arXiv subjects

Boyuan Liu

Publications and source records attributed to Boyuan Liu.

At least 55 records · Page 3Linked to original sources

arXiv2025

EchoVideo: Identity-Preserving Human Video Generation by Multimodal Feature Fusion

Recent advancements in video generation have significantly impacted various downstream applications, particularly in identity-preserving video generation (IPT2V). However, existing methods struggle with "copy-paste" artifacts and low similarity issues, primarily due to their reliance on low-level facial image information. This dependence can result in rigid facial appearances and artifacts reflecting irrelevant details. To address these challenges, we propose EchoVideo, which employs two key strategies: (1) an Identity Image-Text Fusion Module (IITF) that integrates high-level semantic features from text, capturing clean facial identity representations while discarding occlusions, poses, and lighting variations to avoid the introduction of artifacts; (2) a two-stage training strategy, incorporating a stochastic method in the second phase to randomly utilize shallow facial information. The objective is to balance the enhancements in fidelity provided by shallow features while mitigating excessive reliance on them. This strategy encourages the model to utilize high-level features during training, ultimately fostering a more robust representation of facial identities. EchoVideo effectively preserves facial identities and maintains full-body integrity. Extensive experiments demonstrate that it achieves excellent results in generating high-quality, controllability and fidelity videos.

cs.CV↗

arXiv2025

Signatures of Rapidly Rotating Stars with Chemically Homogeneous Evolution in the First Galaxies

The James Webb Space Telescope (JWST) has revealed an unexpectedly high abundance of UV luminous galaxies at redshifts $z\gtrsim 10$, challenging `standard' galaxy formation models. This study investigates the role of rapidly rotating (massive) stars undergoing chemically homogeneous evolution (CHE) in reconciling this potential tension. These stars are more compact, hotter, and exhibit enhanced UV emission. We find that the rest-frame UV luminosity of star-forming galaxies can be significantly enhanced by a factor of $\sim 3-6$ when CHE stars above a minimum initial mass of $m_{\star,\min}^{\rm CHE}\sim 2-10\ \rm M_\odot$ account for more than half of the total stellar mass following a Salpeter initial mass function. As a result, the UV luminosity functions observed at $z\sim 12-16$ can be reproduced with less extreme values of star formation efficiency and UV luminosity stochastic variability. Our results highlight the potential of CHE in explaining the UV-bright galaxy populations detected by JWST and call for future work to explore the broader astrophysical implications of CHE and its associated phenomena in the early universe, such as gamma-ray bursts, compact object binaries, and metal enrichment.

astro-ph.GA↗

arXiv2025

CascadeV: An Implementation of Wurstchen Architecture for Video Generation

Recently, with the tremendous success of diffusion models in the field of text-to-image (T2I) generation, increasing attention has been directed toward their potential in text-to-video (T2V) applications. However, the computational demands of diffusion models pose significant challenges, particularly in generating high-resolution videos with high frame rates. In this paper, we propose CascadeV, a cascaded latent diffusion model (LDM), that is capable of producing state-of-the-art 2K resolution videos. Experiments demonstrate that our cascaded model achieves a higher compression ratio, substantially reducing the computational challenges associated with high-quality video generation. We also implement a spatiotemporal alternating grid 3D attention mechanism, which effectively integrates spatial and temporal information, ensuring superior consistency across the generated video frames. Furthermore, our model can be cascaded with existing T2V models, theoretically enabling a 4$\times$ increase in resolution or frames per second without any fine-tuning. Our code is available at https://github.com/bytedance/CascadeV.

cs.CV↗

arXiv2025

GLIMPSE: An ultra-faint $\simeq$ 10$^{5}$ $M_{\odot}$ Pop III Galaxy Candidate and First Constraints on the Pop III UV Luminosity Function at $z\simeq6-7$

Detecting the first generation of stars, Population III (PopIII), has been a long-standing goal in astrophysics, yet they remain elusive even in the JWST era. Here we present a novel NIRCam-based selection method for PopIII galaxies, and carefully validate it through completeness and contamination simulations. We systematically search ~500 arcmin$^{2}$ across JWST legacy fields for PopIII candidates, including GLIMPSE which, assisted by gravitational lensing, has produced JWST's deepest NIRCam imaging thus far. We discover one promising PopIII galaxy candidate (GLIMPSE-16043) at $z=6.50^{+0.03}_{-0.24}$, a moderately lensed galaxy (mu=2.9) with an intrinsic UV magnitude of $M_{UV}$=-15.89. It exhibits key PopIII features: strong H$α$ emission (rest-frame EW $2810\pm550$Å); a Balmer jump; no dust (UV slope $β=-2.34\pm0.36$); and undetectable metal lines (e.g., [OIII]; [OIII]/H$β$<0.44) implying a gas-phase metallicity of Zgas/Zsun<0.5%. These properties indicate the presence of a nascent, metal-deficient young stellar population (<5Myr) with a stellar mass of $\simeq10^{5}M_{\odot}$. Intriguingly, this source deviates significantly from the extrapolated UV-metallicity relation derived from recent JWST observations at $z=4-10$, consistent with UV enhancement by a top-heavy PopIII initial mass function or the presence of an extremely metal-poor AGN. We also derive the first observational constraints on the PopIII UV luminosity function at z~6-7. The volume density of GLIMPSE-16043 ($\approx10^{-4}$ cMpc$^{-3}$) is in excellent agreement with theoretical predictions, independently reinforcing its plausibility. This study demonstrates the power of our novel NIRCam method to finally reveal distant galaxies even more pristine than the Milky Way's most metal-poor satellites, thereby promising to bring us closer to the first generation of stars than we have ever been before.

astro-ph.GA↗

arXiv2024

An Analytic Model of Gravitational Collapse Induced by Radiative Cooling: Instability Scale, Infall Velocity, and Accretion Rate

We present an analytic description of the spherically symmetric gravitational collapse of radiatively cooling gas clouds, which illustrates the mechanism by which radiative cooling induces gravitational instability at a characteristic mass scale determined by the microphysics of the gas. The approach is based on developing the "one-zone" density-temperature relationship of the gas into a full dynamical model. We convert this density-temperature relationship into a barotropic equation of state, which we use to calculate the density and velocity profiles of the gas. From these quantities, we calculate the time-dependent mass accretion rate onto the center of the cloud. The approach clarifies the mechanism by which radiative cooling induces gravitational instability. In particular, we distinguish the rapid, quasi-equilibrium contraction of a cooling gas core to high central densities from the legitimate instability this contraction establishes in the envelope. We develop a refined criterion for the mass scale of this instability, based only on the chemical-thermal evolution in the core. We explicate our model in the context of a primordial mini-halo cooled by molecular hydrogen, and then provide two further examples, a delayed collapse with hydrogen deuteride cooling and the collapse of an atomic cooling halo. In all three cases, we show that our results agree well with full hydrodynamical treatments.

astro-ph.GA↗

arXiv2024

Physical Pathways for JWST-Observed Supermassive Black Holes in the Early Universe

Observations with the James Webb Space Telescope (JWST) have revealed active galactic nuclei (AGN) powered by supermassive black holes (SMBHs) with estimated masses of $10^7-10^8$ M$_\odot$ at redshifts $z\sim7-9$. Some reside in overmassive systems with higher AGN to stellar mass ratios than locally. Understanding how massive black holes could form so early in cosmic history and affect their environment to establish the observed relations today are some of the major open questions in astrophysics and cosmology. One model to create these massive objects is through direct collapse black holes (DCBHs) that provide massive seeds ($\sim10^5-10^6$ M$_\odot$), able to reach high masses in the limited time available. We use the cosmological simulation code GIZMO to study the formation and growth of DCBH seeds in the early Universe. To grow the DCBHs, we implement a gas swallowing model set to match the Eddington accretion rate as long as the nearby gaseous environment, affected by stellar and accretion disk feedback, provides sufficient fuel. We find that to create massive AGN in overmassive systems at high redshifts, massive seeds accreting more efficiently than the fiducial Bondi-Hoyle model are needed. We assess whether the conditions for such enhanced accretion rates are realistic by considering limits on plausible transport mechanisms. We also examine various DCBH growth histories and find that mass growth is more sustained in overdense cosmological environments, where high gas densities are achieved locally. We discuss the exciting prospect to directly probe the assembly history of the first SMBHs with upcoming, ultra-deep JWST surveys.

astro-ph.GA↗

arXiv2024

How do Primordial Black Holes change the Halo Mass Function and Structure?

We examine the effects of massive primordial black holes (PBHs) on cosmic structure formation, employing both a semi-analytical approach and cosmological simulations. Our simulations incorporate PBHs with a monochromatic mass distribution centered around $10^6 \ \rm M_{\odot}$, constituting a fraction of $10^{-2}$ to $10^{-4}$ of the dark matter (DM) in the universe, with the remainder being collision-less particle dark matter (PDM). Additionally, we conduct a $Λ$CDM simulation for comparative analysis with runs that include PBHs. At smaller scales, halos containing PBHs exhibit similar density and velocity dispersion profiles to those without PBHs. Conversely, at larger scales, PBHs can expedite the formation of massive halos and reside at their centers due to the `seed effect'. To analyze the relative distribution of PBH host halos compared to non-PBH halos, we apply nearest-neighbor (NN) statistics. Our results suggest that PBH host halos, through gravitational influence, significantly impact the structure formation process, compared to the $Λ$CDM case, by attracting and engulfing nearby newly-formed minihalos. Should PBHs constitute a fraction of DM significantly larger than $\sim$$10^{-3}$, almost all newly-formed halos will be absorbed by PBH-seeded halos. Consequently, our simulations predict a bimodal feature in the halo mass function, with most of the massive halos containing at least one PBH at their core and the rest being less massive non-PBH halos.

astro-ph.CO↗

arXiv2024

Gravitational waves from mergers of Population III binary black holes: roles played by two evolution channels

The gravitational wave (GW) signal from binary black hole (BBH) mergers is a promising probe of Population III (Pop III) stars. To fully unleash the power of the GW probe, one important step is to understand the relative importance and features of different BBH evolution channels. We model two channels, isolated binary stellar evolution (IBSE) and nuclear star cluster-dynamical hardening (NSC-DH), in one theoretical framework based on the semi-analytical code A-SLOTH, under various assumptions on Pop III initial mass function (IMF), initial binary statistics and high-$z$ nuclear star clusters (NSCs). The NSC-DH channel contributes $\sim 8-95\%$ of Pop III BBH mergers across cosmic history, with higher contributions achieved by initially wider binary stars, more top-heavy IMFs, and more abundant high-$z$ NSCs. The dimensionless stochastic GW background (SGWB) produced by Pop III BBH mergers has peak values $Ω^{\rm peak}_{\rm GW}\sim 10^{-11}-8\times 10^{-11}$ around observer-frame frequencies $ν\sim 10-100\ \rm Hz$. The Pop III contribution can be a non-negligible ($\sim 2-32\%$) component in the total SGWB at $ν\lesssim 10\ \rm Hz$. The estimated detection rates of Pop III BBH mergers by the Einstein Telescope are $\sim 6-230\ \rm yr^{-1}$ and $\sim 30-1230\ \rm yr^{-1}$ for the NSC-DH and IBSE channels, respectively. Pop III BBH mergers in NSCs are more massive than those from IBSE, so they dominate the Pop III SGWB below $20$ Hz in most cases. Besides, the detection rate of Pop III BBH mergers involving at least one intermediate-mass BH above $100\ \rm M_\odot$ by the Einstein Telescope is $\sim 0.5-200\ \rm yr^{-1}$ in NSCs but remains below $0.1\ \rm yr^{-1}$ for IBSE.

astro-ph.GA↗

arXiv2024

RIGEL: Simulating dwarf galaxies at solar mass resolution with radiative transfer and feedback from individual massive stars

We introduce the RIGEL model, a novel framework to self-consistently model the effects of stellar feedback in the multiphase ISM of dwarf galaxies with radiative transfer (RT) on a star-by-star basis. The RIGEL model integrates detailed implementations of feedback from individual massive stars into the RHD code, AREPO-RT. It forms individual massive stars from the resolved multiphase ISM by sampling the IMF and tracks their evolution individually. The lifetimes, photon production rates, mass-loss rates, and wind velocities of these stars are determined by their initial masses and metallicities based on a library that incorporates a variety of stellar models. The RT equations are solved in seven spectral bins accounting for the IR to HeII ionizing bands, using an M1 RT scheme. The thermochemistry model tracks the non-equilibrium H, He chemistry and the equilibrium abundance of CI, CII, OI, OII, and CO to capture the thermodynamics of all ISM phases. We evaluated the performance of the RIGEL model using $1\,{\rm M}_\odot$ resolution simulations of isolated dwarf galaxies. We found that the SFR and ISRF show strong positive correlations to the metallicity of the galaxy. Photoionization and photoheating can reduce the SFR by an order of magnitude by removing the available cold-dense gas fuel for star formation. The ISRF also changes the thermal structure of the ISM. Radiative feedback occurs immediately after the birth of massive stars and rapidly disperses the molecular clouds within 1 Myr. As a consequence, radiative feedback reduces the age spread of star clusters to less than 2 Myr, prohibits the formation of massive star clusters, and shapes the cluster initial mass function to a steep power-law form with a slope of $\sim-2$. The mass-loading factor of the fiducial galaxy has a median of $\sim50$, while turning off radiative feedback reduces this factor by an order of magnitude.

astro-ph.GA↗

arXiv2024

Towards a universal analytical model for Population III star formation: interplay between feedback and fragmentation

JWST has brought us new insights into Cosmic Dawn with tentative detection of the unique signatures of metal-free Population III (Pop III) stars, such as strong HeII emission, extremely blue UV spectrum, and enhanced nitrogen abundance. Self-consistent theoretical predictions of the formation rates, sites, and masses of Pop III stars are crucial for interpreting the observations, but are challenging due to complex physical processes operating over the large range of length scales involved. One solution is to combine analytical models for the small-scale star formation process with cosmological simulations that capture the large-scale physics such as structure formation, radiation backgrounds, and baryon-dark matter streaming motion that regulate the conditions of Pop III star formation. We build an analytical model to predict the final masses of Pop III stars/clusters from the properties of star-forming clouds, based on the key results of small-scale star formation simulations and stellar evolution models. Our model for the first time considers the interplay between feedback and fragmentation and covers different modes of Pop III star formation ranging from ordinary small ($\sim 10-2000\ \rm M_\odot$) clusters in molecular-cooling clouds to massive ($\gtrsim 10^{4}\ \rm M_\odot$) clusters containing supermassive ($\sim 10^{4}-3\times 10^{5}\ \rm M_\odot$) stars under violent collapse of atomic-cooling clouds. As an example, the model is applied to the Pop III star-forming clouds in the progenitors of typical haloes hosting high-$z$ luminous quasars, which shows that formation of Pop III massive clusters is common ($\sim 20-70\%$) in such biased ($\sim4σ$) regions, and the resulting heavy black hole seeds from supermassive stars can account for a significant fraction of observed luminous ($\gtrsim 10^{46}\ \rm erg\ s^{-1}$) quasars at $z\sim 6$.

astro-ph.GA↗

arXiv2024

Impact of primordial black holes on the formation of the first stars and galaxies

Recent gravitational wave (GW) observations of binary black hole (BH) mergers and the stochastic GW background have triggered renewed interest in primordial black holes (PBHs) in the stellar-mass ($\sim 10 - 100\ \rm M_\odot$) and supermassive regimes ($\sim 10^7 - 10^{11}\ \rm M_\odot$). Although only a small fraction ($\lesssim 1\%$) of dark matter (DM) in the form of PBHs is required to explain such observations, these PBHs may play important roles in early structure/star/galaxy formation. In this chapter, we combine semi-analytical analysis and cosmological simulations to explore the possible impact of PBHs on the formation of the first stars and galaxies, taking into account two (competing) effects of PBHs: acceleration of structure formation and gas heating by BH accretion feedback. We find that the impact of stellar-mass PBHs (allowed by existing observational constraints) on primordial star formation is likely minor, although they do alter the properties of the first star-forming halos/clouds and can potentially trigger the formation of massive BHs, while supermassive PBHs serve as seeds of massive structures that can explain the apparent overabundance of massive galaxies in recent observations. Our tentative models and results call for future studies with improved modeling of the interactions between PBHs, particle DM, and baryons to better understand the impact of PBHs on early star/galaxy/structure formation and their imprints in high-redshift observations.

astro-ph.GA↗

arXiv2024

Rapidly rotating Population III stellar models as a source of primary nitrogen

The first stars might have been fast rotators. This would have important consequences for their radiative, mechanical and chemical feedback. We discuss the impact of fast initial rotation on the evolution of massive Population III models and on their nitrogen and oxygen stellar yields. We explore the evolution of Population III stars with initial masses in the range of 9Msol < Mini < 120Msol starting with an initial rotation on the Zero Age Main Sequence equal to 70% of the critical one. We find that with the physics of rotation considered here, our rapidly-rotating Population III stellar models do not follow a homogeneous evolution. They lose very little mass in case mechanical winds are switched on when the surface rotation becomes equal or larger than the critical velocity. Impact on the ionising flux appears modest when compared to moderately-rotating models. Fast rotation favours, in models with initial masses above ~20Msol, the appearance of a very extended intermediate convective zone around the H-burning shell during the core He-burning phase. This shell has important consequences on the sizes of the He- and CO-cores and thus impacts the final fate of stars. Moreover, it has a strong impact on nucleosynthesis boosting the production of primary 14N. Fast initial rotation impacts significantly the chemical feedback of Population III stars. Observations of extremely metal-poor stars and/or starbursting regions are essential to provide constraints on the properties of the first stars.

astro-ph.SR↗

arXiv2024

Distinguishing the impact and signature of black holes from different origins in early cosmic history

We use semi-analytical models to study the effects of primordial black hole (PBH) accretion on the cosmic radiation background during the epoch of reionization ($z\gtrsim 6$). We consider PBHs floating in the intergalactic medium (IGM), and located inside haloes, where star formation can occur. For stars with a mass $\gtrsim 25 \rm\ M_{\odot}$, formed in suitable host haloes, we assume they quickly burn out and form stellar remnant black holes (SRBHs). Since SRBHs also accrete material from their surroundings, we consider them to have similar radiation feedback as PBHs in the halo environment. To estimate the background radiation level more accurately, we take into account the impact of PBHs on structure formation, allowing an improved modeling of the halo mass function. We consider the radiation feedback from a broad suite of black holes: PBHs, SRBHs, high-mass X-ray binaries (HMXBs), and supermassive black holes (SMBHs). We find that at $z\gtrsim 30$, the radiation background energy density is generated by PBHs accreting in the IGM, whereas at lower redshifts, the accretion feedback power from haloes dominates. We also analyze the total power density by modeling the accretion spectral energy distribution (SED), and break it down into select wavebands. In the UV band, we find that for $f_{\rm PBH} \lesssim 10^{-3}$, the H-ionizing and Lyman-$α$ fluxes from PBH accretion feedback do not violate existing constraints on the timing of reionization, and on the effective Wouthuysen-Field coupling of the 21-cm spin temperature of neutral hydrogen to the kinetic temperature of the IGM. However, in the X-ray band, with the same abundance, PBHs contribute significantly and could account for the unresolved part of the cosmic X-ray background.

astro-ph.CO↗

arXiv2024

Zero Metallicity with Zero CPU Hours: Masses of the First Stars on the Laptop

We develop an analytic model for the mass of the first stars forming in the center of primordial gas clouds as a function of host halo mass, redshift, and degree of rotation. The model is based on the estimation of key timescales determining the following three processes: the collapse of the gas cloud, the accretion onto the protostellar core, and the radiative feedback of the protostellar core. The final stellar mass is determined by the total mass accreted until the radiative feedback halts the accretion. The analytic estimation, motivated by the result of the full numerical simulations, leads to algebraic expressions allowing an extremely fast execution. Despite its simplicity, the model reproduces the stellar mass scale and its parameter dependences observed in state-of-the-art cosmological zoom-in simulations. This work clarifies the basic physical principles undergirding such numerical treatments and provides a path to efficiently calibrating numerical predictions against eventual observations of the first stars.

astro-ph.CO↗

arXiv2023

Population synthesis of Be X-ray binaries: metallicity dependence of total X-ray outputs

X-ray binaries (XRBs) are thought to regulate cosmic thermal and ionization histories during the Epoch of Reionization and Cosmic Dawn ($z\sim 5-30$).Theoretical predictions of the X-ray emission from XRBs are important for modelling such early cosmic evolution. Nevertheless, the contribution from Be-XRBs, powered by accretion of compact objects from decretion disks around rapidly rotating O/B stars, has not been investigated systematically. Be-XRBs are the largest class of high-mass XRBs (HMXBs) identified in local observations and are expected to play even more important roles in metal-poor environments at high redshifts. In light of this, we build a physically motivated model for Be-XRBs based on recent hydrodynamic simulations and observations of decretion disks. Our model is able to reproduce the observed population of Be-XRBs in the Small Magellanic Cloud with appropriate initial conditions and binary stellar evolution parameters. We derive the X-ray output from Be-XRBs as a function of metallicity in the (absolute) metallicity range $Z\in [10^{-4},0.03]$ with a large suite of binary population synthesis (BPS) simulations. The simulated Be-XRBs can explain a non-negligible fraction ($\gtrsim 30\%$) of the total X-ray output from HMXBs observed in nearby galaxies for $Z\sim 0.0003-0.02$. The X-ray luminosity per unit star formation rate from Be-XRBs in our fiducial model increases by a factor of $\sim 8$ from $Z=0.02$ to $Z=0.0003$, which is similar to the trend seen in observations of all types of HMXBs. We conclude that Be-XRBs are potentially important X-ray sources that deserve greater attention in BPS of XRBs.

astro-ph.HE↗

arXiv2023

Observability of Low-Luminosity AGN in the Early Universe with JWST

Active galactic nuclei (AGN) in the early Universe are thought to be prominent sources of energy and ionizing photons that affected the growth of their host galaxy and their environment. However, it is still unclear how the supermassive black holes (SMBHs) that fuel these AGN grew to the observed high masses already at high redshifts. Observations of high-redshift SMBH progenitors or lower-luminosity AGN will thus help characterize the evolution of SMBHs and their impact on the surroundings. With the launch of the JWST, fainter objects at high redshifts can now be detected, including lower-luminosity AGN. We assess the observability of such low luminosity AGN, using the cosmological simulation code GIZMO to provide a realistic environment for black hole growth in the early Universe. Soon after the first stars are born in the simulation run, we insert stellar-remnant black hole seeds of various initial masses, between $300$ and $10^4 {\rm \ M}_{\odot}$, at the center of a dark matter halo and follow their growth until $z\sim6$. Such stellar black hole seeds placed in a typical high-$z$ environment do not significantly accrete and grow to reach masses that can be observed with the JWST under conditions of standard Bondi-Hoyle accretion, as energy input from stellar feedback and chaotic dynamics prevent efficient gas accretion onto the black holes. To be observed with the JWST, rarer but still physically feasible growth regimes, involving Eddington or super-Eddington accretion, would be required. Alternatively, AGN observability may be boosted under even rarer conditions of extreme gravitational lensing.

astro-ph.GA↗

arXiv2022

Drug-target affinity prediction method based on consistent expression of heterogeneous data

The first step in drug discovery is finding drug molecule moieties with medicinal activity against specific targets. Therefore, it is crucial to investigate the interaction between drug-target proteins and small chemical molecules. However, traditional experimental methods for discovering potential small drug molecules are labor-intensive and time-consuming. There is currently a lot of interest in building computational models to screen small drug molecules using drug molecule-related databases. In this paper, we propose a method for predicting drug-target binding affinity using deep learning models. This method uses a modified GRU and GNN to extract features from the drug-target protein sequences and the drug molecule map, respectively, to obtain their feature vectors. The combined vectors are used as vector representations of drug-target molecule pairs and then fed into a fully connected network to predict drug-target binding affinity. This proposed model demonstrates its accuracy and effectiveness in predicting drug-target binding affinity on the DAVIS and KIBA datasets.

q-bio.BM↗

arXiv2022

Impact of Population III homogeneous stellar evolution on early cosmic reionisation

Context: Population III (Pop III) stars may be fast rotating. An expected consequence of fast rotation is strong internal mixing that deeply affects their evolutionary tracks in the Hertzsprung-Russell diagram and hence their ionising power. aims: We investigate the impact on the ionising power of Pop III stars in an extreme case of internal mixing, the one leading to chemically homogeneous evolution (CHE). In that situation, during the main sequence phase, the star keeps the same chemical composition from its center to its surface. Homogeneous stars have larger effective temperatures and luminosities than stars evolving non-homogeneously and thus are stronger ionising sources. Methods: The stellar evolution models are based on $n=3$ polytropes with a time varying hydrogen mass fraction. The ionisation model employs the self-similar champagne flow solution from Shu et al. (2002), as well as numerical simulations for the stochastic treatment of star clusters over a grid of redshifts and halo masses. Results: We find that haloes containing chemically homogeneous stars have an escape fraction of ionising photons about twice that of haloes containing classical Pop III stars. By extrapolating the high-$z$ ionisation history powered by Pop III stars (at $z\gtrsim 15$) to the post-reionisation epoch, we derive the Thomson scattering optical depth $τ$, which is compared with the value measured by $\textit{Planck}$. We find that $τ$ is overproduced by $\sim1.5- 5σ$, when all Pop III stars evolve homogeneously. This indicates that CHE is unlikely to be realised in the majority of Pop III stars, although the present study cannot exclude that a fraction of them undergoes CHE. Conclusions: Fast rotation might have a significant impact on the ionising budget of Pop III stars, and thus on early cosmic reionisation.

astro-ph.SR↗