Liliya L. R. Williams

She/Her/Hers

Director of Undergraduate Studies for MIfA

Professor, School of Physics and Astronomy

Contact

llrw@umn.edu

612-624-1084

285-10 John T. Tate Hall
116 Church Street Se
Minneapolis, MN 55455

Affiliations

Minnesota Institute for Astrophysics (MIfA)

Liliya L. R. Williams

She/Her/Hers

Director of Undergraduate Studies for MIfA

Professor, School of Physics and Astronomy

Research

My research centers on the role of gravity in cosmology: I use gravitational lensing and classical dynamics to study the mass distribution in the Universe, from sub-galactic to galaxy-cluster scales, with the goal of elucidating the nature of dark matter and constraining cosmological parameters. Gravitational lensing is the deflection of light from distant background sources by the intervening mass distribution, like galaxies and clusters of galaxies. Lensing is by far the best tool for the purpose of mapping out the mass distribution, as it does not rely on assumptions about the physical state of the mass. I use multiple images of distant quasars and galaxies to map out in detail the mass distribution of dark matter and ordinary matter (mainly stars) in galaxies and clusters of galaxies. Classical dynamics is a powerful means of addressing the problem of formation, evolution and relaxation of individual galaxies and clusters of galaxies. I use analytical and semi-analytical techniques to gain better understanding of dark matter halos. I am also developing theoretical models to explain the properties of dark matter halos obtained in numerical computer simulations. Our models account for the spatial and velocity distribution of dark matter within galaxy halos. They are based on fundamental physical principles, and promise to connect systems governed by Newtonian gravity with those studied by other branches of physics, like statistical mechanics and thermodynamics.

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Research Tags:

Astrophysics

Biography

Publications & Awards

Selected Publications

Barrera, B., Williams, L.L.R., Coles, J.P., Denzel, P. 2021, "Bridging the Gap Between Simply Parametrized and Free-Form Pixelated Models of Galaxy Lenses: The Case of WFI 2033-4723 Quad " Open Journal of Astroph., Vol.4, 2021.
Agniva Ghosh, Liliya L. R. Williams, Jori Liesenborgs, et al. 2021, "Further support for a trio of mass-to-light deviations in Abell 370: free-form Grale lens inversion using BUFFALO strong lensing data, MNRAS," 506, 6144
Gomer, Matthew R. & Williams, Liliya L.R., Galaxy-lens determination of H₀: the effect of the ellipse + shear modelling assumption, Monthly Notices of the Royal Astronomical Society, Volume 504, Issue 1, June 2021, 1340–1354
Zegeye, David & Williams, Liliya L.R., Two-component mass models of the lensing galaxy in the quadruply imaged supernova iPTF16geu, Open Journal of Astrophysics, Vol 3, September 15, 2020
Ghosh, Agniva; Williams, Liliya L.R.; Liesenborgs, Jori, Free-form Grale lens inversion of galaxy clusters with up to 1000 multiple images, MNRAS, Volume 494, Issue 3, May 2020, 3998–4014
Gomer, Matthew R. & Williams, Liliya L.R,, Galaxy-lens determination of H0: constraining density slope in the context of the mass sheet degeneracy, JCAP 11 (2020) 045
Arora, Arpit & Williams, Liliya L.R., Power law pseudo phase-space density profiles of dark matter halos: fluke of physics?, ApJ 893 53
Young, Anthony M.; Williams, Liliya L. R.; Hjorth, Jens, Ubiquity of density slope oscillations in the central regions of galaxy and cluster-sized systems, Journal of Cosmology and Astroparticle Physics
Priewe, Jett; Williams, Liliya L. R.; Liesenborgs, Jori; Coe, Dan; Rodney, Steven A., Lens Models Under the Microscope: Comparison of Hubble Frontier Field Cluster Magnification Maps, MNRAS, Volume 465, Issue 1, 11 February 2017, 1030–1045
Nolting, Chris; Williams, Liliya L. R.; Boylan-Kolchin, Michael; Hjorth, Jens, Testing DARKexp against energy and density distributions of Millennium-II halos, JCAP 09 (2016) 042
Woldesenbet, Addishiwot G. & Williams, Liliya L. R., Model-free analysis of quadruply imaged gravitationally lensed systems and substructured galaxies, MNRAS, Volume 454, Issue 1, 21 November 2015, 862–875
Massey, Richard; Williams, Liliya, et al., The behaviour of dark matter associated with 4 bright cluster galaxies in the 10kpc core of Abell 3827, MNRAS 449 (2015) 3393
Dhar, Barun Kumar & Williams, Liliya L. R., Surface brightness and intrinsic luminosity of ellipticals, MNRAS, Volume 427, Issue 1, 21 November 2012, 204–244
Williams, Liliya L. R.; Barnes, Eric I.; Hjorth, Jens, Collisionless dynamics in globular clusters, MNRAS, Volume 423, Issue 4, July 2012, 3589–3600
Williams, Liliya L. R. & Saha, Prasenjit , Light/mass offsets in the lensing cluster Abell 3827: evidence for collisional dark matter?, MNRAS, Volume 415, Issue 1, July 2011, Pages 448–460
Hjorth, Jens & Williams, Liliya L. R., Statistical Mechanics of Collisionless Orbits. I. Origin of Central Cusps in Dark-matter Halos, ApJ (2010)
Williams, Liliya L. R. & Hjorth, Jens, Statistical Mechanics of Collisionless Orbits. II. Structure of Halos, ApJ (2010)
Williams, Liliya L. R.; Hjorth, Jens & Wojtak, Radosław, Statistical Mechanics of Collisionless Orbits. III. Comparison with N-body Simulations, ApJ (2010)
Rudnick, L., Brown, S., and Williams, L.L.R., Extragalactic Radio Sources and the WMAP Cold Spot., ApJ, (2007)

Publications

2023

Kelly, P.L., Rodney, S., Treu, T., Oguri, M., Chen, W., Zitrin, A., Birrer, S., Bonvin, V., Dessart, L., Diego, J.M., Filippenko, A.V., Foley, R.J., Gilman, D., Hjorth, J., Jauzac, M., Mandel, K., Millon, M., Pierel, J., Sharon, K., Thorp, S., Williams, L., Broadhurst, T., Dressler, A., Graur, O., Jha, S., McCully, C., Postman, M., Schmidt, K.B., Tucker, B.E., von der Linden, A. (2023). Constraints on the Hubble constant from supernova Refsdal’s reappearance. Science. 380 (6649), [eabh1322].
DOI: 10.1126/science.abh1322

Perera, D., Williams, L.L.R., Scarlata, C. (2023). Constraints on the inner regions of lensing galaxies from central images using a recent AGN offset distribution. Monthly Notices of the Royal Astronomical Society. 522 (2), [1863-1880].
DOI: 10.1093/mnras/stad1110

Meena, A.K., Chen, W., Zitrin, A., Kelly, P.L., Golubchik, M., Zhou, R., Alfred, A., Broadhurst, T., Diego, J.M., Filippenko, A.V., Li, S.K., Oguri, M., Smith, N., Williams, L.L.R. (2023). Flashlights: an off-caustic lensed star at redshift z = 1.26 in Abell 370. Monthly Notices of the Royal Astronomical Society. 521 (4), [5224-5231].
DOI: 10.1093/mnras/stad869

2022

Ghosh, A., Adams, D., Williams, L.L.R., Liesenborgs, J., Alavi, A., Scarlata, C. (2022). An excursion into the core of the cluster lens Abell 1689.
Electronic version

Kelly, P.L., Chen, W., Alfred, A., Broadhurst, T.J., Diego, J.M., Emami, N., Filippenko, A.V., Keen, A., Li, S.K., Lim, J., Meena, A.K., Oguri, M., Scarlata, C., Treu, T., Williams, H., Williams, L.L.R., Zhou, R., Zitrin, A., Foley, R.J., Jha, S.W., Kaiser, N., Mehta, V., Rieck, S., Salo, L., Smith, N., Weisz, D.R. (2022). Flashlights: More than A Dozen High-Significance Microlensing Events of Extremely Magnified Stars in Galaxies at Redshifts z=0.7-1.5.
Electronic version

Meena, A.K., Chen, W., Zitrin, A., Kelly, P.L., Golubchik, M., Zhou, R., Alfred, A., Broadhurst, T., Diego, J.M., Oguri, M., Williams, L.L.R., Filippenko, A.V., Li, S.K. (2022). Flashlights: An Off-Caustic Lensed Star at Redshift $z$ = 1.26 in Abell 370.
Electronic version

Williams, L.L.R., Hjorth, J. (2022). Statistical Mechanics of Collisionless Orbits. V. The Approach to Equilibrium for Idealized Self-gravitating Systems. Astrophysical Journal. 937 (2), [67].
DOI: 10.3847/1538-4357/ac8d06

Shajib, A.J., Vernardos, G., Collett, T.E., Motta, V., Sluse, D., Williams, L.L., Saha, P., Birrer, S., Spiniello, C., Treu, T. (2022). Strong Lensing by Galaxies. In Space Science Reviews.
DOI: 10.48550/arXiv.2210.10790

2021

Barrera, B., Williams, L.L., Coles, J.P., Denzel, P. (2021). Bridging the Gap Between Simply Parametrized and Free-Form Pixelated Models of Galaxy Lenses: The Case of WFI 2033-4723 Quad. The Open Journal of Astrophysics. 4 (1),
DOI: 10.21105/astro.2108.04348 Electronic version

Ghosh, A., Williams, L.L.R., Liesenborgs, J., Acebron, A., Jauzac, M., Koekemoer, A.M., Mahler, G., Niemiec, A., Steinhardt, C., Faisst, A.L., Lagattuta, D., Natarajan, P. (2021). Erratum: Further support for a trio of mass-to-light deviations in Abell 370: Free-form grale lens inversion using BUFFALO strong lensing data (Monthly Notices of the Royal Astronomical Society DOI: 10.1093/mnras/stab1196). Monthly Notices of the Royal Astronomical Society. 506 (4), [6159].
DOI: 10.1093/mnras/stab2096

Meena, A.K., Ghosh, A., Bagla, J.S., Williams, L.L.R. (2021). Exotic image formation in strong gravitational lensing by clusters of galaxies - II. Uncertainties. Monthly Notices of the Royal Astronomical Society. 506 (1), [1526-1539].
DOI: 10.1093/mnras/stab1807

Ghosh, A., Williams, L.L.R., Liesenborgs, J., Acebron, A., Jauzac, M., Koekemoer, A.M., Mahler, G., Niemiec, A., Steinhardt, C., Faisst, A.L., Lagattuta, D., Natarajan, P. (2021). Further support for a trio of mass-to-light deviations in Abell 370: Free-form grale lens inversion using BUFFALO strong lensing data. Monthly Notices of the Royal Astronomical Society. 506 (4), [6144-6158].
DOI: 10.1093/mnras/stab1196

Gomer, M., Williams, L.L.R., Gomer, M. (2021). Galaxy-lens determination of H₀: The effect of the ellipse + shear modelling assumption. Monthly Notices of the Royal Astronomical Society. 504 (1), [1340-1354].
DOI: 10.1093/mnras/stab930

Denzel, P., Coles, J.P., Saha, P., Williams, L.L.R. (2021). The Hubble constant from eight time-delay galaxy lenses. Monthly Notices of the Royal Astronomical Society. 501 (1), [784-801].
DOI: 10.1093/mnras/staa3603

Ding, X., Treu, T., Birrer, S., Chen, G.C.F., Coles, J., Denzel, P., Frigo, M., Galan, A., Marshall, P.J., Millon, M., More, A., Shajib, A.J., Sluse, D., Tak, H., Xu, D., Auger, M.W., Bonvin, V., Chand, H., Courbin, F., Despali, G., Fassnacht, C.D., Gilman, D., Hilbert, S., Kumar, S.R., Lin, J.Y.Y., Park, J.W., Saha, P., Vegetti, S., Van De Vyvere, L., Williams, L.L.R. (2021). Time delay lens modelling challenge. Monthly Notices of the Royal Astronomical Society. 503 (1), [1096-1123].
DOI: 10.1093/mnras/stab484

2020

Liesenborgs, J., Williams, L.L.R., Wagner, J., de Rijcke, S. (2020). Extended lens reconstructions with GRALE: Exploiting time-domain, substructural, and weak lensing information. Monthly Notices of the Royal Astronomical Society. 494 (3), [3253-3274].
DOI: 10.1093/MNRAS/STAA842

Ghosh, A., Williams, L.L.R., Liesenborgs, J. (2020). Free-form grale lens inversion of galaxy clusters with up to 1000 multiple images. Monthly Notices of the Royal Astronomical Society. 494 (3), [3998-4014].
DOI: 10.1093/MNRAS/STAA962

Gomer, M., Williams, L.L.R. (2020). Galaxy-lens determination of H0: constraining density slope in the context of the mass sheet degeneracy. Journal of Cosmology and Astroparticle Physics. 2020 (11), [045].
DOI: 10.1088/1475-7516/2020/11/045

Wagner, J., Williams, L.L.R. (2020). Model-independent and model-based local lensing properties of B0128+437 from resolved quasar images. Astronomy and Astrophysics. [A86].
DOI: 10.1051/0004-6361/201936628

Arora, A., Williams, L.L.R. (2020). Power-law Pseudo-phase-space Density Profiles of Dark Matter Halos: A Fluke of Physics?. Astrophysical Journal. 893 (1), [53].
DOI: 10.3847/1538-4357/ab7f2e

Steinhardt, C.L., Jauzac, M., Acebron, A., Atek, H., Capak, P., Davidzon, I., Eckert, D., Harvey, D., Koekemoer, A.M., Lagos, C.D.P., Mahler, G., Montes, M., Niemiec, A., Nonino, M., Oesch, P.A., Richard, J., Rodney, S.A., Schaller, M., Sharon, K., Strolger, L.G., Allingham, J., Amara, A., Bahé, Y., Bœhm, C., Bose, S., Bouwens, R.J., Bradley, L.D., Brammer, G., Broadhurst, T., Cañas, R., Cen, R., Clément, B., Clowe, D., Coe, D., Connor, T., Darvish, B., Diego, J.M., Ebeling, H., Edge, A.C., Egami, E., Ettori, S., Faisst, A.L., Frye, B., Furtak, L.J., Gómez-Guijarro, C., Remolina González, J.D., Gonzalez, A., Graur, O., Gruen, D., Harvey, D., Hensley, H., Hovis-Afflerbach, B., Jablonka, P., Jha, S.W., Jullo, E., Kneib, J.P., Kokorev, V., Lagattuta, D.J., Limousin, M., Von Der Linden, A., Linzer, N.B., Lopez, A., Magdis, G.E., Massey, R., Masters, D.C., Maturi, M., McCully, C., McGee, S.L., Meneghetti, M., Mobasher, B., Moustakas, L.A., Murphy, E.J., Natarajan, P., Neyrinck, M., O'Connor, K., Oguri, M., Pagul, A., Rhodes, J., Rich, R.M., Robertson, A., Sereno, M., Shan, H., Smith, G.P., Sneppen, A., Squires, G.K., Tam, S.I., Tchernin, C., Toft, S., Umetsu, K., Weaver, J.R., Van Weeren, R.J., Williams, L.L.R., Wilson, T.J., Yan, L., Zitrin, A. (2020). The BUFFALO HST Survey. Astrophysical Journal, Supplement Series. 247 (2), [64].
DOI: 10.3847/1538-4365/ab75ed

Williams, L.L.R., Zegeye, D. (2020). Two-component mass models of the lensing galaxy in the quadruply imaged supernova iPTF16geu. The Open Journal of Astrophysics. 3 (1),
DOI: 10.21105/astro.2006.09391 Electronic version

2019

Sebesta, K., Williams, L.L.R., Liesenborgs, J., Medezinski, E., Okabe, N. (2019). Free-form GRALE reconstruction of Abell 2744: Robustness of uncertainties against changes in lensing data. Monthly Notices of the Royal Astronomical Society. 488 (3), [3251-3261].
DOI: 10.1093/mnras/stz1950

Jones, T.J., Williams, L.L.R., Ertel, S., Hinz, P.M., Vaz, A., Walsh, S., Webster, R. (2019). Image Flux Ratios of Gravitationally Lensed HS 0810+2554 with High-resolution Infrared Imaging. Astronomical Journal. 158 (6), [237].
DOI: 10.3847/1538-3881/ab5108

Chen, W., Kelly, P.L., Diego, J.M., Oguri, M., Williams, L.L.R., Zitrin, A., Treu, T.L., Smith, N., Broadhurst, T.J., Kaiser, N., Foley, R.J., Filippenko, A.V., Salo, L., Hjorth, J., Selsing, J. (2019). Searching for Highly Magnified Stars at Cosmological Distances: Discovery of a Redshift 0.94 Blue Supergiant in Archival Images of the Galaxy Cluster MACS J0416.1-2403. Astrophysical Journal. 881 (1), [8].
DOI: 10.3847/1538-4357/ab297d

Williams, L.L.R., Liesenborgs, J. (2019). The role of multiple images and model priors in measuring H₀ from supernova Refsdal in galaxy cluster MACS J1149.5+2223. Monthly Notices of the Royal Astronomical Society. 482 (4), [5666-5677].
Accepted author manuscriptDOI: 10.1093/mnras/sty3113

2018

Massey, R., Harvey, D., Liesenborgs, J., Richard, J., Stach, S., Swinbank, M., Taylor, P., Williams, L., Clowe, D., Courbin, F., Edge, A., Israel, H., Jauzac, M., Joseph, R., Jullo, E., Kitching, T.D., Leonard, A., Merten, J., Nagai, D., Nightingale, J., Robertson, A., Romualdez, L.J., Saha, P., Smit, R., Tam, S.I., Tittley, E. (2018). Dark matter dynamics in Abell 3827: New data consistent with standard cold dark matter. Monthly Notices of the Royal Astronomical Society. 477 (1), [669-677].
DOI: 10.1093/mnras/sty630

Diego, J.M., Kaiser, N., Broadhurst, T., Kelly, P.L., Rodney, S., Morishita, T., Oguri, M., Ross, T.W., Zitrin, A., Jauzac, M., Richard, J., Williams, L., Vega-Ferrero, J., Frye, B., Filippenko, A.V. (2018). Dark Matter under the Microscope: Constraining Compact Dark Matter with Caustic Crossing Events. Astrophysical Journal. 857 (1), [25].
DOI: 10.3847/1538-4357/aab617

Young, A.M., Williams, L.L.R., Hjorth, J. (2018). Dynamics of merging: Post-merger mixing and relaxation of an Illustris galaxy. Journal of Cosmology and Astroparticle Physics. 2018 (2), [033].
DOI: 10.1088/1475-7516/2018/02/033

Williams, L.L.R., Sebesta, K., Liesenborgs, J. (2018). Evidence for the line-of-sight structure in the Hubble Frontier Field cluster, MACSJ0717.5+3745. Monthly Notices of the Royal Astronomical Society. 480 (3), [3140-3151].
Accepted author manuscriptDOI: 10.1093/mnras/sty2088

Walls, L.G., Williams, L.L.R. (2018). Testing the uniqueness of gravitational lens mass models. Monthly Notices of the Royal Astronomical Society. 481 (1), [655-665].
DOI: 10.1093/mnras/sty2263

Gomer, M.R., Williams, L.L.R. (2018). The impact of ΛCDM substructure and baryon-dark matter transition on the image positions of quad galaxy lenses. Monthly Notices of the Royal Astronomical Society. 475 (2), [1987-2002].
DOI: 10.1093/mnras/stx3294

Rodney, S.A., Balestra, I., Bradac, M., Brammer, G., Broadhurst, T., Caminha, G.B., Chirivì, G., Diego, J.M., Filippenko, A.V., Foley, R.J., Graur, O., Grillo, C., Hemmati, S., Hjorth, J., Hoag, A., Jauzac, M., Jha, S.W., Kawamata, R., Kelly, P.L., McCully, C., Mobasher, B., Molino, A., Oguri, M., Richard, J., Riess, A.G., Rosati, P., Schmidt, K.B., Selsing, J., Sharon, K., Strolger, L.G., Suyu, S.H., Treu, T., Weiner, B.J., Williams, L.L.R., Zitrin, A. (2018). Two peculiar fast transients in a strongly lensed host galaxy. Nature Astronomy. 2 (4), [324-333].
Accepted author manuscriptDOI: 10.1038/s41550-018-0405-4

2017

Priewe, J., Williams, L.L.R., Liesenborgs, J., Coe, D., Rodney, S.A. (2017). Lens models under the microscope: Comparison of Hubble Frontier Field cluster magnification maps. Monthly Notices of the Royal Astronomical Society. 465 (1), [1030-1045].
DOI: 10.1093/mnras/stw2785

Meneghetti, M., Natarajan, P., Coe, D., Contini, E., De Lucia, G., Giocoli, C., Acebron, A., Borgani, S., Bradac, M., Diego, J.M., Hoag, A., Ishigaki, M., Johnson, T.L., Jullo, E., Kawamata, R., Lam, D., Limousin, M., Liesenborgs, J., Oguri, M., Sebesta, K., Sharon, K., Williams, L.L.R., Zitrin, A. (2017). The Frontier Fields lens modelling comparison project. Monthly Notices of the Royal Astronomical Society. 472 (3), [3177-3216].
DOI: 10.1093/mnras/stx2064

2016

Mohammed, I., Saha, P., Williams, L.L.R., Liesenborgs, J., Sebesta, K. (2016). Quantifying substructures in hubble frontier field clusters: Comparison with ΛCDM simulations. Monthly Notices of the Royal Astronomical Society. 459 (2), [1698-1709].
DOI: 10.1093/mnras/stw727

Nolting, C., Williams, L.L.R., Boylan-Kolchin, M., Hjorth, J. (2016). Testing DARKexp against energy and density distributions of Millennium-II halos. Journal of Cosmology and Astroparticle Physics. 2016 (9), [042].
DOI: 10.1088/1475-7516/2016/09/042

Sebesta, K., Williams, L.L.R., Mohammed, I., Saha, P., Liesenborgs, J. (2016). Testing light-traces-mass in Hubble Frontier Fields Cluster MACS-J0416.1-2403. Monthly Notices of the Royal Astronomical Society. 461 (2), [2126-2134].
DOI: 10.1093/mnras/stw1433

Young, A.M., Williams, L.L.R., Hjorth, J. (2016). Ubiquity of density slope oscillations in the central regions of galaxy and cluster-sized systems. Journal of Cosmology and Astroparticle Physics. 2016 (5), [010].
DOI: 10.1088/1475-7516/2016/05/010

2015

Rodney, S.A., Patel, B., Scolnic, D., Foley, R.J., Molino, A., Brammer, G., Jauzac, M., Bradač, M., Broadhurst, T., Coe, D., Diego, J.M., Graur, O., Hjorth, J., Hoag, A., W. Jha, S., Johnson, T.L., Kelly, P., Lam, D., McCully, C., Medezinski, E., Meneghetti, M., Merten, J., Richard, J., Riess, A., Sharon, K., Strolger, L.G., Treu, T., Wang, X., Williams, L.L.R., Zitrin, A. (2015). Illuminating a dark lens: A type ia supernova magnified by the frontier fields galaxy cluster abell 2744. Astrophysical Journal. 811 (1), [70].
DOI: 10.1088/0004-637X/811/1/70

Woldesenbet, A.G., Williams, L.L.R. (2015). Model-free analysis of quadruply imaged gravitationally lensed systems and substructured galaxies. Monthly Notices of the Royal Astronomical Society. 454 (1), [862-875].
DOI: 10.1093/mnras/stv1960

Hjorth, J., Williams, L.L.R., Wojtak, R., McLaughlin, M. (2015). NON-UNIVERSALITY of DARK-MATTER HALOS: CUSPS, CORES, and the CENTRAL POTENTIAL. Astrophysical Journal. 811 (1), [2].
DOI: 10.1088/0004-637X/811/1/2

Sebesta, K., Williams, L.L.R., Mohammed, I., Saha, P., Liesenborgs, J. (2015). Testing light-traces-mass in Hubble Frontier Fields Cluster MACS-J0416.1-240. Proceedings of the International Astronomical Union. 11 (A29B), [785-786].
DOI: 10.1017/S1743921316006827

Massey, R., Williams, L., Smit, R., Swinbank, M., Kitching, T.D., Harvey, D., Jauzac, M., Israel, H., Clowe, D., Edge, A., Hilton, M., Jullo, E., Leonard, A., Liesenborgs, J., Merten, J., Mohammed, I., Nagai, D., Richard, J., Robertson, A., Saha, P., Santana, R., Stott, J., Tittley, E. (2015). The behaviour of dark matter associated with four bright cluster galaxies in the 10 kpc core of Abell 3827. Monthly Notices of the Royal Astronomical Society. 449 (4), [3393-3406].
DOI: 10.1093/mnras/stv467

2014

Mohammed, I., Liesenborgs, J., Saha, P., Williams, L.L.R. (2014). Mass-galaxy offsets in abell 3827, 2218 and 1689: Intrinsic properties or line-of-sight substructures?. Monthly Notices of the Royal Astronomical Society. 439 (3), [2651-2661].
DOI: 10.1093/mnras/stu124

Williams, L.L.R., Hjorth, J., Wojtak, R. (2014). Statistical mechanics of collisionless orbits. IV. Distribution of angular momentum. Astrophysical Journal. 783 (1), [13].
DOI: 10.1088/0004-637X/783/1/13

2012

Williams, L.L.R., Barnes, E.I., Hjorth, J. (2012). Collisionless dynamics in globular clusters. Monthly Notices of the Royal Astronomical Society. 423 (4), [3589-3600].
DOI: 10.1111/j.1365-2966.2012.21158.x

Barnes, E.I., Williams, L.L.R. (2012). Entropy production in collisionless systems. II. Arbitrary phase-space occupation numbers. Astrophysical Journal. 748 (2), [144].
DOI: 10.1088/0004-637X/748/2/144

Dhar, B.K., Williams, L.L. (2012). Surface brightness and intrinsic luminosity of ellipticals. Monthly Notices of the Royal Astronomical Society. 427 (1), [204-244].
DOI: 10.1111/j.1365-2966.2011.20370.x

Woldesenbet, A.G., Williams, L.L.R. (2012). The Fundamental Surface of quad lenses. Monthly Notices of the Royal Astronomical Society. 420 (4), [2944-2955].
DOI: 10.1111/j.1365-2966.2011.20110.x

Advisees & Collaborators