The natural emergence of the SFR-H2 surface density relation in galaxy simulations Alessandro Lupi (Institut d’Astrophysique de Paris) THE ROLE OF GAS IN GALAXY DYNAMICS with: S. Bovino, P. R. Capelo, M. Volonteri, J. Silk October 2nd, 2017 University of Malta
The observed KS relation Bigiel+2008 October 2nd, 2017 University of Malta
H2-based star formation ρ SF = ερ gas Standard prescription: ˙ ( T g < T g , thr ) t ff ρ g > ρ g , thr ρ gas H2-based prescription: ρ SF = ε 0 f H 2 ˙ t ff (Gnedin+09, Christensen+12, Hopkins+14, Tomassetti+15, Pallottini+17, Hopkins+17) BUT Recent theoretical studies have revealed a lack of causal connection between H 2 and SF (Krumholz et al. 2011, Clark et al. 2012). MORE LIKELY The formation of H2 is controlled by SF, or, in general, by the gravitational collapse of atomic gas, not vice versa (Mac Low 2016). October 2nd, 2017 University of Malta
Star formation model (Turbulent magnetized clouds) Padoan & Nordlund 2011 exp[ − ( s − s 0 ) 2 1 p s ( s ) = ] p 2 σ 2 2 πσ 2 s s σ 2 s = ln(1 + b 2 M 2 ) The critical density for SF is related to the magnetic shock jump conditions and to the magnetic critical mass for collapse α vir = 5 σ 2 0 . 067 θ − 2 α vir M 2 ⇤ ⇥ v L/ (6 GM cloud ) s crit = ln " !# � 2 exp(3 " = ✏ ? s − s crit 8 � 2 s ) 1 + erf p 2 � t 2 � 2 s Federrath & Klessen 2012 October 2nd, 2017 University of Malta
Numerical setup KROME GIZMO GIZMO-KROME Non-eq. chemistry mesh-less (Photochemistry) finite mass Galaxy with typical z=3 properties Physically motivated SF NFW DM halo + exp. decay: R vir = 45 kpc SN feedback + Mass losses from low-mass stars M halo = 2x10 11 M ⦿ Interstellar radiation field Stellar + gaseous disc: R 0 = 1.28 kpc Clumping factor M star = 1.6x10 9 M ⦿ ; M gas = 2.4x10 9 M ⦿ Hernquist stellar bulge: a = 0.256 kpc M bulge = 8x10 8 M ⦿ Evolved for 400 Myr in isolation October 2nd, 2017 University of Malta
The Interstellar radiation field We implemented two sub-grid models and compared them with a full-RT simulation. Model ‘S’ τ = σ e ff ( ρ g R max � | r ρ g | R 2 max / 2) m H L i, ? X F = exp( − τ i ) 4 π d 2 i i ρ g X τ = σ j, bin n j λ l Sob = | r ρ g | j October 2nd, 2017 University of Malta
The Interstellar radiation field "X # L i, ? Model ‘T’ F = exp( − τ i ) exp( − τ g ) 4 π d 2 i i Around star: ρ g l Sob = | r ρ g | Around gas: √ π c s λ J = √ G ρ October 2nd, 2017 University of Malta
RT in GIZMO Momentum method with M1 closure scheme (Rosdahl et al. 2013) ∂ I ν 1 ∂ t + n · r I ν = S ν � k ν I ν c ∂ N ⌫ + r · F ⌫ = N ? ⌫ � k ⌫ cN ⌫ ∂ t ∂ F ⌫ ∂ t + c 2 r · P ⌫ = � k ⌫ c F ⌫ Hopkins et al. (in preparation) October 2nd, 2017 University of Malta
The clumping factor R f (H 2 ) = 3 × 10 � 17 n H tot n tot Z/Z � cm � 3 s � 1 PDF averaged rate h R f (H 2 ) i = 3 ⇥ 10 � 17 h n H tot n tot i Z/Z � cm � 3 s � 1 Express using average density h R f (H 2 ) i = 3 ⇥ 10 � 17 h n H tot ih n tot i C ρ Z/Z � cm � 3 s � 1 C ρ = h ρ 2 i h ρ i 2 = exp( σ 2 s ) = 1 + b 2 M 2 October 2nd, 2017 University of Malta
The effect of the interstellar radiation G_RAD_S G_RT G_RAD_T 1 . 0 1 . 0 1 . 0 10 7 10 7 10 7 0 . 8 0 . 8 0 . 8 10 6 10 6 10 6 M (M � ) M (M � ) M (M � ) 0 . 6 0 . 6 0 . 6 f H 2 f H 2 f H 2 10 5 10 5 10 5 0 . 4 0 . 4 0 . 4 0 . 2 0 . 2 0 . 2 10 4 10 4 10 4 0 . 0 0 . 0 0 . 0 10 3 10 3 10 3 � 4 � 2 0 2 4 � 4 � 2 0 2 4 � 4 � 2 0 2 4 log n H tot (cm � 3 ) log n H tot (cm � 3 ) log n H tot (cm � 3 ) 0 0 0 10 7 10 7 10 7 � 1 � 1 � 1 � 2 10 6 � 2 10 6 � 2 10 6 M (M � ) M (M � ) M (M � ) log f H log f H log f H � 3 � 3 � 3 10 5 10 5 10 5 � 4 � 4 � 4 10 4 10 4 10 4 � 5 � 5 � 5 � 6 � 6 � 6 10 3 10 3 10 3 � 4 � 2 0 2 4 � 4 � 2 0 2 4 � 4 � 2 0 2 4 log n H tot (cm � 3 ) log n H tot (cm � 3 ) log n H tot (cm � 3 ) 7 7 7 10 7 10 7 10 7 6 6 6 5 5 5 10 6 10 6 10 6 log T (K) log T (K) log T (K) M (M � ) M (M � ) M (M � ) 4 4 4 10 5 10 5 10 5 3 3 3 10 4 10 4 10 4 2 2 2 10 3 10 3 10 3 1 1 1 � 4 � 2 0 2 4 � 4 � 2 0 2 4 � 4 � 2 0 2 4 log n H tot (cm � 3 ) log n H tot (cm � 3 ) log n H tot (cm � 3 ) October 2nd, 2017 University of Malta
The effect of the interstellar radiation 10 0 10 3 0 . 1 Gyr 1 Gyr G RAD S G RAD S G RT G RT G RAD T G RAD T 10 2 10 � 1 10 Gyr Σ ? (M � / Gyr / pc 2 ) Σ ? (M � / yr / kpc 2 ) 10 1 10 � 2 10 0 ˙ ˙ 10 � 3 10 � 1 10 � 4 10 � 2 10 0 10 1 10 2 10 3 10 � 1 10 0 10 1 10 2 10 3 Σ H 2 (M � / pc 2 ) Σ gas (M � / pc 2 ) October 2nd, 2017 University of Malta
What’s next z fin = 6 M vir ~ 2x10 12 M ⦿ —————————— M gas = ~ 1.5x10 4 M ⦿ /part M DM = ~ 8x10 4 M ⦿ /part —————————— N gas = 6.75x10 7 1) N DM = 6.75x10 7 N DM,low = 2.2x10 7 —————————— 휖 gas,min = 40 cpc | 2.5 pc 휖 DM = 640 cpc | 40 pc 휖 star = 192 cpc | 12 pc 2) Formation of C + in dwarf galaxies, using a more complete network including C, O an Si. October 2nd, 2017 University of Malta
Conclusions Lupi et al. 2017 (submitted) - soon on ArXiv We developed a new model to accurately track H 2 in numerical simulations using the package KROME, including photochemistry, SF, SNe, stellar radiation and shielding (gas, dust, H 2 ). We tested the model on an idealised setup of an isolated galaxy with typical properties of z=3 galaxies, assessing the effect of the different processes included. We found that the correlation between H 2 and SF surface densities can be naturally • reproduced, if we account for all the most important processes and for a self-consistent clumping factor. We found that the correlation is also maintained at low H 2 surface densities. • We concluded that an H 2 -dependent SF prescription is not necessary and also • unmotivated. October 2nd, 2017 University of Malta
Thanks for your attention October 2nd, 2017 University of Malta
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