Research

Two observational paths into the dark matter problem.

My work connects empirical scaling relations, gravitational lensing, and the dynamics of galaxies and clusters. Each is a distinct observational layer; together they provide stringent tests of mass models and gravity.

01A / Scaling relations

BFJR & FP

The baryonic Faber–Jackson relation (BFJR) connects baryonic mass with velocity dispersion across pressure-supported systems. For elliptical galaxies, the BFJR is thought to be a projection of the fundamental plane (FP), which includes the stellar half-mass radius as a third variable. Studied together, the two views test which empirical regularities persist from dwarf and elliptical galaxies to galaxy groups.

Scientific roleBFJR establishes the mass–velocity scaling.The fundamental plane tests how structural scale enters the same phenomenology.

SystemsGalaxy groups, ellipticals, and dwarf galaxies

RelationsBFJR and FP

Representative paperThe Baryonic Faber–Jackson Relation and Fundamental Plane of Galaxy Groups, Elliptical Galaxies, and Dwarf Galaxies ↗

Baryonic Faber-Jackson relation across galaxy groups, elliptical galaxies, and dwarf galaxies — BFJR in galaxy groups, elliptical galaxies, and dwarf galaxies. Left: Total baryonic mass (M_bar) versus velocity dispersion within the effective radius (σ_e) for the full sample. The data points are color-coded by the internal median baryonic acceleration, ⟨g_bar⟩. Middle: BFJR for the low-acceleration subsample only (⟨g_bar⟩ < 0.6a₀). In both panels, the dashed green line shows the MOND prediction in the low-acceleration regime, the solid black line is the best fit from the orthogonal MCMC, and the orange region is its 1σ credible interval. Right: Variation in the fitted parameters with the acceleration cutoff value, ⟨g_bar⟩/a₀: slope (m; top) and intercept (b; bottom). Orange diamonds are the result from orthogonal MCMC fitting, blue circles from vertical MCMC fitting. The number of objects at each cutoff is listed in the upper-right panel. The horizontal dashed lines mark the theoretical expectations from MOND modified gravity theories (m = 4, b = 3.1).Source paper ↗

Baryonic fundamental plane relation across galaxy groups, elliptical galaxies, and dwarf galaxies — FP for pressure-supported systems, including galaxy groups, ellipticals, and dwarf galaxies. The x-axis shows the expected Newtonian dynamical mass, log₁₀(5R_eσ_e²/G), while the y-axis gives the observed baryonic mass, log₁₀(M_bar). The symbols are color-coded by the median baryonic acceleration within the effective radius. The Newtonian expectations (dashed line) are followed only by high-acceleration systems with ⟨g_bar⟩ > a₀, while low-acceleration systems systematically depart from it. The inset presents the MCMC analysis for the subsample restricted to systems with ⟨g_bar⟩ > 6a₀.Source paper ↗

Radial acceleration relation for 20 CLASH galaxy clusters from Tian et al. 2020 — The radial acceleration relation measured at characteristic radii in 20 CLASH galaxy clusters. This is a cluster-scale empirical relation, not by itself a unique physical interpretation.Tian et al. (2020) on NASA ADS ↗

Mass-velocity dispersion relation for HIFLUGCS clusters and MaNGA brightest cluster galaxies — Baryonic mass–velocity dispersion measurements for HIFLUGCS galaxy clusters and MaNGA brightest cluster galaxies, with comparison relations.Tian et al. (2021) on NASA ADS ↗

01B / Scaling relations

BCGs & Galaxy Clusters

Brightest cluster galaxies and galaxy clusters occupy a distinct dynamical regime. Their radial acceleration relation and mass–velocity dispersion relation provide complementary tests of how baryonic and dynamical quantities scale at the high-mass end.

These relations are presented separately from the BFJR and fundamental-plane results because the samples, measured quantities, characteristic scales, and systematic uncertainties are different.

Scientific roleCLASH measurements probe radial acceleration within galaxy clusters.MVDR compares baryonic mass and velocity dispersion for BCG and cluster samples.

SystemsBrightest cluster galaxies and galaxy clusters

RelationsCluster RAR and mass–velocity dispersion relation

Cluster RAR paperThe Radial Acceleration Relation in CLASH Galaxy Clusters ↗BCG MVDR paperMass–Velocity Dispersion Relation in MaNGA Brightest Cluster Galaxies ↗

01C / Research map

Scaling Relations with two possible acceleration scales

This map places the main empirical relations by system and by observational route. It is a guide to how kinematics, dynamics, and lensing connect across scales—not a claim that every entry has the same evidential status.

YT · First authorYT · Co-authorOpen question

Summary of kinematics, dynamics, lensing, and acceleration scales for different astrophysical systems.
System	Kinematics	Dynamics	Lensing	Scales
Solar System	Kepler's laws	Newtonian dynamics	General relativity	—
Spiral galaxies	BTFRMcGaugh (2011)McGaugh (2012)Lelli et al. (2016)Lelli et al. (2019)	RARMcGaugh et al. (2016)Lelli et al. (2017)Li et al. (2018)	RARBrouwer et al. (2021)	g_†
Elliptical galaxies	BFJRSanders (2010)Tian et al. (2026)YT · First author	RARLelli et al. (2017)Rong et al. (2018)Chae et al. (2019)Chae et al. (2020)	RARTian & Ko (2019)YT · First authorBrouwer et al. (2021)	g_†
Brightest cluster galaxies	MVDRTian et al. (2021b)YT · First author	Cluster RARTian et al. (2024)YT · First author	Cluster RARTian et al. (2020)YT · First author	g_‡
Galaxy groups	BFJRSadhu & Tian (2024)YT · Co-authorTian et al. (2026)YT · First author	Open question	Open question	g_†
Galaxy clusters	MVDRTian et al. (2021a)YT · First author	Cluster RARChan & Del Popolo (2020)Sadhu et al. (2021)Eckert et al. (2022)Liu et al. (2023)Tam et al. (2023)Li et al. (2023)YT · Co-author	Cluster RARTian et al. (2020)YT · First author	g_‡

g_† ≈ 1.2 × 10⁻¹⁰ m s⁻²; g_‡ ≈ 2.0 × 10⁻⁹ m s⁻².

Webb image of galaxy cluster G165 and the triply imaged supernova H0pe — Webb image of galaxy cluster PLCK G165.7+67.0 and a magnified view of the triply imaged Type Ia supernova H0pe. The three observed images correspond to light arriving along different paths.NASA source and full credit ↗

Conceptual diagram of light paths deflected by a galaxy cluster lens toward an observer — Temporary conceptual schematic of strong lensing and differing light paths. It is an explanatory aid rather than a reconstructed lens model; a project-specific scientific version will replace it later.

02 / Lensing & time delay

Lensing & Time Delay

Gravitational lensing offers an independent route to the mass distribution around galaxies. My work uses Einstein rings, strong-lensing mass estimates, and time-delay phenomena to test how lensing constraints connect with dynamical acceleration relations. Current work also examines Shapiro time delay in relativistic modified-gravity frameworks, while keeping observable constraints distinct from theoretical interpretation.

ObserveMultiple images and relative arrival times

ModelLens potential and light paths

TestMass distributions and relativistic gravity

SN H0pe is an observational example of the time-delay method, not a result from my own programme. It is included to make the measurable phenomenon concrete.

Representative dataEinstein-ring and time-delay constraints

MethodLensing calculations with explicit theoretical assumptions

Representative paperHubble Constant, Lensing, and Time Delay in Relativistic Modified Newtonian Dynamics ↗

Research principle

“A successful fit is a starting point—not yet a physical explanation.”

Observed relation → phenomenological model → physical interpretation → theoretical framework