1. Miguel CerviñoESAC 23 March 2007 How to use the SEDs produced by synthesis models? Miguel Cerviño (IAA-CSIC/SVO) Valentina Luridiana (IAA-CSIC/SVO)

2. Miguel CerviñoESAC 23 March 2007 What’s VO means in synthesis models context? Scientific vision:  VO requires to explicitly describe your data (you must know what are you doing, without implicit assumptions)  Data models in the VO describe the possible universe of classes of data  Hence: How to describe the whole universe of synthesis models (spectrum) results? How to include a model spectra resulting from a combination of sources in the current spectrum data model?

3. Miguel CerviñoESAC 23 March 2007 Stellar populations are modeled with synthesis models (http://ov.inaoep.mx) +

4. Miguel CerviñoESAC 23 March 2007 Stellar populations are modeled with synthesis models (http://ov.inaoep.mx)

5. Miguel CerviñoESAC 23 March 2007 Step 1: What is a synthesis model?: A stellar population is the result of a combination of spectra Real population: Synthetic population: Assumed representative spectrum Assumed representative evolution and Star Formation birth rate (IMF+SFH) Main issue: What is the accuracy and precision of this assumed representative ingredients?

6. Miguel CerviñoESAC 23 March 2007 Step 2: Synthesis results in VO Spectrum data model Not precision! Do they apply to synthesis models?

7. Miguel CerviñoESAC 23 March 2007 Step 3: Synthesis systematic errors Error sources in ingredients and computation: – Atmosphere libraries Theoretical libraries: – Good coverage in parameter space (log g, T eff, Z,  ) – Real stars could be different... – Observed libraries – They are real stars – Bad coverage in parameter space – How much are they “representative” of a class? – Tracks/Isochrones and Synthesis models algorithms – Isochrone synthesis: (Leitherer, Bruzual...) – Stellar evolution theory – Not all phases agree but observations, specially fast evolutionary phases (WR,TP-AGB, 3rd parameter in HB), but they are the most luminous phases! – Fuel Consumption Theorem: (Only for fast evo. ph.; Buzzoni, Maraston) – Calibrated with observations (different HB morphologies) – How much are they “representative” of a class?

8. Miguel CerviñoESAC 23 March 2007 Step 3a: Synthesis systematic errors Current status: There are groups evaluating errors in tracks/isochrones computations (e.j. Degl'Innocenti et al., Bressan et al....) There are group evaluating the error in isochrone - atmosphere model asignation (e.j. see García Vargas et al. Poster) Summary of systematic errors - Definition of synthesis models must include clearly - Tracks/Isocrones used - Atmosphere library used (and its coverage!) - Algorithms used in the computation of integrated properties - Models will include, in near future, an estimation of systematic errors --> Fitting applications should be created to allow to include (at least) observational errors in data + systematic errors in models (+ probabilistic dispersion in models: see now)

9. Miguel CerviñoESAC 23 March 2007 Step 4: Synthesis probability dispersion/Statistical errors Synthesis models types - Individual Monte Carlo Simulation: (a single spectrum) – No statistical error (since there is no statistical analysis) – But, can a single simulation be representative of a class of objects? - Sets of Monte Carlo simulations (a set of spectra) – Statistical error obtained from the analysis of the whole set. – A particular galaxy would be a point in the whole distribution (but which one?) – The distributions of Monte Carlo simulations are not necessarily gaussian ones!! (it would be needed the skewness and the kurtosis of the resulting distribution) – “Standard” models (a single “spectra”?) – Only give one value of the spectra for given physical parameters (age, metalicity, IMF, SFH) whatever the cluster size. – Probabilistic models – Single mean spectra + variance + skewness + kurtosis for given physical parameters and its variation with the observed cluster size (aperture effects...)

10. Miguel CerviñoESAC 23 March 2007 Standard synthesis models :  Used as deterministic tools  But they return the mean value of the observed properties - not their actual values  don’t give any further information on the distribution

11. Miguel CerviñoESAC 23 March 2007 Monte Carlo simulations and Probabilistic models: Simulations: Barbaro, & Bertelli, 1977, A&A, 54, 243 Chiosi et al.(1988) A&A 196,84 Santos & Frogel 1997, ApJ, 479, 764 Cerviño et al. 2000 A&A 360L Lançon & Mouhcine 2000, ASP C.S.,211, 34 Bruzual 2002, IAU Symp., 207, 616 Girardi 2002, IAU Symp., 207, 625 Cantiello et al. 2003, AJ 125, 2783 Theory (based on Poisson bins) Buzzoni 1989, ApJS, 71, 871 Cerviño et al. 2002, A&A, 381, 51 Cerviño, & Valls-Gabaud 2003 MNRAS 338, 481 González 2004, ApJ, 611, 270 Other approaches Cerviño & Luridiana 2004A&A...413..145 Cerviño & Luridiana 2006A&A...451..475 From Bruzual 2002, IAU Symp., 207, 616

12. Miguel CerviñoESAC 23 March 2007 Probabilistic Synthesis models

13. Miguel CerviñoESAC 23 March 2007 VO implemantation (1st approach): Same age & Z; 90% Confidence Interval Diferent age & same Z; mean valuesl

14. Miguel CerviñoESAC 23 March 2007 Step 4b: Synthesis probabilistic variance/statistical errors Current status: Monte Carlo sets provide statistical errors in model results (Teramo SSP models, B&C stochastic library) Standard models provide only mean values (but it is not enough) Probabilistic models provide variance (e.j. SBFs) + high order moments that allow to estimate if the DISTRIBUTION of INTEGRATED LUMINOSITIES follows a gaussian distribution or not (e.j. Cerviño & Luridiana 2006) Summary of probabilistic variance/statistical errors: - It is possible to use all fields in current spectral data model (may be a bit more of effort is needed in the definition of “error” in order to allow non-gaussian distributions) and all kind of models can be described in a probabilistic unified scheme. (standard models produce a mean, probabilistic models and Monte Carlo sets produce mean, variance + other parameters of the distribution of integrated luminosity, and a single Monte Carlo model is a single “data point” in a distribution) - They will be in the VO (e.j. PGos3 server + TSAP) at the end of summer... - For fitting tools that use synthesis models: precision (  2 fit) or accuracy (include observation errors + models systematic errors + probabilistic dispersion + over-fit test)?

15. Miguel CerviñoESAC 23 March 2007 Final Notes: Best fitted result (precision) is not enough! But the distribution of possible results are also needed The amount of information that we can obtain from a system is limited by the system itself. We can now, with a probabilistic approach, evaluate how much information we can obtain and avoid very precise (but inaccurate) over fitting results