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Project Details
Funding Scheme : General Research Fund
Project Number : 17319316
Project Title(English) : Observational Tests for Competing Theories of Galaxy Formation and the Nature of Dark Matter 
Project Title(Chinese) : 星系形成和暗物質理論的觀察性測試 
Principal Investigator(English) : Prof Lim, Jeremy Jin Leong 
Principal Investigator(Chinese) :  
Department : Dept of Physics
Institution : The University of Hong Kong
E-mail Address : jjlim@hku.hk 
Tel :  
Co - Investigator(s) :
Dr Benítez, Narciso
Prof Bouwens, Rychard J
Prof Broadhurst, Tom
Dr Coe, Dan
Dr Diego, Jose M.
Mr Lam, Daniel
Dr Umetsu, Keiichi
Dr Zitrin, Adi
Panel : Physical Sciences
Subject Area : Physical Sciences
Exercise Year : 2016 / 17
Fund Approved : 540,824
Project Status : Completed
Completion Date : 31-8-2019
Project Objectives :
Robust Lens Models: Our team has developed a hybrid scheme to model lensing by galaxy clusters that includes cluster member galaxies but which makes no assumptions about the distribution of matter on larger spatial scales. Referred to as WSLAP+, this method is well suited to the complexity of the massive merging clusters chosen for HFF. With a reliable correction for lensing, we are able to obtain the intrinsic properties of all the lensed galaxies, including those more weakly lensed and do not produce multiple images. The lensed galaxies reach typically 2–3 magnitudes fainter than those found in the deepest blind-field surveys, and provide the crucial leverage for distinguishing between competing theories for galaxy formation that incorporate different forms of dark matter. We also plan to construct robust lens models for the most powerful lensing clusters in the Cluster Lensing And Supernova survey with Hubble (CLASH) program.
Intrinsic Properties of Multiply-Lensed Sources: With robust lens models in hand, we can maximize the effectiveness of finding multiply-lensed images belonging to the same galaxy by accurately predicting the positions of their counter-images. We also can securely identify each set of lensed images belonging to a given source, derive the geometric redshifts of all the multiply-lensed sources to check against their photometric redshifts (sometimes ambiguous for, especially, galaxies at very high redshifts), and reliably derive their intrinsic properties (luminosity and size). Finally, we can accurately reconstruct the delensed images of well-resolved sources to study their morphology.
Galaxy Luminosity and Size Functions: With knowledge of the intrinsic properties of the lensed galaxies, we can then compute the luminosity and size functions of galaxies. More practically, we can derive their luminosity and size distributions. To derive these distributions, we have developed algorithms to correct for the varying magnification over the cluster and hence the different surface areas at different redshifts probed at different source locations. By comparing the measured luminosity and size distributions against those predicted by theory, we will test competing theories for galaxy formation that incorporate different forms of dark matter. Specifically, we can address whether the galaxy space density increases with decreasing luminosity as might be expected if DM is cold and collisionless, or whether there is an abrupt decrease (turnover) at a particular luminosity indicative of a lower limiting mass for DM halos imposed by its wavelike nature.
Mass distribution of massive cluster members, including mass and location of their supermassive black holes: For lensed images that happen to be projected close to and which therefore experience significant lensing also by individual cluster members, we are able to probe in detail the mass distribution of these cluster members. In particular, such instances provide an opportunity to infer the properties of a supermassive black hole.
Abstract as per original application
(English/Chinese):
Realisation of objectives: We have achieved every objective of our program – and more! 1. We have completed our effort to construct robust free-form lens models for all 6 galaxy clusters in Hubble Frontiers Field (HFF) program: (i) Lam et al. 2014, ApJ, 797, 98. A Rigorous Free-form Lens Model of A2744 to Meet the Hubble Frontier Fields Challenge. (ii) Diego et al. 2015, MNRAS, 447, 3130. Free-form lensing implications for the collision of dark matter and gas in the frontier fields cluster MACS J0416.1-2403. (iii) Diego et al. 2015, MNRAS, 449, 588. The orthogonally aligned dark halo of an edge-on lensing galaxy in the Hubble Frontier Fields: a challenge for modified gravity. (iv) Diego et al. 2015, MNRAS, 451, 3920. Hubble Frontier Field free-form mass mapping of the massive multiple-merging cluster MACSJ0717.5+3745. (v) Diego et al. 2016, MNRAS, 456, 356. A free-form prediction for the reappearance of supernova Refsdal in the Hubble Frontier Fields cluster MACSJ1149.5+2223. (vi) Diego et al. 2016, MNRAS, 459, 3447. A free-form mass model of the Hubble Frontier Fields cluster AS1063 (RXC J2248.7-4431) with over one hundred constraints. (vii) Diego et al. 2018, MNRAS, 473, 4279. A free-form lensing model of A370 revealing stellar mass dominated BCGs, in Hubble Frontier Fields images. (RGC/GRF 17319316) Papers (v)-(vi) were written after this RGC/GRF proposal was submitted and we were awaiting funding results. In addition, we have pioneered an iterative method to construct free-form lens models based on multiply-lensed images having a mixture of spectroscopic and photometric redshifts. This method was applied to a galaxy cluster in the Cluster Lensing And Supernova survey with Hubble (CLASH) program: (viii) Chan et al. 2020, ApJ, 888, 35. Redshift Determinations from a Self-consistent Grid-based Lens Model for the Hubble Frontiers Field Cluster RXC J2248.7−4431 (AS1063). (RGC/GRF 17319316) This work was part of Chan’s MPhil thesis, supervised by the PI and co-supervised by a proposal Collaborator (T. Broadhurst). 2. We have derived geometric redshifts to multiply-lensed galaxies with only photometric redshifts in all the papers mentioned above, including papers (vii)-(viii) conducted in this proposal. In addition, we have measured the geometric redshift of the candidate highest-redshift gravitationally-lensed galaxy known to date, confirming its very high redshift: (ix) Chan et al. 2017, ApJ, 835, 44. Geometric Corroboration of the Earliest Lensed Galaxy at z ≃ 10.8 from Robust Free-form Modelling. (RGC/GRF 17319316) This work was part of Chan’s MPhil thesis, supervised by the PI and co-supervised by a proposal Collaborator (T. Broadhurst). 3. Taking advantage of gravitational lensing by galaxy clusters to magnify the brightness of background galaxies in the Hubble Frontiers Field (HFF) program, we have derived the luminosity function of high-redshift galaxies. We showed that the measured luminosity function is inconsistent with the prediction of Cold Dark Matter (CDM), but consistent with those of wavelike Dark Matter (ψDM): (x) Leung et al. 2018, ApJ, 862, 156. Magnification Bias of Distant Galaxies in the Hubble Frontier Fields: Testing Wave Versus Particle Dark Matter Predictions. (RGC/GRF 17319316) This work was part of Leung’s MPhil thesis, supervised by the PI and co-supervised by a proposal Collaborator (T. Broadhurst). 4. We have pinpointed the location and derived the mass of a supermassive black hole in the dominant galaxy of a galaxy cluster in the Hubble Frontiers Field (HFF) program. This work constitutes the first direct measurement of the mas of a supermassive black hole at intermediate redshifts, critical for studying the co-evolution – or otherwise – of supermassive black holes and their host galaxies: (xi) Chen et al. 2018, ApJ, 863, 135. A Likely Supermassive Black Hole Revealed by Its Einstein Radius in Hubble Frontier Fields Images. (RGC/GRF 17319316)
Summary of objectives addressed:
Objectives Addressed Percentage achieved
1.Robust Lens Models: Our team has developed a hybrid scheme to model lensing by galaxy clusters that includes cluster member galaxies but which makes no assumptions about the distribution of matter on larger spatial scales. Referred to as WSLAP+, this method is well suited to the complexity of the massive merging clusters chosen for HFF. With a reliable correction for lensing, we are able to obtain the intrinsic properties of all the lensed galaxies, including those more weakly lensed and do not produce multiple images. The lensed galaxies reach typically 2–3 magnitudes fainter than those found in the deepest blind-field surveys, and provide the crucial leverage for distinguishing between competing theories for galaxy formation that incorporate different forms of dark matter. We also plan to construct robust lens models for the most powerful lensing clusters in the Cluster Lensing And Supernova survey with Hubble (CLASH) program.Yes100%
2.Intrinsic Properties of Multiply-Lensed Sources: With robust lens models in hand, we can maximize the effectiveness of finding multiply-lensed images belonging to the same galaxy by accurately predicting the positions of their counter-images. We also can securely identify each set of lensed images belonging to a given source, derive the geometric redshifts of all the multiply-lensed sources to check against their photometric redshifts (sometimes ambiguous for, especially, galaxies at very high redshifts), and reliably derive their intrinsic properties (luminosity and size). Finally, we can accurately reconstruct the delensed images of well-resolved sources to study their morphology.Yes100%
3.Galaxy Luminosity and Size Functions: With knowledge of the intrinsic properties of the lensed galaxies, we can then compute the luminosity and size functions of galaxies. More practically, we can derive their luminosity and size distributions. To derive these distributions, we have developed algorithms to correct for the varying magnification over the cluster and hence the different surface areas at different redshifts probed at different source locations. By comparing the measured luminosity and size distributions against those predicted by theory, we will test competing theories for galaxy formation that incorporate different forms of dark matter. Specifically, we can address whether the galaxy space density increases with decreasing luminosity as might be expected if DM is cold and collisionless, or whether there is an abrupt decrease (turnover) at a particular luminosity indicative of a lower limiting mass for DM halos imposed by its wavelike nature.Yes100%
4.Mass distribution of massive cluster members, including mass and location of their supermassive black holes: For lensed images that happen to be projected close to and which therefore experience significant lensing also by individual cluster members, we are able to probe in detail the mass distribution of these cluster members. In particular, such instances provide an opportunity to infer the properties of a supermassive black hole.Yes100%
Research Outcome
Major findings and research outcome: We have completed our effort to construct robust free-form lens models for all 6 galaxy clusters in Hubble Frontiers Field (HFF) program, the last of which published in fulfillment of this proposal (Paper 2). All but perhaps one of these galaxy clusters are in the process of merging, and therefore have complex mass distributions that cannot be easily or completely captured by parametric lensing algorithms, as is the common approach used in other works. In addition, we have pioneered an iterative method to construct free-form lens models based on multiply-lensed images having a mixture of spectroscopic and photometric redshifts, and applied this method to a galaxy cluster in the Cluster Lensing And Supernova survey with Hubble (CLASH) program (Paper 5). We have applied the lens models constructed to: (i) determine the geometric redshift of the most distant gravitationally lensed galaxy discovered to date (Paper 1) (ii) determine the geometric redshift of multiply-lensed galaxies having only photometrically determined redshifts (Papers 2, 5) (iii) pinpoint the position and measure the mass of a supermassive black hole in a galaxy at an intermediate redshift, constituting the first direct measurement of the mass of a supermassive black hole beyond the local universe (Paper 4) (iv) measured the luminosity function of galaxies at high redshifts, and demonstrated that the luminosity function of these galaxies is inconsistent with the predictions of Cold Dark Matter but consistent with those of wave-like Dark Matter (Paper 3)
Potential for further development of the research
and the proposed course of action:		 The astrophysical applications of gravitational lensing - the first step of which is to construct a robust lens model for the lensing object - is one of my core research projects. The work conducted for (and before) this proposal laid the foundation for the follow-up proposal RGC/GRF 17304519, which received excellent reviews and was maximally funded.
Layman's Summary of
Completion Report:		 Gravitational lensing by galaxies constitute natural cosmic telescopes to magnify the brightnesses and sizes of distant background galaxies - permitting the detection of galaxies otherwise too dim to be seen, and the study of their morphology otherwise too small in size to show any features. Under suitable geometries, the background galaxy is multiply lensed, so that each image constitutes a magnified, brightened, but distorted view of the actual background galaxy. We use the geometrical arrangement of such multiply-lensed images in the sky to derive lens models for the lensing galaxies - i.e., the distribution of matter, including invisible Dark Matter, in the lensing galaxies. From the lens models thus constructed, we can reconstruct the actual appearance of lensed galaxies, and even derive - based on geometry - their distances. In this project, we use the lens models constructed for massive galaxy clusters to: (i) determine the geometric redshift of the most distant gravitationally lensed galaxy discovered to date (ii) determine the geometric redshift of multiply-lensed galaxies having only photometrically determined redshifts (iii) pinpoint the position and measure the mass of a supermassive black hole in a galaxy at an intermediate redshift, constituting the first direct measurement of the mass of a supermassive black hole beyond the local universe (iv) measured the luminosity function of galaxies at high redshifts, and demonstrated that the luminosity function of these galaxies is inconsistent with the predictions of Cold Dark Matter but consistent with those of wave-like Dark Matter
Research Output
Peer-reviewed journal publication(s)
arising directly from this research project :
(* denotes the corresponding author)
Year of
Publication		 Author(s) Title and Journal/Book Accessible from Institution Repository
2017 Brian M. Y. Chan*, Tom Broadhurst, Jeremy Lim, Jose M. Diego, Adi Zitrin, Dan Coe, & Holland C. Ford  Geometric Corroboration of the Earliest Lensed Galaxy at z ≃ 10.8 from Robust Free-form Modelling  No 
2018 Jose M. Diego*, Kasper B. Schmidt, Tom Broadhurst, Daniel Lam, Jesús Vega-Ferrero, Wei Zheng, Slanger Lee, Takahiro Morishita, Gary Bernstein, Jeremy Lim, Joseph Silk, & Holland Ford  A free-form lensing model of A370 revealing stellar mass dominated BCGs, in Hubble Frontier Fields images  No 
2018 Enoch Leung*, Tom Broadhurst, Jeremy Lim, Tzihong Chiueh, Hsi-Yu Schive, & Rogier Windhorst  Magnification Bias of Distant Galaxies in the Hubble Frontiers Fields: Testing Wave vs. Particle Dark Matter Predictions  No 
2018 Mandy C. Chen*, Tom Broadhurst, Jeremy Lim, Jose M. Diego, Holland Ford, & Narciso Benítez  A Likely Super Massive Black Hole Revealed by its Einstein Radius in Hubble Frontier Field Images  No 
2020 Brian M. Y. Chan, Tom Broadhurst, Jeremy Lim, Jess Wong, Jose M. Diego, & Dan Coe  Redshift Determinations from a Self-consistent Grid-based Lens Model for the Hubble Frontiers Field Cluster RXC J2248.7−4431 (AS1063)  No 
Recognized international conference(s)
in which paper(s) related to this research
project was/were delivered :
Month/Year/City Title Conference Name
Leiden 1. Geometric redshift confirmation of the second most distant candidate galaxy (poster) 2. Direct measurement of the mass of a supermassive black hole at z=0.55 (oral)  From theory to applications: celebrating a century of gravitational lensing 
Other impact
(e.g. award of patents or prizes,
collaboration with other research institutions,
technology transfer, etc.):
  SCREEN ID: SCRRM00542