arXiv subjects

Lu Shen

Publications and source records attributed to Lu Shen.

At least 55 records · Page 3Linked to original sources

arXiv2023

CEERS: MIRI deciphers the spatial distribution of dust-obscured star formation in galaxies at $0.1<z<2.5$

[Abridged] We combined HST images from the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey with JWST images from the Cosmic Evolution Early Release Science (CEERS) survey to measure the stellar and dust-obscured star formation distributions of a mass-complete ($>10^{10}M_\odot$) sample of 69 star-forming galaxies (SFGs) at $0.1 75$; 35 galaxies). At lower $S/N$, simulations show that simultaneous measurements of the size and Sérsic index become unreliable. We extended our study to fainter sources ($S/N>10$; 69 galaxies) by fixing their Sérsic index to unity. The Sérsic index of bright galaxies ($S/N>75$) has a median value of 0.7, which, together with their axis ratio distribution, suggests a disk-like morphology in the rest-MIR. Galaxies above the main sequence (MS; i.e., starbursts) have rest-MIR sizes that are a factor 2 smaller than their rest-optical sizes. The median rest-optical to rest-MIR size ratio of MS galaxies increases with stellar mass, from 1.1 at $10^{9.8}M_\odot$ to 1.6 at $10^{11}M_\odot$. This mass-dependent trend resembles the one found in the literature between the rest-optical and rest-near-infrared sizes of SFGs, suggesting that it is due to radial color gradients affecting rest-optical sizes and that the sizes of the stellar and star-forming components of SFGs are, on average, consistent at all masses. There is, however, a small population of SFGs (15%) with a compact star-forming component embedded in a larger stellar structure. This could be the missing link between galaxies with an extended stellar component and those with a compact stellar component, the so-called blue nuggets.

astro-ph.GA↗

arXiv2023

CEERS: 7.7 $μ$m PAH Star Formation Rate Calibration with JWST MIRI

We test the relationship between UV-derived star formation rates (SFRs) and the 7.7 $μ$m polycyclic aromatic hydrocarbon (PAH) luminosities from the integrated emission of galaxies at z ~ 0 - 2. We utilize multi-band photometry covering 0.2 - 160 $μ$m from HST, CFHT, JWST, Spitzer, and Herschel for galaxies in the Cosmic Evolution Early Release Science (CEERS) Survey. We perform spectral energy distribution (SED) modeling of these data to measure dust-corrected far-UV (FUV) luminosities, $L_{FUV}$, and UV-derived SFRs. We then fit SED models to the JWST/MIRI 7.7 - 21 $μ$m CEERS data to derive rest-frame 7.7 $μ$m luminosities, $L_{770}$, using the average flux density in the rest-frame MIRI F770W bandpass. We observe a correlation between $L_{770}$ and $L_{FUV}$, where log $L_{770}$ is proportional to (1.27+/-0.04) log $L_{FUV}$. $L_{770}$ diverges from this relation for galaxies at lower metallicities, lower dust obscuration, and for galaxies dominated by evolved stellar populations. We derive a "single-wavelength" SFR calibration for $L_{770}$ which has a scatter from model estimated SFRs (${σ_{ΔSFR}}$) of 0.24 dex. We derive a "multi-wavelength" calibration for the linear combination of the observed FUV luminosity (uncorrected for dust) and the rest-frame 7.7 $μ$m luminosity, which has a scatter of ${σ_{ΔSFR}}$ = 0.21 dex. The relatively small decrease in $σ$ suggests this is near the systematic accuracy of the total SFRs using either calibration. These results demonstrate that the rest-frame 7.7 $μ$m emission constrained by JWST/MIRI is a tracer of the SFR for distant galaxies to this accuracy, provided the galaxies are dominated by star-formation with moderate-to-high levels of attenuation and metallicity.

astro-ph.GA↗

arXiv2023

CEERS MIRI Imaging: Data Reduction and Quality Assessment

The Cosmic Evolution Early Release Science Survey (CEERS), targeting the Extended Groth Strip extragalactic field, is one of the JWST Director's Discretionary Early Release Science programs. To date, all observations have been executed and include NIRCam/MIRI imaging and NIRSpec/NIRCam spectroscopic exposures. Here, we discuss the MIRI imaging, which includes eight pointings, four of which provide deep imaging with the bluer bands (F560W, F770W) and four with contiguous wavelength coverage in F1000W, F1280W, F1500W, and F1800W, where two of these also include coverage in F770W and F2100W. We present a summary of the data, the data quality, and data reduction. The data reduction is based on the JWST Calibration Pipeline combined with custom modifications and additional steps designed to enhance the output quality, including improvements in astrometry and the removal of detector artifacts. We estimate the image depth of the reduced mosaics, and show that these generally agree with expectations from the Exposure Time Calculator. We compare the MIRI F560W and F770W flux densities for bright sources to measurements from Spitzer/IRAC Ch3 (5.8 $μ$m) and Ch4 (8.0 $μ$m), and we find that they agree with systematic differences of $<0.1$ mag. For the redder MIRI bands, we assess their quality by studying the spectral energy distributions (SEDs) of Galactic stars. The SEDs are consistent with the expected Rayleigh-Jeans law with a deviation $\sim 0.03$ mag, indicating that the MIRI colors are reliable. We also discuss all publicly released data products (images and source catalogs), which are available on the CEERS website (https://ceers.github.io/).

astro-ph.GA↗

arXiv2023

The High-Redshift Clusters Occupied by Bent Radio AGN (COBRA) Survey: Investigating the Role of Environment on Bent Radio AGNs using LOFAR

Bent radio AGN morphology depends on the density of the surrounding gas. However, bent sources are found inside and outside clusters, raising the question of how environment impacts bent AGN morphology. We analyze new LOw-Frequency Array Two-metre Sky Survey (LoTSS) Data Release II observations of 20 bent AGNs in clusters and 15 not in clusters from the high-$z$ Clusters Occupied by Bent Radio AGN (COBRA) survey (0.35 $<$ $z$ $<$ 2.35). We measure the impact of environment on size, lobe symmetry, and radio luminosity. We find that the most asymmetric radio lobes lie outside of clusters and we uncover a tentative correlation between the total projected physical area and cluster overdensity. Additionally, we, for the first time, present spectral index measurements of a large sample of high-$z$ bent sources using LoTSS and Very Large Array Faint Images of the Radio Sky at Twenty-centimeters (VLA FIRST) observations. We find that the median spectral index for the cluster sample is -0.76 $\pm$ 0.01, while the median spectral index for the non-cluster sample median is -0.81 $\pm$ 0.02. Furthermore, 13 of 20 cluster bent AGNs have flat cores ($α$ $\geq$ -0.6) compared to 4 of 15 of non-clusters, indicating a key environmental signature. Beyond core spectral index, bent AGNs inside and outside clusters are remarkably similar. We conclude that the non-cluster sample may be more representative of bent AGNs at large offsets from the cluster center ($>$ 1.2Mpc) or bent AGNs in weaker groups rather than the field.

astro-ph.GA↗

arXiv2023

Elentári: A $z\sim3.3$ Proto-Supercluster in COSMOS

Motivated by spectroscopic confirmation of three overdense regions in the COSMOS field at $z\sim3.35$, we analyze the uniquely deep multi-wavelength photometry and extensive spectroscopy available in the field to identify any further related structure. We construct a three dimensional density map using the Voronoi tesselation Monte Carlo method and find additional regions of significant overdensity. Here we present and examine a set of six overdense structures at $3.20 5σ$ overdensity separated by up to 70 cMpc, suggestive of a proto-supercluster similar to the Hyperion system at $z\sim2.45$. Upcoming photometric surveys with JWST such as COSMOS-Web, and further spectroscopic follow-up will enable more extensive analysis of the evolutionary effects that such an environment may have on its component galaxies at these early times.

astro-ph.GA↗

arXiv2023

Discovery of spectacular quasar-driven superbubbles in red quasars

Quasar-driven outflows on galactic scales are a routinely invoked ingredient for galaxy formation models. We report the discovery of ionized gas nebulae as traced by [O III] $λ$5007 AA emission surrounding three luminous red quasars at $z \sim 0.4$ from Gemini Integral Field Unit (IFU) observations. All these nebulae feature unprecedented pairs of "superbubbles" extending $\sim$20 kpc in diameter, and the line-of-sight velocity difference between the red- and blue-shifted bubbles reaches up to $\sim$1200 km s$^{-1}$. Their spectacular dual-bubble morphology (in analogy to the Galactic "Fermi bubbles") and their kinematics provide unambiguous evidence for galaxy-wide quasar-driven outflows, in parallel with the quasi-spherical outflows similar in size from luminous Type-1 and -2 quasars at concordant redshift. These bubble pairs manifest themselves as a signpost of the short-lived superbubble ``break-out'' phase, when the quasar wind drives the bubbles to escape the confinement from the dense environment and plunge into the galactic halo with a high-velocity expansion.

astro-ph.GA↗

arXiv2023

CEERS: Spatially Resolved UV and mid-IR Star Formation in Galaxies at 0.2 < z < 2.5: The Picture from the Hubble and James Webb Space Telescopes

We present the mid-IR (MIR) morphologies for 64 star-forming galaxies at $0.2 10^{9}~M_\odot}$ using JWST MIRI observations from the Cosmic Evolution Early Release Science survey (CEERS). The MIRI bands span the MIR (7.7--21~$μ$m), enabling us to measure the effective radii ($R_{\rm{eff}}$) and Sérsic indexes of these SFGs at rest-frame 6.2 and 7.7 $μ$m, which contains strong emission from Polycyclic aromatic hydrocarbon (PAH) features, a well-established tracer of star formation in galaxies. We define a ``PAH-band'' as the MIRI bandpass that contains these features at the redshift of the galaxy. We then compare the galaxy morphologies in the PAH-bands to those in rest-frame Near-UV (NUV) using HST ACS/F435W or ACS/F606W and optical/near-IR using HST WFC3/F160W imaging from UVCANDELS and CANDELS, where the NUV-band and F160W trace the profile of (unobscured) massive stars and the stellar continuum, respectively. The $R_{\rm{eff}}$ of galaxies in the PAH-band are slightly smaller ($\sim$10\%) than those in F160W for galaxies with $\rm{M_*\gtrsim10^{9.5}~M_\odot}$ at $z\leq1.2$, but the PAH-band and F160W have a similar fractions of light within 1 kpc. In contrast, the $R_{\rm{eff}}$ of galaxies in the NUV-band are larger, with lower fractions of light within 1 kpc compared to F160W for galaxies at $z\leq1.2$. Using the MIRI data to estimate the $\rm{SFR_{\rm{IR}}}$ surface density, we find the correlation between the $\rm{SFR_{\rm{IR}}}$ surface density and stellar mass has a steeper slope than that of the $\rm{SFR_{\rm{UV}}}$ surface density and stellar mass, suggesting more massive galaxies having increasing amounts of obscured fraction of star formation in their inner regions. This paper demonstrates how the high-angular resolution data from JWST/MIRI can reveal new information about the morphology of obscured-star formation.

astro-ph.GA↗

arXiv2023

CEERS Key Paper IV: Galaxies at $4 < z < 9$ are Bluer than They Appear -- Characterizing Galaxy Stellar Populations from Rest-Frame $\sim 1$ micron Imaging

We present results from the Cosmic Evolution Early Release Survey (CEERS) on the stellar-population parameters for 28 galaxies with redshifts $4<z<9$ using imaging data from the James Webb Space Telescope (JWST) Mid-Infrared Instrument (MIRI) combined with data from the Hubble Space Telescope and the Spitzer Space Telescope. The JWST/MIRI 5.6 and 7.7 $μ$m data extend the coverage of the rest-frame spectral-energy distribution (SED) to nearly 1 micron for galaxies in this redshift range. By modeling the galaxies' SEDs the MIRI data show that the galaxies have, on average, rest-frame UV (1600 Å) $-$ $I$-band colors 0.4 mag bluer than derived when using photometry that lacks MIRI. Therefore, the galaxies have lower (stellar)-mass-to-light ratios. The MIRI data reduce the stellar masses by $\langle Δ\log M_\ast\rangle=0.25$ dex at $4<z<6$ (a factor of 1.8) and 0.37 dex at $6<z<9$ (a factor of 2.3). This also reduces the star-formation rates (SFRs) by $\langle Δ\log\mathrm{SFR} \rangle=0.14$ dex at $4<z<6$ and 0.27 dex at $6<z<9$. The MIRI data also improve constraints on the allowable stellar mass formed in early star-formation. We model this using a star-formation history that includes both a "burst' at $z_f=100$ and a slowly varying ("delayed-$τ$") model. The MIRI data reduce the allowable stellar mass by 0.6 dex at $4<z< 6$ and by $\approx$1 dex at $6<z<9$. Applying these results globally, this reduces the cosmic stellar-mass density by an order of magnitude in the early universe ($z\approx9$). Therefore, observations of rest-frame $\gtrsim$1 $μ$m are paramount for constraining the stellar-mass build-up in galaxies at very high-redshifts.

astro-ph.GA↗

arXiv2023

The Next Generation Deep Extragalactic Exploratory Public (NGDEEP) Survey

We present the Next Generation Deep Extragalactic Exploratory Public (NGDEEP) Survey, a deep slitless spectroscopic and imaging Cycle 1 JWST treasury survey designed to constrain feedback mechanisms in low-mass galaxies across cosmic time. NGDEEP targets the Hubble Ultra Deep Field (HUDF) with NIRISS slitless spectroscopy (f~1.2e-18 erg/s/cm^2, 5sigma) to measure metallicities and star-formation rates (SFRs) for low-mass galaxies through the peak of the cosmic SFR density (0.5 12, constraining the slope of the faint-end of the rest-ultraviolet luminosity function. NGDEEP overlaps with the deepest HST ACS optical imaging in the sky: F435W in the HUDF (m=29.6), and F814W in HUDF-Par2 (m=30), making this a premier HST+JWST Deep Field. As a treasury survey, NGDEEP data is public immediately, and we will rapidly release data products and catalogs in the spirit of previous deep field initiatives. In this paper we present the NGDEEP survey design, summarize the science goals, and detail plans for the public release of NGDEEP reduced data products.

astro-ph.GA↗

arXiv2022

An overdensity of red galaxies around the hyperluminous dust-obscured quasar W1835$+$4355 at $z=2.3$

\emph{Wide-field Infrared Survey Explorer} all-sky survey has discovered a new population of hot dust-obscured galaxies (Hot DOGs), which has been confirmed to be dusty quasars. Previous statistical studies have found significant overdensities of sub-millimeter and mid-IR selected galaxies around Hot DOGs, indicating they may reside in dense regions. Here we present the near-infrared ($J$ and $K_s$ bands) observations over a $7.5'\times 7.5'$ field centered on a Hot DOG W1835$+$4355 at $z \sim 2.3$ using the wide-field infrared camera on the Palomar 200-inch telescope. We use the color criterion $J-K_s>2.3$ for objects with $K_s<20$, to select Distant Red Galaxies (DRGs). We find a significant excess of number density of DRGs in W1835$+$4355 field compared to three control fields, by a factor of about 2. The overdensity of red galaxies around W1835$+$4355 are consistent with the multi-wavelength environment of Hot DOGs, suggesting that Hot DOGs may be a good tracer for dense regions at high redshift. We find that W1835$+$4355 do not reside in the densest region of the dense environment traced by itself. A possible scenario is that W1835$+$4355 is undergoing merging process, which lowers the local number density of galaxies in its surrounding region.

astro-ph.GA↗

arXiv2022

The ALPINE-ALMA [CII] survey: The infrared-radio correlation and AGN fraction of star-forming galaxies at z $\sim$ 4.4-5.9

We present the radio properties of 66 spectroscopically-confirmed normal star-forming galaxies (SFGs) at $4.4<z<5.9$ in the COSMOS field that were [C II] detected in the Atacama Large Millimeter Array (ALMA) Large Program to INvestigate [C II] at Early times (ALPINE). We separate these galaxies ("CII-detected-all") into lower redshift ("CII-detected-lz", $\langle z\rangle=4.5$) and higher redshift ("CII-detected-hz", $\langle z\rangle=5.6$) sub-samples and stack multi-wavelength imaging for each sub-sample from X-ray to radio bands. A radio signal is detected in the stacked 3 GHz image of CII-detected-all and -lz samples at $\gtrsim3σ$. We find that the infrared-radio correlation of our sample, quantified by $q_{\mathrm{TIR}}$, is lower than the local relation for normal SFGs at $\sim$3$σ$ significance level, and is instead broadly consistent with that of bright sub-mm galaxies at $2<z<5$. Neither of these samples show evidence of dominant AGN activity in their stacked Spectral Energy Distributions (SEDs), rest-frame UV spectra, or X-ray images. Although we cannot rule out the possible effect of the assumed spectral index and the applied infrared SED templates as at least partially causing these differences, the lower obscured fraction of star formation than at lower redshift can alleviate the tension between our stacked $q_{\mathrm{TIR}}$s and that of local normal SFGs. It is possible that the dust buildup, which primarily governs the IR emission in addition to older stellar populations, has not had enough time to occur fully in these galaxies, whereas the radio emission can respond on a more rapid timescale. Therefore, we might expect a lower $q_{\mathrm{TIR}}$ to be a general property of high-redshift SFGs.

astro-ph.GA↗

arXiv2022

Uncertainty-Guided Lung Nodule Segmentation with Feature-Aware Attention

Since radiologists have different training and clinical experiences, they may provide various segmentation annotations for a lung nodule. Conventional studies choose a single annotation as the learning target by default, but they waste valuable information of consensus or disagreements ingrained in the multiple annotations. This paper proposes an Uncertainty-Guided Segmentation Network (UGS-Net), which learns the rich visual features from the regions that may cause segmentation uncertainty and contributes to a better segmentation result. With an Uncertainty-Aware Module, this network can provide a Multi-Confidence Mask (MCM), pointing out regions with different segmentation uncertainty levels. Moreover, this paper introduces a Feature-Aware Attention Module to enhance the learning of the nodule boundary and density differences. Experimental results show that our method can predict the nodule regions with different uncertainty levels and achieve superior performance in LIDC-IDRI dataset.

eess.IV↗

arXiv2022

Evidence for quasar fast outflows being accelerated at the scale of tens of parsecs

Quasar outflows may play a crucial role in regulating the host galaxy, although the spatial scale of quasar outflows remain a major enigma, with their acceleration mechanism poorly understood. The kinematic information of outflow is the key to understanding its origin and acceleration mechanism. Here, we report the galactocentric distances of different outflow components for both a sample and an individual quasar. We find that the outflow distance increases with velocity, with a typical value from several parsecs to more than one hundred parsecs, providing direct evidence for an acceleration happening at a scale of the order of 10 parsecs. These outflows carry ~1% of the total quasar energy, while their kinematics are consistent with a dust driven model with a launching radius comparable to the scale of a dusty torus, indicating that the coupling between dust and quasar radiation may produce powerful feedback that is crucial to galaxy evolution.

astro-ph.GA↗

arXiv2021

B2 0003+38A: a classical flat-spectrum radio quasar hosted by a rotation-dominated galaxy with a peculiar massive outflow

We present a detailed analysis of the single-slit optical spectrum of the Flat-Spectrum Radio Quasar (FSRQ) B2 0003+38A, taken by the Echellette Spectrograph and Imager (ESI) on the Keck II telescope. This classical low-redshift FSRQ ($z=0.22911$, as measured from the stellar absorption lines) remains underexplored in its emission lines, though its broad-band continuum properties from radio to X-ray is well-studied. After removing the unresolved quasar nucleus and the starlight from the host galaxy, we obtain a spatially-resolved 2-D spectrum, which clearly shows three components, indicating a rotating disk, an extended emission line region (EELR) and an outflow. The bulk of the EELR, with a characteristic mass $M_{\rm EELR}\sim 10^{7}~\rm M_{\odot}$, and redshifted by $v_{\rm EELR}\approx 120$ km s$^{-1}$ with respect to the quasar systemic velocity, shows a one-sided structure stretching to a projected distance of $r_{\rm EELR}\sim 20$ kpc from the nucleus. The rotation curve of the rotating disk is well consistent with that of a typical galactic disk, suggesting that the FSRQ is hosted by a disk galaxy. This conclusion is in accordance with the facts that strong absorption in the HI 21-cm line was previously observed, and that Na I$λ\lambda5891,5897$ and Ca II$λ\lambda3934,3969$ doublets are detected in the optical ESI spectrum. B2 0003+38A will become the first FSRQ discovered to be hosted by a gas-rich disk galaxy, if this is confirmed by follow-up deep imaging and/or IFU mapping with high spatial resolution. These observations will also help unravel the origin of the EELR.

astro-ph.GA↗

arXiv2021

Estimating air quality co-benefits of energy transition using machine learning

Estimating health benefits of reducing fossil fuel use from improved air quality provides important rationales for carbon emissions abatement. Simulating pollution concentration is a crucial step of the estimation, but traditional approaches often rely on complicated chemical transport models that require extensive expertise and computational resources. In this study, we develop a novel and succinct machine learning framework that is able to provide precise and robust annual average fine particle (PM2.5) concentration estimations directly from a high-resolution fossil energy use data set. The accessibility and applicability of this framework show great potentials of machine learning approaches for integrated assessment studies. Applications of the framework with Chinese data reveal highly heterogeneous health benefits of reducing fossil fuel use in different sectors and regions in China with a mean of \$34/tCO2 and a standard deviation of \$84/tCO2. Reducing rural and residential coal use offers the highest co-benefits with a mean of \$360/tCO2. Our findings prompt careful policy designs to maximize cost-effectiveness in the transition towards a carbon-neutral energy system.

econ.GN↗

arXiv2021

Implications of the Environments of Radio-detected AGN in a Complex Protostructure at z$\sim$3.3

Radio Active Galactic Nuclei (RAGNs) are mainly found in dense structures (i.e., clusters/groups) at redshifts of z$<$2 and are commonly used to detect protoclusters at higher redshift. Here, we attempt to study the host and environmental properties of two relatively faint ($\mathrm L_\mathrm{1.4GHz} \sim10^{25}$ W Hz$^{-1}$) RAGNs in a known protocluster at z=3.3 in the PCl J0227-0421 field, detected using the latest radio observation obtained as part of the Observations of Redshift Evolution in Large-Scale Environments (ORELSE) Survey. Using new spectroscopic observations obtained from Keck/MOSFIRE as part of the Charting Cluster Construction with the VIMOS Ultra-Deep Survey (VUDS) and ORELSE (C3VO) survey and previous spectroscopic data obtained as part of the VIMOS-VLT Deep Survey (VVDS) and VUDS, we revise the three-dimensional overdensity field around this protocluster. The protocluster is embedded in a large scale overdensity protostructure. This protostructure has an estimated total mass of $\sim$2.6$\times10^{15} M_\odot$ and contains several overdensity peaks. Both RAGNs are hosted by very bright and massive galaxies, while their hosts show extreme differences color, indicating that they have different ages and are in different evolutionary stages. Furthermore, we find that they are not in the most locally dense parts of the protostructure, but are fairly close to the centers of their parent overdensity peaks. We propose a scenario where merging might already have happened in both cases, which lowered the local density of their surrounding area and boosted their stellar mass. This work is the first time that two RAGNs at low luminosity have been found and studied within a high redshift protostructure.

astro-ph.GA↗

arXiv2021

An Extraordinary Response of Iron Emission to the Central Outburst in a Tidal Disruption Event Candidate

Understanding the origin of \feii\ emission is important because it is crucial to construct the main sequence of Active Galactic Nuclei (AGNs). Despite several decades of observational and theoretical effort, the location of the optical iron emitting region and the mechanism responsible for the positive correlation between the \feii\ strength and the black hole accretion rate remain open questions as yet. In this letter, we report the optical \feii\ response to the central outburst in PS1-10adi, a candidate tidal disruption event (TDE) taking place in an AGN at $z = 0.203$ that has aroused extensive attention. For the first time, we observe that the \feii\ response in the rising phase of its central luminosity is significantly more prominent than that in the decline phase, showing a hysteresis effect. We interpret this hysteresis effect as a consequence of the gradual sublimation of the dust grains situating at the inner surface of the torus into gas when the luminosity of the central engine increases. It is the iron element released from the sublimated dust that contributes evidently to the observed \feii\ emission. This interpretation, together with the weak response of the \hb\ emission as we observe, naturally explains the applicability of relative \feii\ strength as a tracer of the Eddington ratio. In addition, optical iron emission of this origin renders the \feii\ time lag a potential "standard candle" with cosmological implications.

astro-ph.GA↗

arXiv2020

A sharp rise in the detection rate of broad absorption line variations in a quasar SDSS J141955.26+522741.1

We present an analysis of the variability of broad absorption lines (BALs) in a quasar SDSS J141955.26+522741.1 at $z=2.145$ with 72 observations from the Sloan Digital Sky Survey Data Release 16 (SDSS DR16). The strong correlation between the equivalent widths of BAL and the continuum luminosity, reveals that the variation of BAL trough is dominated by the photoionization. The photoionization model predicts that when the time interval $ΔT$ between two observations is longer than the recombination timescale $t_{\rm rec}$, the BAL variations can be detected. This can be characterized as a "sharp rise" in the detection rate of BAL variation at $ΔT=t_{\rm rec}$. For the first time, we detect such a "sharp rise" signature in the detection rate of BAL variations. As a result, we propose that the $t_{\rm rec}$ can be obtained from the "sharp rise" of the detection rate of BAL variation. It is worth mentioning that the BAL variations are detected at the time-intervals less than the $t_{\rm rec}$ for half an order of magnitude in two individual troughs. This result indicates that there may be multiple components with different $t_{\rm rec}$ but the same velocity in an individual trough.

astro-ph.GA↗