-- The most original work Lai did in this area concerns how strong-field QED (vacuum birefringence) affects radiative transfer in magnetized neutron star (NS) atmospheres/plasmas. A representative paper is Transfer of Polarized Radiation in Strongly Magnetized Plasmas: Effect of Vacuum Polarization (Lai & Ho 2003 ApJ) (see also LH02). He showed that in highly magnetized plasmas of NSs, the combined effects of plasma and vacuum polarization gives rise to a "vacuum resonance". A polarized photon traversing the resonance can convert from one linearly polarized mode into the other, with dramatic change in photon opacities. The underlying physics of this mode conversion is analogous to MSW neutrino oscillation that takes place inside the Sun. In a series of related papers (all with students), he showed that this QED-induced photon mode conversion significantly changes the observed thermal radiation spectrum of magnetars and gives rise to a unique, clean x-ray polarization signature even for "ordinary" magnetic NSs (HL03, LH03 PRL, VL06, WL09). Recently (2023), he showed that the detected polarized X-rays from two magnetars by IXPE are consistent the prediction of the QED resonance effects , although more work is needed (by future x-ray polarimeter space mission like eXTP).

-- Lai has carried out some pioneering first-principle quantum mechanical calculations of atoms, molecules and condensed matter in strong magnetic fields, and have studied the magnetic field effects on the property of neutron star surfaces and interiors and their observational implications (LS91, LSS92, LS97, ML06, ML07). These and related works are reviewed in L01 and HL06.

-- Lai has carried out some pioneering study on neutrino transfer in superstrong magentic fields, including the effect of parity violation (LQ98, AL99, AL99). His theoretical works have helped constrain and elucidate the physical mechanisms of supernova kicks (LBV95, LG00, WLH06). The paper CC01 gives a critical assessment of various NS kick mechanisms (still up to date) and contains the correct calculation of the electromagnetic rocket effect.

-- The most original work Lai did in this area is Magnetically Driven Warping, Precession, and Resonances in Accretion Disks (Lai 1999 ApJ) , where he showed that inner region of the accretion disk onto a rotating magnetized star (neutron star, white dwarf, or T Tauri star) is subjected to magnetic torques that induce warping and precession of the disk. The new magnetic effects provide a paragidm to explain a number of observatoinal puzzles, ranging from variabilities in T Tauri stars to quasi-periodic oscillations in accreting neutron stars and white dwarfs. They may also have implications for the observed stellar obliquities in (exo)planetary systems (LFL11).

-- In the last few years, Lai (with student and postdoc) initiated a series of numerical studies on circumbinary accretion (accretion onto binary stars or binary black holes) (ML16, MML17, MML19, MLKM20). These works reveal several new dynamical behaviors (e.g. short and long-term variabilities) of the accretion process. Most importantly, these works show that a comparable-mass binary can gain angular momentum via circumbinary accretion and therefore expands in orbit while accreting -- this result contradicts decades-old assumptions and previous numerical works (but has now been confirmed by more recent works from various groups), and significantly impacts our understanding of the evolution of supermassive black-hole binaries and the formation of binary stars. A theoretical paper (ZL18) elucidates the inclination evolution of disks around eccentric binaries (some polar-aligned disks were later observed). Here is an ARAA article.

-- With his postdoc and other collaborators, Lai studied the hydrodynamics of BH binaries embedded in AGN disks (LL22, LL23), including the first study of gas-assisted binary formation (LDLLL).

-- Lai has made original contributions to the understanding of hydrodynamical processes in coalescing neutron star binaries: he gave the first complete analytic/correct expression of gravitational wave (GW) phase shift due to static tides (LRS94) and discovered the related tidal instability (LRS93, LW96, WL00) -- these can be used to constrain the tidal deformability and equation of state of neutron stars using GWs; he pioneered the study of resonant tides and tidal heating (L94, HL99, LW06, XL17) and magnetic effect (L12) in merging NS binaries.

-- Lai showed that young neutron stars undergoing nonlinear bar-mode instability produces a unique, characteristic gravitational waveform (LS95).

-- Since the detection of GWs by LIGO, Lai has studied dynamical formation of binary black holes ("tertiary-induced mergers"), examining the signatures of spin-orbit misalignments (LL17, LL18, LLW19, SLL21), new GR effects in triples (LLW19, LL20), and hierarchical mergers (LL21). With students, Lai studied the formation and merger of BH binaries due to GW bremsstrahlung in AGN disks (LLR23). Several recent works examine the hydrodynamical evolution of BH binaries in AGN disks (LL22).

-- As noted above, Lai's works on circumbinary accretion (ML16, MML17, MML19, MLKM20). are important our understanding of the evolution of supermassive black-hole binaries (which are LISA and PTA sources).

-- Since 2010, Lai has devoted a large part of his research to exoplanet dynamics and formation. A representative paper is Tidal dissipation in planet-hosting stars: damping of spin-orbit misalignment and survival of hot Jupiters (Lai 2012 MNRAS), in which he showed that tidal damping of spin-orbit misalignment can in principle involve different physical processes than tidal decay of planetary orbit, and this difference could allow hot Jupiter's orbit to align with the spin axis of the host star while avoiding orbital decay.

-- With students, Lai carried out comprehensive studies on the formation of hot Jupiters through high-eccentricity migration via Lidov-Kozai effects (ASL16, MLL16 and VLA19) and "secular chaos" effect (TLV19). Most significantly, he showed that stellar spin dynamics (often chaotic) driven by migrating planets plays a crucial role in determining the observed stellar obliquities (SAL14 Science, ASL16), and developed the corresponding theory of "spin chaos due to overlapping resonances" (SL15, SL17) that explain the numerical results. A recent work along these lines may provide an explanation for the observed "perpendicular hot Jupiters" (VSL23).

-- Proposed a new formation mechanism ("low-e migration") for ultra-short-period planets that explain all key observations of these new class of planets (PL19).

-- Carried out some pioneering studies on the effects of mass transfer and magnetic interactions in close-in planet systems (LHv10, L12).

-- Lai has explored several new mechanisms of producing spin-orbit misalignments in exoplanetary systems, which shed light on the formation and evolution of these systems: magnetic effect (LFL11), proto-stellar disk with binary companion (L14 and ZL18), stellar spin-down and spin-orbit resonance (AL18).

-- Dynamics of planets and disks in binary systems: ML15 PNAS predicts circumbinaty planets misaligned with the binary; ML15 examines disk truncation by binary companion, FL14 and ZL17 study eccentric and warped disks in binaries, ZL18 explains polar-aligned disks.

-- Dynamical influences of external companions/planets on the inner multi-planet systems: LP17, PL18, LAP18, PL21, RL21. The effects of stellar flybys: RSL21, RL22.

-- Planetary obliquities: LL20 and LLAP21 calculated spin and onliquity from planet-planet collisions and derived the relevant scaling relations; three recent papers made progress on the classical problem of "Colombo's top", including analytical calculation of transition probability in separatrox crossing: SL20 studied the generation of obliquity from planet-disk interaction, SL22a studied tidal-Cassini equilibiria (tides do not erase obliquity), and SL22b discovered new "mix-mode" Cassini equilibria. These works are relevant to the spin obliquities of super-Earths and have implications for the future observations of these objects.

-- Origin of planets and debris around white dwarfs: OL20, OLL21, OTL22.

-- With student, Lai has studied dynamical tides in compact binary white dwarfs (FL12), heartbeat stars (FL12) and highly eccentric binaries (L97). A recent work elucidates the dynamics of "chaotic tides" (VL18).

-- Lai developed the theory of corotational excitation of global oscillations of accretion disks around black holes in an attempt to understand QPOs (LT09, TL09, FL09, FL11) -- while the theory is beautiful (GR really makes the mode grow), he could not be sure this is "the" explanation of QPOs (L13; alas, BH accretion disks are messy...).

-- On Solar system subjects, Lai suggested "mode mixing" ("avoided crossing") mechansim to explain the small frequency splitting of Saturn's oscillation modes (FLS14) -- this idea was pushed forward by others to include the stratification effect (see DMFLX21), computed Sun's obliquity generated by putative Planet 9 (L16), and developed an efficient method to compute Jupiter's dynamical Love number (L21).

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