Speccal @ MPIA galaxy coffee

First presentation of speccal at MPIA galaxy coffee on August 6th, 2015

Transcript

1. How the Stellar IMF taught me about Flexible Noise Models Dan Weisz University of Washington Hubble Fellow Charlie Conroy (CfA) Ben Johnson (CfA) Dan Foreman-Mackey (UW) David W. Hogg (NYU) Galaxy Coffee MPIA 6.8.2015
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5. F475W-F814W F475W PHAT: High-mass Stellar IMF from Resolved Stars Photometry ~50 pc Brighter Fainter Hotter Cooler
6. F475W-F814W F475W PHAT: High-mass Stellar IMF from Resolved Stars Photometry ~50 pc M odel CM D Probability distributions for Age, Extinction, IMF slope, … Weisz+ 2015 (1502.06621) Brighter Fainter Hotter Cooler
7. Ground HST Limitations of resolved stellar pops Even HST becomes “crowding limited”
8. Ground HST Limitations of resolved stellar pops Even HST becomes “crowding limited” Need another way to measure the IMF…
9. High-Mass Stellar IMF from Integrated Light F475W-F814W F475W Resolved Stars M31 cluster HST photometry MMT Spectrum Integrated spectrum & photometry IMF slope, age, metallicity, mass, …
10. Common problem in astronomy: ‣ Have spectroscopy and photometry: want to use all information. ‣ Spectrum contains more information than photometry, but suffers from systematics. M31 cluster HST photometry MMT Spectrum
11. Some possible solutions: Common problem in astronomy: ‣ Have spectroscopy and photometry: want to use all information. ‣ Spectrum contains more information than photometry, but suffers from systematics. M31 cluster HST photometry MMT Spectrum
12. Some possible solutions: ‣ Model photometry first, use results as prior on spectral model. Common problem in astronomy: ‣ Have spectroscopy and photometry: want to use all information. ‣ Spectrum contains more information than photometry, but suffers from systematics. M31 cluster HST photometry MMT Spectrum
13. Some possible solutions: ‣ Model photometry first, use results as prior on spectral model. ‣ Assign relative weights to spectrum & photometry. Common problem in astronomy: ‣ Have spectroscopy and photometry: want to use all information. ‣ Spectrum contains more information than photometry, but suffers from systematics. M31 cluster HST photometry MMT Spectrum
14. Some possible solutions: ‣ Model photometry first, use results as prior on spectral model. ‣ Assign relative weights to spectrum & photometry. ‣ Convert spectrum into photometric indices. Common problem in astronomy: ‣ Have spectroscopy and photometry: want to use all information. ‣ Spectrum contains more information than photometry, but suffers from systematics. M31 cluster HST photometry MMT Spectrum
15. Some possible solutions: ‣ Model photometry first, use results as prior on spectral model. ‣ Assign relative weights to spectrum & photometry. ‣ Convert spectrum into photometric indices. ‣ Model photometry and spectrum independently, combine PDFs. Common problem in astronomy: ‣ Have spectroscopy and photometry: want to use all information. ‣ Spectrum contains more information than photometry, but suffers from systematics. M31 cluster HST photometry MMT Spectrum
16. Our Solution: Use a flexible noise model. M31 cluster HST photometry MMT Spectrum Common problem in astronomy: ‣ Have spectroscopy and photometry: want to use all information. ‣ Spectrum contains more information than photometry, but suffers from systematics.
17. Our Solution: Use a flexible noise model. M31 cluster HST photometry MMT Spectrum ‣ Model spectroscopy and photometry together. ‣ Photometry: absolute flux, spectral shape ‣ Spectroscopy: line information Common problem in astronomy: ‣ Have spectroscopy and photometry: want to use all information. ‣ Spectrum contains more information than photometry, but suffers from systematics.
18. Our Solution: Use a flexible noise model. M31 cluster HST photometry MMT Spectrum ‣ Physical parameters marginalized over data calibration. ‣ Learn about data/telescope calibration properties. Common problem in astronomy: ‣ Have spectroscopy and photometry: want to use all information. ‣ Spectrum contains more information than photometry, but suffers from systematics.
19. How does this work schematically? BDJ ET AL measure- metric cal- alibration- to produce pect to the can be ex- However, gth ranges, calibration ynomials) It is there- odel of the n the like- lization of hat allows ntroduced dified log- ⇤ smaller `. The multiplication by µn µn0 in the kernel function signifies that it is defined in fractional terms. Using a high order polynomial can result in strong degeneracies between model and polynomial parameters, whereas the Gaussian Pro cess BDJ make this more precise and correct likelihood only reduces the penalty for residuals on the scale of ` with ampli tude a that can’t be fit by the mean model. The two log-likelihoods, for photometry and spectroscopy are combined into a single likelihood function, ln p(ds,dp |✓,↵,b) = ln pspec(ds |✓,↵)+ln pphot(dp |✓,b) . (10 where now ds is the spectroscopic data and dp is the photo metric data. The spectroscopic likelihood pspec is given by equation (3) and pphot is given by equation (2). 3. DATA AND EXPERIMENTAL SETUP We are now left to demonstrate that, by including photom etry as well as spectroscopy, it is possible to infer the param eters of interest ✓ while marginalizing over the calibration pa ds : spectroscopy dP : photometry
20. How does this work schematically? BDJ ET AL measure- metric cal- alibration- to produce pect to the can be ex- However, gth ranges, calibration ynomials) It is there- odel of the n the like- lization of hat allows ntroduced dified log- ⇤ smaller `. The multiplication by µn µn0 in the kernel function signifies that it is defined in fractional terms. Using a high order polynomial can result in strong degeneracies between model and polynomial parameters, whereas the Gaussian Pro cess BDJ make this more precise and correct likelihood only reduces the penalty for residuals on the scale of ` with ampli tude a that can’t be fit by the mean model. The two log-likelihoods, for photometry and spectroscopy are combined into a single likelihood function, ln p(ds,dp |✓,↵,b) = ln pspec(ds |✓,↵)+ln pphot(dp |✓,b) . (10 where now ds is the spectroscopic data and dp is the photo metric data. The spectroscopic likelihood pspec is given by equation (3) and pphot is given by equation (2). 3. DATA AND EXPERIMENTAL SETUP We are now left to demonstrate that, by including photom etry as well as spectroscopy, it is possible to infer the param eters of interest ✓ while marginalizing over the calibration pa Physical Model (IMF, Av, mass, redshift, velocity, …) http://dan.iel.fm/python-fsps ds : spectroscopy dP : photometry
21. How does this work schematically? BDJ ET AL measure- metric cal- alibration- to produce pect to the can be ex- However, gth ranges, calibration ynomials) It is there- odel of the n the like- lization of hat allows ntroduced dified log- ⇤ smaller `. The multiplication by µn µn0 in the kernel function signifies that it is defined in fractional terms. Using a high order polynomial can result in strong degeneracies between model and polynomial parameters, whereas the Gaussian Pro cess BDJ make this more precise and correct likelihood only reduces the penalty for residuals on the scale of ` with ampli tude a that can’t be fit by the mean model. The two log-likelihoods, for photometry and spectroscopy are combined into a single likelihood function, ln p(ds,dp |✓,↵,b) = ln pspec(ds |✓,↵)+ln pphot(dp |✓,b) . (10 where now ds is the spectroscopic data and dp is the photo metric data. The spectroscopic likelihood pspec is given by equation (3) and pphot is given by equation (2). 3. DATA AND EXPERIMENTAL SETUP We are now left to demonstrate that, by including photom etry as well as spectroscopy, it is possible to infer the param eters of interest ✓ while marginalizing over the calibration pa Physical Model (IMF, Av, mass, redshift, velocity, …) http://dan.iel.fm/python-fsps low order polynomial to capture broad variations spectroscopic noise model Gaussian Process to model small- scale residuals (2 parameters) & http://dan.iel.fm/george/ ds : spectroscopy dP : photometry
22. How does this work schematically? BDJ ET AL measure- metric cal- alibration- to produce pect to the can be ex- However, gth ranges, calibration ynomials) It is there- odel of the n the like- lization of hat allows ntroduced dified log- ⇤ smaller `. The multiplication by µn µn0 in the kernel function signifies that it is defined in fractional terms. Using a high order polynomial can result in strong degeneracies between model and polynomial parameters, whereas the Gaussian Pro cess BDJ make this more precise and correct likelihood only reduces the penalty for residuals on the scale of ` with ampli tude a that can’t be fit by the mean model. The two log-likelihoods, for photometry and spectroscopy are combined into a single likelihood function, ln p(ds,dp |✓,↵,b) = ln pspec(ds |✓,↵)+ln pphot(dp |✓,b) . (10 where now ds is the spectroscopic data and dp is the photo metric data. The spectroscopic likelihood pspec is given by equation (3) and pphot is given by equation (2). 3. DATA AND EXPERIMENTAL SETUP We are now left to demonstrate that, by including photom etry as well as spectroscopy, it is possible to infer the param eters of interest ✓ while marginalizing over the calibration pa Physical Model (IMF, Av, mass, redshift, velocity, …) http://dan.iel.fm/python-fsps low order polynomial to capture broad variations spectroscopic noise model Gaussian Process to model small- scale residuals (2 parameters) & http://dan.iel.fm/george/ include ‘jitter’ term for each photometric point photometric noise model ds : spectroscopy dP : photometry
23. How does this work schematically? BDJ ET AL measure- metric cal- alibration- to produce pect to the can be ex- However, gth ranges, calibration ynomials) It is there- odel of the n the like- lization of hat allows ntroduced dified log- ⇤ smaller `. The multiplication by µn µn0 in the kernel function signifies that it is defined in fractional terms. Using a high order polynomial can result in strong degeneracies between model and polynomial parameters, whereas the Gaussian Pro cess BDJ make this more precise and correct likelihood only reduces the penalty for residuals on the scale of ` with ampli tude a that can’t be fit by the mean model. The two log-likelihoods, for photometry and spectroscopy are combined into a single likelihood function, ln p(ds,dp |✓,↵,b) = ln pspec(ds |✓,↵)+ln pphot(dp |✓,b) . (10 where now ds is the spectroscopic data and dp is the photo metric data. The spectroscopic likelihood pspec is given by equation (3) and pphot is given by equation (2). 3. DATA AND EXPERIMENTAL SETUP We are now left to demonstrate that, by including photom etry as well as spectroscopy, it is possible to infer the param eters of interest ✓ while marginalizing over the calibration pa Physical Model (IMF, Av, mass, redshift, velocity, …) http://dan.iel.fm/python-fsps low order polynomial to capture broad variations spectroscopic noise model Gaussian Process to model small- scale residuals (2 parameters) & http://dan.iel.fm/george/ include ‘jitter’ term for each photometric point photometric noise model ds : spectroscopy dP : photometry Apply priors and use emcee to sample posterior http://dan.iel.fm/emcee
24. Graphical Schematic of Spectroscopic Noise Model Flux Physical model
25. Graphical Schematic of Spectroscopic Noise Model Flux Physical model ~10-100% x Flux Smooth Noise Component
26. Graphical Schematic of Spectroscopic Noise Model Flux Physical model ~1-10% x Flux Gaussian process (operates on residual) ~10-100% x Flux Smooth Noise Component
27. Graphical Schematic of Spectroscopic Noise Model Flux Physical model ~1-10% x Flux Gaussian process (operates on residual) ~10-100% x Flux Smooth Noise Component Model Spectrum = Physical Model x (Smooth + GP)
28. COMBINING SPECTROSCOPY AND PHOTOMETRY 11 Figure 5. Results of inference from the combination of uncalibrated spectroscopy and all the photometric data points. Panels and are as in Figure 2. residual Age (Gyr) Log Z/Z⊙ M (105 M⊙ ) v Application to Mock Globular Cluster calibration from Schiavon+ (2005)
29. COMBINING SPECTROSCOPY AND PHOTOMETRY 11 Figure 5. Results of inference from the combination of uncalibrated spectroscopy and all the photometric data points. Panels and are as in Figure 2. residual Age (Gyr) Log Z/Z⊙ M (105 M⊙ ) v Application to Mock Globular Cluster calibration from Schiavon+ (2005)
30. COMBINING SPECTROSCOPY AND PHOTOMETRY 11 Figure 5. Results of inference from the combination of uncalibrated spectroscopy and all the photometric data points. Panels and are as in Figure 2. residual Age (Gyr) Log Z/Z⊙ M (105 M⊙ ) v Application to Mock Globular Cluster calibration from Schiavon+ (2005)
31. 14 BDJ ET AL Only grizJ photometry Spectroscopy + g photometry Spectroscopy + grizJ Truth Sensitivity Tests with a mock Globular Cluster
32. 16 BDJ ET AL Figure 11. The value of more photometry in combination with optical spectroscopy. Marginalized posterior PDFs obtained from mock spectra and photometry, for different numbers of photometric bands. The medians of the posterior PDFs are shown as connected black circles, the 16th and 84th percentile of the posteriors are indicated by the gray shaded region. Sensitivity of various physical parameters Spectrum + various photometric bands Bias [dex]
33. HST photometry MMT Spectrum Application to M31 Cluster
34. ‘Truth’ from CMD HST photometry MMT Spectrum Application to M31 Cluster
35. ‘Truth’ from CMD HST photometry MMT Spectrum Application to M31 Cluster MMT fiber size
36. ‘Truth’ from CMD HST photometry MMT Spectrum Application to M31 Cluster MMT fiber size Killed by Stochasticity (for now)
37. Conclusions A Flexible Noise Model readily allows you to model spectroscopic and photometric data together ‣ use all the available information; can be disjoint in wavelength ‣ no ad hoc weighting of data ‣ no need to subtract/normalize continuum ‣ physical parameters marginalized over data calibration ‣ learn about data/telescope calibration ‣ planned applications: stars, clusters, galaxies, … But not without some challenges… ‣ non-trivial to implement correctly ‣ modestly expensive to compute ‣ stochasticity http://dan.iel.fm/python-fsps http://dan.iel.fm/george/