@article{astropy1,
Adsnote = {Provided by the SAO/NASA Astrophysics Data System},
Adsurl = {http://adsabs.harvard.edu/abs/2013A%26A...558A..33A},
Archiveprefix = {arXiv},
Author = {{Astropy Collaboration} and {Robitaille}, T.~P. and {Tollerud}, E.~J. and {Greenfield}, P. and {Droettboom}, M. and {Bray}, E. and {Aldcroft}, T. and {Davis}, M. and {Ginsburg}, A. and {Price-Whelan}, A.~M. and {Kerzendorf}, W.~E. and {Conley}, A. and {Crighton}, N. and {Barbary}, K. and {Muna}, D. and {Ferguson}, H. and {Grollier}, F. and {Parikh}, M.~M. and {Nair}, P.~H. and {Unther}, H.~M. and {Deil}, C. and {Woillez}, J. and {Conseil}, S. and {Kramer}, R. and {Turner}, J.~E.~H. and {Singer}, L. and {Fox}, R. and {Weaver}, B.~A. and {Zabalza}, V. and {Edwards}, Z.~I. and {Azalee Bostroem}, K. and {Burke}, D.~J. and {Casey}, A.~R. and {Crawford}, S.~M. and {Dencheva}, N. and {Ely}, J. and {Jenness}, T. and {Labrie}, K. and {Lim}, P.~L. and {Pierfederici}, F. and {Pontzen}, A. and {Ptak}, A. and {Refsdal}, B. and {Servillat}, M. and {Streicher}, O.},
Doi = {10.1051/0004-6361/201322068},
Eid = {A33},
Eprint = {1307.6212},
Journal = {\aap},
Keywords = {methods: data analysis, methods: miscellaneous, virtual observatory tools},
Month = oct,
Pages = {A33},
Primaryclass = {astro-ph.IM},
Title = {{Astropy: A community Python package for astronomy}},
Volume = 558,
Year = 2013,
Bdsk-Url-1 = {https://dx.doi.org/10.1051/0004-6361/201322068}}
@article{astropy2,
Adsnote = {Provided by the SAO/NASA Astrophysics Data System},
Adsurl = {https://ui.adsabs.harvard.edu/#abs/2018AJ....156..123T},
Author = {{Price-Whelan}, A.~M. and {Sip{\H{o}}cz}, B.~M. and {G{\"u}nther}, H.~M. and {Lim}, P.~L. and {Crawford}, S.~M. and {Conseil}, S. and {Shupe}, D.~L. and {Craig}, M.~W. and {Dencheva}, N. and {Ginsburg}, A. and {VanderPlas}, J.~T. and {Bradley}, L.~D. and {P{\'e}rez-Su{\'a}rez}, D. and {de Val-Borro}, M. and {Paper Contributors}, (Primary and {Aldcroft}, T.~L. and {Cruz}, K.~L. and {Robitaille}, T.~P. and {Tollerud}, E.~J. and {Coordination Committee}, (Astropy and {Ardelean}, C. and {Babej}, T. and {Bach}, Y.~P. and {Bachetti}, M. and {Bakanov}, A.~V. and {Bamford}, S.~P. and {Barentsen}, G. and {Barmby}, P. and {Baumbach}, A. and {Berry}, K.~L. and {Biscani}, F. and {Boquien}, M. and {Bostroem}, K.~A. and {Bouma}, L.~G. and {Brammer}, G.~B. and {Bray}, E.~M. and {Breytenbach}, H. and {Buddelmeijer}, H. and {Burke}, D.~J. and {Calderone}, G. and {Cano Rodr{\'\i}guez}, J.~L. and {Cara}, M. and {Cardoso}, J.~V.~M. and {Cheedella}, S. and {Copin}, Y. and {Corrales}, L. and {Crichton}, D. and {D{\textquoteright}Avella}, D. and {Deil}, C. and {Depagne}, {\'E}. and {Dietrich}, J.~P. and {Donath}, A. and {Droettboom}, M. and {Earl}, N. and {Erben}, T. and {Fabbro}, S. and {Ferreira}, L.~A. and {Finethy}, T. and {Fox}, R.~T. and {Garrison}, L.~H. and {Gibbons}, S.~L.~J. and {Goldstein}, D.~A. and {Gommers}, R. and {Greco}, J.~P. and {Greenfield}, P. and {Groener}, A.~M. and {Grollier}, F. and {Hagen}, A. and {Hirst}, P. and {Homeier}, D. and {Horton}, A.~J. and {Hosseinzadeh}, G. and {Hu}, L. and {Hunkeler}, J.~S. and {Ivezi{\'c}}, {\v{Z}}. and {Jain}, A. and {Jenness}, T. and {Kanarek}, G. and {Kendrew}, S. and {Kern}, N.~S. and {Kerzendorf}, W.~E. and {Khvalko}, A. and {King}, J. and {Kirkby}, D. and {Kulkarni}, A.~M. and {Kumar}, A. and {Lee}, A. and {Lenz}, D. and {Littlefair}, S.~P. and {Ma}, Z. and {Macleod}, D.~M. and {Mastropietro}, M. and {McCully}, C. and {Montagnac}, S. and {Morris}, B.~M. and {Mueller}, M. and {Mumford}, S.~J. and {Muna}, D. and {Murphy}, N.~A. and {Nelson}, S. and {Nguyen}, G.~H. and {Ninan}, J.~P. and {N{\"o}the}, M. and {Ogaz}, S. and {Oh}, S. and {Parejko}, J.~K. and {Parley}, N. and {Pascual}, S. and {Patil}, R. and {Patil}, A.~A. and {Plunkett}, A.~L. and {Prochaska}, J.~X. and {Rastogi}, T. and {Reddy Janga}, V. and {Sabater}, J. and {Sakurikar}, P. and {Seifert}, M. and {Sherbert}, L.~E. and {Sherwood-Taylor}, H. and {Shih}, A.~Y. and {Sick}, J. and {Silbiger}, M.~T. and {Singanamalla}, S. and {Singer}, L.~P. and {Sladen}, P.~H. and {Sooley}, K.~A. and {Sornarajah}, S. and {Streicher}, O. and {Teuben}, P. and {Thomas}, S.~W. and {Tremblay}, G.~R. and {Turner}, J.~E.~H. and {Terr{\'o}n}, V. and {van Kerkwijk}, M.~H. and {de la Vega}, A. and {Watkins}, L.~L. and {Weaver}, B.~A. and {Whitmore}, J.~B. and {Woillez}, J. and {Zabalza}, V. and {Contributors}, (Astropy},
Doi = {10.3847/1538-3881/aabc4f},
Eid = {123},
Journal = {\aj},
Keywords = {methods: data analysis, methods: miscellaneous, methods: statistical, reference systems, Astrophysics - Instrumentation and Methods for Astrophysics},
Month = Sep,
Pages = {123},
Primaryclass = {astro-ph.IM},
Title = {{The Astropy Project: Building an Open-science Project and Status of the v2.0 Core Package}},
Volume = {156},
Year = 2018,
Bdsk-Url-1 = {https://doi.org/10.3847/1538-3881/aabc4f}}
@article{PyLops,
abstract = {Linear operators and optimisation are at the core of many algorithms used in signal and image processing, remote sensing, and inverse problems. For small to medium-scale problems, existing software packages (e.g., MATLAB, Python numpy and scipy) allow for explicitly building dense (or sparse) matrices and performing algebraic operations (e.g., computation of matrix-vector products and manipulation of matrices) with syntax that closely represents their corresponding analytical forms. However, many real application, large-scale operators do not lend themselves to explicit matrix representations, usually forcing practitioners to forego of the convenient linear-algebra syntax available for their explicit-matrix counterparts. PyLops is an open-source Python library providing a flexible and scalable framework for the creation and combination of so-called linear operators, class-based entities that represent matrices and inherit their associated syntax convenience, but do not rely on the creation of explicit matrices. We show that PyLops operators can dramatically reduce the memory load and CPU computations compared to explicit-matrix calculations, while still allowing users to seamlessly use their existing knowledge of compact matrix-based syntax that scales to any problem size because no explicit matrices are required.},
archivePrefix = {arXiv},
arxivId = {1907.12349},
author = {Ravasi, Matteo and Vasconcelos, Ivan},
eprint = {1907.12349},
file = {:home/jammy/Documents/Papers/Software/PyLops.pdf:pdf},
title = {{PyLops -- A Linear-Operator Python Library for large scale optimization}},
url = {http://arxiv.org/abs/1907.12349},
year = {2019}
}
@article{colossus,
abstract = {This paper introduces Colossus, a public, open-source python package for calculations related to cosmology, the large-scale structure (LSS) of matter in the universe, and the properties of dark matter halos. The code is designed to be fast and easy to use, with a coherent, well-documented user interface. The cosmology module implements Friedman-Lemaitre-Robertson-Walker cosmologies including curvature, relativistic species, and different dark energy equations of state, and provides fast computations of the linear matter power spectrum, variance, and correlation function. The LSS module is concerned with the properties of peaks in Gaussian random fields and halos in a statistical sense, including their peak height, peak curvature, halo bias, and mass function. The halo module deals with spherical overdensity radii and masses, density profiles, concentration, and the splashback radius. To facilitate the rapid exploration of these quantities, Colossus implements more than 40 different fitting functions from the literature. I discuss the core routines in detail, with particular emphasis on their accuracy. Colossus is available at bitbucket.org/bdiemer/colossus.},
archivePrefix = {arXiv},
arxivId = {1712.04512},
author = {Diemer, Benedikt},
doi = {10.3847/1538-4365/aaee8c},
eprint = {1712.04512},
file = {:home/jammy/Documents/Papers/Software/Collosus2018.pdf:pdf},
issn = {0067-0049},
journal = {The Astrophysical Journal Supplement Series},
keywords = {cosmology,cosmology: theory,methods: numerical,methods,numerical,theory},
number = {2},
pages = {35},
publisher = {IOP Publishing},
title = {{COLOSSUS: A Python Toolkit for Cosmology, Large-scale Structure, and Dark Matter Halos}},
url = {http://dx.doi.org/10.3847/1538-4365/aaee8c},
volume = {239},
year = {2018}
}
@article{corner,
  doi = {10.21105/joss.00024},
  url = {https://doi.org/10.21105/joss.00024},
  year  = {2016},
  month = {jun},
  publisher = {The Open Journal},
  volume = {1},
  number = {2},
  pages = {24},
  author = {Daniel Foreman-Mackey},
  title = {corner.py: Scatterplot matrices in Python},
  journal = {The Journal of Open Source Software}
}
@article{dynesty,
abstract = {We present dynesty, a public, open-source, python package to estimate Bayesian posteriors and evidences (marginal likelihoods) using the dynamic nested sampling methods developed by Higson et al. By adaptively allocating samples based on posterior structure, dynamic nested sampling has the benefits of Markov chain Monte Carlo (MCMC) algorithms that focus exclusively on posterior estimation while retaining nested sampling's ability to estimate evidences and sample from complex, multimodal distributions. We provide an overview of nested sampling, its extension to dynamic nested sampling, the algorithmic challenges involved, and the various approaches taken to solve them in this and previous work. We then examine dynesty's performance on a variety of toy problems along with several astronomical applications. We find in particular problems dynesty can provide substantial improvements in sampling efficiency compared to popular MCMC approaches in the astronomical literature. More detailed statistical results related to nested sampling are also included in the appendix.},
archivePrefix = {arXiv},
arxivId = {1904.02180},
author = {Speagle, Joshua S},
doi = {10.1093/mnras/staa278},
eprint = {1904.02180},
file = {:home/jammy/Documents/Papers/PPLs/Dynesty.pdf:pdf},
issn = {0035-8711},
journal = {Monthly Notices of the Royal Astronomical Society},
keywords = {data analysis,methods,statistical},
number = {3},
pages = {3132--3158},
title = {{dynesty: a dynamic nested sampling package for estimating Bayesian posteriors and evidences}},
volume = {493},
year = {2020}
}
@article{emcee,
abstract = {We introduce a stable, well tested Python implementation of the affine-invariant ensemble sampler for Markov chain Monte Carlo (MCMC) proposed by Goodman {\&} Weare (2010). The code is open source and has already been used in several published projects in the astrophysics literature. The algorithm behind emcee has several advantages over traditional MCMC sampling methods and it has excellent performance as measured by the autocorrelation time (or function calls per independent sample). One major advantage of the algorithm is that it requires hand-tuning of only 1 or 2 parameters compared to {\$}\backslashsim N{\^{}}2{\$} for a traditional algorithm in an N-dimensional parameter space. In this document, we describe the algorithm and the details of our implementation and API. Exploiting the parallelism of the ensemble method, emcee permits any user to take advantage of multiple CPU cores without extra effort. The code is available online at http://dan.iel.fm/emcee under the MIT License.},
archivePrefix = {arXiv},
arxivId = {1202.3665},
author = {Foreman-Mackey, Daniel and Hogg, David W. and Lang, Dustin and Goodman, Jonathan},
doi = {10.1086/670067},
eprint = {1202.3665},
file = {:home/jammy/Documents/Papers/PPLs/Emcee.pdf:pdf},
issn = {00046280},
journal = {Publications of the Astronomical Society of the Pacific},
number = {925},
pages = {306--312},
title = {{emcee : The MCMC Hammer }},
volume = {125},
year = {2013}
}
@article{matplotlib,
  Author    = {Hunter, J. D.},
  Title     = {Matplotlib: A 2D graphics environment},
  Journal   = {Computing in Science \& Engineering},
  Volume    = {9},
  Number    = {3},
  Pages     = {90--95},
  abstract  = {Matplotlib is a 2D graphics package used for Python for
  application development, interactive scripting, and publication-quality
  image generation across user interfaces and operating systems.},
  publisher = {IEEE COMPUTER SOC},
  doi       = {10.1109/MCSE.2007.55},
  year      = 2007
}
@article{numba,
abstract = {Dynamic, interpreted languages, like Python, are attractive for domain-experts and scientists experimenting with new ideas. However, the performance of the interpreter is of-ten a barrier when scaling to larger data sets. This paper presents a just-in-time compiler for Python that focuses in scientific and array-oriented computing. Starting with the simple syntax of Python, Numba compiles a subset of the language into efficient machine code that is comparable in performance to a traditional compiled language. In addi-tion, we share our experience in building a JIT compiler using LLVM[1].},
author = {Lam, Siu Kwan and Pitrou, Antoine and Seibert, Stanley},
doi = {10.1145/2833157.2833162},
file = {:home/jammy/Documents/Papers/Software/numba{\_}sc15.pdf:pdf},
isbn = {9781450340052},
journal = {Proceedings of the Second Workshop on the LLVM Compiler Infrastructure in HPC - LLVM '15},
keywords = {2,a jit for numeric,com-,compiler,jit,just-in-time,llvm,numba is a function-at-a-time,python},
pages = {1--6},
title = {{Numba: a LLVM-based Python JIT compiler}},
url = {http://dl.acm.org/citation.cfm?doid=2833157.2833162},
year = {2015}
}
@article{numpy,
  author={S. {van der Walt} and S. C. {Colbert} and G. {Varoquaux}},
  journal={Computing in Science   Engineering},
  title={The NumPy Array: A Structure for Efficient Numerical Computation},
  year={2011},
  volume={13},
  number={2},
  pages={22-30},
  doi={10.1109/MCSE.2011.37}}

@misc{pyautofit,
  author = {​James Nightingale and Richard Hayes},
  title = {PyAutoFit: A classy Probabilistic Programming Language for Complex Model-fitting},
  year = {2020},
  publisher = {​GitHub},
  journal = {​GitHub repository},
  url = {https://github.com/rhayes777/PyAutoFit}
}
@article{multinest,
abstract = {We present further development and the first public release of our multimodal nested sampling algorithm, called MultiNest. This Bayesian inference tool calculates the evidence, with an associated error estimate, and produces posterior samples from distributions that may contain multiple modes and pronounced (curving) degeneracies in high dimensions. The developments presented here lead to further substantial improvements in sampling efficiency and robustness, as compared to the original algorithm presented in Feroz and Hobson, which itself significantly outperformed existing Markov chain Monte Carlo techniques in a wide range of astrophysical inference problems. The accuracy and economy of the MultiNest algorithm are demonstrated by application to two toy problems and to a cosmological inference problem focusing on the extension of the vanilla $\Lambda$ cold dark matter model to include spatial curvature and a varying equation of state for dark energy. The MultiNest software, which is fully parallelized using MPI and includes an interface to CosmoMC, is available at http://www.mrao.cam.ac.uk/software/multinest/. It will also be released as part of the SuperBayeS package, for the analysis of supersymmetric theories of particle physics, at http://www.superbayes.org. {\textcopyright} 2009 RAS.},
archivePrefix = {arXiv},
arxivId = {0809.3437},
author = {Feroz, F. and Hobson, M. P. and Bridges, M.},
doi = {10.1111/j.1365-2966.2009.14548.x},
eprint = {0809.3437},
isbn = {0035-8711},
issn = {00358711},
journal = {Monthly Notices of the Royal Astronomical Society},
keywords = {Methods: Data analysis,Methods: Statistical},
number = {4},
pages = {1601--1614},
pmid = {29176},
title = {{MultiNest: An efficient and robust Bayesian inference tool for cosmology and particle physics}},
volume = {398},
year = {2009}
}
@article{pymultinest,
abstract = {Context. Aims. Active galactic nuclei are known to have complex X-ray spectra that depend on both the properties of the accreting super-massive black hole (e.g. mass, accretion rate) and the distribution of obscuring material in its vicinity (i.e. the "torus"). Often however, simple and even unphysical models are adopted to represent the X-ray spectra of AGN, which do not capture the complexity and diversity of the observations. In the case of blank field surveys in particular, this should have an impact on e.g. the determination of the AGN luminosity function, the inferred accretion history of the Universe and also on our understanding of the relation between AGN and their host galaxies. Methods. We develop a Bayesian framework for model comparison and parameter estimation of X-ray spectra. We take into account uncertainties associated with both the Poisson nature of X-ray data and the determination of source redshift using photometric methods. We also demonstrate how Bayesian model comparison can be used to select among ten different physically motivated X-ray spectral models the one that provides a better representation of the observations. This methodology is applied to X-ray AGN in the 4 Ms Chandra Deep Field South. Results. For the {\~{}}350 AGN in that field, our analysis identifies four components needed to represent the diversity of the observed X-ray spectra: (1) an intrinsic power law; (2) a cold obscurer which reprocesses the radiation due to photo-electric absorption, Compton scattering and Fe-K fluorescence; (3) an unabsorbed power law associated with Thomson scattering off ionised clouds; and (4) Compton reflection, most noticeable from a stronger-than-expected Fe-K line. Simpler models, such as a photo-electrically absorbed power law with a Thomson scattering component, are ruled out with decisive evidence (B {\textgreater} 100). We also find that ignoring the Thomson scattering component results in underestimation of the inferred column density, NH, of the obscurer. Regarding the geometry of the obscurer, there is strong evidence against both a completely closed (e.g. sphere), or entirely open (e.g. blob of material along the line of sight), toroidal geometry in favour of an intermediate case. Conclusions. Despite the use of low-count spectra, our methodology is able to draw strong inferences on the geometry of the torus. Simpler models are ruled out in favour of a geometrically extended structure with significant Compton scattering. We confirm the presence of a soft component, possibly associated with Thomson scattering off ionised clouds in the opening angle of the torus. The additional Compton reflection required by data over that predicted by toroidal geometry models, may be a sign of a density gradient in the torus or reflection off the accretion disk. Finally, we release a catalogue of AGN in the CDFS with estimated parameters such as the accretion luminosity in the 2-10 keV band and the column density, NH, of the obscurer. {\textcopyright} ESO, 2014.},
archivePrefix = {arXiv},
arxivId = {1402.0004},
author = {Buchner, J. and Georgakakis, A. and Nandra, K. and Hsu, L. and Rangel, C. and Brightman, M. and Merloni, A. and Salvato, M. and Donley, J. and Kocevski, D.},
doi = {10.1051/0004-6361/201322971},
eprint = {1402.0004},
file = {:home/jammy/Documents/Papers/Stats/ButchnerPyMultiNest.pdf:pdf},
issn = {14320746},
journal = {Astronomy and Astrophysics},
keywords = {Accretion, accretion disks,Galaxies: high-redshift,Galaxies: nuclei,Methods: data analysis,Methods: statistical,X-rays: galaxies},
pages = {A125},
title = {{X-ray spectral modelling of the AGN obscuring region in the CDFS: Bayesian model selection and catalogue}},
volume = {564},
year = {2014}
}
@article{pynufft,
abstract = {A Python non-uniform fast Fourier transform (PyNUFFT) package has been developed to accelerate multidimensional non-Cartesian image reconstruction on heterogeneous platforms. Since scientific computing with Python encompasses a mature and integrated environment, the time efficiency of the NUFFT algorithm has been a major obstacle to real-time non-Cartesian image reconstruction with Python. The current PyNUFFT software enables multi-dimensional NUFFT accelerated on a heterogeneous platform, which yields an efficient solution to many non-Cartesian imaging problems. The PyNUFFT also provides several solvers, including the conjugate gradient method, 1 total variation regularized ordinary least square (L1TV-OLS), and 1 total variation regularized least absolute deviation (L1TV-LAD). Metaprogramming libraries have been employed to accelerate PyNUFFT. The PyNUFFT package has been tested on multi-core central processing units (CPUs) and graphic processing units (GPUs), with acceleration factors of 6.3–9.5× on a 32-thread CPU platform and 5.4–13× on a GPU.},
author = {Lin, Jyh Miin},
doi = {10.3390/jimaging4030051},
file = {:home/jammy/Documents/Papers/Software/jimaging-04-00051-v2.pdf:pdf},
issn = {2313433X},
journal = {Journal of Imaging},
keywords = {Graphic processing unit (GPU),Heterogeneous system architecture (HSA),Magnetic resonance imaging (MRI),Multi-core system,Total variation (TV)},
number = {3},
pages = {1--22},
title = {{Python non-uniform fast fourier transform (PyNUFFT): An accelerated non-cartesian MRI package on a heterogeneous platform (CPU/GPU)}},
volume = {4},
year = {2018}
}
@software{pyquad,
  author       = {Ashley J. Kelly},
  title        = {pyquad},
  month        = jul,
  year         = 2020,
  publisher    = {Zenodo},
  version      = {0.6.4},
  doi          = {10.5281/zenodo.3936959},
  url          = {https://doi.org/10.5281/zenodo.3936959}
}
@article{pyswarms,
    author  = {Lester James V. Miranda},
    title   = "{P}y{S}warms, a research-toolkit for {P}article {S}warm {O}ptimization in {P}ython",
    journal = {Journal of Open Source Software},
    year    = {2018},
    volume  = {3},
    issue   = {21},
    doi     = {10.21105/joss.00433},
    url     = {https://doi.org/10.21105/joss.00433}
}
 @book{python,
 author = {Van Rossum, Guido and Drake, Fred L.},
 title = {Python 3 Reference Manual},
 year = {2009},
 isbn = {1441412697},
 publisher = {CreateSpace},
 address = {Scotts Valley, CA}
}
@article{scikit-image,
  title={scikit-image: image processing in Python},
  author={Van der Walt, Stefan and Sch{\"o}nberger, Johannes L and Nunez-Iglesias, Juan and Boulogne, Fran{\c{c}}ois and Warner, Joshua D and Yager, Neil and Gouillart, Emmanuelle and Yu, Tony},
  journal={PeerJ},
  volume={2},
  pages={e453},
  year={2014},
  publisher={PeerJ Inc.}
}
@article{scikit-learn,
 title={Scikit-learn: Machine Learning in {P}ython},
 author={Pedregosa, F. and Varoquaux, G. and Gramfort, A. and Michel, V.
         and Thirion, B. and Grisel, O. and Blondel, M. and Prettenhofer, P.
         and Weiss, R. and Dubourg, V. and Vanderplas, J. and Passos, A. and
         Cournapeau, D. and Brucher, M. and Perrot, M. and Duchesnay, E.},
 journal={Journal of Machine Learning Research},
 volume={12},
 pages={2825--2830},
 year={2011}
}
@article{scipy,
       author = {{Virtanen}, Pauli and {Gommers}, Ralf and {Oliphant},
         Travis E. and {Haberland}, Matt and {Reddy}, Tyler and
         {Cournapeau}, David and {Burovski}, Evgeni and {Peterson}, Pearu
         and {Weckesser}, Warren and {Bright}, Jonathan and {van der Walt},
         St{\'e}fan J.  and {Brett}, Matthew and {Wilson}, Joshua and
         {Jarrod Millman}, K.  and {Mayorov}, Nikolay and {Nelson}, Andrew
         R.~J. and {Jones}, Eric and {Kern}, Robert and {Larson}, Eric and
         {Carey}, CJ and {Polat}, {\.I}lhan and {Feng}, Yu and {Moore},
         Eric W. and {Vand erPlas}, Jake and {Laxalde}, Denis and
         {Perktold}, Josef and {Cimrman}, Robert and {Henriksen}, Ian and
         {Quintero}, E.~A. and {Harris}, Charles R and {Archibald}, Anne M.
         and {Ribeiro}, Ant{\^o}nio H. and {Pedregosa}, Fabian and
         {van Mulbregt}, Paul and {Contributors}, SciPy 1. 0},
        title = "{SciPy 1.0: Fundamental Algorithms for Scientific
                  Computing in Python}",
      journal = {Nature Methods},
      year = "2020",
      volume={17},
      pages={261--272},
      adsurl = {https://rdcu.be/b08Wh},
      doi = {10.1038/s41592-019-0686-2},
}
@article{Alexander2019,
abstract = {Dark matter substructure has the potential to discriminate between broad classes of dark matter models. With this in mind, we construct novel solutions to the equations of motion governing condensate dark matter candidates, namely axion Bose-Einstein condensates and superfluids. These solutions are highly compressed along one axis and thus have a disk-like geometry. We discuss linear stability of these solutions, consider the astrophysical implications as a large-scale dark disk or as small scale substructure, and find a characteristic signal in strong gravitational lensing. This adds to the growing body of work that indicates that the morphology of dark matter substructure is a powerful probe of the nature of dark matter.},
archivePrefix = {arXiv},
arxivId = {1901.03694},
author = {Alexander, Stephon and Bramburger, Jason J. and McDonough, Evan},
doi = {10.1016/j.physletb.2019.134871},
eprint = {1901.03694},
file = {:home/jammy/Documents/Papers/PyAutoLens/Alexander2018DiskSuperfliod.pdf:pdf},
issn = {03702693},
journal = {Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics},
pages = {1--7},
title = {{Dark disk substructure and superfluid dark matter}},
url = {http://arxiv.org/abs/1901.03694},
volume = {797},
year = {2019}
}
@article{Bolton2012,
abstract = {We present an analysis of the evolution of the central mass-density profile of massive elliptical galaxies from the SLACS and BELLS strong gravitational lens samples over the redshift interval z ≈ 0.1-0.6, based on the combination of strong-lensing aperture mass and stellar velocity-dispersion constraints. We find a significant trend toward steeper mass profiles (parameterized by the power-law density model with $\rho$ ∝ r-$\gamma$) at later cosmic times, with magnitude d 〈$\gamma$〉/dz = -0.60 ± 0.15. We show that the combined lens-galaxy sample is consistent with a non-evolving distribution of stellar velocity dispersions. Considering possible additional dependence of 〈$\gamma$〉 on lens-galaxy stellar mass, effective radius, and S{\'{e}}rsic index, we find marginal evidence for shallower mass profiles at higher masses and larger sizes, but with a significance that is subdominant to the redshift dependence. Using the results of published Monte Carlo simulations of spectroscopic lens surveys, we verify that our mass-profile evolution result cannot be explained by lensing selection biases as a function of redshift. Interpreted as a true evolutionary signal, our result suggests that major dry mergers involving off-axis trajectories play a significant role in the evolution of the average mass-density structure of massive early-type galaxies over the past 6Gyr. We also consider an alternative non-evolutionary hypothesis based on variations in the strong-lensing measurement aperture with redshift, which would imply the detection of an "inflection zone" marking the transition between the baryon-dominated and dark-matter halo-dominated regions of the lens galaxies. Further observations of the combined SLACS+BELLS sample can constrain this picture more precisely, and enable a more detailed investigation of the multivariate dependences of galaxy mass structure across cosmic time. {\textcopyright} 2012. The American Astronomical Society. All rights reserved.},
archivePrefix = {arXiv},
arxivId = {1201.2988},
author = {Bolton, Adam S. and Brownstein, Joel R. and Kochanek, Christopher S. and Shu, Yiping and Schlegel, David J. and Eisenstein, Daniel J. and Wake, David A. and Connolly, Natalia and Maraston, Claudia and Arneson, Ryan A. and Weaver, Benjamin A.},
doi = {10.1088/0004-637X/757/1/82},
eprint = {1201.2988},
issn = {15384357},
journal = {Astrophysical Journal},
keywords = {Galaxies: elliptical and lenticular, cD,Galaxies: evolution,Galaxies: structure,Gravitational lensing: strong},
number = {1},
pages = {82},
title = {{The BOSS emission-line lens survey. II. Investigating mass-density profile evolution in the SLACS+BELLS strong gravitational lens sample}},
url = {http://arxiv.org/abs/1201.2988},
volume = {757},
year = {2012}
}
@article{Collett2015,
abstract = {Ongoing and future imaging surveys represent significant improvements in depth, area, and seeing compared to current data sets. These improvements offer the opportunity to discover up to three orders of magnitude more galaxy-galaxy strong lenses than are currently known. In this work we forecast the number of lenses that will be discoverable in forthcoming surveys and simulate their properties. We generate a population of statistically realistic strong lenses and simulate observations of this population for the Dark Energy Survey (DES), the Large Synoptic Survey Telescope (LSST), and Euclid surveys. We verify our model against the galaxy-scale lens search of the Canada-France-Hawaii Telescope Legacy Survey, predicting 250 discoverable lenses compared to 220 found by Gavazzi et al. The predicted Einstein radius distribution is also remarkably similar to that found by Sonnenfeld et al. For future surveys we find that, assuming Poisson limited lens galaxy subtraction, searches of the DES, LSST, and Euclid data sets should discover 2400, 120000, and 170000 galaxy-galaxy strong lenses, respectively. Finders using blue-minus-red (g - i) difference imaging for lens subtraction can discover 1300 and 62000 lenses in DES and LSST. The uncertainties on the model are dominated by the high-redshift source population, which typically gives fractional errors on the discoverable lens number at the level of tens of percent. We find that doubling the signal-to-noise ratio required for a lens to be detectable approximately halves the number of detectable lenses in each survey, indicating the importance of understanding the selection function and the sensitivity of future lens finders in interpreting strong lens statistics. We make our population forecasting and simulated observation codes publicly available so that the selection function of strong lens finders can easily be calibrated.},
archivePrefix = {arXiv},
arxivId = {1507.02657},
author = {Collett, Thomas E.},
doi = {10.1088/0004-637X/811/1/20},
eprint = {1507.02657},
isbn = {0004-637x},
issn = {15384357},
journal = {Astrophysical Journal},
keywords = {gravitational lensing: strong},
number = {1},
pages = {20},
title = {{The population of galaxy-galaxy strong lenses in forthcoming optical imaging surveys}},
url = {http://arxiv.org/abs/1507.02657},
volume = {811},
year = {2015}
}
@article{Czoske2012,
abstract = {This paper presents the full Very Large Telescope (VLT)/VIMOS-IFU data set and related data products from an ESO Large Programme with the observational goal of obtaining two-dimensional kinematic data of early-type lens galaxies, out to one effective radius. The sample consists of 17 early-type galaxies (ETGs) selected from the SLACS gravitational-lens survey. The galaxies cover the redshift range from 0.08 to 0.35 and have stellar velocity dispersions between 200 and 350 kms-1. This programme is complemented by a similar observational programme on Keck, using long-slit spectroscopy. In combination with multi-band imaging data, the kinematic data provide stringent constraints on the inner mass profiles of ETGs beyond the local Universe. Our Large Programme thus extends studies of nearby ETGs (e.g. SAURON/ATLAS3D) by an order of magnitude in distance and towards higher masses. We provide an overview of our observational strategy, the data products (luminosity-weighted spectra andHubble Space Telescopeimages) and derived products (i.e. two-dimensional fields of velocity dispersions and streaming motions) that have been used in a number of published and forthcoming lensing, kinematic and stellar-population studies. These studies also pave the way for future studies of ETGs atz≈ 1 with the upcoming extremely large telescopes. {\textcopyright} 2011 The Authors Monthly Notices of the Royal Astronomical Society {\textcopyright} 2011 RAS.},
archivePrefix = {arXiv},
arxivId = {1108.0577},
author = {Czoske, Oliver and Barnab{\`{e}}, Matteo and Koopmans, L{\'{e}}on V.E. and Treu, Tommaso and Bolton, Adam S.},
doi = {10.1111/j.1365-2966.2011.19726.x},
eprint = {1108.0577},
isbn = {00358711},
issn = {00358711},
journal = {Monthly Notices of the Royal Astronomical Society},
keywords = {Galaxies: elliptical and lenticular, cD,Galaxies: kinematics and dynamics,Galaxies: structure,Gravitational lensing: strong,Techniques: spectroscopic},
number = {1},
pages = {656--668},
title = {{Two-dimensional kinematics of SLACS lenses - IV. The complete VLT-VIMOS data set}},
volume = {419},
year = {2012}
}
@article{Dye2014,
abstract = {We have determined the mass density radial profiles of the first five strong gravitational lens systems discovered by the Herschel Astrophysical Terahertz Large Area Survey. We present an enhancement of the semilinear lens inversion method of Warren {\&} Dye which allows simultaneous reconstruction of several different wavebands and apply this to dual-band imaging of the lenses acquired with the Hubble Space Telescope. The five systems analysed here have lens redshifts which span a range 0.22 ≤ z ≤ 0.94. Our findings are consistent with other studies by concluding that: (1) the logarithmic slope of the total mass density profile steepens with decreasing redshift; (2) the slope is positively correlated with the average total projected mass density of the lens contained within half the effective radius and negatively correlated with the effective radius; (3) the fraction of dark matter contained within half the effective radius increases with increasing effective radius and increases with redshift. {\textcopyright} 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.},
archivePrefix = {arXiv},
arxivId = {1311.5893},
author = {Dye, S. and Negrello, M. and Hopwood, R. and Nightingale, J. W. and Bussmann, R. S. and Amber, S. and Bourne, N. and Cooray, A. and Dariush, A. and Dunne, L. and Eales, S. A. and Gonzalez-Nuevo, J. and Ibar, E. and Ivison, R. J. and Maddox, S. and Valiante, E. and Smith, M.},
doi = {10.1093/mnras/stu305},
eprint = {1311.5893},
issn = {13652966},
journal = {Monthly Notices of the Royal Astronomical Society},
keywords = {Galaxies: evolution,Galaxies: structure},
number = {3},
pages = {2013--2025},
title = {{Herschel*-ATLAS: Modelling the first strong gravitational lenses}},
volume = {440},
year = {2014}
}
@article{Enia2018,
abstract = {We perform lens modelling and source reconstruction of Sub-millimetre Array (SMA) data for a sample of 12 strongly lensed galaxies selected at 500$\mu$m in the Herschel Astrophysical Terahertz Large Area Survey (H-ATLAS). A previous analysis of the same data set used a single S{\'{e}}rsic profile to model the light distribution of each background galaxy. Here we model the source brightness distribution with an adaptive pixel scale scheme, extended to work in the Fourier visibility space of interferometry. We also present new SMA observations for seven other candidate lensed galaxies from theH-ATLAS sample. Our derived lens model parameters are in general consistent with previous findings. However, our estimated magnification factors, ranging from 3 to 10, are lower. The discrepancies are observed in particular where the reconstructed source hints at the presence of multiple knots of emission.We define an effective radius of the reconstructed sources based on the area in the source plane where emission is detected above 5s. We also fit the reconstructed source surface brightness with an elliptical Gaussian model. We derive a median value reff {\~{}} 1.77 kpc and a median Gaussian full width at half-maximum {\~{}}1.47 kpc. After correction for magnification, our sources have intrinsic star formation rates (SFR) {\~{}} 900-3500M⊙ yr-1, resulting in a median SFR surface density $\Sigma$SFR {\~{}} 132M⊙ yr-1 kpc-2 (or {\~{}}218M⊙ yr-1 kpc-2 for the Gaussian fit). This is consistent with that observed for other star-forming galaxies at similar redshifts, and is significantly below the Eddington limit for a radiation pressure regulated starburst.},
archivePrefix = {arXiv},
arxivId = {1801.01831},
author = {Enia, A. and Negrello, M. and Gurwell, M. and Dye, S. and Rodighiero, G. and Massardi, M. and {De Zotti}, G. and Franceschini, A. and Cooray, A. and van der Werf, P. and Birkinshaw, M. and Michalowski, M. J. and Oteo, I.},
doi = {10.1093/mnras/sty021},
eprint = {1801.01831},
file = {:home/jammy/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Enia et al. - 2018 - The Herschel-ATLAS Magnifications and physical sizes of 500-$\mu$m-selected strongly lensed galaxies.pdf:pdf},
issn = {13652966},
journal = {Monthly Notices of the Royal Astronomical Society},
keywords = {Galaxies: structure,Gravitational lensing: strong,Instrumentation: interferometers},
number = {3},
pages = {3467--3484},
title = {{The Herschel-ATLAS: Magnifications and physical sizes of 500-$\mu$m-selected strongly lensed galaxies}},
url = {http://arxiv.org/abs/1801.01831},
volume = {475},
year = {2018}
}
@article{Hermans2019,
abstract = {Posterior inference with an intractable likelihood is becoming an increasingly common task in scientific domains which rely on sophisticated computer simulations. Typically, these mechanistic models do not admit tractable densities forcing practitioners to rely on approximations during inference. This work proposes a novel approach to address the intractability of the likelihood and the marginal model. We achieve this by learning a flexible estimator which approximates the likelihood-to-evidence ratio. The resulting amortized ratio estimator is embedded in MCMC samplers such as Metropolis-Hastings and Hamiltonian Monte Carlo to approximate the likelihood-ratio between consecutive states in the Markov chain, allowing us to draw samples from the intractable posterior. Techniques are presented to improve the numerical stability. We demonstrate our approach on a variety of benchmarks and compare against well-established approximate inference techniques. Scientific applications in high energy and astrophysics with high-dimensional observations show its applicability.},
archivePrefix = {arXiv},
arxivId = {1903.04057},
author = {Hermans, Joeri and Begy, Volodimir and Louppe, Gilles},
eprint = {1903.04057},
file = {:home/jammy/Documents/Papers/PyAutoLens/Hermanns2019LikelihoodFree.pdf:pdf},
number = {i},
title = {{Likelihood-free MCMC with Amortized Approximate Likelihood Ratios}},
url = {http://arxiv.org/abs/1903.04057},
year = {2019}
}
@article{Koopmans2009,
abstract = {Based on 58 SLACS strong-lens early-type galaxies (ETGs) with direct total-mass and stellar-velocity dispersion measurements, we find that inside one effective radius massive elliptical galaxies with M eff ≳ 3 × 1010 M⊙ are well approximated by a power-law ellipsoid, with an average logarithmic density slope of 〈$\gamma$′ LD〉 ≡ -dlog($\rho$tot)/dlog(r) = 2.085 +0.025-0.018 (random error on mean) for isotropic orbits with $\beta$r = 0, 0.1 (syst.) and intrinsic scatter (all errors indicate the 68{\%} CL). We find no correlation of $\gamma$′LD with galaxy mass (M eff), rescaled radius (i.e., R einst/R eff) or redshift, despite intrinsic differences in density-slope between galaxies. Based on scaling relations, the average logarithmic density slope can be derived in an alternative manner, fully independent from dynamics, yielding 〈$\gamma$′SR〉 = 1.959 0.077. Agreement between the two values is reached for 〈$\beta$r〉 = 0.45 0.25, consistent with mild radial anisotropy. This agreement supports the robustness of our results, despite the increase in mass-to-light ratio with total galaxy mass: M eff L 1.3630.056V,eff. We conclude that massive ETGs are structurally close to homologous with close to isothermal total density profiles (≲10{\%} intrinsic scatter) and have at most some mild radial anisotropy. Our results provide new observational limits on galaxy formation and evolution scenarios, covering 4 Gyr look-back time. {\textcopyright} 2009. The American Astronomical Society.},
archivePrefix = {arXiv},
arxivId = {0906.1349},
author = {Koopmans, L. V.E. and Bolton, A. and Treu, T. and Czoske, O. and Auger, M. W. and Barnab{\`{e}}, M. and Vegetti, S. and Gavazzi, R. and Moustakas, L. A. and Burles, S.},
doi = {10.1088/0004-637X/703/1/L51},
eprint = {0906.1349},
isbn = {1522-1601 (Electronic)$\backslash$r0161-7567 (Linking)},
issn = {15384357},
journal = {Astrophysical Journal},
keywords = {Galaxies: structure,Gravitational lensing},
number = {1 PART 2},
pages = {L51--L54},
pmid = {25414243},
title = {{The structure and dynamics of massive early-type galaxies: On homology, isothermality, and isotropy inside one effective radius}},
url = {http://stacks.iop.org/1538-4357/703/i=1/a=L51?key=crossref.0217bdab14c5f868ab70f18136b0acdd},
volume = {703},
year = {2009}
}
@article{McCully2014,
abstract = {In strong gravitational lens systems, the light bending is usually dominated by one main galaxy, but may be affected by other mass along the line of sight (LOS). Shear and convergence can be used to approximate the contributions from less significant perturbers (e.g. those that are projected far from the lens or have a small mass), but higher order effects need to be included for objects that are closer or more massive. We develop a framework for multiplane lensing that can handle an arbitrary combination of tidal planes treated with shear and convergence and planes treated exactly (i.e. including higher order terms). This framework addresses all of the traditional lensing observables including image positions, fluxes, and time delays to facilitate lens modelling that includes the non-linear effects due to mass along the LOS. It balances accuracy (accounting for higher order terms when necessary) with efficiency (compressing all other LOS effects into a set of matrices that can be calculated up front and cached for lens modelling). We identify a generalized multiplane mass sheet degeneracy, in which the effective shear and convergence are sums over the lensing planes with specific, redshift-dependent weighting factors. {\textcopyright} 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.},
archivePrefix = {arXiv},
arxivId = {1401.0197},
author = {McCully, Curtis and Keeton, Charles R. and Wong, Kenneth C. and Zabludoff, Ann I.},
doi = {10.1093/mnras/stu1316},
eprint = {1401.0197},
issn = {13652966},
journal = {Monthly Notices of the Royal Astronomical Society},
keywords = {Gravitational lensing: strong,Gravitational lensing: weak},
month = {oct},
number = {4},
pages = {3631--3642},
title = {{A new hybrid framework to efficiently model lines of sight to gravitational lenses}},
volume = {443},
year = {2014}
}
@article{Negrello2014,
abstract = {We report on deep near-infrared observations obtained with the Wide Field Camera-3 (WFC3) onboard the Hubble Space Telescope (HST) of the first five confirmed gravitational lensing events discovered by the Herschel Astrophysical Terahertz Large Area Survey (H-ATLAS). We succeed in disentangling the background galaxy from the lens to gain separate photometry of the two components. The HST data allow us to significantly improve on previous constraints of the mass in stars of the lensed galaxy and to perform accurate lens modelling of these systems, as described in the accompanying paper by Dye et al. We fit the spectral energy distributions of the background sources from near-IR to millimetre wavelengths and use the magnification factors estimated by Dye et al. to derive the intrinsic properties of the lensed galaxies. We find these galaxies to have star-formations rates (SFR) {\~{}} 400-2000 M⊙ yr-1, with {\~{}}(6-25) × 1010 M⊙ of their baryonic mass already turned into stars. At these rates of star formation, all remaining molecular gas will be exhausted in less than {\~{}}100 Myr, reaching a final mass in stars of a few 1011 M⊙. These galaxies are thus proto-ellipticals caught during their major episode of star formation, and observed at the peak epoch (z {\~{}} 1.5-3) of the cosmic star formation history of the Universe.},
archivePrefix = {arXiv},
arxivId = {1311.5898},
author = {Negrello, M. and Hopwood, R. and Dye, S. and da Cunha, E. and Serjeant, S. and Fritz, J. and Rowlands, K. and Fleuren, S. and Bussmann, R. S. and Cooray, A. and Dannerbauer, H. and Gonzalez-Nuevo, J. and Lapi, A. and Omont, A. and Amber, S. and Auld, R. and Baes, M. and Buttiglione, S. and Cava, A. and Danese, L. and Dariush, A. and {De Zotti}, G. and Dunne, L. and Eales, S. and Ibar, E. and Ivison, R. J. and Kim, S. and Leeuw, L. and Maddox, S. and Michalowski, M. J. and Massardi, M. and Pascale, E. and Pohlen, M. and Rigby, E. and Smith, D. J.B. and Sutherland, W. and Temi, P. and Wardlow, J.},
doi = {10.1093/mnras/stu413},
eprint = {1311.5898},
issn = {13652966},
journal = {Monthly Notices of the Royal Astronomical Society},
keywords = {Galaxies: elliptical and lenticular, cD,Galaxies: evolution,Galaxies: formation,Gravitational lensing: strong,Infrared: galaxies,Submillimetre: galaxies},
number = {3},
pages = {1999--2012},
title = {{Herschel *-ATLAS: Deep HST/WFC3 imaging of strongly lensed submillimetre galaxies}},
url = {http://arxiv.org/abs/1311.5898},
volume = {440},
year = {2014}
}
@article{Nightingale2015,
abstract = {We present a new pixelized method for the inversion of gravitationally lensed extended source images which we term adaptive semi-linear inversion (SLI). At the heart of the method is an h-means clustering algorithm which is used to derive a source plane pixelization that adapts to the lens model magnification. The distinguishing feature of adaptive SLI is that every pixelization is derived from a random initialization, ensuring that data discretization is performed in a completely different and unique way for every lens model parameter set. We compare standard SLI on a fixed source pixel grid with the new method and demonstrate the shortcomings of the former when modelling singular power-law ellipsoid (SPLE) lens profiles. In particular, we demonstrate the superior reliability and efficiency of adaptive SLI which, by design, fixes the number of degrees of freedom (NDOF) of the optimization and thereby removes biases present with other methods that allow the NDOF to vary. In addition, we highlight the importance of data discretization in pixel-based inversion methods, showing that adaptive SLI averages over significant systematics that are present when a fixed source pixel grid is used. In the case of the SPLE lens profile, we show how the method successfully samples its highly degenerate posterior probability distribution function with a single nonlinear search. The robustness of adaptive SLI provides a firm foundation for the development of a strong lens modelling pipeline, which will become necessary in the short-term future to cope with the increasing rate of discovery of new strong lens systems.},
archivePrefix = {arXiv},
arxivId = {1412.7436},
author = {Nightingale, J. W. and Dye, S.},
doi = {10.1093/mnras/stv1455},
eprint = {1412.7436},
issn = {13652966},
journal = {Monthly Notices of the Royal Astronomical Society},
keywords = {Galaxies: evolution,Galaxies: structure,Methods: observational},
month = {sep},
number = {3},
pages = {2940--2959},
title = {{Adaptive semi-linear inversion of strong gravitational lens imaging}},
volume = {452},
year = {2015}
}
@article{Nightingale2018,
abstract = {This work presents AutoLens, the first entirely automated modeling suite for the analysis of galaxy-scale strong gravitational lenses. AutoLens simultaneously models the lens galaxy's light and mass whilst reconstructing the extended source galaxy on an adaptive pixel-grid. The method's approach to source-plane discretization is amorphous, adapting its clustering and regularization to the intrinsic properties of the lensed source. The lens's light is fitted using a superposition of Sersic functions, allowing AutoLens to cleanly deblend its light from the source. Single-component mass models representing the lens's total mass density profile are demonstrated, which in conjunction with light modeling can detect central images using a centrally cored profile. Decomposed mass modeling is also shown, which can fully decouple a lens's light and dark matter and determine whether the two components are geometrically aligned. The complexity of the light and mass models is automatically chosen via Bayesian model comparison. These steps form AutoLens's automated analysis pipeline, such that all results in this work are generated without any user intervention. This is rigorously tested on a large suite of simulated images, assessing its performance on a broad range of lens profiles, source morphologies, and lensing geometries. The method's performance is excellent, with accurate light, mass, and source profiles inferred for data sets representative of both existing Hubble imaging and future Euclid wide-field observations.},
archivePrefix = {arXiv},
arxivId = {1708.07377},
author = {Nightingale, J. W. and Dye, S. and Massey, Richard J.},
doi = {10.1093/mnras/sty1264},
eprint = {1708.07377},
file = {:home/jammy/Documents/Papers{\_}Me/AutoLensChangesMarked.pdf:pdf},
issn = {13652966},
journal = {Monthly Notices of the Royal Astronomical Society},
keywords = {Galaxy: structure,Gravitational lensing,Methods: data analysis},
number = {4},
pages = {4738--4784},
title = {{AutoLens: Automated modeling of a strong lens's light, mass, and source}},
url = {https://academic.oup.com/mnras/article/478/4/4738/5001434},
volume = {478},
year = {2018}
}
@article{Nightingale2019,
abstract = {We investigate how strong gravitational lensing can test contemporary models of massive elliptical (ME) galaxy formation, by combining a traditional decomposition of their visible stellar distribution with a lensing analysis of their mass distribution. As a proof of concept, we study a sample of three ME lenses, observing that all are composed of two distinct baryonic structures, a 'red' central bulge surrounded by an extended envelope of stellar material. Whilst these two components look photometrically similar, their distinct lensing effects permit a clean decomposition of their mass structure. This allows us to infer two key pieces of information about each lens galaxy: (i) the stellar mass distribution (without invoking stellar populations models) and (ii) the inner dark matter halo mass. We argue that these two measurements are crucial to testing models of ME formation, as the stellar mass profile provides a diagnostic of baryonic accretion and feedback whilst the dark matter mass places each galaxy in the context of LCDM large-scale structure formation. We also detect large rotational offsets between the two stellar components and a lopsidedness in their outer mass distributions, which hold further information on the evolution of each ME. Finally, we discuss how this approach can be extended to galaxies of all Hubble types and what implication our results have for studies of strong gravitational lensing.},
archivePrefix = {arXiv},
arxivId = {1901.07801},
author = {Nightingale, James W. and Massey, Richard J. and Harvey, David R. and Cooper, Andrew P. and Etherington, Amy and Tam, Sut Ieng and Hayes, Richard G.},
doi = {10.1093/mnras/stz2220},
eprint = {1901.07801},
file = {:home/jammy/Documents/Papers{\_}Me/Gal{\_}Structure{\_}Final/GalaxyStructure.pdf:pdf},
issn = {13652966},
journal = {Monthly Notices of the Royal Astronomical Society},
keywords = {Galaxies: Evolution,Galaxies: Formation,Gravitational lensing: Strong},
number = {2},
pages = {2049--2068},
title = {{Galaxy structure with strong gravitational lensing: Decomposing the internal mass distribution of massive elliptical galaxies}},
url = {http://arxiv.org/abs/1901.07801},
volume = {489},
year = {2019}
}
@article{Sonnenfeld2015,
abstract = {We investigate the cosmic evolution of the internal structure of massive early-type galaxies over half of the age of the universe. We perform a joint lensing and stellar dynamics analysis of a sample of 81 strong lenses from the Strong Lensing Legacy Survey and Sloan ACS Lens Survey and combine the results with a hierarchical Bayesian inference method to measure the distribution of dark matter mass and stellar initial mass function (IMF) across the population of massive early-type galaxies. Lensing selection effects are taken into account. We find that the dark matter mass projected within the inner 5 kpc increases for increasing redshift, decreases for increasing stellar mass density, but is roughly constant along the evolutionary tracks of early-type galaxies. The average dark matter slope is consistent with that of a Navarro-Frenk-White profile, but is not well constrained. The stellar IMF normalization is close to a Salpeter IMF at log M ∗ = 11.5 and scales strongly with increasing stellar mass. No dependence of the IMF on redshift or stellar mass density is detected. The anti-correlation between dark matter mass and stellar mass density supports the idea of mergers being more frequent in more massive dark matter halos.},
archivePrefix = {arXiv},
arxivId = {1410.1881},
author = {Sonnenfeld, Alessandro and Treu, Tommaso and Marshall, Philip J. and Suyu, Sherry H. and Gavazzi, Rapha{\"{e}}l and Auger, Matthew W. and Nipoti, Carlo},
doi = {10.1088/0004-637X/800/2/94},
eprint = {1410.1881},
issn = {15384357},
journal = {Astrophysical Journal},
keywords = {galaxies: elliptical and lenticular, cD,galaxies: evolution,gravitational lensing: strong},
number = {2},
pages = {94},
title = {{The sl2s galaxy-scale lens sample. V. Dark matter halos and stellar imf of massive early-type galaxies out to redshift 0.8}},
url = {http://arxiv.org/abs/1410.1881},
volume = {800},
year = {2015}
}
@article{Suyu2016,
abstract = {Strong gravitational lens systems with time delays between the multiple images allow measurements of time-delay distances, which are primarily sensitive to the Hubble constant that is key to probing dark energy, neutrino physics and the spatial curvature of the Universe, as well as discovering new physics. We present H0LiCOW (H0 Lenses in COSMOGRAIL's Wellspring), a program that aims to measure H0 with {\textless} 3.5 per cent uncertainty from five lens systems (B1608+656, RXJ1131-1231, HE 0435-1223, WFI2033-4723 and HE 1104-1805). We have been acquiring (1) time delays through COSMOGRAIL and Very Large Array monitoring, (2) high-resolution Hubble Space Telescope imaging for the lens mass modelling, (3) wide-field imaging and spectroscopy to characterize the lens environment and (4) moderate-resolution spectroscopy to obtain the stellar velocity dispersion of the lenses for mass modelling. In cosmological models with one-parameter extension to flat $\Lambda$ cold dark matter, we expect to measure H0 to {\textless} 3.5 per cent in most models, spatial curvature $\Omega$k to 0.004, w to 0.14 and the effective number of neutrino species to 0.2 (1$\sigma$ uncertainties) when combined with current cosmic microwave background (CMB) experiments. These are, respectively, a factor of {\~{}}15, {\~{}}2 and {\~{}}1.5 tighter than CMB alone. Our data set will further enable us to study the stellar initial mass function of the lens galaxies, and the co-evolution of supermassive black holes and their host galaxies. This program will provide a foundation for extracting cosmological distances from the hundreds of time-delay lenses that are expected to be discovered in current and future surveys.},
archivePrefix = {arXiv},
arxivId = {1607.00017},
author = {Suyu, S. H. and Bonvin, V. and Courbin, F. and Fassnacht, C. D. and Rusu, C. E. and Sluse, D. and Treu, T. and Wong, K. C. and Auger, M. W. and Ding, X. and Hilbert, S. and Marshall, P. J. and Rumbaugh, N. and Sonnenfeld, A. and Tewes, M. and Tihhonova, O. and Agnello, A. and Blandford, R. D. and Chen, G. C.F. and Collett, T. and Koopmans, L. V.E. and Liao, K. and Meylan, G. and Spiniello, C.},
doi = {10.1093/mnras/stx483},
eprint = {1607.00017},
file = {:home/jammy/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Suyu et al. - 2017 - H0LiCOW - I. H0 Lenses in COSMOGRAIL's Wellspring Program overview.pdf:pdf},
issn = {13652966},
journal = {Monthly Notices of the Royal Astronomical Society},
keywords = {Cosmological parameters,Distance scale,Galaxies: structure,Gravitational lensing: strong,HE 0435-1223,HE 1104-1805,Quasars: individual:B1608+656,RXJ1131-1231,WFI2033-4723},
number = {3},
pages = {2590--2604},
title = {{H0LiCOW - I. H0 Lenses in COSMOGRAIL's Wellspring: Program overview}},
url = {http://arxiv.org/abs/1607.00017{\%}0Ahttp://dx.doi.org/10.1093/mnras/stx483},
volume = {468},
year = {2017}
}
@article{Treu2009,
abstract = {We study the relation between the internal structure of early-type galaxies and their environment using 70 strong gravitational lenses from the SLACS Survey. The Sloan Digital Sky Survey (SDSS) database is used to determine two measures of overdensity of galaxies around each lens - the projected number density of galaxies inside the tenth nearest neighbor ($\Sigma$10) and within a cone of radius one h -1 Mpc (D 1). Our main results are as follows. (1) The average overdensity is somewhat larger than unity, consistent with lenses preferring overdense environments as expected for massive early-type galaxies (12/70 lenses are in known groups/clusters). (2) The distribution of overdensities is indistinguishable from that of "twin" nonlens galaxies selected from SDSS to have the same redshift and stellar velocity dispersion $\sigma$*. Thus, within our errors, lens galaxies are an unbiased population, and the SLACS results can be generalized to the overall population of early-type galaxies. (3) Typical contributions from external mass distribution are no more than a few percent in local mass density, reaching 10-20{\%} (0.05-0.10 external convergence) only in the most extreme overdensities. (4) No significant correlation between overdensity and slope of the mass-density profile of the lens galaxies is found. (5) Satellite galaxies (those with a more luminous companion) have marginally steeper mass-density profiles (as quantified by f SIE = $\sigma$*/$\sigma$SIE = 1.12 ± 0.05 versus 1.01 ± 0.01) and smaller dynamically normalized mass enclosed within the Einstein radius ($\Delta$log M Ein/M dim differs by -0.09 ± 0.03 dex) than central galaxies (those without). This result suggests that tidal stripping may affect the mass structure of early-type galaxies down to kpc scales probed by strong lensing, when they fall into larger structures. {\textcopyright} 2009. The American Astronomical Society. All rights reserved.},
archivePrefix = {arXiv},
arxivId = {0806.1056},
author = {Treu, Tommaso and Gavazzi, Rapha{\"{e}}l and Gorecki, Alexia and Marshall, Philip J. and Koopmans, L{\'{e}}on V.E. and Bolton, Adam S. and Moustakas, Leonidas A. and Burles, Scott},
doi = {10.1088/0004-637X/690/1/670},
eprint = {0806.1056},
issn = {15384357},
journal = {Astrophysical Journal},
keywords = {Galaxies: elliptical and lenticular, cD,Galaxies: evolution,Galaxies: formation,Galaxies: structure,Gravitational lensing},
number = {1},
pages = {670--682},
title = {{The slacs survey. VIII. the relation between environment and internal structure of early-type galaxies}},
url = {http://stacks.iop.org/0004-637X/690/i=1/a=670?key=crossref.f6cfae6390f195584737e04966a8c778},
volume = {690},
year = {2009}
}
@article{Vegetti2009,
abstract = {We introduce a new adaptive and fully Bayesian grid-based method to model strong gravitational lenses with extended images. The primary goal of this method is to quantify the level of luminous and dark mass substructure in massive galaxies, through their effect on highly magnified arcs and Einstein rings. The method is adaptive on the source plane, where a Delaunay tessellation is defined according to the lens mapping of a regular grid on to the source plane. The Bayesian penalty function allows us to recover the best non-linear potential-model parameters and/or a grid-based potential correction and to objectively quantify the level of regularization for both the source and potential. In addition, we implement a Nested-Sampling technique to quantify the errors on all non-linear mass model parameters - marginalized over all source and regularization parameters - and allow an objective ranking of different potential models in terms of the marginalized evidence. In particular, we are interested in comparing very smooth lens mass models with ones that contain mass substructures. The algorithm has been tested on a range of simulated data sets, created from a model of a realistic lens system. One of the lens systems is characterized by a smooth potential with a power-law density profile, 12 include a Navarro, Frenk and White (NFW) dark matter substructure of different masses and at different positions and one contains two NFW dark substructures with the same mass but with different positions. Reconstruction of the source and lens potential for all of these systems shows the method is able, in a realistic scenario, to identify perturbations with masses ≳107 M ⊙ when located on the Einstein ring. For positions both inside and outside of the ring, masses of at least 109 M⊙ are required (i.e. roughly the Einstein ring of the perturber needs to overlap with that of the main lens). Our method provides a fully novel and objective test of mass substructure in massive galaxies. {\textcopyright} 2008 RAS.},
archivePrefix = {arXiv},
arxivId = {0805.0201},
author = {Vegetti, S. and Koopmans, L. V.E.},
doi = {10.1111/j.1365-2966.2008.14005.x},
eprint = {0805.0201},
isbn = {0892-0915 (Print)$\backslash$r0892-0915 (Linking)},
issn = {00358711},
journal = {Monthly Notices of the Royal Astronomical Society},
keywords = {Dark matter,Galaxies: haloes,Galaxies: structure,Gravitational lensing},
month = {jan},
number = {3},
pages = {945--963},
pmid = {20829068},
title = {{Bayesian strong gravitational-lens modelling on adaptive grids: Objective detection of mass substructure in Galaxies}},
volume = {392},
year = {2009}
}
@article{Vegetti2014,
abstract = {We present the results of a search for galaxy substructures in a sample of 11 gravitational lens galaxies from the Sloan Lens ACS Survey by Bolton et al. We find no significant detection of mass clumps, except for a luminous satellite in the system SDSS J0956+5110. We use these non-detections, in combination with a previous detection in the system SDSS J0946+1006, to derive constraints on the substructure mass function in massive early-type host galaxies with an average redshift zlens {\~{}}0.2 and an average velocity dispersion seff {\~{}}270 km s-1. We perform a Bayesian inference on the substructure mass function, within a median region of about 32 kpc2 around the Einstein radius (Rein {\~{}}4.2 kpc). We infer a mean projected substructure mass fraction f = 0.0076+0.0208-0.0052 at the 68 per cent confidence level and a substructure mass function slopea {\textless} 2.93 at the 95 per cent confidence level for a uniform prior probability density on a. For a Gaussian prior based on cold dark matter (CDM) simulations, we infer f = 0.0064+0.0080-0.0042 and a slope of a =1.90+0.098-0.098 at the 68 per cent confidence level. Since only one substructure was detected in the full sample, we have little information on the mass function slope, which is therefore poorly constrained (i.e. the Bayes factor shows no positive preference for any of the two models). The inferred fraction is consistent with the expectations from CDM simulations and with inference from flux ratio anomalies at the 68 per cent confidence level. {\textcopyright} 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.},
archivePrefix = {arXiv},
arxivId = {1405.3666},
author = {Vegetti, S. and Koopmans, L. V.E. and Auger, M. W. and Treu, T. and Bolton, A. S.},
doi = {10.1093/mnras/stu943},
eprint = {1405.3666},
issn = {13652966},
journal = {Monthly Notices of the Royal Astronomical Society},
keywords = {Galaxies,Structure},
month = {aug},
number = {3},
pages = {2017--2035},
title = {{Inference of the cold dark matter substructure mass function at z = 0.2 using strong gravitational lenses}},
volume = {442},
year = {2014}
}
@article{Atek2015,
abstract = {Exploiting the power of gravitational lensing, the Hubble Frontier Fields (HFF) program aims at observing six massive galaxy clusters to explore the distant universe far beyond the limits of blank field surveys. Using the complete Hubble Space Telescope observations of the first HFF cluster A2744, we report the detection of 50 galaxy candidates at z ∼ 7 and eight candidates at z ∼ 8 in a total survey area of 0.96 arcmin2 in the source plane. Three of these galaxies are multiply imaged by the lensing cluster. Using an updated model of the mass distribution in the cluster we were able to calculate the magnification factor and the effective survey volume for each galaxy in order to compute the ultraviolet galaxy luminosity function (LF) at both redshifts 7 and 8. Our new measurements reliably extend the z ∼ 7 UV LF down to an absolute magnitude of MUV ∼ -15.5. We find a characteristic magnitude of M∗UV = -20.90-0.73+0.90 mag and a faint-end slope $\alpha$ = -2.01-0.28+0.20,close to previous determinations in blank fields. We show here for the first time that this slope remains steep down to very faint luminosities of 0.01 L∗. Although prone to large uncertainties, our results at z ∼ 8 also seem to confirm a steep faint-end slope below 0.1 L∗. The HFF program is therefore providing an extremely efficient way to study the faintest galaxy populations at z {\textgreater} 7 that would otherwise be inaccessible with current instrumentation. The full sample of six galaxy clusters will provide even better constraints on the buildup of galaxies at early epochs and their contribution to cosmic reionization.},
archivePrefix = {arXiv},
arxivId = {1409.0512},
author = {Atek, Hakim and Richard, Johan and Kneib, Jean Paul and Jauzac, Mathilde and Schaerer, Daniel and Clement, Benjamin and Limousin, Marceau and Jullo, Eric and Natarajan, Priyamvada and Egami, Eiichi and Ebeling, Harald},
doi = {10.1088/0004-637X/800/1/18},
eprint = {1409.0512},
file = {:home/jammy/Documents/Papers/StrongLensCluster/Atek2015HFFUV.pdf:pdf},
issn = {15384357},
journal = {Astrophysical Journal},
keywords = {Galaxies: evolution,Galaxies: high-redshift,Galaxies: luminosity function, mass function,Gravitational lensing: strong},
number = {1},
title = {{New constraints on the faint end of the UV luminosity function at z ∼ 7-8 using the gravitational lensing of the hubble frontier fields cluster A2744}},
volume = {800},
year = {2015}
}
@article{Jullo2010,
abstract = {Current efforts in observational cosmology are focused on characterizing the mass-energy content of the universe. We present results from a geometric test based on strong lensing in galaxy clusters. Based on Hubble Space Telescope images and extensive ground-based spectroscopic follow-up of the massive galaxy cluster Abell 1689, we used a parametric model to simultaneously constrain the cluster mass distribution and dark energy equation of state. Combining our cosmological constraints with those from x-ray clusters and the Wilkinson Microwave Anisotropy Probe 5-year data gives $\Omega$m = 0.25 ±0.05 and Wx = -0.97 ±0.07, which are consistent with results from other methods. Inclusion of our method with all other available techniques brings down the current 2$\sigma$ contours on the dark energy equation-of-state parameter wx by ∼30{\%}.},
archivePrefix = {arXiv},
arxivId = {1008.4802},
author = {Jullo, Eric and Natarajan, Priyamvada and Kneib, Jean Paul and D'Aloisio, Anson and Limousin, Marceau and Richard, Johan and Schimd, Carlo},
doi = {10.1126/science.1185759},
eprint = {1008.4802},
file = {:home/jammy/Documents/Papers/StrongLensCluster/Jullo2008CosmologicalConstraints.pdf:pdf},
issn = {00368075},
journal = {Science},
number = {5994},
pages = {924--927},
title = {{Cosmological constraints from strong gravitational lensing in clusters of galaxies}},
volume = {329},
year = {2010}
}
@article{Richard2014,
abstract = {Extending over three Hubble Space Telescope (HST) cycles, the Hubble Frontier Fields (HFF) initiative constitutes the largest commitment ever of HST time to the exploration of the distant Universe via gravitational lensing by massive galaxy clusters. Here, we present models of the mass distribution in the six HFF cluster lenses, derived from a joint strong- and weak-lensing analysis anchored by a total of 88 multiple-image systems identified in existing HST data. The resulting maps of the projected mass distribution and of the gravitational magnification effectively calibrate the HFF clusters as gravitational telescopes. Allowing the computation of search areas in the source plane, these maps are provided to the community to facilitate the exploitation of forthcoming HFF data for quantitative studies of the gravitationally lensed population of background galaxies. Our models of the gravitational magnification afforded by the HFF clusters allow us to quantify the lensing-induced boost in sensitivity over blank-field observations and predict that galaxies at z {\textgreater} 10 and as faint as m(AB) = 32 will be detectable, up to 2 mag fainter than the limit of the Hubble Ultra Deep Field.},
author = {Richard, Johan and Jauzac, Mathilde and Limousin, Marceau and Jullo, Eric and Cl{\'{e}}ment, Benjamin and Ebeling, Harald and Kneib, Jean Paul and Atek, Hakim and Natarajan, Priya and Egami, Eiichi and Livermore, Rachael and Bower, Richard},
doi = {10.1093/mnras/stu1395},
file = {:home/jammy/Documents/Papers/StrongLensCluster/Richard2017HFFModels.pdf:pdf},
issn = {13652966},
journal = {Monthly Notices of the Royal Astronomical Society},
keywords = {Galaxies clusters: individual: A1063S,Galaxies clusters: individual: Abell 370,Galaxies clusters: individual: MACS J0416.1-2403,Galaxies clusters: individual: MACS J0717.5+3745,Galaxies clusters: individual: MACS J1149.5+2223,galaxies clusters: individual: Abell 2744},
number = {1},
pages = {268--289},
title = {{Mass and magnification maps for the hubble space telescope frontier fields clusters: Implications for high-redshift studies}},
volume = {444},
year = {2014}
}
@article{Powell2020,
abstract = {We present a new gravitational lens modelling technique designed to model high-resolution interferometric observations with large numbers of visibilities without the need to pre-average the data in time or frequency. We demonstrate the accuracy of the method using validation tests on mock observations. Using small data sets with ∼103 visibilities, we first compare our approach with the more traditional direct Fourier transform (DFT) implementation and direct linear solver. Our tests indicate that our source inversion is indistinguishable from that of the DFT. Our method also infers lens parameters to within 1 to 2 per cent of both the ground truth and DFT, given sufficiently high signal-to-noise ratio (SNR). When the SNR is as low as 5, both approaches lead to errors of several tens of per cent in the lens parameters and a severely disrupted source structure, indicating that this is related to the SNR and choice of priors rather than the modelling technique itself. We then analyze a large data set with ∼108 visibilities and a SNR matching real global Very Long Baseline Interferometry observations of the gravitational lens system MG J0751+2716. The size of the data is such that it cannot be modelled with traditional implementations. Using our novel technique, we find that we can infer the lens parameters and the source brightness distribution, respectively, with an RMS error of 0.25 and 0.97 per cent relative to the ground truth.},
archivePrefix = {arXiv},
arxivId = {2005.03609},
author = {Powell, Devon and Vegetti, Simona and McKean, John P and Spingola, Cristiana and Rizzo, Francesca and Stacey, Hannah R},
doi = {10.1093/mnras/staa2740},
eprint = {2005.03609},
file = {:home/jammy/Documents/Papers/Strong{\_}Lens/Powell2020interfermeter.pdf:pdf},
issn = {0035-8711},
journal = {Monthly Notices of the Royal Astronomical Society},
keywords = {data analysis,gravitational lensing,high angular resolution,image,methods,processing,strong,techniques},
number = {October},
pages = {1--16},
title = {{A novel approach to visibility-space modelling of interferometric gravitational lens observations at high angular resolution}},
volume = {16},
year = {2020}
}
@article{Birrer2018a,
abstract = {We present lenstronomy, a multi-purpose open-source gravitational lens modelling pythonpackage. lenstronomy is able to reconstruct the lens mass and surface brightness distributions of strong lensing systems using forward modelling. lenstronomy supports a wide range of analytic lens and light models in arbitrary combination. The software is also able to reconstruct complex extended sources (Birrer et. al 2015) as well as being able to model point sources. We designed lenstronomy to be stable, flexible and numerically accurate, with a clear user interface that could be deployed across different platforms. Throughout its development, we have actively used lenstronomy to make several measurements including deriving constraints on dark matter properties in strong lenses, measuring the expansion history of the universe with time-delay cosmography, measuring cosmic shear with Einstein rings and decomposing quasar and host galaxy light. The software is distributed under the MIT license. The documentation, starter guide, example notebooks, source code and installation guidelines can be found at https://lenstronomy.readthedocs.io.},
archivePrefix = {arXiv},
arxivId = {1803.09746},
author = {Birrer, Simon and Amara, Adam},
doi = {10.1016/j.dark.2018.11.002},
eprint = {1803.09746},
file = {:home/jammy/Documents/Papers/Strong{\_}Lens/Biirrer2018lenstronomy.pdf:pdf},
issn = {22126864},
journal = {Physics of the Dark Universe},
keywords = {Gravitational lensing,Image simulations,Software},
pages = {189--201},
title = {{lenstronomy: Multi-purpose gravitational lens modelling software package}},
volume = {22},
year = {2018}
}
@ARTICLE{spilker16a,
  author = {{Spilker}, J.~S. and {Marrone}, D.~P. and {Aravena}, M. and
	{B{\'e}thermin}, M. and {Bothwell}, M.~S. and {Carlstrom}, J.~E. and
	{Chapman}, S.~C. and {Crawford}, T.~M. and {de Breuck}, C. and
	{Fassnacht}, C.~D. and {Gonzalez}, A.~H. and {Greve}, T.~R. and
	{Hezaveh}, Y. and {Litke}, K. and {Ma}, J. and {Malkan}, M. and
	{Rotermund}, K.~M. and {Strandet}, M. and {Vieira}, J.~D. and
	{Weiss}, A. and {Welikala}, N.},
  title = "{ALMA Imaging and Gravitational Lens Models of South Pole Telescope{\mdash}Selected Dusty, Star-Forming Galaxies at High Redshifts}",
  journal = {\apj},
  archivePrefix = "arXiv",
  eprint = {1604.05723},
  keywords = {galaxies: high-redshift, galaxies: ISM, galaxies: star formation },
  year = 2016,
  month = aug,
  volume = 826,
  eid = {112},
  pages = {112},
  doi = {10.3847/0004-637X/826/2/112},
  adsurl = {http://adsabs.harvard.edu/abs/2016ApJ...826..112S},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
