Preamble

Vol. 43, No. 2

June 2025

PROGRESS IN ASTRONOMY Vol. 43, No. 2 June., 2025 doi: 10.3969/j.issn.1000-8349.2025.02.04

Research Progress on Velocity Shifts of Quasar Absorption Lines

LIN Yingru, LU Weijian, QIN Huanchang, PAN Caijuan (Baise University, Baise 533000, China)

Abstract: Outflows serve as a crucial feedback mechanism in quasars, playing a significant role in understanding the co-evolution processes between quasars and their host galaxies. This paper collects and organizes literature on the research of velocity shifts in outflow absorption lines, compares and analyzes the identification methods, challenges, and generation mechanisms of such velocity shifts, and discusses potential future research directions. While current empirical cases of absorption line velocity shifts are limited and their underlying physical mechanisms remain unclear, the growth of quasar survey data and advancements in data processing techniques are expected to lead to breakthroughs in this field. Such progress will not only deepen our understanding of quasar outflow phenomena, but also offer new perspectives for galaxy evolution studies.

Key words: quasar; outflow; absorption line; velocity shift

CLC number: P157.9 Document code: A

1 Introduction

Astrophysicists widely acknowledge that active galactic nucleus (AGN) feedback mechanisms play a pivotal role in the co-evolution of black holes and galaxies [1{4]. AGN produce broadband electromagnetic radiation through accretion onto supermassive black holes at their centers, exhibiting observational characteristics such as high luminosity, small scales (compact nuclear regions), multi-band variability (timescales ranging from hours to years), and emission lines of varying widths (10^3 (cid:24) 10^4 km (cid:1) s (cid:0) 1) [1]. These unique observational features provide astronomers with a window to deeply investigate galaxy evolution processes and the extreme physical events occurring within them [5].

Through long-term observations and research, astronomers have classified AGN into categories including quasars, Seyfert galaxies, radio galaxies, optically violent variable quasars (OVV quasar), and BL Lacertae objects (BL Lac). Among these, quasars, as one of the four major astronomical discoveries of the 1960s, have rapidly become a research focus due to their extreme luminosity and activity characteristics.

It is generally believed that outflows generated from the bright accretion disks at quasar centers can interact with surrounding interstellar medium [6{14], eventually propagating to galactic scales and forming large-scale outflow phenomena. Consequently, outflows play a vital role in galaxy evolution by transporting heavy elements away from host galaxies, limiting the growth of central supermassive black holes [15], and providing energy and momentum to interstellar and intergalactic media [16]. Despite the widely recognized importance of outflows, key aspects such as their formation causes, physical states, locations, acceleration mechanisms, and three-dimensional structures remain to be thoroughly investigated.

Broad absorption lines frequently detected in quasars serve as compelling evidence for outflows [17]. Most ultraviolet broad absorption lines exhibit blueshifts, suggesting they are produced by outflows moving away from the central source. In addition to broad absorption lines, some quasars also show narrow absorption lines in the UV band. The classification criteria typically designate absorption lines with full width at half maximum (FWHM) exceeding 2,000 km (cid:1) s (cid:0) 1 as broad, those with FWHM less than 500 km (cid:1) s (cid:0) 1 as narrow, with intermediate-width absorption lines falling between these values. Many studies do not distinguish between broad and intermediate-width absorption lines, differentiating only between narrow and broad absorption lines, primarily because the former are often difficult to attribute definitively to outflows driven by AGN or star formation processes versus absorption from circumgalactic medium (CGM), intergalactic medium (IGM), or foreground gas.

Research analyzing broad and intermediate-width absorption lines in quasars has revealed that the enormous kinetic energy carried by outflows exerts significant feedback effects on host galaxies. For example, He et al. [18] confirmed the substantial impact of outflow kinetic energy on galaxy evolution based on a sample of 915 variable broad absorption line quasars from the Sloan Digital Sky Survey (SDSS) [19], with Hamann et al. [20] further corroborating this conclusion using SDSS-III BOSS data. In contrast, studies on narrow absorption line outflows remain insufficient. Although sporadic reports have explored individual sources, systematic large-sample studies evaluating their feedback effects are lacking. Furthermore, the formation mechanisms for these three absorption line morphologies (broad, narrow, and intermediate-width) remain inconclusive, with general consensus attributing them to differences in the observer's sightline angle relative to the outflow axis [21] or different evolutionary stages of outflows [22].

Analyzing variations in the intensity, profile, and velocity of outflow absorption lines may provide a method to study the physical properties of quasar outflows, offering constraints on aspects such as outflow structure, location, and dynamics [23{25]. Studies have shown that changes in intensity and profile of broad, intermediate-width, and narrow absorption lines are common on timescales of months to years [25{48]. These variations may stem from absorption gas moving perpendicular to the line of sight [26{32], transitions in the ionization state of absorbing gas [25, 33{38], or a combination of both [49{51]. For the former case, using the variability timescale as an upper limit on the recombination time allows calculation of a lower limit on the gas density; for the latter, broad absorption line variability timescales can constrain the distance between absorbers and the central black hole [52, 53].

While variations in intensity and profile of outflow absorption lines have been confirmed to be widespread, cases of velocity shifts remain rare [50, 54{60]. Absorption line velocity shift refers to the overall offset of the absorption line center wavelength across continuous observations while the absorption line profile remains essentially unchanged (as shown in Figure 1 [FIGURE:1]). Velocity shifts can trend toward either the red or blue end of the spectrum. The formation mechanisms of outflow absorption line velocity shifts remain controversial within the academic community. Although theories propose that velocity shifts may result from real acceleration/deceleration of outflows along the line of sight or from outflows crossing the line of sight during circular motion around the central massive black hole, these theories have yet to be fully validated by observational data [50, 55, 61{63].

When velocity shifts reflect real acceleration or deceleration of outflows, they can not only reveal kinematic characteristics and dynamic mechanisms of outflows [59], but also test hypotheses regarding outflows as mediators of galaxy feedback. For example, galaxy feedback models explain outflow deceleration as follows [1{3]: when outflows are sufficiently distant from the central source, they may interact with host galaxy material, potentially leading to outflow deceleration [64]. In such cases, the interaction also alters the ionization and thermal state of the outflow, consequently changing absorption line profiles. The absence of observed deceleration may indicate that the outflow remains very close to the central black hole and has not yet undergone significant interaction with host galaxy material. Most broad absorption lines maintain average velocity fluctuations within a 3% range, and Grier et al. [59] concluded from this result that broad absorption line clouds may not have traveled to effective distances where they would significantly interact with their surroundings. Verifying this viewpoint requires more observational data on broad absorption line deceleration. Recent studies have also proposed that genuine broad absorption line acceleration or deceleration events may provide unique insights into the origins of quasar reddening and weak radio emission [65, 66].

The physical mechanisms underlying outflow absorption line velocity shifts remain controversial. Although some scholars suggest these may result from real velocity changes of outflow material along the line of sight or from their circular motion around the central massive black hole, these explanations lack conclusive observational evidence, and theoretical predictions differ from observational results [50, 55, 61{63]. For instance, studies have found that broad absorption line accelerations exhibit inconsistent behavior across different timescales, which traditional accretion disk wind models and geometric projection effects struggle to explain [59]. Additionally, research has discovered that broad absorption line velocity shifts are accompanied by coordinated enhancement of absorption line equivalent width, weakening of the continuum, and enhancement of emission lines, suggesting that central source radiation may play a driving role in this process [54, 56]. Therefore, the complex mechanisms of outflow absorption line velocity shifts require further in-depth investigation.

This paper collects literature on absorption line velocity shifts and introduces research achievements in this field from four aspects: identification methods (Section 2), identification challenges (Section 3), case studies (Section 4), and generation mechanisms (Section 5). Section 6 proposes future research directions, followed by a summary in the final section. All "time" mentioned in this paper refers to quasar rest-frame time.

2 Identification Methods for Broad Absorption Line Velocity Shifts

Currently, three primary methods exist for identifying broad absorption line velocity shifts from spectral data: the integer pixel offset method, the cross-correlation function combined with chi-square test method, and visual inspection method.

2.1 Integer Pixel Offset Method

Gibson et al. [67] established an upper limit of 1 Å for velocity shifts for each source, then divided by the source's sampling time interval to derive an upper limit on acceleration. This method's limitations manifest in two aspects: (1) it only uses a small range of the absorption trough for calculation, failing to reflect changes in the complete broad absorption trough; (2) it assumes a velocity offset upper limit of one pixel to derive the acceleration upper limit, making it unable to identify drift values smaller than one pixel.

2.2 Cross-Correlation Function and Chi-Square Test Method

Cross-correlation functions are commonly used to measure time delays in light curves [68] or radial velocities of exoplanets [69]. Grier et al. [59] combined cross-correlation functions with chi-square test methods to screen broad absorption line acceleration/deceleration candidates from large samples. Their screening criteria were: (1) the p-value between spectra without broad absorption line velocity shifts and subsequent spectra should be less than 0.1, indicating significant differences in the absorption line between these two observations; (2) the (cid:31) value and p-value between the first spectrum showing broad absorption line velocity shifts and its subsequent spectrum should meet certain conditions to ensure statistical significance of the velocity difference between the two observations.

The advantages of the cross-correlation function and chi-square test combination method include: (1) high sensitivity to velocity shifts, capable of detecting drifts smaller than one pixel; (2) ability to treat the entire (or at least part of) broad absorption trough as a whole to identify whether changes result from velocity variations or other factors; (3) capacity to quantify errors and derive reliable upper limits on velocity shifts.

It should be noted that when screening criteria are set to be strict, this method excludes targets exhibiting both velocity shifts and profile or intensity changes. For instance, Grier et al. [59] used this method to exclude absorption lines with profile or intensity changes, retaining only pure acceleration/deceleration candidates.

2.3 Visual Inspection Method

As the most direct and original method, visual inspection allows researchers to identify velocity shifts based on experience. This approach avoids misjudgment caused by parameter setting issues, such as the problem where cross-correlation function and chi-square test methods may exclude absorption lines with simultaneous velocity shifts and profile/intensity changes. Lu and Lin [54, 56] and Yao et al. [57] both employed visual inspection methods to identify broad absorption lines with velocity shifts from quasar spectra. However, when facing large numbers of spectra, visual inspection becomes time-consuming and demands high professional expertise and experience from researchers. Nevertheless, visual inspection remains an indispensable method for confirming broad absorption line velocity shifts.

3 Difficulties in Identifying Broad Absorption Line Velocity Shifts

Identifying broad absorption line velocity shifts in spectra can be influenced by various factors, including sampling frequency and interval, spectral resolution and signal-to-noise ratio, intrinsic complexity of broad absorption lines themselves, and the need to determine whether the zero point has drifted between two spectral observations (which can be assessed using characteristic absorption or emission lines such as [O III]).

3.1 Sampling Frequency and Interval

Broad absorption lines may exhibit apparent velocity shifts between two observations due to changes in profile or absorption intensity. If the shape remains unchanged across multiple observations, this confirms that velocity shifts have occurred in the same absorption line rather than other types of changes. Therefore, having three or more observations at different epochs enhances the reliability of observed velocity shift phenomena. Second, the sampling interval needs to be sufficiently long. Grier et al. [59] demonstrated that within 2.5(cid:24)5.5 a, the average velocity variation of most C IV broad absorption lines remains within a 3% range. Consequently, if the sampling interval is not long enough, the magnitude of velocity shifts may be too small to be detected.

Wheatley et al. [60] clearly demonstrated the impact of sampling frequency and interval on velocity shift measurements using an example. Grier et al. [70] studied 32 observations of quasar SDSS J141007.72+541203.6 within one year and found significant changes in the equivalent width of a C IV broad absorption line. Subsequently, Hemler et al. [71] studied follow-up observations over three years and found that the broad absorption line intensity weakened slightly without significant changes in equivalent width. Wheatley et al. [60] added 70 spectra from the subsequent four years and discovered that the broad absorption line exhibited changes in equivalent width, intensity, and profile, as well as velocity shifts. This illustrates that with small sample sizes, insufficient sampling frequency or short sampling intervals may cause velocity shift candidates to be missed.

3.2 Limitations of Spectral Resolution and Signal-to-Noise Ratio

The importance of high-resolution spectra for analyzing quasar absorption line velocity shifts is self-evident. As shown in Table 1 [TABLE:1], the outflow absorption line acceleration values measured by Vilkoviskij and Irwin [72] and Rupke et al. [73] are one to two orders of magnitude smaller than those from other researchers' work, possibly because their spectra had higher resolution and signal-to-noise ratios, enabling detection of more subtle velocity shifts. High-resolution spectra are crucial for precisely measuring velocity shift values and studying absorption line variability and line-locking characteristics. Only with high-resolution spectra can one accurately decompose components of an (unsaturated) broad absorption trough without relying on models, which is essential for verifying whether line-locking components truly exist in broad absorption lines.

3.3 Intrinsic Complexity of Broad Absorption Lines

The third difficulty in identifying broad absorption line velocity shifts stems from the intrinsic complexity of broad absorption lines themselves. This complexity first manifests in potential self-blending effects, where mutual mixing of blue and red subcomponents may mask velocity shifts. In recent research, Wheatley et al. [60] demonstrated how to distinguish or decompose subcomponents of broad absorption lines and measure their individual velocity shifts, comparing these with the velocity shift of the entire broad absorption line before decomposition.

Beyond self-blending effects, widespread changes in absorption line intensity, equivalent width, or profile can also interfere with velocity shift identification. Filiz et al. [25] found that 50%(cid:24)60% of C IV and Si IV broad absorption lines undergo intensity or profile changes within several years. Hemler et al. [71] discovered that among 27 quasars in the Sloan Digital Sky Survey Reverberation Mapping project (SDSS-RM [74, 75]), more than half showed significant changes in C IV broad absorption line equivalent width even over short timescales (within 10 d in the rest frame). When broad absorption line velocity shifts occur simultaneously with intensity, equivalent width, or profile changes, accurately measuring the magnitude of velocity shifts may be difficult even with long-term, high-quality, and high-sampling-rate spectral data [76{78].

Additionally, outflows undergoing acceleration may not necessarily show velocity shifts in their spectral absorption lines. For example, when our sightline passes through the main body of an outflow ejected perpendicular to the accretion disk [79], the portion of the outflow within our line of sight may be continuous and maintain constant velocity. In such cases, despite the outflow itself accelerating, the absorption lines appearing in the spectrum may not exhibit obvious velocity shifts [6, 80, 81].

4 Case Studies of Absorption Line Velocity Shifts

4.1 Early Sporadic Reports

Research on outflow absorption line velocity shifts began in the early 20th century, with initial studies focusing on individual sources. For example, Vilkoviskij and Irwin [72], Rupke et al. [73], and Hall et al. [63] reported outflow broad absorption lines with accelerations of 0.03(cid:24)0.1 cm/s^2 within 1(cid:24)5 a. In 2003, Gabel et al. [62] discovered the first case of decelerating narrow absorption lines, finding that C IV, Si IV, and N V narrow absorption lines in Seyfert galaxy NGC 3783 all showed deceleration over 9(cid:24)13 months. Subsequently, Gibson et al. [67] and Capellupo et al. [24] attempted to detect broad absorption line velocity shifts in small samples but found none. In 2019, Misawa et al. [82] conducted a 2.8(cid:24)5.5 a tracking study of intrinsic narrow absorption lines in six quasars, likewise finding no obvious velocity shift phenomena. Nevertheless, these studies provided methods and suggestions for understanding outflow absorption line velocity shift phenomena.

4.2 First Large-Sample Detection

In 2016, based on 140 broad absorption line quasars selected from the Sloan Digital Sky Survey, Grier et al. [59] reported the first successful large-sample search for broad absorption line velocity shifts. Although this sample was significantly larger than previous studies, the results identified only three broad absorption lines with velocity shifts, two showing acceleration and one deceleration, suggesting the rarity of broad absorption line velocity shifts.

Grier et al. [59] attempted to explain the origin of the two accelerating broad absorption lines using the classical disk-wind model. Using disk-wind model formulas from Murray et al. [6] and Murray and Chiang [83], they calculated the acceleration change rate of the outflow and found the results differed from measured values, particularly as the disk-wind model could not explain the large acceleration magnitude. Additionally, Grier et al. [59] derived the conclusion that within 2.5(cid:24)5.5 a, the average velocity variation of most broad absorption lines does not exceed 3% based on further screening of 76 C IV broad absorption lines.

4.3 X-ray Bright Quasar Discoveries

In 2014, Joshi et al. [50] detected deceleration of C IV broad absorption lines in two X-ray bright quasars. Within 3.11 a and 2.34 a, these two C IV broad absorption lines exhibited average accelerations of (cid:0)0:7 cm (cid:1) s (cid:0) 2 and (cid:0)2:0 cm (cid:1) s (cid:0) 2, respectively. They evaluated several mainstream velocity shift mechanisms to explain the measured values and, combined with the X-ray bright characteristics of these quasars, concluded that the movement of numerous small self-shielding clouds along curved trajectories provided the most reasonable explanation.

4.4 Coordinated Multi-line Velocity Shifts

In 2019, Joshi et al. [55] discovered deceleration in both C IV and Si IV broad absorption lines with identical redshifts in another X-ray bright quasar. Synthesizing their 2014 and 2019 studies, Joshi et al. summarized common features among these three sources: (1) decelerating components typically have high ejection velocities exceeding 10,000 km (cid:1) s (cid:0) 1; (2) other absorption lines without velocity shifts exist in lower velocity intervals of the spectra; (3) the optical continuum shows no significant changes. Furthermore, they noted that accelerated broad absorption line phenomena have not been observed in X-ray bright quasars. Verifying this finding in large samples will help us understand the physical origins of broad absorption lines in X-ray bright (or weak) quasars.

4.5 Highest Acceleration Case at the Time

Xu et al. [58] studied spectra of quasar SDSS J1042+1646 from 2011 and 2017, discovering velocity shifts in a broad absorption line. The velocity centroid of this broad absorption line changed from (cid:0)19,500 km (cid:1) s (cid:0) 1 to (cid:0)21,050 km (cid:1) s (cid:0) 1 within 3.2 a, representing a drift of approximately (cid:0)1,550 km (cid:1) s (cid:0) 1, corresponding to an acceleration of 1.52 cm/s^2. This was the maximum reported acceleration of absorption line outflows at that time. The velocity shift manifested not only in the separated double peaks of Ne VIII (cid:21)(cid:21)770.41, 780.32, but also in the O V (cid:21)629.73 and Mg X (cid:21)(cid:21)609.79, 624.94 absorption doublets. After excluding photoionization changes and absorbers moving in and out of the sightline as potential causes, Xu et al. attributed the velocity shifts to outflow acceleration.

4.6 Narrow Absorption Line Velocity Shifts

In 2020, based on two spectral observations of quasar SDSS J143530.49+142338.4, Yao et al. [57] reported for the first time a narrow absorption line system (including C IV (cid:21)(cid:21)1548, 1551 and N V (cid:21)(cid:21)1239, 1243) simultaneously showing increased equivalent width and velocity shifts. Given the significant weakening of the continuum, they speculated that changes in outflow ionization state might be one cause of the increased equivalent width of this absorption system. Yao et al. conducted preliminary analysis on the mechanism causing velocity shifts in this absorption system, but limited to only two SDSS observations, they could not yet provide a reasonable explanation.

4.7 Low-Ionization Broad Absorption Line Velocity Shifts

In 2020, Lu and Lin [56] discovered that Mg II and Al III broad absorption lines in quasar SDSS J134444.33+315007.6 underwent velocity shifts of approximately (cid:0)1,101 km (cid:1) s (cid:0) 1 and (cid:0)1,170 km (cid:1) s (cid:0) 1, respectively, within 3.21 a, representing the first report of low-ionization broad absorption line velocity shifts. Additionally, they identified other significant spectral changes, including notable continuum weakening, synchronous enhancement of multiple emission lines such as Mg II, C III, and Al III, and synchronous enhancement of three Al III absorption troughs. These features all indicate that background radiation energy significantly influenced the observations, leading to the inference that the broad absorption line velocity shifts likely originated from acceleration of the outflow along the line of sight caused by radiation pressure from the central source.

4.8 Highest Recorded Acceleration

In 2021, Aromal et al. [84] reported two distinct C IV broad absorption lines in a quasar, where the bluer broad absorption line accelerated while simultaneously showing equivalent width changes, while the redder broad absorption line exhibited complex profile changes. The two absorption components within the redder broad absorption line also showed acceleration and equivalent width changes, and their acceleration and equivalent width variations correlated with those of the bluer broad absorption line. The acceleration of the bluer broad absorption line between the second and third observations was (8.84(cid:6)3.62) cm (cid:1) s (cid:0) 2, the highest acceleration discovered in broad absorption line quasars to date.

4.9 First Case of Constant Acceleration

For sources with more than two spectral observations, comparing velocity shift values between each pair of observations reveals that the magnitude of velocity shift variation is not constant. For example, in Joshi et al.'s 2019 study [55], the deceleration rate of the C IV broad absorption line in quasar J092345+512710 measured between the second and fourth observations was approximately 1.4 times that between the first and second observations. Similarly, Grier et al. [59] found from three observations of quasar J012415.53-003318.4 that the average acceleration of the broad absorption line was 0.9 cm/s^2 between the first two observations but decreased to 0.37 cm (cid:1) s (cid:0) 2 between the latter two observations.

In 2024, Yi et al. [85] reported four low-ionization broad absorption line acceleration/deceleration candidates, finding that for three candidates, the broad absorption line acceleration increased sharply in the initial stage before leveling off. However, the remaining candidate showed a broad absorption line profile that remained essentially unchanged and exhibited a linear relationship between sampling interval and velocity shift across three consecutive spectral samplings, representing the first case of constant acceleration in a broad absorption line outflow. Recently, Wheatley et al. [60] also discovered non-constant outflow absorption line acceleration from 130 observations over 8 a of quasar SDSS J141007.72+541203.6.

5 Generation Mechanisms of Absorption Line Velocity Shifts

Currently, the physical mechanisms believed to cause broad absorption line velocity shifts mainly include the following [61{63]: (1) real acceleration or deceleration of outflows; (2) changes in line-of-sight velocity as outflows undergo circular motion around the central massive black hole; (3) velocity shifts caused by changes in physical properties such as ionization state and column density of outflow material. However, these mechanisms have not obtained strong observational support, and theoretical predictions differ substantially from actual observational data.

5.1 Real Acceleration/Deceleration of Outflows

Acceleration/deceleration of absorbing clouds along radial directions under the gravitational influence of the central object may explain absorption line velocity shifts. To evaluate whether this mechanism can reasonably explain observed velocity shifts, researchers estimate the distance between absorbing clouds and the central source and compare their actual velocities with theoretical escape velocities. For example, Joshi's team [50, 55] studied three velocity shift cases and found that theoretically estimated outflow escape velocities were far lower than the observed velocity shift rates, thus ruling out gravity-dominated outflow acceleration/deceleration. It should be noted that accurately estimating the distance between absorbing clouds and quasars requires high signal-to-noise ratio, high-resolution spectral data covering multiple ions.

Researchers also employ other methods to infer whether velocity shifts originate from real outflow acceleration/deceleration. For instance, Lu and Lin [54, 56] analyzed C IV broad absorption line acceleration in quasar J1208+0355 and Mg II and Al III broad absorption line acceleration in quasar J1344+3150, discovering that these broad absorption lines showed coordinated enhancement of equivalent width, significant continuum weakening, and emission line enhancement simultaneously with velocity shifts. These features indicate that outflows in these sources may be influenced by central source radiation, leading to the inference that their broad absorption line velocity shifts likely originated from outflow acceleration driven by central source radiation.

When analyzing spectral data of quasar J1042+1646 from 2011 and 2017, Xu et al. [58] also discovered velocity shifts in a broad absorption line. After excluding photoionization changes and absorbers moving in and out of the sightline as explanations, they attributed the observed velocity shifts to outflow acceleration.

5.2 Curvilinear Motion of Outflow Material Crossing the Line of Sight

During curvilinear motion of outflow material, deflection of its movement direction may cause changes in the line-of-sight velocity of absorption lines. In this scenario, the measured absorption line velocity shift value actually represents only the change in the line-of-sight velocity component of the outflow material (see Figure 3 [FIGURE:3] in reference [62]).

For example, Joshi et al. [50] discovered velocity shifts in C IV broad absorption lines in two X-ray bright quasars (J0855+3757 and J0911+0550) and concluded that such velocity shifts could be reasonably explained by the curvilinear motion of outflows. Their conclusion was based on estimates that these outflows' motion paths were sufficiently curved to produce the measured velocity shift values (217 (cid:24) 620 km (cid:1) s (cid:0) 1 (cid:1) a (cid:0) 1).

5.3 Changes in Physical Properties of Outflows

Changes in the ionization state of the quasar central source can trigger changes in physical properties such as ionization state and column density of outflow material, manifesting spectrally as absorption line intensity changes and possible accompanying velocity shifts. Wheatley et al. [60] clearly demonstrated how changes in parameters (center/width/amplitude) of two subcomponents of a broad absorption line affect measurements of the entire broad absorption line's center (see Figures 12 [FIGURE:12] and 16 [FIGURE:16] in that reference).

Photoionization models [44] can serve as auxiliary tools to determine whether absorption line intensity changes originate from central source ionization state changes. For example, Joshi et al. [50] attempted to use photoionization models to analyze the cause of C IV broad absorption line intensity changes in quasar J0911+0550. In the photoionization model, the absence of Si IV or N V absorption lines in all five observational spectra could infer that this C IV absorption line was in a stage where it would strengthen when the central source's ionization degree decreased. However, Joshi et al. [50] obtained results from the spectra showing that both the continuum and C IV absorption line weakened; therefore, they excluded photoionization changes as the cause of this C IV absorption line intensity change, indirectly ruling out photoionization changes as the cause of its velocity shift.

Similarly, Xu et al. [58] studied quasar SDSS J1042+1646 and found a broad absorption line that underwent a velocity shift of approximately (cid:0)1,550 km (cid:1) s (cid:0) 1 within 3.2 a. They hypothesized that this change was not caused by outflow acceleration but by photoionization changes. In this mechanism, absorption line changes are explained by variations in quasar ionization. To explain the appearance and disappearance of these two stationary outflows, significant changes in the quasar's ionization state between the two observations would be required (detailed ionization state analysis process see Section 5.1 in reference [58]). However, four other absorption lines in the two spectra of this quasar showed no changes during this period, including some unsaturated doublets; thus Xu et al. excluded photoionization changes as the explanation.

5.4 Geometric Projection Effects from Accretion Disk Rotation

Accretion disk rotation produces geometric projection effects. If broad absorption line material is assumed to be emitted from a rotating accretion disk, then as the accretion disk rotates, the projected position and velocity of the absorbing material in the observer's line of sight will change. This variation can cause observed broad absorption lines to exhibit velocity shift phenomena [86]. Grier et al. [59] attempted to explain the acceleration/deceleration phenomena of broad absorption lines observed in three quasars using geometric projection effects. They analyzed the rotation period of accretion disk material to calculate the timescale over which broad absorption line acceleration or deceleration could be observed; the results indicated that the accretion disk did not undergo significant rotation relative to the observer's line of sight during the observation period, making geometric projection effects from accretion disk rotation an unlikely cause of these broad absorption line velocity shifts.

6 Research Prospects

The above research progress reveals two major limitations in current studies of outflow absorption line velocity shifts: (1) empirical cases are scarce, with only 20 cases reported; (2) the physical mechanisms behind velocity shifts remain unclear, with mainstream mechanisms lacking strong observational support. Based on these deficiencies, this paper proposes the following prospects for future research directions in this field.

6.1 Expanding Repeated Observation Samples

As shown in Table 1, currently only 20 cases of velocity shifts have been discovered. Such a small number of empirical cases limits further research on velocity shifts. Fortunately, we are in an era of rapidly developing survey projects. For example, the Sloan Digital Sky Survey (SDSS) has released spectral data for over 750,000 quasars by its 16th data release. China's Guoshoujing Telescope (LAMOST) survey has also observed more than 70,000 quasars. Quasars with repeated observations in large survey projects such as SDSS and LAMOST can form large samples for searching broad absorption line velocity shifts.

Grier et al. [59] conducted the only successful search for absorption line velocity shifts from a relatively large sample to date, but they limited their study objects to quasars observed at least three times, which greatly restricted the search scope and resulted in only three velocity shift cases from 140 quasars. Of course, Grier et al.'s goal was to screen outflow acceleration candidates rather than simply find cases with velocity shifts, so setting strict screening criteria was reasonable. However, to discover more velocity shift cases, we recommend expanding the search scope to include quasars with only two observations. Searching for velocity shift candidates first from quasars with only two observations and then conducting multiple high-resolution observations of these candidates would have a relatively higher success rate compared to searching directly from samples with at least three observations, helping to construct a statistically meaningful sample of broad absorption line velocity shifts.

6.2 Comprehensive Study with Line-Locking Features

The line-locking phenomenon is a concept proposed based on the Doppler effect of absorption line gas clouds, where two outflow absorbers move parallel to the line of sight with a velocity difference consistent with the spacing of specific ion doublets [87{89]. Studying this phenomenon is crucial for understanding the physical mechanisms of radiation-driven outflows in quasars and is therefore considered a unique signature of radiation-driven outflows [88, 89]. However, how radiation-driven mechanisms cause line-locking phenomena remains unresolved. Researchers have attempted to explain the origin of line-locking phenomena through models: (1) Scargle proposed the "S73 model" [88]; (2) Braun and Milgrom proposed the "BM89 model" [89]. However, neither model has received strong support from observational data [90, 91]. The S73 model is a steady-state model requiring nearly equal outward and inward forces in the line-locking system [88], which means no velocity shifts would occur; the BM89 model is a non-steady-state model that does not require equal forces but only requires that the acceleration differences between "locked" subcomponents remain nearly constant. Therefore, according to the BM89 model, absorption lines showing line-locking may accompany velocity shift phenomena [89]. If we search for velocity shifts while simultaneously identifying line-locking observational features, we can test the S73 and BM89 models and reveal the physical mechanisms of radiation-driven outflows.

6.3 Integration with Variability Characteristics

Analyzing equivalent width variability of quasar absorption lines plays a non-negligible role in studying outflow spatial distribution, velocity structure, and ionization structure [19, 33, 92]. Equivalent width variability of quasar absorption lines is a common observational characteristic of quasars [38, 71, 91, 93{99], with current understanding suggesting two main mechanisms: (1) absorbers moving across the line of sight [26]; (2) changes in absorber ionization state [34]. Both mechanisms provide valuable clues for understanding outflow origins [26, 34, 39] and are important for investigating outflow physical conditions. For instance, under the first mechanism, we can use broad absorption line variability timescales to constrain the distance between absorbers and the central black hole [52, 53]; under the second mechanism, we can set the variability timescale as an upper limit on the recombination timescale of outflow gas, thereby calculating a lower limit on absorber density.

Studies based on SDSS quasar spectral samples [38, 93, 95, 96] have found that absorption line equivalent width changes exhibit a significant anti-correlation with quasar UV continuum changes. This discovery indicates that most equivalent width changes result from absorber ionization state responses to central source variability.

Furthermore, He et al. [19] utilized a spectral sample of nearly 1,000 quasars from SDSS to conduct an in-depth investigation of outflow scales and kinetic luminosity distributions. This research revealed the tremendous potential of using absorption line equivalent width variability to determine outflow scales. Therefore, research methods combining absorption line velocity shifts with variability characteristics will provide new perspectives and tools for deeply understanding outflow origins, acceleration processes, and impacts on galaxy evolution.

7 Summary

This paper reviews research progress on quasar absorption line velocity shifts from four aspects: detection methods, search challenges, case studies, and generation mechanisms. Related research is beneficial for revealing outflow structure, location, dynamic characteristics, and the complex physical environments within quasars.

Current understanding of broad absorption line velocity shifts remains limited. First, the severe scarcity of empirical cases restricts research on this phenomenon, with only 20 cases reported to date. Second, although several physical mechanisms have been proposed to explain velocity shifts, all lack sufficient observational support.

Based on these deficiencies, this paper proposes prospects for future research directions on quasar absorption line velocity shifts. With the accumulation of quasar survey observational data and technological advancements, we anticipate that research on absorption line velocity shifts can be further expanded and deepened, providing not only more data support for quasar outflow dynamic models but also new clues for revealing complex physical processes within quasars. Ultimately, progress in this field will help us understand the essential laws of quasar evolution more comprehensively and profoundly.

We sincerely thank the two reviewers for their careful review and valuable comments, which have improved both the writing quality and content completeness of this paper.

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