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Cedric Lacey

Multi-wavelength modelling of galaxy evolution: Lecture 2: Semi-analytical models of galaxy formation. Cedric Lacey. Outline. Why multi-wavelength modelling of galaxy evolution? Basics of semi-analytical galaxy formation models A tale of 2 models - does the IMF vary?

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Cedric Lacey

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  1. Multi-wavelength modelling of galaxy evolution:Lecture 2: Semi-analytical models of galaxy formation Cedric Lacey Foz de Iguacu

  2. Outline • Why multi-wavelength modelling of galaxy evolution? • Basics of semi-analytical galaxy formation models • A tale of 2 models - does the IMF vary? • Chemical evolution in hierarchical models - further evidence for a variable IMF? Foz de Iguacu

  3. Why multi-wavelength modelling? Foz de Iguacu

  4. Why do we need multi-wavelength models of galaxy evolution? (i.e models which cover wavelengths from UV to IR or radio) • Different wavelengths provide complementary information - sensitive to different physical processes • Multi-wavelength view of galaxy evolution now becoming observationally accessible - GALEX satellite in far-UV, SPITZER in IR, SCUBA-2 in sub-mm, VLA in radio…. Foz de Iguacu

  5. 2 different views of the Hubble Deep Field optical sub-mm Universe looks very different at different wavelengths! Foz de Iguacu

  6. Key Motivation: Understand Star Formation History of universe • Cosmic SFR history describes how baryons converted into stars over history of universe - fundamental quantity in models of galaxy formation • Many attempts to determine SFR history observationally - but different methods each have own limitations, and final answer still uncertain Foz de Iguacu

  7. Methods to measure SFR For distant galaxies, cannot observe individual stars, so must infer SFR from some property of integrated light: • Far-UV continuum from stars (912 < < 3000A) • IR or sub-mm continuum from dust (10 m < < 1 mm) • Emission lines from HII regions • Radio continuum (usually non-thermal) (> 10 cm) Foz de Iguacu

  8. 1. SFR from far-UV continuum • In galaxies with significant star formation, non-ionizing far-UV (FUV) continuum dominated by O & B stars with lifetimes < 100 Myr • So if could measure L(FUV) without dust extinction, could infer formation rate of stars with m > 5 Mo • However, in most galaxies, dust extinction in FUV very large • Furthermore, no reliable & accurate way to measure this dust extinction from FUV continuum alone (various empirical methods, but do not work for all types of galaxies) Foz de Iguacu

  9. 2. SFR from IR & sub-mm continuum • Most star formation appears to happen in dusty regions with UV) > 1 • most UV luminosity from young stars absorbed by dust grains & then re-radiated in IR & sub-mm • total IR luminosity (integrated over 10 < 1000 m) should provide good measure of formation rate of m > 5 Mo stars in most cases • However, measurement of L(total IR) only currently possible for local galaxies Foz de Iguacu

  10. For high-z galaxies, can only measure L in mid-IR or sub-mm, then convert to L(total IR) based on assumed SED shape • But SED shapes in IR/sub-mm vary, so this is uncertain (mid-IR & sub-mm both miss peak of dust emission in far-IR, m) Foz de Iguacu

  11. 3. SFR from HII region emission lines • HII region emission lines (e.g. Ly, H, [OII]) produced by gas ionized by O & B stars (lifetimes < 10 Myr) • If could measure unextincted luminosities of H-recombination lines (e.g. H) would give direct measure of rate of H-ionization, hence formation rate of stars with m > 10 Mo • Can try to estimate dust extinction observationally from recomination-line ratios (e.g. HH) - but only works for simple dust geometries, and v.difficult at high-z Foz de Iguacu

  12. 4. SFR from radio continuum • Low-frequency radio continuum in star-forming galaxies dominated by synchrotron emission • Synchrotron emission thought to be powered by Type II supernova explosions • So L(radio) should provide measure of SNII rate, hence formation rate of stars with m > 8 Mo • Advantage: L(radio) not affected by dust • Disadvantage: conversion L(radio)/rate(SNII) might depend on magnetic fields Foz de Iguacu

  13. Measuring SFRs: the IMF uncertainty • All methods (1) - (4) only measure formation rate of massive stars (m > 5-10 Mo) • To get total SFR, have to extrapolate down to low masses (m = 0.1 Mo) based on an assumed IMF • What if the IMF varies with environment? - e.g. if it is different in normal & starburst galaxies ? Foz de Iguacu

  14. Measuring cosmic SFR: the LF uncertainty • Want to obtain total SFR/(comoving volume) as function of redshift z • This requires summing SFRs of ALL galaxies in representative volume of universe • In practice, at high-z only observe highest luminosity galaxies • Have to extrapolate contribution of low-L galaxies based on assumed luminosity function (LF) • But LF shape varies with wavelength & redshift, so this introduces further uncertainties Foz de Iguacu

  15. Example of observational data on cosmic SFR history • variety of methods shown: far-UV, H, sub-mm • with/without corrections for dust extinction Foz de Iguacu

  16. How to test cosmic SFR history predicted by a galaxy formation model against observations? • Since current obsns only probe some ranges of wavelength & luminosity • also given uncertainties from dust extinction & IMF => most robust way to compare models with obsns is to compare predicted & observed LFs at wavelengths actually observed • Multi-wavelength modelling allows one to do this Foz de Iguacu

  17. Semi-analytical models of galaxy formation Foz de Iguacu

  18. Galaxy formation in the CDM model: key physical processes • Assembly of dark matter halos • Shock-heating and radiative cooling of gas within halos • Star formation and feedback • Production of heavy elements • Galaxy mergers Foz de Iguacu

  19. Semi-analytical models • Start from initial density fluctuations • Use analytical and/or Monte Carlo modelling for the different physical processes • Predict galaxy properties (mass, radius, luminosity, metallicity etc) and their evolution with redshift Foz de Iguacu

  20. Some references on semi-analytical models • White & Rees (1978) • White & Frenk (1991), Lacey et al (1991) • Kauffmann, White & Guiderdoni (1993), Cole et al (1994) • Somerville & Primack (1999) • Cole et al (2000), Granato et al (2000) • Guiderdoni et al (2001), Nagashima et al (2001), Menci et al (2002) • Baugh et al (2005) • and many more…… Foz de Iguacu

  21. Assembly of dark matter halos: Merger trees • Assembly history of halo described by merger tree • 2 approaches: • Monte Carlo based on conditional Press-Schechter mass function • Extract from N-body simulations • similar results from both approaches Foz de Iguacu

  22. Shock-heating & cooling of gas in halos • Infalling gas all shock-heated to halo virial temperature • Radiative cooling of gas from static spherical distribution • Disk size related to angular momentum of gas which cools Foz de Iguacu

  23. Shock-heating & cooling of gas: more details • Assume halo gas shock-heated to uniform temperature: • Assume halo density profile: or Foz de Iguacu

  24. Assume gas density follows dark matter, or modified profile with core, e.g. • Radiative cooling time in halo then depends on radius through: where L(T,Z) is radiative cooling function for collisional ionization equlibrium • At time t after halo has formed, gas cools out to radius rcool(t) given by: Foz de Iguacu

  25. Disk radius • if it conserves its angular momentum, cooled gas collapses to form rotationally-supported disk with radius roughly: where is halo spin parameter • more detailed calcn of disk radius depends on halo profile and disk self-gravity Foz de Iguacu

  26. Star formation & feedback • stars form in disks • supernova feedback ejects gas from galaxies Foz de Iguacu

  27. Star formation timescale in disks • A popular choice is: where dyn is dynamical time in disk • Another popular choice: • or some combination of these… Foz de Iguacu

  28. Supernova feedback • Usually assume SN feedback efficiency of form where hot & Vhot are parameters • hot =2 corresponds to constant efficiency of converting SNII explosion energy into gas ejection energy Foz de Iguacu

  29. Galaxy mergers & morphology • halos merge • galaxies merge by dynamical friction • major mergers make galactic spheroids from disks • mergers trigger starbursts • spheroids can grow new disks Foz de Iguacu

  30. Effects of galaxy mergers • Galaxy mergers with mass ratio M2/M1 > 0.3 cause major changes in galaxy morphologies - trigger re-arrangement of stellar disks into spheroids - these are MAJOR MERGERs • Smaller mass ratios produce minor morphological changes - these are MINOR MERGERS • Major mergers trigger STARBURSTS which consume remaining gas • Minor mergers may also trigger bursts (but with lower efficiency) Foz de Iguacu

  31. Modelling galaxy SEDs use GRASIL model to compute emission from stars, extinction and emission by dust, and radio emission (Silva et al 1998) Foz de Iguacu

  32. semi-analytical model tracks evolution of metallicity of stars & gas • assume dust/gas proportional to gas metallicity • optical depth for dust depends on both dust mass and galaxy radius Foz de Iguacu

  33. Example Model SED (1) • unextincted starlight • (+ radio) Foz de Iguacu

  34. Example Model SED (2) • starlight with dust extinction Foz de Iguacu

  35. Example Model SED (3) • starlight with dust extinction • emission from diffuse dust Foz de Iguacu

  36. Example Model SED (4) • starlight with dust extinction • emission from diffuse dust + molecular clouds Foz de Iguacu

  37. Example Model SED (5) • starlight with dust extinction • emission from diffuse dust + molecular clouds • total Foz de Iguacu

  38. Two models of galaxy formation - both based on same CDM cosmology Foz de Iguacu

  39. Model 1 (Cole et al 2000, Granato et al 2000) • Star formation timescale in disks: - scaling with dyn implies much shorter disk SFR timescales at high-z • Starbursts triggered by major mergers only • Normal solar neighbourhood IMF for all star formation Foz de Iguacu

  40. Model 2 (Baugh et al 2005) • Star formation timescale in disks: - longer disk SFR timescales at high-z c.f. Model 1 => high-z disks more gas-rich • Starbursts triggered by major & minor mergers => Starbursts make much larger contribution to total SFR at high-z Foz de Iguacu

  41. Model 2 (cont’d) • Normal solar neighbourhood IMF for stars formed quiescently in galaactic disks • Top-heavy (x=0) IMF for stars formed in bursts triggered by galaxy mergers => Starbursts much more luminous because of larger fraction of high-mass stars Foz de Iguacu

  42. Choice of free parameters • For both Models 1 & 2, adjust free parameters to fit wide range of observational data on present-day galaxies: - luminosity functions in optical, near-IR, far-IR; disk sizes & circular velocities; gas fractions, metallicities, mix of morphological types etc Foz de Iguacu

  43. Star formation history both models model 1 model 2 quiescent quiescent quiescent bursts bursts bursts model 2 has more star formation in bursts at high z Foz de Iguacu

  44. Present-day optical & near-IR luminosity functions (Model 1) B-band K-band Foz de Iguacu

  45. Present-day far-IR LF (Model 1) 60 m quiescent bursts Foz de Iguacu

  46. Present-day optical & near-IR LFs (Model 2) B-band K-band total total no dust quiescent quiescent no dust bursts bursts Very similar to Model 1 - this is because free parameters in model chosen to try to match present-day galaxies Foz de Iguacu

  47. Present day luminosity LFs in far-IR & radio (Model 2) far-IR (60 m) radio (1.4 GHz) total quiescent bursts Again, not much difference between Models 1 & 2 Foz de Iguacu

  48. So both models predict very similar properties for local universe • At high redshift however, predictions differ dramatically…. Foz de Iguacu

  49. Sub-mm (850 m) source counts (Model 1 vs Model 2) Model 1 Model 2 total bursts quiescent Foz de Iguacu

  50. Interpretation of sub-mm counts • Sub-mm source counts appear to be dominated by ultra-luminous dusty starbursts at z~2 • the 2 models make very different predictions for the number of these • what are the main reasons for the difference? Foz de Iguacu

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