The Besancon Galaxy Model, a population synthesis tool for galactic - - PowerPoint PPT Presentation
The Besancon Galaxy Model, a population synthesis tool for galactic structure and evolution studies A.C. Robin, C. Reyl, B. Debray OSU THETA, Institut UTINAM Besanon, France Outlines Population synthesis approach Model ingredients
A.C. Robin, C. Reylé, B. Debray OSU THETA, Institut UTINAM Besançon, France
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Population synthesis approach Model ingredients Setting the model to photometric large scale surveys
comparison with SDSS+2MASS surveys Model web service Conclusions and perspectives
статистического исследования звездного населения:
– подсчет звезд в различных диапазонах блеска в
выделенных площадках, определение дифференциальной и интегральной функций блеска:
Решение обратной задачи звездной статистики (интегральное уравнение звездной статистики Шварцшильда, связывающее звёздную плотность и функцию светимости (φ(M(m,r,Av)) – абсолютная звездная величина) с наблюдаемой функцией блеска: Не слишком успешно: проблемы с неравномерным и неопределенным распределением поглощающей материи
Сделать предположение о модели, рассчитать ожидаемые результаты в терминах наблюдательных параметров (количество звезд на единицу звездной величины на бин цвета), и итерировать модель, добиваясь согласия расчетов с наблюдениями в пределах оцениваемых ошибок.
Sky survey data:
Color-magnitude diagram
given direction
Problem: how to
extract informations? Data on distances are not available.
thin disc stars thick disc stars halo Galaxies
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Inversion : deduce one or several parameters from observations (ex a velocity dispersion for a given set of stars, a luminosity function...) Require a priori knowledge, theoretical and empirical (or guesses) When a “reasonable scenario” points out : synthesis approach With surveys : complex multivariate analysis Allow comparisons of hypothesis/scenario with observations (even large data sets) of different types (multiwavelength, multiparameter...) Very powerful test method
Должна правильно отвечать на вопросы:
звезд мы видим в этом направлении?
распределение звезд
параметров можно определить, базируясь на знаниях о солнечной окрестности
Start with a mass of gas Tranform into stars as functions of IMF and SFR Stars evolve on evolutionary tracks and populate the HR diagram After a time (10 Gyr for the thin disc)
φ(Mv, Teff, log g, age)
Population synthesis
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Star formation rate history : How many stars are formed at a given time Initial Mass Function (IMF) : How many stars of a given mass Stellar models (evolutionary tracks): How stars evolve with time Stellar atmosphere models : How the physical state of the star atmosphere
are observed (getting magnitudes and colors)
Stellar density distributions: How the star density changes across the sky Chemical evolution : How the chemical abundances of the stars change with
their birth time
Dynamical consistency: How to include dynamical constraints (based on
gravity, conservation of energy, conservation of mass and of angular momentum)
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Star formation rate history : How many stars are formed at a given time
N(t) (one single burst, constant SFR)
Initial Mass Function (IMF) : How many stars of a given mass are formed,
N(m)dm~m-α.
Chemical evolution : How the chemical abundances of the stars change with
their birth time
Stellar density distributions: How the star density changes across the sky
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Stellar models (evolutionary tracks): How stars evolve with time
Boltzmann constraint (isothermal and relaxed thin disc population)
}
Star counts modelled as:
Computation of the number of stars of a given type on a given line of sight, by summing the contributions, and modulating with star density.
Volume elements on a line of sight Sommations on whole Hess diagram for each population Computation of catalogues of simulated stars with observable parameters : atmosphere models and extinction => Apparent magnitudes, colors kinematics => proper motions, radial velocities Add Observational errors Interstellar extinction
Production of star counts and distributions of observables
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Star formation history, Evolutionary tracks Atmosphere models Kinematics :
Extinction distribution (3D) Observational errors φ(Mv, Teff, Age, Z) Apparent magnitude, colours Proper motions, Vrad Equation of stellar statistics A(m)=∫φ(M)ρ(r)Ωr2dr Star counts Simulated catalogues
– Тонкий диск – Толстый диск – Балдж – Гало – Внешнее (темное) гало
не взаимодействуют (взаимопроникновение) -> можно моделировать отдельно. + Распределение поглощающей материи (модель поглощения)
4 populations : thin disc, thick disc, spheroid, bulge
Scenario : Thin disc : 10 Gyr, with cste SFR, 2 slope -IMF renormalised to the solar neighborhood (Hipparcos + CNS3) axisymmetric, kinematics and [Fe/H] function of age Thick disc : single burst, 11 Gyr, power law IMF density, IMF and kinematics constrainted by obs. Spheroid : single burst, 14 Gyr, power law IMF density, IMF and kinematics constrainted by obs. Bulge : single burst, 10 Gyr, power law IMF density constrained by NIR star counts
Star counts as a function of latitudes for longitudes 90° and 270° (rotation and anti-rotation) Comparison with observed star counts
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physics sufficiently understood ?
Use of multi-wavelength data (visible, IR, UV, X) Use of multiparameter data (photometry / spectroscopy / astrometry) Step by step approach (less parameters to start with, adding parameters when required, adding self-consistency loops when possible)
Тестирование гипотез и получение ограничений на их параметры
previous knowledge (common values in the literature for example). Then if it happens that there is a discrepancy between model predictions and data, we have to identify the parameter(s) that are bad and should be adjusted.
suitable to constrain certain parameters (like star counts in a set of directions as a function of magnitude and colors for example). Then we run simulations for the same directions, but varying the adjusted parameters and test the likelihood
constrained and better parameters for it.
Все составляющие модели – комплексы многопараметрических гипотезы (пример: эволюционные модели: lg L, Teff, lg g (m, z, lg t)) Есть параметры, связанные с другими, и есть свободные параметры (авторы стремятся уменьшить их число, исходя из физических соображений). Ниже приводятся примеры процесса уточнения связанных и свободных параметров.
magnitude 22, whole sky Hipparcos catalogue from 5 to 9, Tycho2 to 12th mag, Sloan Digital Sky Survey to 21th mag.
pole, Cosmos field)
Данные больших обзоров дополняют друг друга: разные диапазоны излучения, разные области неба, разная полнота
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Comparison of the model with 2MASS star counts
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Solution : bulge region fit with 2 structures (Robin, Marshall, Schultheis, Reylé, (2012) A&A 538, A106)
contribution of the thick disc Attempt to fit the bulge region 200 fields
K/J-K star counts K<12-14 (completeness limit) Extinction: 3D model from Marshall et al (2006).
Model Model Residuals with 2 components with 1 component Residuals
Model Robin et al 2012 Model Robin et al 2014
scale length)
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Data Model Residuals Significant residuals=> change warp slope
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Data Model Residuals New warp slope=> good agreement, no significant residuals
Fit SDSS fields with no streams (photometry) (F1,F2,F3,F4 patches) Add 2MASS fields at intermediate latitudes and a larger longitude range
2MASS fields in green, galactic coordinates
Exploration of the space of model parameters using a Metropolis- Hasting sampling method and MCMC (fit models to data by exploring
randomly at the beginning the parameter space of the possible models, compare them to data by computing a goodness-of-fit (can be a xi2 test or likelihood for example). Then it uses the result to optimize the way to explore the parameter space in order not to compute the goodness-of-fit for each of the possible models. It is very efficient if the dimension of the parameter space is
The choice is to do according to the type of the problem to solve.)
Observations: star counts in magnitude/color bins ( n = 14830) in 121 directions Models: from 10 to 18 parameters (2 thick disc shapes, 12 isochrones Age/[Fe/H]), 3 halos shapes, 3 thin disc models)
Scale height (local) 535 pc xsi=660 pc scale length : 2.3 kpc not exponential vertically ! Old thick disc flaring in the outer galaxy (scale height going up to ~1000 pc at Rgal=15 kpc) Thick disc contracting (scale length from 3 to 2 kpc, scale height from 800 et 350 pc when one goes from 12 to 10 Gyr)
Model Web page http://model.obs-besancon.fr
Email where to send the results Simulations are deposited on a ftp site and kept for ~1 week for the user to download
Model accessed via web: outputs
Model outputs
Model outputs
Model output: Example of predicted star counts in a given direction
Model output: Exemple of a predicted star catalogue
PLATO, Euclid, …)
model to compute a probability that a star has a given type, a given age
by computing this probability for a simulation of the field where the star is)
Robin, Luri, Reylé, et al, 2012, catalogue available at CDS Distribution of stars visible by Gaia
Galactic stars near a cluster, a dwarf galaxy, … (Sollima et al, 2014)
mission (Penny et al, 2013)
Galactic bulge
Predictions of optical depth in the bulge in V (comparaison MACHO, EROS, OGLE, MOA) Sum of all pairs source/lens simulated by BGM, taking into account extinction => event rate and distribution of time scale
Organisation of the web service
Responsable
Web interface Data base of simulations Technical support to users
Model development Scientific support to users
Extinction model
(CEA) Microlensing simulations Mabuls
(Manchester) http://model.obs-besancon.fr
2011 2012 2013 Total simulations 18276 21780 66932 Total nb of diff users 348 288 298 Total volume 300 Gb 492 Gb 1031 Gb Nb of countries 30 24 ~30
Statistics of model usage on the web not including particular simulations for Gaia, APOGEE, PLATO
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Population synthesis models are useful tools for data interpretation Although imperfect they allow a better understanding
make useful simulations for preparing future surveys Gaia, PLATO,Eucli d, LSST,…