How we look inside stars: stellar evolution codes & Mathieu - PowerPoint PPT Presentation

Computational Astrophysics – 18/01/16 How we “look” inside stars: stellar evolution codes & Mathieu Renzo, PhD student @ API, UvA “Traditional scientific knowledge has generally taken the form of either theory or experimental data. However, where theory and experiment stumble, simulations may offer a third way.” Simulation, Johannes Lenhard et al. 1 / 24

Outline The most important thing What is (Computational) “Stellar Astrophysics”? The stellar evolution code • Basic Assumptions • Discretization • Translation of the Physics for the Computer • Example of input Physics: Nuclear Reaction Networks • How the Computer Solves the Equations What do I do with it? 2 / 24

Outline The most important thing What is (Computational) “Stellar Astrophysics”? The stellar evolution code • Basic Assumptions • Discretization • Translation of the Physics for the Computer • Example of input Physics: Nuclear Reaction Networks • How the Computer Solves the Equations What do I do with it? 3 / 24

The most important thing This is what should not happen grep is your friend! (see man grep on *nix) 4 / 24

Outline The most important thing What is (Computational) “Stellar Astrophysics”? The stellar evolution code • Basic Assumptions • Discretization • Translation of the Physics for the Computer • Example of input Physics: Nuclear Reaction Networks • How the Computer Solves the Equations What do I do with it? 5 / 24

How can we “look” inside a star? Figures Credits: NASA ? ⇒ 6 / 24

How can we “look” inside a star? Figures Credits: NASA ? ⇒ We simply can’t!! Other Q: How can we observe how one star evolves? 6 / 24

So what to do? Advantages • Full control over the parameters 1 Build a theory from first ⇒ Numerical Experiments; principles; • Allow to focus on interesting 2 Plug it in a computer; things (e.g. no reddening!); • Allow to deal with long-lasting, 3 Get out a model ; rare, inaccessible phenomena; 4 Find a smart way to Drawbacks compare it to what we • Numerical errors; can observe. • Limited computational resources; • Nature ≫ Theory ≫ Model. “All models are wrong, but some are useful” – G. Box 7 / 24

Outline The most important thing What is (Computational) “Stellar Astrophysics”? The stellar evolution code • Basic Assumptions • Discretization • Translation of the Physics for the Computer • Example of input Physics: Nuclear Reaction Networks • How the Computer Solves the Equations What do I do with it? 8 / 24

The Stellar Evolution Code: is a tool , not a theory! What does it stand for? References: Modules for Paxton et al. 2011, ApJs192,3 Experiments in Paxton et al. 2013, ApJs208,4 Paxton et al. 2015, ApJs220,15 Stellar mesa.sourceforge.net mesastar.org Astrophysics Open Source ⇔ Open Know How “An algorithm must be seen to be believed” – D. Knuth How to get MESA: svn co -r 7624 svn://svn.code.sf.net/p/mesa/code/trunk mesa 9 / 24

Modules overview 10 / 24

Numerical Methods: 1D (or 1.5D) Prohibitive computational cost of 3D simulations ⇒ 1D, but stars are not spherical-symmetric! Need of parametric approximations for: • Rotation ⇒ “Shellular Approximation”; • Magnetic Fields; • Convection ⇒ Mixing Length Theory (MLT); • (Some) mixing processes; • ... Beware of systematic errors! (Recall: Nature ≫ Model) 11 / 24

Numerical Methods: Hydrostatic code... dr = − Gm ( r ) ρ dP r 2 ... but stars are not necessarily static! Other examples: • He flash, • Outburst and Eruptions, • Impulsive mass loss, • RLOF , • ... Figure: η Car, APOD. 12 / 24

Numerical Methods: Discretization For numerical solutions: dx → f ( x k + 1 ) − f ( x k ) df x k + 1 − x k ⇒ Discretization of space (mesh or grid) and time (timesteps) (Recall: Nature ≫ Model) 13 / 24

Spatial Discretization (Meshing) toward surface face k-1 m k − 1 , r k − 1 , L k − 1 , v k − 1 , ... cell k-1 dm k − 1 ρ k − 1 , T k − 1 , X i , k − 1 , P k − 1 , ... • Intensive quantities face k (e.g. T , ρ ) averaged dm k m k , r k , L k , v k , σ F i , k , P k , T k , ∇ T k , , k by mass within each cell; cell k dm k ρ k , T k , X i , k , P k , ∇ , , ad , k ε nuc , k ε grav , k • Extensive quantities (e.g. m , L ) calculated face k + 1 m k + 1 , r k + 1 , L k + 1 , v k + 1 , k + 1 , F i , k + 1 , ... σ at outer cell boundary. toward center Figure: From Paxton et al. 2011, ApJs, 192, 3 Need to check that your physical results do not depend on the way you discretize space. 14 / 24

Numerical Methods: Timestep selection ∆ t n : Large enough, but � τ KH , τ ˙ M , etc. Need to find the best ∆ t n at each step – few × 100 � total n � few × 10 4 15 / 24

Reformulation of the (1D–) Equations Physical Theory: Numerical Implementation: � � dr = − Gm ( r ) ρ dP F + ⇔ r 2 4 π r 2 dm dr = 4 π r 2 ρ ⇔ κρ L dT 3 dr = − ⇔ 16 π ac r 2 T 3 dL dr = 4 π r 2 ρε ⇔ P ≡ P ( ρ , µ , T ) ⇔ � � � � � dX i � σ i ∇ 2 X i = P j , i ( T , ρ ) − ∑ D i , k ( T , rho , ) + ∑ � dt � j k r ⇔ 16 / 24

Reformulation of the (1D–) Equations Physical Theory: Numerical Implementation: � � P k − 1 − P k dr = − Gm ( r ) ρ 0 . 5 ( dm k − 1 − dm k ) = − Gm k a k dP F + ⇔ k − r 2 4 π r 2 4 π r 4 4 π r 2 k � � dm ln ( r k ) = 1 k + 1 + 3 dm k dr = 4 π r 2 ρ r 3 ⇔ 3 ln 4 π ρ k � � � ˜ T k − 1 − T k κρ L T k dT 3 dP � dr = − ⇔ ( dm k − 1 − dm k ) / 2 = −∇ T , k � ˜ 16 π ac r 2 T 3 dm P k � k dL dr = 4 π r 2 ρε ⇔ L k − L k + 1 = dm k { ε nuc − ε ν + ε grav } P ≡ P ( ρ , µ , T ) ⇔ P ≡ P ( ρ , µ , T ) � � � � � dX i � σ i ∇ 2 X i = P j , i ( T , ρ ) − ∑ D i , k ( T , rho , ) + ∑ � dt � j k r ⇔ � � dX i , k nuc + ( X i , k − X i , k − 1 ) σ k ∆ t n + 1 X i , k ( t n + ∆ t n + 1 ) = X i , k ( t n ) + ∆ t n + 1 0 . 5 ( dm k − 1 − dm k ) dt 16 / 24

Reformulation of the (1D–) Equations Physical Theory: Numerical Implementation: � � P k − 1 − P k dr = − Gm ( r ) ρ 0 . 5 ( dm k − 1 − dm k ) = − Gm k a k dP F + ⇔ k − r 2 4 π r 2 4 π r 4 4 π r 2 k � � dm ln ( r k ) = 1 k + 1 + 3 dm k dr = 4 π r 2 ρ r 3 ⇔ 3 ln 4 π ρ k � � � ˜ T k − 1 − T k κρ L T k dT 3 dP � dr = − ⇔ ( dm k − 1 − dm k ) / 2 = −∇ T , k � ˜ 16 π ac r 2 T 3 dm P k � k dL dr = 4 π r 2 ρε ⇔ L k − L k + 1 = dm k { ε nuc − ε ν + ε grav } P ≡ P ( ρ , µ , T ) ⇔ P ≡ P ( ρ , µ , T ) � � � � � dX i � σ i ∇ 2 X i = P j , i ( T , ρ ) − ∑ D i , k ( T , rho , ) + ∑ � dt � j k r ⇔ � � dX i , k nuc + ( X i , k − X i , k − 1 ) σ k ∆ t n + 1 X i , k ( t n + ∆ t n + 1 ) = X i , k ( t n ) + ∆ t n + 1 0 . 5 ( dm k − 1 − dm k ) dt 16 / 24

Reformulation of the (1D–) Equations Physical Theory: Numerical Implementation: � � P k − 1 − P k dr = − Gm ( r ) ρ 0 . 5 ( dm k − 1 − dm k ) = − Gm k a k dP F + ⇔ k − r 2 4 π r 2 4 π r 4 4 π r 2 k � � dm ln ( r k ) = 1 k + 1 + 3 dm k dr = 4 π r 2 ρ r 3 ⇔ 3 ln 4 π ρ k � � � ˜ T k − 1 − T k κρ L T k dT 3 dP � dr = − ⇔ ( dm k − 1 − dm k ) / 2 = −∇ T , k � ˜ 16 π ac r 2 T 3 dm P k � k dL dr = 4 π r 2 ρε ⇔ L k − L k + 1 = dm k { ε nuc − ε ν + ε grav } P ≡ P ( ρ , µ , T ) ⇔ P ≡ P ( ρ , µ , T ) � � � � � dX i � σ i ∇ 2 X i = P j , i ( T , ρ ) − ∑ D i , k ( T , rho , ) + ∑ � dt � j k r ⇔ � � dX i , k nuc + ( X i , k − X i , k − 1 ) σ k ∆ t n + 1 X i , k ( t n + ∆ t n + 1 ) = X i , k ( t n ) + ∆ t n + 1 0 . 5 ( dm k − 1 − dm k ) dt 16 / 24

Reformulation of the (1D–) Equations Physical Theory: Numerical Implementation: � � P k − 1 − P k dr = − Gm ( r ) ρ 0 . 5 ( dm k − 1 − dm k ) = − Gm k a k dP F + ⇔ k − r 2 4 π r 2 4 π r 4 4 π r 2 k � � dm ln ( r k ) = 1 k + 1 + 3 dm k dr = 4 π r 2 ρ r 3 ⇔ 3 ln 4 π ρ k � � � ˜ T k − 1 − T k κρ L T k dT 3 dP � dr = − ⇔ ( dm k − 1 − dm k ) / 2 = −∇ T , k � ˜ 16 π ac r 2 T 3 dm P k � k dL dr = 4 π r 2 ρε ⇔ L k − L k + 1 = dm k { ε nuc − ε ν + ε grav } P ≡ P ( ρ , µ , T ) ⇔ P ≡ P ( ρ , µ , T ) � � � � � dX i � σ i ∇ 2 X i = P j , i ( T , ρ ) − ∑ D i , k ( T , rho , ) + ∑ � dt � j k r ⇔ � � dX i , k nuc + ( X i , k − X i , k − 1 ) σ k ∆ t n + 1 X i , k ( t n + ∆ t n + 1 ) = X i , k ( t n ) + ∆ t n + 1 0 . 5 ( dm k − 1 − dm k ) dt 16 / 24

Numerical Methods: Nuclear Networks (Ex. of) tricks under the hood: • Compound reactions, e.g. 3 α : � 12 C + γ ; α + α → � 8 Be + α → • (Quasi Statistical Equilibrium Networks for advanced burning stages); High impact on: What matters: • Computational cost ( ∝ N 2 • Total Number iso ) ⇒ Run time; of Isotopes N iso ; • ε nuc ⇒ L , T c , ρ c , etc.; • Which Isotopes; • Free electrons ( Y e ) ⇒ • Number of Nuclear Final fate (BH,NS, WD, etc.) Reactions. 17 / 24