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Heating the Early Universe: Numerical Methods and Their Analysis
Stockholm University, Faculty of Science, Department of Astronomy. (Reionization)
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

During the epoch when the first collapsed structures formed (6<z<50) our Universe went through an extended period of changes. Some of the radiation from the first stars and accreting black holes in those structures escaped and changed the state of the Intergalactic Medium (IGM). The era of this global phase change in which the state of the IGM was transformed from cold and neutral to warm and ionized, is called the Epoch of Reionization.In this thesis we focus on numerical methods to calculate the effects of this escaping radiation. We start by considering the performance of the cosmological radiative transfer code C2-Ray. We find that although this code efficiently and accurately solves for the changes in the ionized fractions, it can yield inaccurate results for the temperature changes. We introduce two new elements to improve the code. The first element, an adaptive time step algorithm, quickly determines an optimal time step by only considering the computational cells relevant for this determination. The second element, asynchronous evolution, allows different cells to evolve with different time steps. An important constituent of methods to calculate the effects of ionizing radiation is the transport of photons through the computational domain or ``ray-tracing''. We devise a novel ray tracing method called PYRAMID which uses a new geometry - the pyramidal geometry. This geometry shares properties with both the standard Cartesian and spherical geometries. This makes it on the one hand easy to use in conjunction with a Cartesian grid and on the other hand ideally suited to trace radiation from a radially emitting source. A time-dependent photoionization calculation not only requires tracing the path of photons but also solving the coupled set of photoionization and thermal equations. Several different solvers for these equations are in use in cosmological radiative transfer codes. We conduct a detailed and quantitative comparison of four different standard solvers in which we evaluate how their accuracy depends on the choice of the time step. This comparison shows that their performance can be characterized by two simple parameters and that the C2-Ray generally performs best.

Place, publisher, year, edition, pages
Stockholm: Department of Astronomy, Stockholm University , 2016.
Keyword [en]
cosmology
National Category
Astronomy, Astrophysics and Cosmology
Research subject
Astronomy
Identifiers
URN: urn:nbn:se:su:diva-130436ISBN: 978-91-7649-427-1 (print)OAI: oai:DiVA.org:su-130436DiVA: diva2:930331
Public defence
2016-09-02, FP41, AlbaNova universitetscentrum, Roslagstullsbacken 33, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 2: Submitted. Paper 3: Submitted.

Available from: 2016-06-09 Created: 2016-05-23 Last updated: 2016-08-23Bibliographically approved
List of papers
1. Efficient photoheating algorithms in time-dependent photoionization simulations
Open this publication in new window or tab >>Efficient photoheating algorithms in time-dependent photoionization simulations
2016 (English)In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 455, no 4, 4406-4425 p.Article in journal (Refereed) Published
Abstract [en]

We present an extension to the time-dependent photoionization code C-2-RAY to calculate photoheating in an efficient and accurate way. In C-2-RAY, the thermal calculation demands relatively small time-steps for accurate results. We describe two novel methods to reduce the computational cost associated with small time-steps, namely, an adaptive time-step algorithm and an asynchronous evolution approach. The adaptive time-step algorithm determines an optimal time-step for the next computational step. It uses a fast ray-tracing scheme to quickly locate the relevant cells for this determination and only use these cells for the calculation of the time-step. Asynchronous evolution allows different cells to evolve with different time-steps. The asynchronized clocks of the cells are synchronized at the times where outputs are produced. By only evolving cells which may require short time-steps with these short time-steps instead of imposing them to the whole grid, the computational cost of the calculation can be substantially reduced. We show that our methods work well for several cosmologically relevant test problems and validate our results by comparing to the results of another time-dependent photoionization code.

Keyword
radiative transfer, methods: numerical, H II regions, intergalactic medium, dark ages reionization first stars
National Category
Astronomy, Astrophysics and Cosmology
Research subject
Astronomy
Identifiers
urn:nbn:se:su:diva-126887 (URN)10.1093/mnras/stv2556 (DOI)000368009300077 ()
Available from: 2016-02-22 Created: 2016-02-16 Last updated: 2017-11-30Bibliographically approved
2. PYRAMID - a novel ray-tracing method
Open this publication in new window or tab >>PYRAMID - a novel ray-tracing method
(English)In: Computational Astrophysics and Cosmology, ISSN 2197-7909Article in journal (Refereed) Submitted
National Category
Astronomy, Astrophysics and Cosmology
Research subject
Astronomy
Identifiers
urn:nbn:se:su:diva-130437 (URN)
Available from: 2016-05-23 Created: 2016-05-23 Last updated: 2016-06-01Bibliographically approved
3. Mathematical Analysis of the Coupled Ionization and Thermal Equations
Open this publication in new window or tab >>Mathematical Analysis of the Coupled Ionization and Thermal Equations
(English)In: Computational Astrophysics and Cosmology, ISSN 2197-7909Article in journal (Refereed) Submitted
National Category
Astronomy, Astrophysics and Cosmology
Research subject
Astronomy
Identifiers
urn:nbn:se:su:diva-130438 (URN)
Available from: 2016-05-23 Created: 2016-05-23 Last updated: 2016-06-01Bibliographically approved

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