year for at least 10 years Expected to yield ~250 000 SN Ia per year for at least 10 years

7. Timeline 1 million

8. Spectra Hurt! z>0.5 spectra require large telescopes z>0.5 spectra require large telescopes Integration time ~(1+z) 3,6 Even if all 8m class telescopes worldwide only took SNe spectra they would still only cover less than 20% of LSST detections per year Even if all 8m class telescopes worldwide only took SNe spectra they would still only cover less than 20% of LSST detections per year

9. Light-curve fitting is not perfect In the SDSS II SN (2006)  In the SDSS II SN (2006)  6 candidates were incorrectly identified as SN Ia from the lightcurves 6 candidates were incorrectly identified as SN Ia from the lightcurves Spectra revealed they were in fact Spectra revealed they were in fact Type Ib,c,II 6/150 ~ 4% of Sample 6/150 ~ 4% of Sample Extrapolating to LSST – 4% of 10 6 =4x10 4 – how can we deal with these unavoidable contaminants to LSST? Extrapolating to LSST – 4% of 10 6 =4x10 4 – how can we deal with these unavoidable contaminants to LSST?

10. Contaminated data Best SN Ia fit Best SN II fit SN Ia template was the best fit, while the candidate was actually a Type II

11. Contaminated Data I θ

12. Contaminated data II

13. Contaminated data III

14. Probability notation Probability of X given that Y is true Probability of X and Y (the probability that they are both true)

15. Marginalisation

16. Bayes’ Theorem Posterior – what we want to estimate Likelihood of observing the data given the parameter/theory Prior - Probability distribution before Bayesian evidence – (generally) arbitrary normalisation

17. Posterior: P i = P(t i =1) t i = 1 if SN Ia 0 if non-Ia 0 if non-IaMarginalisation D, t have N entries Bayes Independent Priors on θ,t

18. Uncorrelated data : P(D|θ,t ) separates into independent factors for Ia and non-Ia distributions Combining the two Ia distribution Non-Ia distribution Combinatorial simplification (Press)

19. Bayesian Estimation Applied to Multiple Species BEAMS results in a posterior that weights likelihoods obtained by assuming that the data is of each type with the probability that it is indeed that type.

20. Testing BEAMS Compare with other methods 1. Including only those candidates with P i > P cut in standard χ 2 analysis 2. Weighting the data from each candidate by P i N 3. Modify the error: σ i 2  σ i 2 + 1/P i N -1

21. How far away is our estimation from the true value? The error on the measurement – how ‘well’ do we estimate the value? Better Performance for 10 spectroscopic vs 1000 photometric

22. Better

23. Better Increasing P cut Performance for 10 spectroscopic vs 1000 photometric

24. Better Increasing N Performance for 10 spectroscopic vs 1000 photometric

25. Better Increasing M Performance for 10 spectroscopic vs 1000 photometric

26. Better Error for 1000 Spectroscopic points

27. Better Performance for 10 spectroscopic vs 1000 photometric

28. BEAMS Errors for distributions with different Errors for distributions with different

29. Making BEAMS robust What if there is a systematic error in the P i ’s ? Probabilities key to using BEAMS We allow for this with a nuisance parameter and marginalise over it to correct for error (bias) in the P i ’s.

30. BEAMS estimates the true mean correctly and can recover the systematic error (shift) in the probabilities m A =m-10

31. Iterative conservatism Beams can be made as conservative as one likes by adding extra parameters and marginalising over them to parameterize one’s ignorance

32. When the input data from SN Ia and contaminating distributions is analysed using BEAMS… Distribution Characteristics I

33. …we recover the distribution characteristics of the contaminants Distribution Characteristics II

34. BEAMS TRIP TO ARNISTON ”

35. BEAMS ‘washes whiter’ BEAMS allows for full use of the available information – automatically taking contamination into account: BEAMS allows for full use of the available information – automatically taking contamination into account: no discarded data, no bias BEAMS corrects for systematic errors in the probabilities BEAMS corrects for systematic errors in the probabilities BEAMS gives insight into the contaminant distribution itself BEAMS gives insight into the contaminant distribution itself

36. Changes to assumptions: Changes to assumptions: ▫ Uncorrelated data set – independent likelihoods – using block diagonal C ij ▫ Gaussianity for the non-Ia distribution Extend the BEAMS method to estimate photometric redshift: estimation straight from lightcurve data – collaboration with fitting techniques of Swedish group? Extend the BEAMS method to estimate photometric redshift: estimation straight from lightcurve data – collaboration with fitting techniques of Swedish group? Future Work - Theory

37. Future Work - Application Simulate LSST data – predict survey constraints Simulate LSST data – predict survey constraints Run BEAMS on large LSST data set – cluster? Run BEAMS on large LSST data set – cluster? 17 th mag limit

38. Future Work - Application Apply BEAMS to real SNe data from SDSS SN Survey Apply BEAMS to real SNe data from SDSS SN Survey Can we improve error estimates on Can we improve error estimates on w 0,w a using the photometric candidates? How do probabilites (and inferred cosmology) change with light-curve fitting techniques? How do probabilites (and inferred cosmology) change with light-curve fitting techniques?

40. Probabilities Probabilities key to using BEAMS Probabilities key to using BEAMS Often one may only know global probability, or P i ’s with associated errors Often one may only know global probability, or P i ’s with associated errors We can replace P i with distribution p (P i ) and marginalise over posterior – estimate global probability from the data We can replace P i with distribution p (P i ) and marginalise over posterior – estimate global probability from the data

41. Global Uncertainty We could instead ignore all probability information entirely – marginalise over posterior probability We could instead ignore all probability information entirely – marginalise over posterior probability Example – sending the wrong data! Example – sending the wrong data!

42. Distribution Characteristics Prior for the non-Ia data: Prior for the non-Ia data: (Marginalisation) (Marginalisation) So by including b,S in MCMC as free variables we gain insight into distribution characteristics of contaminants So by including b,S in MCMC as free variables we gain insight into distribution characteristics of contaminants

43. Maximum Likelihood Parameter Estimation Likelihood is defined as:

44. ● Thermonuclear explosions of WD ● Accretion in binary systems ● As WD reaches Chandrasekhar mass limit 1.44M o - no longer support itself against gravitational collapse The physics of Type Ia Supernovae

45. SALT image of distant supernova SDSS SN131951 This common mass at detonation believed to result in standard candle This common mass at detonation believed to result in standard candle Variation in intrinsic magnitude still exists, yet SNe Ia are still used as standard candles… Variation in intrinsic magnitude still exists, yet SNe Ia are still used as standard candles…

46. Standardizing SNe Ia   m 15 = change in m during 15 d after maximum 15 days

47. Garnavich et al. ‘The Bright ones last longer’ Peak luminosity Rate of decline Peak luminosity shown to be empirically correlated with the light curve decline rate (Phillips 1993)

48. Kim et al. Lightcurves as measured Lightcurve timescale ‘stretch factor’ corrected This correlation reduces the dispersion in intrinsic magnitude (s≈0.4m  ≈0.15m) – resulting in true ‘standard candle’

49. Why the correlation? Both peak luminosity and light curve decline rate are generally believed to be linked to the Nickel abundance in the stars Both peak luminosity and light curve decline rate are generally believed to be linked to the Nickel abundance in the stars More Ni Higher L peak Higher Temp increased κ, takes decreased photon λ Longer decline

51. Why SNe Ia anyway? SNe Ia have been used to probe the accelerating expansion of the Universe, and might allow us to determine the nature of dark energy (w=P de /ρ de ) http://blogs.chron.com/sciguy/archives/2006/11/the_dark_energ y.html

52. Using SNe Ia as standard candles