arXiv subjects

Weijia Sun

Publications and source records attributed to Weijia Sun.

At least 19 recordsLinked to original sources

arXiv2026

On-sky Fibre-Target-Alignment of the 4MOST instrument: calibration and performance

The 4-metre Multi-Object Spectroscopic Telescope (4MOST) is a new wide-field, fibre-fed spectroscopic survey facility for the VISTA telescope at ESOs Paranal Observatory. The instrument enables the simultaneous acquisition of 2436 spectra across a 4.2 square deg field of view, using a tilting spine fibre positioner feeding three dedicated spectrographs. In this paper, we describe the calibration process, and performance verification of the Fibre-Target-Alignment (FTA) process for 4MOST. We show the complete FTA process, including calibration of the individual hardware- and software components. Namely the Metrology camera system, the Fibre Positioner AESOP, a spine based Secondary Guiding System, the sky to focal surface projection software, and residual minimization via raster scans. In total, the FTA system required one special tool, a large calibration target for the focal surface, and approximately 1 month of accumulated calibration work on the telescope. The FTA process reached approx. 24 um (0.4 arc sec) RMS distance between fibres and targets on sky about 3 weeks after installation of the final hardware components of 4MOST, which is when 4MOST had its first light event. By the time of writing this paper, i.e. 6 months later, we reach approx. 16 um (0.27 arc sec) RMS. Currently, we far exceed our requirements in terms of accuracy, and are doing trade-off studies to maximize scientific returns.

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arXiv2026

TwinSpecNet: Extending APOGEE's chemical reach to low-S/N spectra via empirical paired learning

Large spectroscopic surveys rely on automated pipelines to deliver homogeneous stellar labels, but a substantial fraction of observations are at low signal-to-noise ratio (S/N), where label estimates become imprecise or are omitted. In APOGEE, these low-S/N spectra visits sample faint and distant populations -- the bulge, outer halo, and satellite systems -- yet still encode recoverable chemical information. We present TwinSpecNet (TSN), a paired-learning framework that exploits APOGEE's multi-visit observing strategy: by training on empirical low-/high-S/N spectral twins of the same stars, TSN learns to suppress stochastic noise while preserving the ASPCAP label scale. TSN employs a Vision Transformer encoder with dual objectives: reconstructing high-S/N flux from low-S/N visits and predicting stellar parameters and abundances with calibrated uncertainties. TSN reduces label scatter relative to visit-level ASPCAP for S/N<60 visits. TSN reproduces the ASPCAP scale with residual scatters of $\sigma$< 19 K in $T_{\mathrm{eff}}$, $\sigma\sim$0.06 dex in $\log g$, and $\sigma\sim$0.03 dex in Fe/H. TSN tightens intra-cluster abundance dispersions, recovers cleaner chemical sequences in inner-disk and bulge and satellite samples, and improves C/N-based age precision for APOKASC giants from 1.70 to 1.59 Gyr. By learning survey-specific noise patterns from repeated observations, TSN demonstrates how empirical paired learning can extend the chemical reach of existing spectroscopic data, providing a template applicable to other multi-visit surveys.

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arXiv2025

Observational constraints on the origin of the elements. X. Combining NLTE and machine learning for chemical diagnostics of 4 million stars in the 4MIDABLE-HR survey

We present the 4MOST-HR resolution Non-Local Thermal Equilibrium (NLTE) Payne artificial neural network (ANN), trained on $404\,793$ new FGK spectra with 16 elements computed in NLTE. This network will be part of the Stellar Abundances and atmospheric Parameters Pipeline (SAPP), which will analyse 4 million stars during the five year long 4MOST consortium 4: 4MOST MIlky way Disc And BuLgE High-Resolution (4MIDABLE-HR) survey. A fitting algorithm using this ANN is also presented that is able to fully-automatically and self-consistently derive both stellar parameters and elemental abundances. The ANN is validated by fitting 121 observed spectra of low-mass FGKM type stars, including main-sequence dwarf, subgiant and giant stars down to [Fe/H] $\approx -3.3$ degraded to 4MOST-HR resolution of $R\approx20\,000$, and comparing the derived abundances with the output of the classical radiative transfer code TSFitPy. We are able to recover all 18 elemental abundances with a bias~$<0.13$ and spread~$<0.16$\,dex, although the typical values are $<0.09$ dex for most elements. These abundances are compared to the OMEGA+ Galactic Chemical Evolution model, showcasing for the first time, the expected performance and results obtained from high-resolution spectra of the quality expected to be obtained with 4MOST. The expected Galactic trends are recovered, and we highlight the potential of using many chemical elements to constrain the formation history of the Galaxy.

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arXiv2025

A hybrid SLAM-Payne framework for atmospheric parameter and abundance determination of early-type Stars from LAMOST DR9 low-resolution Spectra

Early-type stars are key drivers of Galactic chemical evolution, enriching the interstellar medium with alpha elements through powerful stellar winds and core-collapse supernovae, fueled by their short lifetimes and high masses. However, their spectra remain challenging to analyse due to rapid rotation, weak metal lines, and non-LTE effects. While large spectroscopic surveys provide extensive low-resolution data, extracting reliable parameters remains difficult due to methodological limitations for hot stars. Our goal is to develop a unified framework combining data-driven and synthetic spectral approaches to determine atmospheric parameters and abundances for hot stars using low-resolution spectra, addressing limitations in current methodologies while retaining critical spectral information. We present a hybrid approach integrating the Stellar LAbel Machine (SLAM) and the Payne frameworks, for low-resolution ($R\sim 1800$) spectra from LAMOST DR9. Our method preserves full spectral information including Balmer series and metal-line blends, employing neural-network interpolation for efficient parameter estimation ($T_\mathrm{eff}$, $\log g$, and $v\sin i$) and abundance determination for O, Mg, Si, and Fe, across 8000 - 20000 K. We derive stellar parameters and abundances for 315,822 stars with $\mathrm{SNR} \geqslant 10$ in the $r$-band. Additionally, we detect abundance trends ([$\alpha$/Fe]-[Fe/H]) that exhibit temperature-dependent systematics and a distinct $\alpha$-poor stellar population within $0.0 \leqslant \mathrm{[Fe/H]} \leqslant 0.5$ dex. The radial abundance gradients are negative and consistent with that derived from Cepheids, with a slope of $-0.070\pm0.007$ in \feh in the region $6 \leqslant R_\mathrm{GC}\leqslant 15$ kpc.

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arXiv2024

The rotation properties of $\delta$ Sct and $\gamma$ Dor stars

Based on the LAMOST spectroscopy and TESS time-series photometry, we have obtained a main-sequence star sample of $\delta$ Scuti and $\gamma$ Doradus stars. The sample includes 1534 $\delta$ Sct stars, 367 $\gamma$ Dor stars, 1703 $\delta$ Sct$| \gamma$ Dor stars, 270 $\gamma$ Dor$| \delta$ Sct stars, along with 105 '$\delta$ Sct candidates' and 32 '$\gamma$ Dor candidates'. After correcting for projection effects, we derived the equatorial rotational velocity distribution for $\delta$ Sct and $\gamma$ Dor stars and compared it with that of normal stars. The rotational velocity distributions of $\delta$ Sct and $\gamma$ Dor stars are extremely similar, with the only difference potentially due to the rotational variable stars that have not been completely removed. In contrast, the rotational velocity distribution of normal stars is more dispersed compared to pulsating stars. Additionally, the peak rotational velocity of the pulsating stars is about 10 km s$^{-1}$ higher than that of normal stars. Unlike the normal stars, which show a monotonic increase in peak velocity with mass between 1.8 and 2.5 $M_{\odot}$, the rotational velocity distribution of $\delta$ Sct stars does not exhibit a strong mass dependence. We also found that normal stars accelerate during the late main-sequence evolutionary phase, while $\delta$ Sct stars decelerate. Furthermore, there may still be unclassified stars with diverse rotational properties in the normal star sample compared to the $\delta$ Sct stars, which is likely to be an important contributor to the broader dispersion observed in its rotational velocity distribution. The photometric amplitude in $\delta$ Sct stars is modulated with rotational velocity, with high-amplitude stars typically rotating slowly and low-amplitude stars showing a broad distribution of rotational velocities.

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arXiv2024

Exploring the Stellar Rotation of Early-type Stars in the LAMOST Medium-resolution Survey. III. Evolution

Stellar rotation significantly shapes the evolution of massive stars, yet the interplay of mass and metallicity remains elusive, limiting our capacity to construct accurate stellar evolution models and to better estimate the impact of rotation in chemical evolution of galaxies. Our goal is to investigate how mass and metallicity influence the rotational evolution of A-type stars on the main sequence (MS). We seek to identify deviations in rotational behaviors that could serve as new constraints to existing stellar models. Using the LAMOST median-resolution survey Data Release 9, we derived stellar parameters for a population of 104,752 A-type stars. Our study focused on the evolution of surface rotational velocities and their dependence on mass and metallicity in 84,683 `normal' stars. Normalized surface rotational revealed a prevailing evolutionary profile from 1.7 to 4.0 $M_\odot$. This profile features an initial rapid acceleration until $t/t_\mathrm{ms} = 0.25$, potentially a second acceleration peak near $t/t_\mathrm{ms} = 0.55$ for stars heavier than 2.5 $M_\odot$, followed by a steady decline and a `hook' feature at the end. Surpassing theoretical expectations, the initial acceleration likely stems from a concentrated distribution of angular momentum at ZAMS, resulting in a prolonged increase in speed. The inverse circulation becomes more efficient at lower metallicity, explaining the correlation of the slope of this deceleration phase with metallicity from -0.3 dex up to 0.1 dex. The metal-poor subsample suggests a mechanism dependent on metallicity for removing angular momentum during star formation. The proportion of fast rotators decreases with an increase in metallicity, up to $\log(Z/Z_\odot)\sim -0.2$, a trend consistent with observations of OB-type stars found in the Small and Large Magellanic Clouds.

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arXiv2024

Extended Main Sequences in Star Clusters

Extended main sequences (eMSs) and extended main-sequence turnoffs (eMSTOs) are fascinating phenomena that are routinely observed in star clusters. These phenomena strongly challenge the current canonical "simple stellar population" picture of star clusters, which postulates that star clusters are coeval and chemically homogeneous and can thus be described by a single, unique isochrone. Detections of eMSs and eMSTOs provide valuable insights into stellar physics and the evolution of star clusters. This comprehensive review delves into the observational characteristics, underlying mechanisms, and astrophysical implications of the eMSs and eMSTOs observed in young (less than 600 million years) and intermediate-age (600 to 2000 million years) star clusters. Several scenarios or hypotheses have been proposed to explain these phenomena, including the presence of an age spread, binary interactions, variable stars, and differences in stellar rotation rates. This review discusses the advantages and limitations of current models. Among contemporary models and hypotheses, stellar rotation has been demonstrated as the most plausible mechanism to explain the occurrence of eMSs and eMSTOs. Research on stellar rotation and its connection to eMSs has opened up a myriad of fascinating avenues, such as investigations of the magnetic braking mechanism in stars, searches for tidally locked binary systems in star clusters, and investigations as to whether binary mergers can give rise to massive magnetars. These endeavors have yielded valuable insights and significantly enriched our understanding of stellar astrophysics.

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arXiv2024

Rotation in Stellar Evolution: Probing the Influence on Population Synthesis in High-Redshift Galaxies

Stellar population synthesis (SPS) is essential for understanding galaxy formation and evolution. However, the recent discovery of rotation-driven phenomena in star clusters warrants a review of uncertainties in SPS models caused by overlooked factors, including stellar rotation. In this study, we investigate the impact of rotation on SPS specifically using the PARSEC V2.0 rotation model and its implications for high redshift galaxies with the JWST. Rotation enhances the ultraviolet (UV) flux for up to $\sim 400$ Myr after the starburst, with the slope of UV increasing as the population gets faster rotating and more metal-poor. Using the Prospector tool, we construct simulated galaxies and deduce their properties associated with dust and star formation. Our results suggest that rapid rotation models result in a gradual UV slope up to 0.1 dex higher and an approximately 50\% increase in dust attenuation for identical wide-band spectral energy distributions. Furthermore, we investigate biases if the stellar population should be characterized by rapid rotation and demonstrate that accurate estimation can be achieved for rotation rates up to $ω_\text{i}=0.6$. Accounting for the bias in the case of rapid rotation aligns specific star formation rates more closely with predictions from theoretical models. Notably, this also implies a slightly higher level of dust attenuation than previously anticipated, while still allowing for a `dust-free' interpretation of the galaxy. The impact of rapid rotation SPS models on the rest-UV luminosity function is found to be minimal. Overall, our findings have potentially important implications for comprehending dust attenuation and mass assembly history in the high-redshift Universe.

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arXiv2023

The role of tidal interactions in the formation of slowly rotating early-type stars in young star clusters

The split main sequences found in the colour-magnitude diagrams of star clusters younger than ~600 Myr are suggested to be caused by the dichotomy of stellar rotation rates of upper main-sequence stars. Tidal interactions have been suggested as a possible explanation of the dichotomy of the stellar rotation rates. This hypothesis proposes that the slow rotation rates of stars along the split main sequences are caused by tidal interactions in binaries. To test this scenario, we measured the variations in the radial velocities of slowly rotating stars along the split main sequence of the young Galactic cluster NGC 2422 (~90 Myr) using spectra obtained at multiple epochs with the Canada-France-Hawai'i Telescope. Our results show that most slowly rotating stars are not radial-velocity variables. Using the theory of dynamical tides, we find that the binary separations necessary to fully or partially synchronise our spectroscopic targets, on time-scales shorter than the cluster age, predict much larger radial velocity variations across multiple-epoch observations, or a much larger radial velocity dispersion at a single epoch, than the observed values. This indicates that tidal interactions are not the dominant mechanism to form slowly rotating stars along the split main sequences. As the observations of the rotation velocity distribution among B- and A-type stars in binaries of larger separations hint at a much stronger effect of braking with age, we discuss the consequences of relaxing the constraints of the dynamical tides theory.

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arXiv2022

The role of binarity and stellar rotation in the split main sequence of NGC 2422

In addition to the extended main-sequence turnoffs widely found in young and intermediate-age (~ 600 Myr-2 Gyr-old) star clusters, some younger clusters even exhibit split main sequences (MSs). Different stellar rotation rates are proposed to account for the bifurcated MS pattern, with red and blue MSs (rMS and bMS) populated by fast and slowly rotating stars, respectively. Using photometry from Gaia Early Data Release 3, we report a Galactic open cluster with a bifurcated MS, NGC 2422 ( ~ 90 Myr). We exclude the possibilities that the bifurcated MS pattern is caused by photometric noise or differential reddening. We aim to examine if stellar rotation can account for the split MSs. We use spectra observed with the Canada-France-Hawaii Telescope and the Southern African Large Telescope, and directly measured v sin i, the projected rotational velocities, for stars populating the bMS and rMS. We find that their v sin i values are weakly correlated with their loci in the color-magnitude diagram because of contamination caused by a large fraction of rMS stars with low projected rotational velocities. Based on the spectral energy distribution fitting method, we suggest that these slowly rotating stars at the rMS may hide a binary companion, which breaks the expected v sin i-color correlation. Future time-domain studies focusing on whether these slowly rotating stars are radial velocity variables are crucial to test the roles of stellar rotation and binarity in generating the split MSs.

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arXiv2021

Exploring the stellar rotation of early-type stars in the LAMOST Medium-Resolution Survey. II. Statistics

Angular momentum is a key property regulating star formation and evolution. However, the physics driving the distribution of the stellar rotation rates of early-type main-sequence stars is as yet poorly understood. Using our catalog of 40,034 early-type stars with homogeneous $v\sin i$ parameters, we review the statistical properties of their stellar rotation rates. We discuss the importance of possible contaminants, including binaries and chemically peculiar stars. Upon correction for projection effects and rectification of the error distribution, we derive the distributions of our sample's equatorial rotation velocities, which show a clear dependence on stellar mass. Stars with masses less than $2.5\ {M_\odot}$ exhibit a unimodal distribution, with the peak velocity ratio increasing as stellar mass increases. A bimodal rotation distribution, composed of two branches of slowly and rapidly rotating stars, emerges for more massive stars ($M>2.5\ {M_\odot}$). For stars more massive than $3.0\ {M_\odot}$, the gap between the bifurcated branches becomes prominent. For the first time, we find that metal-poor ([M/H] $< -0.2$ dex) stars only exhibit a single branch of slow rotators, while metal-rich ([M/H] $> 0.2$ dex) stars clearly show two branches. The difference could be attributed to unexpectedly high spin-down rates and/or in part strong magnetic fields in the metal-poor subsample.

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arXiv2021

Exploring the stellar rotation of early-type stars in the LAMOST Medium-Resolution Survey. I. Catalog

We derive stellar parameters and abundances (`stellar labels') of 40,034 late-B and A-type main-sequence stars extracted from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope Medium Resolution Survey (LAMOST--MRS). The primary selection of our early-type sample was obtained from LAMOST Data Release 7 based on spectral line indices. We employed the Stellar LAbel Machine (SLAM) to derive their spectroscopic stellar parameters, drawing on Kurucz spectral synthesis models with 6000 K $< T_\mathrm{eff} <$ 15,000 K and $-1$ dex $< \mathrm{[M/H]} <$ 1 dex. For a signal-to-noise ratio of $\sim 60$, the cross-validated scatter is $\sim$75 K, 0.06 dex, 0.05 dex, and $\sim 3.5\,\mathrm{km\,s^{-1}}$ for $T_\mathrm{eff}$, $\log g$, [M/H], and $v\sin i$, respectively. A comparison with objects with prior, known stellar labels shows great consistency for all stellar parameters, except for $\log g$. Although this is an intrinsic caveat that comes from the MRS's narrow wavelength coverage, it only has a minor effect on estimates of the stellar rotation rates because of the decent spectral resolution and the profile-fitting method employed. The masses and ages of our early-type sample stars were inferred from non-rotating stellar evolution models. This paves the way for reviewing the properties of stellar rotation distributions as a function of stellar mass and age.

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arXiv2021

Further evidence of shocks in the first-overtone RR Lyrae pulsators: first detection of shock-triggered magnesium emissions

The behavior of the shock wave in the atmosphere of the non-fundamental mode RR Lyrae pulsator remains a mystery. In this work, we firstly report a blueshifted Mg triplet emission in continuous spectroscopic observations for a non-Blazhko RRc pulsator (Catalina-1104058050978) with LAMOST medium resolution spectra. We analyse the photometric observations from Catalina Sky Survey of this RRc pulsator with pre-whitening sequence method and provide the ephemeris and phases. An additional frequency signal with $P_1/P_x = 0.69841$ is detected and discussed. The redshift and radial velocity of the spectra are provided by fitting process with $S\acute{e}rsic$ functions and cross-correlation method. Moreover, we plot the variation of H$α$ and Mg lines in a system comoving with the pulsation. Clear evolution of comoving blueshifted hydrogen and Mg emission is observed, which further confirms the existence of shock waves in RRc pulsators. The shock-triggered emission lasts over $15\%$ of the pulsation cycle, which is much longer than the previous observations.

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arXiv2021

Blueshifted hydrogen emission and shock wave of RR Lyrae variables in SDSS and LAMOST

Hydrogen emissions of RR Lyrae variables are the imprints of shock waves traveling through their atmospheres. We develop a pattern recognition algorithm, which is then applied to single-epoch spectra of SDSS and LAMOST. These two spectroscopic surveys covered $\sim$ 10,000 photometrically confirmed RR Lyrae stars. We discovered in total 127 RR Lyrae stars with blueshifted Balmer emission feature, including 103 fundamental mode (RRab), 20 first-overtone (RRc), 3 double-mode (RRd), and 1 Blazhko type (temporary classification for RR Lyrae stars with strong Blazhko modulation in Catalina sky survey that cannot be characterized) RR Lyrae variable. This forms the largest database to date of the properties of hydrogen emission in RR Lyrae variables. Based on ZTF DR5, we carried out a detailed light-curve analysis for the Blazhko type RR Lyrae star with hydrogen emission of long-term modulations. We characterize the Blazhko type RR Lyrae star as an RRab and point out a possible Blazhko period. Finally, we set up simulations on mock spectra to test the performance of our algorithm and on the real observational strategy to investigate the occurrence of the "first apparition".

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arXiv2021

Binary-driven stellar rotation evolution at the main-sequence turn-off in star clusters

The impact of stellar rotation on the morphology of star cluster colour-magnitude diagrams is widely acknowledged. However, the physics driving the distribution of the equatorial rotation velocities of main-sequence turn-off (MSTO) stars is as yet poorly understood. Using Gaia Data Release 2 photometry and new Southern African Large Telescope medium-resolution spectroscopy, we analyse the intermediate-age ($\sim1\,$Gyr-old) Galactic open clusters NGC 3960, NGC 6134 and IC 4756 and develop a novel method to derive their stellar rotation distributions based on SYCLIST stellar rotation models. Combined with literature data for the open clusters NGC 5822 and NGC 2818, we find a tight correlation between the number ratio of slow rotators and the clusters' binary fractions. The blue-main-sequence stars in at least two of our clusters are more centrally concentrated than their red-main-sequence counterparts. The origin of the equatorial stellar rotation distribution and its evolution remains as yet unidentified. However, the observed correlation in our open cluster sample suggests a binary-driven formation mechanism.

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arXiv2021

Eclipsing Binary Populations across the Northern Galactic Plane from the KISOGP survey

We present a catalog of eclipsing binaries in the northern Galactic Plane from the Kiso Wide-Field Camera Intensive Survey of the Galactic Plane (KISOGP). We visually identified 7055 eclipsing binaries spread across $\sim$330 square degrees, including 4197 W Ursa Majoris/EW-, 1458 $β$ Lyrae/EB-, and 1400 Algol/EA-type eclipsing binaries. For all systems, $I$-band light curves were used to obtain accurate system parameters. We derived the distances and extinction values for the EW-type objects from their period--luminosity relation. We also obtained the structure of the thin disk from the distribution of our sample of eclipsing binary systems, combined with those of high-mass star-forming regions and Cepheid tracers. We found that the thin disk is inhomogeneous in number density as a function of Galactic longitude. Using this new set of distance tracers, we constrain the detailed structure of the thin disk. Finally, we report a global parallax zero-point offset of $ Δπ=-42.1\pm1.9\mbox{(stat.)}\pm12.9\mbox{(syst.)}$ $μ$as between our carefully calibrated EW-type eclipsing binary positions and those provided by Gaia Early Data Release 3. Implementation of the officially recommended parallax zero-point correction results in a significantly reduced offset. Additionally, we provide a photometric characterization of our EW-type eclipsing binaries that can be applied to further analyses.

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arXiv2020

Physical Parameters of Late-type Contact Binaries in the Northern Catalina Sky Survey

We present the physical parameters of 2335 late-type contact binary (CB) systems extracted from the Catalina Sky Survey (CSS). Our sample was selected from the CSS Data Release 1 by strictly limiting the prevailing temperature uncertainties and light-curve fitting residuals, allowing us to almost eliminate any possible contaminants. We developed an automatic Wilson--Devinney-type code to derive the relative properties of CBs based on their light-curve morphology. By adopting the distances derived from CB (orbital) period--luminosity relations (PLRs), combined with the well-defined mass--luminosity relation for the systems' primary stars and assuming solar metallicity, we calculated the objects' masses, radii, and luminosities. Our sample of fully eclipsing CBs contains 1530 W-, 710 A-, and 95 B-type CBs. A comparison with literature data and with the results from different surveys confirms the accuracy and coherence of our measurements. The period distributions of the various CB subtypes are different, hinting at a possible evolutionary sequence. W-type CBs are clearly located in a strip in the total mass versus mass ratio plane, while A-type CBs may exhibit a slightly different dependence. There are no significant differences among the PLRs of A- and W-type CBs, but the PLR zero points are affected by their mass ratios and fill-out factors. Determination of zero-point differences for different types of CBs may help us improve the accuracy of the resulting PLRs. We demonstrate that automated approaches to deriving CB properties could be a powerful tool for application to the much larger CB samples expected to result from future surveys.

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arXiv2019

The Next Generation Virgo Cluster Survey. XVII. A Search for Planetary Nebulae in Virgo Cluster Globular Clusters

The occurrence of planetary nebulae (PNe) in globular clusters (GCs) provides an excellent chance to study low-mass stellar evolution in a special (low-metallicity, high stellar density) environment. We report a systematic spectroscopic survey for the [O{\sc iii}] 5007 emission line of PNe in 1469 Virgo GCs and 121 Virgo ultra-compact dwarfs (UCDs), mainly hosted in the giant elliptical galaxies M87, M49, M86, and M84. We detected zero PNe in our UCD sample and discovered one PN ($M_{5007} = -4.1$ mag) associated with an M87 GC. We used the [O{\sc iii}] detection limit for each GC to estimate the luminosity-specific frequency of PNe, $α$, and measured $α$ in the Virgo cluster GCs to be $α\sim 3.9_{-0.7}^{+5.2}\times 10^{-8}\mathrm{PN}/L_\odot$. $α$ in Virgo GCs is among the lowest values reported in any environment, due in part to the large sample size, and is 5--6 times lower than that for the Galactic GCs. We suggest that $α$ decreases towards brighter and more massive clusters, sharing a similar trend as the binary fraction, and the discrepancy between the Virgo and Galactic GCs can be explained by the observational bias in extragalactic surveys toward brighter GCs. This low but non-zero efficiency in forming PNe may highlight the important role played by binary interactions in forming PNe in GCs. We argue that a future survey of less massive Virgo GCs will be able to determine whether PN production in Virgo GCs is governed by internal process (mass, density, binary fraction), or is largely regulated by external environment.

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