WRITING, STRUCTURING AND DEVELOPING MONTE CARLO RADIATIVE TRANSFER CODES ANTONIA BEVAN, UCL ST ANDREWS MONTE CARLO SUMMER SCHOOL 2017

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1 WRITING, STRUCTURING AND DEVELOPING MONTE CARLO RADIATIVE TRANSFER CODES ANTONIA BEVAN, UCL ST ANDREWS MONTE CARLO SUMMER SCHOOL 2017

2 Me in Oct 2012 just after I started my PhD

3 Herschel, Planck and Spitzer imaging data for Cas A (De Looze+ 17)

4 FLUX DOPPLER VELOCITY observer dust clumps DUST IN CCSN EJECTA CAUSES BLUE- SHIFTED EMISSION LINE PROFILES IN OPTICAL AND IR

5 First observed in SN 1987A [OI] 6300,6363Å (d529) (d739) Lucy et al. 1989

6 CHALLENGE: WRITE A MONTE CARLO RADIATIVE TRANSFER CODE THAT WILL?

7 Dust absorption and scattering Smooth or clumped dust distribution 3D Monte Carlo radiative transfer code Smooth or clumped emissivity distribution Dust A ffected Models O f C haracteristic L ine E mission in S upernovae Simple electron scattering Velocity field v α r at fixed time Any dust grain size distribution Any combination of dust species

8 ASK YOURSELF QUESTIONS Where will this go? Will I want to add capacity in future? Is there anything I can do now to make that easier? What are the inputs? What are the outputs? Which processes/physics/stats/magic will take you from your inputs to your outputs? What can/can t you assume? What are you going to do with your outputs?

9 MAP OUT YOUR PROBLEM MCRT CODES: SAME BASIC PREMISE DIFFERENT PHYSICS/ PROCESSES/PRO DUCTS ETC.

10 Read inputs any user defined variables, optical constants etc. Set up general variables such as loop counters, physical constants etc. Set any default values Write out outputs Perform any comparison to observations/experimental results? Turn written outputs (grids, lists of numbers etc.) into graphics, images, plots etc.

11 INITIALISE Initialise

12 What now? You re going to need to make some decisions about your tools Fortran or C or Python or or or? [you may choose to use multiple] OpenMP or MPI? IDE? text editor? Compiler? Computer! Which version control Git, SVN etc.? QUESTIONS TO ASK USE VERSION CONTROL

13 DAMOCLES development: Fortran 95 + Python (historically also matlab) Tools I use: Eclipse IDE with Photran Sublime Text & emacs for text editing GitHub for version control gcc compilers DAMOCLES Develop on my macbook and run on servers at UCL

14 USE MODULES

15 USE MODULES

16 USE MODULES

17 USE MODULES

18 USE MODULES

19 USE MODULES

20 MODULAR STRUCTURE We re building up the program block by block Program file runs the main body of the code calling functions and subroutines Break up your code into sections and save them in different files FORTRAN if module A uses module B, then all variables, subroutines and functions declared in module B can be seen and updated by module A I put all my variables, subroutines and functions in modules grouped by categories e.g. dust RECAP

21 DESCRIBE THE ENVIRONMENT Initialise

22 What is it made of? Dust? Gas? Skin? Rocks? Can I describe how light interacts with it? Where is it? Density distribution Smooth? Clumpy? Layered? Physical extent how big is it [and how do I want to describe that]? How should I describe it? Formula? Grid? QUESTIONS TO ASK

23 Cartesian grid of dust densities Each grid cell has constant properties Can describe any distribution with some defaults included: Shell with a smooth power-law Any fraction of dust in clumps Arbitrary distributions Mie theory gives extinction efficiencies Velocity proportional to radius DAMOCLES

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25 USE LIBRARIES AND PACKAGES

26 USE LIBRARIES AND PACKAGES

27 TEST TWICE (AT LEAST!)

28 TEST TWICE (AT LEAST!)

29 Build up each section of code as you go Test each section as you go Use benchmark tests and analytical results Use sense checks and count checks Consider writing unit tests Calculate the properties of your medium in advance and store Grids allow for flexibility properties in a given grid cell are constant RECAP

30 LAUNCH PACKETS Initialise

31 Frequency distribution P(υ) α? Blackbody? Monochromatic? Emissivity distribution i(x,y,z) α? Proportional to density? Radial distribution? Point source? Arbitrary distribution? Propagation direction Isotropic? Non-isotropic? Plane parallel? QUESTIONS TO ASK

32 DAMOCLES uses monochromatic (i.e. line photons) Emissivity distribution is default coupled to the dust density distribution with i(x,y,z) α ρ 2? Can have an arbitrary distribution Packets are emitted isotropically Packets must be frequency shifted when launched (moving atmosphere) DAMOCLES

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34 PROPAGATION DIRECTION: E.G. SAMPLE FROM AN ISOTROPIC DISTRIBUTION cosq = 2z -1 f = 2px

35 POSITION: E.G. RADIAL POWER LAW IN 1D For P(r) = Cr n where r Î [r min,r max ] CARE WITH RANDOM NUMBERS r =[(r n+1 max - r n+1 min )g +r n+1 n+1 min ] 1 UNIFORM RANDOM NUMBERS IN [0,1) CAN BE CONVERTED TO OTHER DISTRIBUTIONS

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37 RECAP Packets should be instantiated with a position, a direction and any other properties Frequency? Weight? Flags? (e.g. continuum packet, line packet etc.) Random numbers can be used to sample position and direction vectors Take care with random numbers (seeds, parallel s )

38 PROPAGATE PACKETS & ABSORPTION/SCATTERING/RE-EMISSION Initialise

39 What happens to absorbed? Do I need to use weighted? With what direction are scattered reemitted? Isotropic? Phase function? Are ted immediately? Do I need to iterate? Update grid properties? Determine thermal balance? QUESTIONS TO ASK

40 DAMOCLES Absorbed removed from simulation since outside wavelength range Packets are weighted at each scattering event by ratio of frequencies Dust scattering is calculated using Henyey- Greenstein approximation (non-isotropic scattering) No need for iteration since dust opacities not temperature dependent

41 PARALLEL WORKS VERY WELL

42 PARALLEL WORKS VERY WELL

43 A PACKET S PATH THROUGH THE EJECTA IN DAMOCLES (note, no reemission )

44 Packets do not interact so RECAP can process one until it escapes before launching another can run multiple at once Monte Carlo very, very parallel (and fairly easy to do so) Lots of required ( typical): can be slow so parallelisation helps Random numbers determine random walk but also events along the way

45 COLLECT PACKETS & VISUALISE Initialise

46 What information should be collected? Weights, frequencies, positions, directions How should the information be collated? Binning what resolution? Viewing angles? QUESTIONS TO ASK What visualisation/analysis can be used to explore the results of the simulation? What graphics/images best represent the model? Convolve to observation?

47 All binned into a grid of frequencies (summation over their weights) All also binned into a number of lines of sight d as a line profile by plotting the outputted histogram DAMOCLES The profile flux is scaled to the observations and compared

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50 VISUALISATION IS IMPORTANT It is how your model is seen by the outside world It allows you to easily assess and analyse the results Normally worth writing scripts for visualising then packaging with the code Many tools and libraries in e.g. Python, matlab

51 Important part of the code RECAP Normally worth investing time in writing postprocessing scripts for visualising results Try to collect as many outputs as you might be interested in Make output automated e.g. automated file names based on date/time or input parameters etc.

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53 It didn t quite go like that SPHERICAL GRID DUST ABSORPTION CARTESIAN GRID DUST SCATTERING SMOOTH + ELECTRON SCATTERING DUST + CLUMPED + CLUMPED DISTRIBUTION ANY DISTRIBUTION DUST YOU EMISSIVITY LIKE MONOCHROMATIC DISTRIBUTION DISTRIBUTION LINE PACKETS BUT ALSO AND DOUBLETS TRIPLETS BAYESIAN MCMC WRAPPER IN PYTHON

54 S U P E R N O V A 1987A ( I I P ) END RESULT! FITS TO THE SN 1987A [OI] DOUBLET

55 Bayesian Modelling SN 1987A Hα day 714 smooth gas & dust coupled

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57 HINTS & TIPS Use version control Use modules Use libraries and packages Test twice (at least!) Take care with random numbers Parallelise Don t assume that only you will be using your code Comments Clear variable and module names Ask questions!