Modelling SEDs with Artificial Neural Networks
Laura Silva (INAF/Trieste)
GianLuigi Granato (INAF/Trieste), Andrew Schurer (INAF/Padova), Cesario Almeida, Carlton Baugh,
Cedric Lacey, Carlos Frenk (ICC/Durham)
Outline:
• SED modelling- approaches vs aims • GRASIL and application to SAM• Modelling SED with ANN
Multi- SED modelling – approaches vs aims
*Stellar pop. synthesis
*SFR(t)+Mgas(t),Z(t) exponentials, chemical evol. or galaxy formation models
* UV/optical attenuation and IR emission
T
SSP dttZtTLtSFRTL0
))(,()()(
Semi-empirical: attenuation curve for LIR + IR shapePros: non time consuming –analysis of large data sets . Cons: not great predictive power
Theoretical: Explicit computation of radiative transfer and dust emissionPros: broader interpretative/predictive powerCons: time consuming
Modelling UV to radio SEDs with GRA(phite)SIL(icate)
Star- forming MCs
Diffuse dust
Extincted stars
1) Realistic and flexible SED modelling
Stars and dust in a bulge (King profile) + disk (double exponential)
Dust: big grains, very small grains and PAHs. Emission is appropriately computed for each component
Stars are born within MCs and gradually escape as a function of their age age-dependent extinction
3 dusty environments: dense (star forming Molecular Clouds), diffuse (cirrus) ( clumping of stars and dust), dusty envelopes of AGB stars
UV-to radio SEDs (continuum & nebular lines)
2) Reasonable computing time
Radiative transfer exactly solved for opt thick MCs, with approximation in the cirrus (real bottle-neck)
Presence of symmetries
No Monte Carlo
Computing SEDs in Semi-Analytical galaxy formation Models• SAM: DM with gravity-only N-body or MC, baryons with analytical recipes – compare with widest range of observed galaxy properties
• Outputs: simulated catalogues of galaxies at different redshift slices; SFR(t), Mgas(t), Z(t), morphology, scale radii for stars & dust• Associate to each mock galaxy its “real” SED but:complexities in treating radiative effects - unknown dust properties - computing time fundamental issue for cosmological volumes
Semi-empirical treatment: fix v (L or f(Mgas, Z)) + dependence + uniform distrib. of stars and dust in a 1D slab• SAMs with theoretical SED:
GALFORM+GRASIL (Granato+00, Silva+01, Baugh+05, Lacey+08)MORGANA+GRASIL (Monaco+07, Fontanot+07, 08)Anti-hierar.BarionicCollapse+GRASIL(Granato+04, Silva+05,Lapi+06)
SAM + GRASIL
SAM + [C&F00 + slab]
SF histories from the Semi-Analytical Model for galaxy formation MORGANA SED by: *GRASIL (colored) *Empirical [attenuation curve with C&F + slab] (hatched)
Fontanot, Somerville, Silva+08
Different treatments predict different SED for the same SFR(t)
Fontanot, Somerville, Silva+08
SAM+GRASIL
SAM+ templates[Chary&Elbaz01, Lagache+04, Devriendt+99]
SF histories from SAM MORGANA
SED by: *GRASIL (black) *Templates (color)
Different treatments predict different SED for the same SFR(t)
GALFORM + GRASIL (Granato+00, Silva+01, Baugh+05, Lacey+08)
But high-z universe : Revised model: reproduce multi- LFs and counts/ z-distr with top-heavy IMF in starbursts850m
Old model
850mNew model
Local universe :
0.2 m B-band K-band 60 m
Spectral variance for a GALFORM + GRASIL catalogue
=>ANN: Mathematical algorithms for data analysis, introduced to replicate the brain behavior - learn from examples
• SEDs : complex, non-linear, high dimensionality and large variance functions of some galaxy properties
ANN is a black box that is trained to predict the SED from controlling parameters using a suitable precomputed training set (many couples input-output)
Improving the computing time: Modelling SEDs with Artificial Neural Neworks
Input layer: parameters determining the SED
Output layer: SED, one unit for each L()
Hidden layers: black box!
wjk nj=wjkik
oj=f(nj)
Propagation rule: the output from each unit is weighted and summed to form the input for the upper layer units: nj=wjkik The new output is oj=f(nj) , f=non linear function
Learning: the ANN is trained with a given target- weights are adjusted to best approximate a given set of inputs/outputs
ANN & SED: 2 methods“Universal” and very fast (Silva+08): input = physical quantities determining the SED of MCs and Cirrus – one single trained net
• MCs: Optical depth , R/Rsubl.• Cirrus: Ldust, Mdust, Polar &
Equatorial opt depth, R*/Rdust, z*/R*, zdust/Rdust, Hardness of the rad. field
• “ANN mode” implemented in GRASIL: compute extinction and predict IR SEDs with separately trained ANN for MCs and Cirrus - ~ 1 sec. -> large cosmological volumes
“Less universal” and super-fast (Almeida+08): input = galaxy properties – re-train the net for different realizations
• Mstar, Zstar, Zgas, Lbol, vcirc, R1/2 (bulge & disc), V, Mburst, tlast burst …
• Each simulated catalogue from a SAM requires a trained net
• << 1 sec -> exploit the whole Millennium Simulation
Examples: single objects
M82
ARP220
m12.00zv2.50 @ 0.25 Gyr m13.00zv3.50 @ 0.25 Gry
m13.20zv3.50 @ 0.1 Gyr m13.20zv3.50 @ 0.5 Gyr
FULL/ANN Tot: black/redMC: dark /light greenCirr: blue/cyan
Examples: models extracted from ABC SAM (G04, S05)
Examples: models extracted from a GALFORM+GRASIL catalogue
Almeida et al.
…and one catastrophe ….work in progress…..
m12.00zv2.50 @ 0.1 Gyr
Improving the reconstructed SED by splitting the output neurons
GALFORM+GRASIL catalogue:
>70% with error < 10% - MIR and submm have larger variance
B-band 24 m
850 m
100(1-Lpredicted/Loriginal) vs Loriginal
Almeida et al.
Colours for z=0 GALFORM+GRASIL catalogue
Almeida et al.
ABC SAM – Galaxy counts
FULL: redANN: blue
24 m
850 m
24 mz=0.5
0.17 mz=3
850 mz=2GALFORM+GRASIL:
Luminosity Functions
______ original- - - - - - recontructed
Almeida et al.
Summary
• Multi-wavelength modelling as a tool to quantitatively deconvolve/ interpret observations – make predictions/ constrain galaxy formation models
• Different treatments predict different SEDs for the same SFR(t)-> necessity of a reliable computation of the SED for proper interpretations of observations and predictions of galaxy formation models
• The treatment of dust reprocessing of UV/optical in the IR requires a proper computation – time cosuming for some applications
• For large cosmological applications: promising solution with ANN