Quasar Winds Caught on Acceleration and Deceleration

We present an observational study of wind acceleration based on four low-ionization broad absorption line (BAL) quasars (J0136, J1238, J1259, and J1344). J0136 and J1344 (group 1) are radio-quiet and show large BAL-velocity shifts as opposed to stable line-locking associated absorption lines (AALs). Notably, J1344 displays a linear relation between BAL-velocity shift and time interval over three consecutive epochs, characteristic of compelling evidence for BAL acceleration. J1238 and J1259 (group 2) exhibit small BAL-velocity shifts along with steep-spectrum, weak radio emission at 3.0 and 1.4 GHz. All four quasars have spectral energy distributions (SEDs) with a peak at λ rest ∼ 10 μm, suggesting a link between the BAL acceleration and hot dust emission. The group-2 quasars are redder than group-1 quasars and have a steeper rise at 1 μm < λ rest < 3 μm in their SEDs. All but J1238 exhibit a steep rise followed by a plateau-like time evolution in BAL-velocity shift. Our investigations, combined with previous studies of BAL acceleration, indicate that (1) the coupling process between the BALs and the interstellar medium (ISM) is one of the major avenues for the origin of quasar reddening and patchy obscuration, (2) AAL outflows are ubiquitous and likely signify large-scale remnants of BAL winds coupled to the ISM, and (3) wind deceleration that is closely linked to the BAL–ISM coupling process may produce weak radio emission in otherwise radio-quiet quasars.


INTRODUCTION
Broad absorption line (BAL; Weymann et al. 1991) features imprinted on quasar spectra are unambiguous evidence for intrinsic outflows, whose kinetic power could be sufficient for triggering active galactic nuclear (AGN) feedback and hence control the growth of supermassive black holes (SMBHs; Fabian 2012).BAL winds are believed to be launched from the accretions disks that have a typical size of ∼0.01 pc if driven by a SMBH with ∼ 10 9 M ⊙ (Murray et al. 1995;Proga et al. 2000).Observationally, however, many studies suggest that the vast majority of BAL winds are likely to be located at a range of ∼1-1000 pc from their SMBHs (e.g., Capellupo et al. 2011;McGraw et al. 2017;Arav et al. 2018;He et al. 2019).Therefore, probing inner physics of BAL winds, such as the acceleration mechanisms and the impact on ISM, has become a topic of increasing interest.
BAL quasars are divided into two major classes, namely high-ionization BAL (HiBAL) and low-ionization BAL (LoBAL) quasars (e.g., Weymann et al. 1991;Trump et al. 2006).A bona fide BAL is characterized by an absorption trough, whose width is broader than 2000 km s −1 under 90% of the continuum level with a minimum line-of-sight (LOS) velocity of > 3000 km s −1 (Weymann et al. 1991).To form such remarkable absorption features, acceleration of BAL winds must somehow play a role during the lifetime of BAL quasars.Grier et al. (2016) conducted the first systematic investigation of BAL acceleration, from which they found only 2 out of 140 quasars showing solid evidence of BAL acceleration.Such a low incidence (∼1.43%) of BAL acceleration is likely underestimated since their work is based on the search for monolithic velocity shifts across the entire BAL trough over multiple spectroscopic epochs.Nevertheless, one would expect from a sample of ∼100,000 BAL quasars (Lyke et al. 2020) that a fairly large number of objects could be caught on BAL acceleration even with an incidence of ∼1.43%.Hall et al. (2007a) reported one of the first cases of a quasar exhibiting BAL-acceleration signatures, whose average acceleration magnitude is consistent with that estimated from a longer-time sampling interval in a subsequent study (Byun, Arav, & Hall 2022), although more data are needed before drawing a firm conclusion of BAL acceleration.This point is particularly true when notic-Yi et al.
ing the "jerk" phenomena of BAL acceleration; that is, the change in acceleration with time (e.g., Capellupo et al. 2011;Filiz Ak et al. 2013;Rogerson et al. 2016;Grier et al. 2016).For example, Rogerson et al. (2016) identified a quasar showing BAL emergence at two widely separated velocities.Specifically, trough A showed a fluctuating velocity centroid due to trough profile variability; however, trough B showed an increasing outflow velocity over three epochs, which if confirmed to be acceleration would represent rest-frame 16 and 55 cm s −2 between the 1st & 2nd and 2nd & 3rd epochs, respectively.Simple radiative acceleration models can match such values at small radii (see their section 4.1.2),but would have to invoke strong ionizing continuum variability to explain such large changes in acceleration.Similarly, Aromal, Srianand, & Petitjean (2021) reported a quasar having two distinct BAL troughs, one of which is consistent with BAL acceleration along with variability in rest equivalent width (REW) while the other exhibits complex variations in profile.Recently, Xu et al. (2020) argued for the largest BAL acceleration detected in a quasar, despite with only two sampling-epoch spectra.Perhaps a more ambiguous example for acceleration is NGC 3783, a local AGN that has been extensively studied from nearly two decades of high spectral resolution observations, for which Gabel et al. (2003) proposed an explanation of radial deceleration; however, this argument appears to be increasingly uncertain in later studies (e.g., Scott et al. 2014;Kriss et al. 2019).
Another major difficulty for the analysis of BAL phenomena is the prevalence of BAL-profile variability among BAL quasars.As introduced above, time variability has become a widely used tool for probing the formation, acceleration, and evolution of BAL winds, due primarily to the fact that the vast majority of quasars and their host galaxies cannot be spatially resolved by current instruments.Generally, well-separated, multi-epoch spectroscopy is a powerful technique for identifying genuine BAL acceleration cases and for placing valuable constraints on the BAL physics, lifetime, and location (e.g., Aromal, Srianand, & Petitjean 2021;Yi et al. 2022).In reality, however, BAL acceleration and BAL-profile variability may occur simultaneously, making a firm identification of BAL acceleration difficult or sometimes impossible, even with the aid of long-term, high-quality, and high-cadence sampling spectra (e.g., Kriss et al. 2019;Yi & Timlin 2021;Byun, Arav, & Hall 2022).This situation can be easily understood given the complex nature of BAL winds typically characterized by many subflows that are independent from each other and vary stochastically.Regarding the analysis of BAL acceleration, another three facts are needed to be taken into account.First, the majority of BAL quasars have not been spectroscopically observed more than three times, rendering any attempts at identifying genuine acceleration difficult.Secondly, BALs may be transient during the spectroscopic monitoring time.Thirdly, the decomposition of a complex, seemingly single BAL trough is notoriously difficult due to blending and/or partial covering along our LOS.Nevertheless, genuine BAL acceleration or deceleration events may provide unique insights into the origin of quasar reddening and weak radio emission, an interesting yet open question invoked by recent studies (e.g., Klindt et al. 2019;Calistro Rivera et al. 2021).
In this work, we conduct a systematic analysis of BAL acceleration from the LoBAL variability sample in Yi et al. (2019) and the HiBAL acceleration sample in Grier et al. (2016), from which we identified 4 BAL-acceleration quasars.The first two (and in one case four) epochs of spectroscopic observations of the four quasars were performed in various phases of the Sloan Digital Sky Survey (SDSS; York et al. 2000;Eisenstein et al. 2011;Blanton et al. 2017) and were accessed from the SDSS public database.Additional observations were obtained with a variety of other facilities (see Section 2.2).The new data were designed to systematically investigate LoBAL acceleration and to bridge the gap over HiBAL acceleration.We emphasize that (1) all time intervals are in the quasar rest frame; (2) the term "acceleration" refers to either actual acceleration or deceleration unless stated otherwise; (3) velocity or kinematic shift, by definition, is a relative quantity and does not depend on the accuracy of systemic redshift; and (4) zero velocity is converted by the shorter-wavelength component of each doublet at systemic redshift throughout this work.

Candidate selection
We began with the selection of BAL-acceleration candidates from the LoBAL-variability sample in Yi et al. (2019), where a few quasars were found to show apparent velocity shifts within the sampling epochs.Following Grier et al. (2016), we first searched for quasar candidates of BAL acceleration from Yi et al. (2019) by requiring monolithic velocity shifts in BAL profile over at least three spectroscopic epochs for each quasar.However, none of the quasars from that work satisfy the requirement, probably because (1) the majority of quasars from Yi et al. (2019) have been observed only two times, (2) the occurrence of BAL acceleration is intrinsically rare, (3) BAL-profile changes are ubiquitous as reported in previous studies, and/or (4) it is impossible to assess BAL acceleration from BAL-transient events without sufficient sampling epochs before its disappearance.
Unfortunately, we did not find any quasars with three or more different-epoch spectra from Yi et al. (2019) that displayed monolithic BAL shifts, i.e., they often exhibit large BAL-profile changes and pose great challenges to ascertain the origin of their BAL variability.Therefore, we then searched for monolithic velocity shifts among these quasars having only two different-epoch spectra and found three candidates, namely SDSS J134444.32+315007.6,SDSS J123820.19+175039.1,SDSS J125942.79+121312.6 (hereafter J1344, J1238, J1259) meeting the requirement.We also add the strongest BAL-acceleration candidate, namely SDSS J013656.31−004623.8 (hereafter J0136), from Grier et al. (2016) into our final BAL-acceleration list, due partly to the presence of LoBAL species which was mentioned only in passing in that work.
The early-epoch spectra of the four BAL-acceleration candidates are retrieved directly from the SDSS DR16 archive (see Lyke et al. 2020); in addition, we also quantify the variability both in the Mg ii-BAL and continuum shape for J0136 following the same prescription in Yi & Timlin (2021).Interestingly, like the six quasars reported in Yi & Timlin (2021), J0136 is also undergoing a LoBAL→HiBAL transformation along with a decrease of dust; in stark contrast, the other three BAL-acceleration candidates having small fractional REW changes become redder in later epochs.Below we illustrate them in detail with the aid of archived multi-wavelength photometry and new spectroscopic observations.

New observations
To facilitate the assessment of BAL acceleration, we placed these objects into the target list of our spectroscopic monitoring campaign of subsequent BAL variability for individual quasars of interest.We obtained additional optical spectra for these quasars using the Low-Resolution Spectrograph-2 (LRS2; Chonis et al. 2014) mounted on the Hobby-Eberly Telescope (HET; Ramsey et al. 1998).These newly obtained spectroscopic data were processed with the LRS2 pipeline9 , which incorporates an improved procedure for flux calibration with a typical uncertainty of ∼15% (Hill et al. 2021).Long-slit (2.5 ′′ in width) spectra were mainly acquired by the Yunnan Faint Object Spectrograph and Camera (YFOSC) mounted on the Lijiang 2.4 m Telescope (LJT;Fan et al. 2015;Wang et al. 2019).We also obtained another longslit (1.0 ′′ in width) spectrum for the faintest quasar J1259 using the multi-object double spectrographs (MODS) mounted on the Large Binocular Telescope (LBT), which covers a wide wavelength range of 0.33-1.03µm.These long-slit data were processed using standard IRAF routines, including bias subtraction, flat field correction, cosmic ray removal, spectral extraction, wavelength identification, and flux calibration.
Near-IR spectroscopic observations were performed with the TripleSpec spectrograph at the Palomar Hale 200 inch telescope (P200/TripleSpec; Wilson et al. 2004) for J0136 and J1238.TripleSpec provides a wide wavelength coverage (0.95-2.46 µm) at an average spectral resolution of ∼ 2700, allowing simultaneous observations in the J/H/K bands.A slit width of one arcsecond and the ABBA dither pattern along the slit were chosen to improve the sky subtraction during the observations.We carefully examined the data quality flags and wavelength calibration in each epoch for each quasar, and did not find significant instrumental artifacts from the spectral regions of interest.
The log of observations are summarized in Table 1 and the multi-epoch optical spectra of each candidate are presented in Fig. 1 for an overall view.

OF BAL ACCELERATION
Following a similar procedure from Yi et al. (2019), we first model the local continuum of interest by fitting a reddened power-law function to the relatively line-free spectral regions identified through visual inspection for each quasar.The BALs and BELs are then normalized by the fitted continuum from each epoch for each quasar.Finally, the quantities such as REW are measured by the continuum normalized spectra over the epochs, which allow us to quantify the BALs and BELs and the related time variability therein for each quasar.
We highlight that the REW alone may fail to quantify BAL variability, especially in cases where BALs show velocity shifts over different epochs but lack significant changes in their profiles, leading to an approximately equal REW for the two BALs chosen from two different epochs.This issue must be addressed before performing a further analysis of BAL acceleration, given that one would naturally expect to see velocity shifts of the BAL over multiple epochs from BAL-acceleration candidates.Therefore, it is mandatory to examine the BAL-profile variability in detail and, whenever possible, to identify independent or correlated BAL subflows from epoch to epoch for each quasar.Such an investigation is important given the diversity of BAL-profile variability that may reflect different-velocity components in a single BAL trough arising from largely different physical regions (e.g., Arav et al. 2015;Yi et al. 2019;Yi & Timlin 2021).This is also one of the most challenging issues for the analysis of BAL variability.
Ideally, high-resolution and high-S/N spectroscopy can provide powerful diagnostics to probe the detailed variability for a given BAL trough, but in reality it is almost impossible to obtain multi-epoch, high-resolution spectra for the majority of quasars given their faint apparent magnitudes.We circumvent this challenge by taking advantage of well-separated, intermediate-resolution spectra for each quasar selected.All but the LJT/YFOSC spectra displayed below are smoothed by a 3-pixel Boxcar filter (∼ 200 km s −1 ) for optimal visual inspection.

The criteria of BAL acceleration
As mentioned in the Introduction, identifications of BAL-acceleration events from apparent velocity shifts are often challenging due to the complex nature of BAL winds.This issue can be alleviated to some extent by placing stringent criteria to select BAL-acceleration candidates (Grier et al. 2016); however, the requirement of a monolithic shift for BAL acceleration in their work, such that the entire BAL trough is clearly shifted but remains generally unchanged in profile, could potentially miss cases of genuine BAL acceleration, given the prevalence of BAL-profile variability both on long and short timescales (e.g., Capellupo et al. 2011;Yi et al. 2019;Hemler et al. 2019).To further mitigate this issue and search for potentially more BAL-acceleration cases, we require three prerequisites: (1) at least three different epochs spanning more than one rest-frame year are required for a quasar, (2) the BAL of interest is similar in profile and has an overlap in velocity from epoch to epoch, and (3) the BAL of interest must be free of strong overlapping absorption produced by different ions.Based upon the above preconditions, we classify tentative, strong, and compelling cases of BAL acceleration using the following criteria.
1. Tentative case: the entire BAL trough of interest is characterized by a monolithic velocity shift, or the same BAL subflow is persistent and shows a velocity shift over multiple epochs.
2. Strong case: the BAL velocity exhibits a monotonic change over at least three consecutive spectroscopic epochs.
3. Compelling case: in addition to criterion-2, the measured velocity shifts fall into the same linear relation with time interval.
Following the prescription of Grier et al. (2016), we perform a cross-correlation function (CCF) analysis to measure the monolithic velocity shift between two different epochs for a BAL of interest.Specifically, we run the cross-correlation analysis for each of the 10000 iterations via a Monte Carlo approach (see the bottom-left panel of Fig. 2).
Then, we adopt the median of these cross-correlation peaks as the best velocity shift, with an error bar depicting the 90% percentile confidence level.We also performed a similar analysis (Monte Carlo simulations) for the BAL of interest using the reduced χ 2 12 (see Yi et al. 2019 for its definition).This exercise found that the velocity shift and uncertainty are in excellent agreement with those derived by the CCF analysis.For simplicity, we adopt the CCF analysis as a standard routine to measure the BAL-velocity shifts and to quantify their uncertainties.We identified one compelling, one strong, and two tentative cases of BAL acceleration based on the above criteria.
3.2.J1344: a case with compelling evidence for BAL acceleration J1344 is one of the quasars having two distinct BALs from the sample of Yi et al. (2019); moreover, one of the BALs contains a variable region based on the measurements from the two different-epoch SDSS spectra as recorded in the catalog.A subsequent analysis of this quasar using the two SDSS spectra was performed by Lu & Lin (2020), where they found large velocity shifts traced by both Al iii and Mg ii for the high-velocity BAL, and hence speculated that it could be associated with actual BAL acceleration.However, as mentioned above, at least three spectroscopic epochs are required to assess the possibility of BAL acceleration in a robust manner.To achieve this goal, we have obtained three additional spectra by HET/LRS-2 and LJT/YFOSC.Although the YFOSC spectrum at MJD=58224 has a low spectral resolution and signal-to-noise ratio (S/N), a reliable velocity shift can be measured via the CCF approach; moreover, it is helpful for visual inspection and can be used for flux calibration of the HET/LRS-2 spectrum obtained at MJD=58489, when assuming that there is negligible variability in continuum over such a short time interval.In combination with the well time-separated optical spectra spanning nearly two decades, we can now investigate BAL acceleration in a robust manner for this quasar.One can see from Fig. 3 that there are some interesting features from the normalized spectra: (1) The high-velocity BAL-1 and low-velocity BAL-2 are detected in Mg ii, Al iii, and C iv over the sampling epochs; (2) The BAL-1 profiles are similar over the epochs either in Al iii or Mg ii except for small changes in trough depth; (3) The BAL-1 velocity increased monotonically from MJD=53503 to 58224 and then appears to level off or perhaps decelerate after that epoch; (4) The Mg ii BAL-2 remains unchanged in trough depth over the epochs, despite a large increase in trough width and a slight increase in centroid velocity; (5) A third Al iii BAL with v LOS ∼ −11000 km s −1 is significantly detected only at MJD=56363, for which we cannot assess its variability in detail.
Using the first epoch spectrum as a benchmark, we separate the five epochs into four time intervals in an ascending order.To measure the velocity shifts in a robust manner, the Mg ii BAL-1 that has a higher S/N than the corresponding Al iii BAL-1 is treated as the main tracer for the cross-correlation analysis.The measured velocity shifts are 1120 +70 −260 , 1780 +360 −60 , 1670 +200 −65 , 1650 +260 −130 km s −1 over the four intervals via this method.Similarly, performing a CCF analysis to the Al iii BAL-1 yields 980 +230 −430 , 1620 +390 −390 , 1570 +230 −330 , 1410 +400 −260 km s −1 for the four time intervals, respectively (see the MJD vs. ∆v LOS panel in Fig. 3).The velocity shifts derived by the two different methods are consistent within the error bars, reinforcing the argument for BAL acceleration.In combination with the same linear relation over the two consecutive time intervals before MJD=58224, we believe that the observations provide compelling evidence for BAL acceleration.On the other hand, by closely examining the Al iii BAL-1 profiles, we identified the same subflow with three absorption peaks presumably linked to three different-velocity, blueward components of Al iii doublets from the three spectra with relatively high S/N (see left subpanels of Figure 3 for details).This identification is further supported by blueward components of Mg ii doublets at the same velocities corresponding to the Al iii BAL-1 subflow in each epoch (see the vertical dotted lines in Figure 3), although a shorter-velocity split of the doublet in Mg ii than in Al iii makes it somewhat uncertain.Notably, the velocity shifts traced by the subflow are in excellent agreement with those derived from the entire BAL via the CCF method over the three epochs, reinforcing the argument for acceleration.
For the analysis of BEL variability, a velocity range of −2600 < v LOS < 2500 km s −1 is chosen to characterize their core-emission features based on visual inspection of the C iv, Al iii, and Mg ii BELs.Note that Fe ii emission contributes only slightly to the core portion of the Mg ii BEL.Surprisingly, the Al iii BEL nearly disappeared by MJD=59384 while the Mg ii BEL varied only slightly in fractional REW over the epochs.In addition, the C iv BEL experienced a sharp drop in REW after MJD=58224.Such dramatic variability of C iv BEL has been rarely reported (Ross et al. 2020).
Regarding the evolution of BALs, it is clear that the BAL-1 and BAL-2 REWs exhibit an overall opposite time-variability pattern after MJD=56363 (see the REW vs. MJD panel in Fig. 3), which may be related to transverse motions caused by multiple streams moving across our LOS or acceleration/deceleration events (see Section 5).Interestingly, the Al iii BAL-1 and BEL be-come weakened after MJD=56363, while the Al iii BAL-2 and BEL show an opposite time-variability trend in REW after MJD=56363 (see the MJD vs. REW panel of Fig. 3), suggestive of the BEL having a stronger link to BAL-1 in Al iii.To provide additional diagnostics for the analysis of the observed BAL/BEL variability, we added a panel of MJD vs. f 1700 (the continuum flux at λ rest = 1700 Å) to Fig. 3 for comparison.Clearly, the time-variability pattern of f 1700 is opposite to those of the BALs/BELs from MJD=53503 to 56363, such that the BALs/BELs strengthened when the continuum f 1700 dimmed by a factor of ∼2; in addition, the BAL-1 and BELs (in Al iii and Mg ii) show a similar time-variability trend to that of f 1700 after MJD=56363.Conversely, f 1700 Å and velocity shift (∆v LOS ) exhibit an opposite time-variability pattern before MJD=58224; in addition, the BAL-1 and BAL-2 show an opposite time-variability pattern in trough width at the 95% continuum level (w 95 ) over the five epochs.Implications of these observational results will be discussed in Section 5.
3.3.J0136: a case with strong evidence for BAL acceleration J0136 was considered the strongest candidate of acceleration in Grier et al. (2016) based on the analysis of the C iv BAL profiles over different epochs.But the Al iii BAL was mentioned only in passing in their work due to its shallow depth.Through a careful examination of the different-ion absorption features in velocity space, we found that this BAL absorber consists of Si iv, C iv, Al iii, and Mg ii.However, we did not explore Si iv in this work as it lies at the CCD blue edge.The Mg ii absorption was detected only in the first two epochs and completely disappeared in later epochs.Such a phenomenon, in which lower-ionization BAL species disappear faster than higher-ionization BAL species at the same velocity, has been also reported in other quasars from the literature (see Wang et al. 2015;Yi & Timlin 2021).
Through a detailed comparison between the C iv and Al iii BALs over five epochs, we identified a number of interesting properties.(1) The centroid velocity of the Al iii BAL increases monotonically with time, such that the velocity shifts relative to MJD=55,444 are −690±70, 210±70, and 230±70 km s −1 over the three time intervals (see cyan squares from the MJD vs. ∆v LOS panel in Fig. 4 .Left: Continuum-normalized spectra of the group-1 quasar J0136 over five epochs.The comb-like symbol, again, indicates a line-locking feature in C iv. Right: MJD vs. velocity shifts of the C iv BAL relative to MJD=55444, REWs for the BALs and BELs, and continuum flux at λrest = 1700 Å, respectively, which depict the time-variability behaviors of these quantities.The C iv BAL profiles are identical (CCF coefficient >0.9) to that from MJD=55444 and the velocity shifts in each interval measured by the two different methods are consistent within measurement errors.The Mg ii was caught on the disappearance as opposed to the persistence of C iv from the BAL flow.
them.However, a full investigation of the BEL variability requires higher-cadence spectroscopic observations on longer timescales, which is beyond the scope of this work.
J0136 shows kinematic acceleration signatures traced by both the C iv and Al iii BAL troughs, in which the latter completely disappeared by MJD=59516 characteristic of a LoBAL→HiBAL transformation in tandem with the acceleration.Examining the MJD vs. f 1700 panel, the continuum flux density at λ rest = 1700 Å brightened by a factor of ∼2 during the BAL transformation, a variability pattern that was also reported in another LoBAL quasar undergoing the same transformation (Yi et al. 2022).However, the variability relation between velocity shift and continuum flux is unclear for J0136, given both the same and opposite trends observed over different time intervals, such that the largest velocity shift occurred in the interval with no or small-amplitude continuum variability, while the largest-amplitude continuum variability was detected in the interval having only a small velocity shift along with the Mg ii BAL disappearance.These results will be discussed in Section 5.
3.4.J1238: a case with tentative evidence for BAL acceleration The spectra of J1238 show that the Mg ii BAL profiles are closely similar to each other and contain at least three BAL subflows in each epoch (see the left panel of Fig. 5).Although each subflow may be composed of many Mg ii doublets, we are unable to identify them due to saturation, self-blending, insufficient spectral resolution, and potentially overlapping with Fe ii.The deepest two BAL subflows, at λ rest ∼ 2700 and ∼ 2735 Å, vary in depth and velocity from epoch to epoch, while the shallowest BAL subflow at λ rest ∼ 2650 Å appears not to change in depth.In addition, the He i* λ10830 BAL profile is closely similar to the Mg ii BAL trough except for trough depth (see Section 4.2).
The continuum flux density, however, increases monotonically with time over the four epochs as observed by the V -band magnitudes (see the black circles in the MJD vs. Mag panel of Fig. 5, in which the last two V -band magnitudes are converted from their ZTF-g/r magnitudes; see Jester et al. 2005).Interestingly, the Mg ii/He i* λ3889 BAL strength decreased/increased between MJD=54243 and 56035 while both increased between MJD=58198 and 59306, despite the increase of continuum flux over both intervals.Such complex BALvariability behaviors are consistent with previous studies that disfavor the pure ionization-change scenario (Mc-Graw et al. 2017;Yi et al. 2019).
In the analysis of BEL variability, one must keep in mind that the complex emission at 2750 < λ rest < 3000 Å appears to be dominated by Fe ii rather than Mg ii, given the generally unchanged Mg ii BEL as opposed to large variability in the Fe ii BEL at 2815 < λ rest < 2900 Å from MJD=54234 to 58198.Nevertheless, the Mg ii BEL profile is asymmetric and exhibits a blueshift relative to systemic redshift; in addition, the Mg ii BEL weakened dramatically from the first to last epoch, perhaps leading to the apparent increase of the Mg ii BEL blueshift.The Mg ii BAL and BEL show an overall opposite timevariability pattern, which will be discussed in Section 5 in conjunction with J0136 and J1344.
Compared to the BAL-1 in J1344, which exhibits a large kinematic shift over the rest-frame 6.6 years, the Mg ii BAL in J1238 has much smaller kinematic shifts (∆v LOS = −257 +60 −33 , +150 +220 −330 , −210 +67 −130 km s −1 ) relative to the first epoch over the three time intervals after performing the CCF analysis as demonstrated above, perhaps indicative of milder acceleration/deceleration events.The evidence for BAL acceleration remains tentative due to the low spectral resolution at MJD=58198.Alternatively, using the deepest BAL subflow, we found that its characteristic velocity has also experienced a decrease→increase→decrease process.These results support both acceleration and deceleration events occurring at least for the deepest BAL subflow, if not for the entire BAL trough.No clear relations, again, have been found between velocity shift (∆v LOS ) and continuum flux, in agreement with J0136.This variability behavior will be discussed in Section 5.
3.5.J1259: a case with tentative evidence for BAL acceleration As reported in the discovery paper from Hall (2007b), the optical spectrum of J1259 is notably characterized by Balmer absorption features, a rare phenomenon observed in BAL quasars.Since a BAL seen in a singlet like H9 is naturally expected to be narrower than that from a doublet like C iv, we treat these Balmer absorption features in J1259 as "BALs" throughout this work.Note that these Balmer troughs have an overlap to the Mg ii BAL in LOS velocity and at least the Hγ trough at MJD=58216 is consistent with a bona fide BAL.From subsequent studies of this quasar (e.g., Shi et al. 2016;Yi et al. 2019), significant variations were detected for both the Balmer and Mg ii BALs based on the analysis of the two SDSS spectra (MJD=53473 and 55983).Although Shi et al. (2016) proposed that BAL acceleration likely occurred in this quasar, evidence for acceleration remains lacking due to limited sampling epochs in their work.With the aid of additional four optical spectra obtained by HET/LRS-2, LJT/YFOSC, and LBT/MODS, we are now able to assess BAL acceleration in considerable detail by analyzing the similarities and differences among the six different-epoch (over ∼9 rest-frame yr) spectra for this quasar.
To alleviate contamination from telluric absorption and blending with other ions (for details see Hall 2007b;Shi et al. 2016) during the analysis, we choose to examine the H9 and Hγ absorption features since they consist primarily of a single ion with relatively high spectral S/N.It is obvious from Fig. 6 that the two BAL profiles varied most dramatically during the time interval from the first to second epoch, but changed only slightly over the later epochs.Therefore we adopt the second-epoch spectrum as the benchmark when applying the CCF analysis to this quasar.The CCF coefficient (ρ=0.74) is lowest for the epoch pair between MJD=53473 and 55983, consistent with our visual inspection that the Hγ BAL profile at the first epoch is somewhat apparently different from those at other epochs.In addition, we visually examine the absorption peaks across the two different-ion BAL troughs over the epochs, whose differences may trace the velocity shift when assuming the same BAL subflow persistent in each epoch.
The  among these Balmer lines, so it is used as a benchmark to search for absorption peaks and velocity shifts over the epochs for this quasar.In Fig. 6 the red vertical line indicates the peak absorption at the first epoch and is shown in the same column for easy comparison, while the peak-absorption positions are indicated by the blue vertical lines in the other five epochs.The Hγ absorption peak is consistent with that of the H9 BAL in each epoch.Therefore, using the deepest absorption feature as a characteristic velocity of the BAL absorber, we also found that the BAL velocity increases monotonically from MJD=53473 to 58601 and decreases slightly over the later two epochs, indicative of BAL acceleration and perhaps deceleration for this quasar.Quantitatively, the velocity shifts traced by the peak absorption of Hγ over the other five successive epochs are 657±70, 795±70, 1072±260, 806±70, 855±70 km s −1 relative to the first epoch.The last four velocity shifts are therefore 138±70, 415±260, 149±70, 198±70 relative to the second epoch, which are in agreement with those (173 +140 −70 , 410 +117 −117 , 242 +13 −69 , 311 +20 −69 km s −1 relative to the trough at MJD=55983) derived from the CCF analyses to all but the first-epoch spectra having an overall identical Hγ BAL profile as tested by the maximum CCF coefficient (ρ >0.9 vs. ρ =0.74).This result reinforces the argument for BAL acceleration.However, the above results provide only tentative evidence of BAL deceleration, due to a large uncertainty from the low-S/N, low-resolution spectrum at MJD=58601.
It is worth noting that the [O ii] emission line in J1259, at first glance, appears to have experienced a sudden disappearance at MJD=58894 and a reappearance at MJD=59308 (see Fig. 6).However, both the IFU data at MJD=58216 and 59308 reveal a similar one-sided, offnuclear [O ii] emission nebula with a projected size of ∼25 kpc (Yi et al. in prep).Therefore, a long-slit spectroscopic observation that was targeting the quasar core could make the [O ii] emission photocenter fall out of the slit with PA=328 • , leading to the apparent [O ii] disappearance from the long-slit, background-subtracted spectrum at MJD=58894.On the other hand, the [O iii] emission exhibits a blueshifted, broad-wing feature in each epoch, suggesting that some of the BAL winds may be closely linked to the forbidden-line outflows.A dedicated study, especially via spatially resolved 3D spectroscopy, would be valuable to gain unique insights into the origin of the giant [O ii] nebula; this effort is beyond the scope of this work.We briefly discuss the implications of these results in Section 5 after combining the other three quasars, particularly in the context of hot dust and weak radio emission.

An overall view of BAL acceleration
The two quasars from group-1 possess multiple BALacceleration signatures.J1344 is the most convincing example of BAL acceleration known to date, given that (1) the BAL profiles of interest are similar over the epochs except for differences in velocity shift; (2) the velocity shifts over each time interval measured by two different methods are approximately equal; (3) its largest BALvelocity shift in Mg ii (1780 km s −1 ) is much higher than the median value (98 km s −1 ) of positive velocity shifts + 3σ uncertainties from Table 4 2016) derived by the median values of velocity shifts + 3σ positive/negative uncertainties.J1344, J0136, and J1259 all show a similar trend, such that they have a steep rise followed by a plateau-like time evolution in BAL-velocity shift.
(see Fig. 7); and (4) most importantly, our data reveal the velocity shift in J1344 as a linear function of time interval over three well-separated, consecutive epochs, which is highly unlikely caused by BAL-profile variability and other random effects.For J0136 (another quasar in group-1), it has all but property-(4) listed above, which can be considered a less robust but still convincing example of BAL acceleration.
In contrast, BAL-acceleration signatures of the two quasars from group-2 are less convincing than those from group-1, due to smaller BAL shifts and the lack of wideseparation doublets such as Al iii that can be well resolved by the intermediate-resolution spectroscopy.The Mg ii doublet has a shorter-wavelength separation than Al iii and is often unidentifiable from a BAL trough due to saturation and blending with Fe ii.However, the group-2 quasars still have negative BAL-velocity shifts at a significant level relative to the measurement uncertainties (-260±70/-270±70 km s −1 for J1238/J1259); moreover, these negative shifts are almost 3 times higher than the median value (-102 km s −1 ) of negative velocity shifts -3σ uncertainties from Grier et al. (2016), supportive of BAL deceleration.Note that the smaller the BAL-velocity shift between two epochs, the greater the chance that the shift could be due to velocitydependent trough depth changes caused by ionization changes and/or transverse motions, and not bulk acceleration or deceleration.Table 2 provides an overall view of the spectral measurements.

The SED properties
This section explores the spectral energy distribution (SED) properties for each of the four quasars, with a particular attention focusing on variability of the restframe UV reddening between two different epochs.J0136 and J1344 are BAL-acceleration candidates without significant radio detections from FIRST, while J1238 and J1259 exhibit both BAL acceleration and deceleration signatures, along with weak radio emission and a much redder color as indicated by the W3/SDSS-i ratio.
Fig. 8 displays the SEDs of the four quasars, whose photometric data are retrieved from GALEX, SDSS,  2MASS, WISE, and FIRST sky surveys (see Lyke et al. 2020 and references therein).To highlight variability in the rest-frame UV continuum, we display the early/late epoch spectra in red/blue color for each quasar.In addition, the near-IR spectra obtained by P200/TripleSpec for J0136 and J1238 are flux-corrected by the photometric data from 2MASS and included in their SEDs for comparison.All the four SEDs have a peak at λ rest ∼ 10 µm; in particular, the group-2 quasars have a steeper rise of the SED shape than the group-1 quasars at 1 < λ rest < 3 µm.
J0136 is the only one among the four quasars undergoing a LoBAL→HiBAL transformation and becoming brighter/bluer in the rest-frame UV band in later epochs.Interestingly, such a time-variability trend is also seen in six LoBAL quasars that were caught on a LoBAL→HiBAL transformation (Yi & Timlin 2021); in particular, the C iv, Al iii, and Mg ii BAL-variability trends in J0136 resemble closely another LoBAL quasar (J0827) that was captured of shedding its dust cocoon, despite the emergence of a new C iv BAL in J0827 (see Figure 4 in Yi et al. 2022).Given the persistence of the BAL in J0136 and the LoBAL→HiBAL→non-BAL evolutionary path proposed in Yi & Timlin (2021), we argue that the SED of J0136 will become increasingly bluer/brighter, and ultimately like the vast majority of non-BAL blue quasars, peak at the rest-frame UV band as time passes.In contrast, J1344 is still in a LoBAL state and becomes conspicuously dimmer (a factor of ∼2) in the UV continuum over the later epochs, although it has an even larger BAL-acceleration magnitude than J0136 (1.14 vs. 0.74 cm s −2 ; see   VLASS and FIRST (star).The early/late epoch spectra are shown in red/blue for each quasar, complemented with a near-IR (cyan) spectrum if it exists.J0136 and J1344 (group-1) have BAL-acceleration signatures and are radio quiet; in addition, J0136 is undergoing a LoBAL→HiBAL transformation along with an increase of brightness over the epochs, while J1344 remains to be in a LoBAL state along with a decrease of brightness.J1238 and J1259 (group-2) exhibit BAL-acceleration/-deceleration signatures and weak radio emission, with f 3GHz /f 1.4GHz = 2.5/5.84mJy and 0.8/2.0mJy for the former and latter, respectively.The GALEX photometry for J1259 should be treated with caution given its large flag values.The median SED of red quasars from Calistro Rivera et al. ( 2021) is scaled to the W3-band.v LOS [km s 1 ] Figure 9. Left panels: The spectral fits (thick gray) to the Mg ii (bottom panel), Hβ and Hα (top panel) emission for J0136, which include the Fe ii (blue dotted), the broad Gaussians (orange), the narrow Gaussians (green), and the continuum fits (dashed).The BAL feature (green) was masked during the fit.The thin grey lines indicate spectral errors.The fits indicate that the FWHM (Mg ii) is ∼ 4650 km s −1 in broad emission as opposed to FWHM (Hβ) ∼ 2750 km s −1 , and that blueshifted emission/absorption features exist in Mg ii but not in Hβ, suggestive of the former being more affected by outflows.Right panels: The He i* λ10830 and λ3889 BAL profiles for J1238.For comparison, a subpanel of the Mg ii BAL profile is added over the four epochs, above which the He i* λ10830 BAL is displayed.Unlike the He i* λ10830 and Mg ii BALs having three major subflows, only one He i* λ3889 BAL feature was detected at v LOS ∼ −6000 km s −1 , whose strength remains generally unchanged over the epochs.are valuable to advance our understanding of the BAL nature, which will be discussed in Section 5 in conjunction with the multi-wavelength data at hand.

4.2.
Near-IR spectroscopy for J1238 and J0136 We have performed near-IR spectroscopic observations using the P200/TripleSpec for J1238 and J0136.The near-IR spectrum of J0136 at MJD=59503 exhibits strong Fe ii and weak Hβ emission (see left panels of Fig. 9).Following Yi et al. (2022), we use a model with two Gaussians and one Fe ii component to fit the Hα and Hβ lines.Our spectral fit reveals that the Hα/Hβ emission can be well fitted by two/one Gaussians, when their FWHMs are tied to each other and the Hα/Hβ flux ratio is constrained within a range between 2.9 and 3.5 for one set of the Gaussians during the fit.The Hβ FWHM of the broad-emission component is derived to be 2750 ± 120 km s −1 ; in addition, the Hα FWHM measured from a combination of the two broad Gaussians is 3200 ± 50 km s −1 , which is still narrower than that measured from the broad Mg ii emission (4650 ± 19 km s −1 ; see Table 3 for individual components) at MJD=55444.This difference is expected in the context of stratified structures of the BLR for the Mg ii and Hα emission, especially in the scenario where BAL winds are shaping the Mg ii-BEL profile (see an example from Yi et al. 2022).Indeed, our spectral fit to the Mg ii BEL reveals a blueshifted, narrow Gaussian that well characterizes the blueshifted-wing emission in Mg ii (also see Fig. 4 for a similar blueshifted feature over the other epochs), suggesting the presence of the Mg ii emission-line outflows and hence making it less robust than Hβ in the study of BLR physics.We caution that the Hα and Hβ FWHMs may be underestimated due to the CCD edge effect.
The near-IR spectrum of J1238 reveals a dramatic He i* λ10830 absorption feature aligning exactly with the Mg ii BAL trough in velocity space, whose kinematics is highly similar to the Mg ii BAL trough characterized by three major BAL subflows (see right panels of Fig. 9).However, the multi-epoch optical spectra indicate that the corresponding He i* λ3889 absorption is detected only for the BAL subflow at v LOS ∼ −6000 km s −1 and remains generally unchanged over the epochs, characteristic of an absorber with a partial covering factor in He i* and being more saturated than other subflows across the entire He i* BAL trough.Nevertheless, both the He i* and Mg ii troughs must be saturated to some extent, because theoretically the optical-depth ratio between He I* λ10830 and λ3889 for optically-thin gas is 23.3 (Leighly, Dietrich, & Barber 2011), whereas this ratio in the spectra of J1238 is only ∼6.5 from the velocity range where the λ3889 feature is seen, according to the apparent optical depth τ a (v) = ln[I 0 (v)/I obs (v)], where I 0 (v) and I obs (v) are the intrinsic and observed fluxes at velocity v, respectively.

Implications from joint analyses
The four quasars, especially from group-1, are promising candidates of BAL acceleration based on our analyses, although other possibilities may contribute secondarily to the BAL-velocity shift.They will be treated as actual BAL-acceleration quasars throughout the following sections to explore some of the key questions of quasar feedback, such as the driving force of BAL acceleration, the process of BAL winds coupling to ambient medium, and potentially observable imprints during the BAL-acceleration phase.Acceleration is the simplest and most straightforward interpretation for a monolithic velocity shift of a BAL seen from multi-epoch spectra, i.e., one would expect to see increasing/decreasing portions of the BAL blue/red wings in acceleration cases or decreasing/increasing portions of the BAL blue/red wings in deceleration cases.Below we explore the implications of BAL acceleration and then deceleration in conjunction with the multi-wavelength data at hand.

The driving mechanisms of BAL acceleration
One of the long-standing questions about BAL winds is the driving mechanism.Theoretically, BAL winds with LOS velocities beyond 5000 km s −1 are thought to be driven by UV radiation pressure on ionized gas within R ≲1 pc from the quasar center, when noticing that the typical SED of normal quasars peak at the UV band, despite some debates about the role of shielding gas (e.g., Murray et al. 1995;Proga et al. 2000;Hamann et al. 2019).This scenario is supported by observations and appears particularly true for LoBAL quasars, in that they are more likely X-ray weak and tend to possess softer ionizing SEDs than normal quasars (e.g., Trump et al. 2006;Gallagher et al. 2006;Hamann et al. 2019).
In addition to UV radiation-driven winds on small scales, IR radiation pressure on dust, e.g., via IR photon trapping and multi-scattering processes, may provide an additional force to accelerate ionized outflows on large scales, particularly when they are mildly optically thick to IR radiation and effectively coupled to dust (e.g., Costa et al. 2018).Other driving mechanisms, such as magnetic fields or cosmic rays, may be also at work or coexist with the above two forces for accelerating BAL winds, but we are unable to assess these possibilities using the current data.Therefore, throughout the discussion we will ignore them and focus only on the UV/IR radiation driven scenarios.
Unlike high-velocity, UV-radiation-driven disk winds that are thought to be launched at R ∼ 0.01 pc, IRradiation-driven outflows must exist on large-scale regions (R ≳ 1 pc) at which dust can survive; hence, relatively low-velocity (< 3000 km s −1 ) outflows and small acceleration magnitudes may be expected if driven solely by IR radiation (e.g, Roth et al. 2012;Faucher-Giguère & Quataert 2012;Costa et al. 2018).Recently, He et al. (2022) found from a small sample that BAL velocities appear to increase with galactocentric distances, from Yi et al. which they interpreted as UV-radiation-pressure on dust as the driving force of BAL acceleration, despite the lack of investigations in kinematic shift as adopted routinely in previous studies for acceleration and the unknown coupling efficiency between dust and gas in that work.Nevertheless, IR radiation pressure on dust can exert an additional force to a high-velocity BAL wind that is located at relatively large radii (e.g., R > 1 pc), leading to mild BAL acceleration as seen in group-2 quasars.
Although the IR-radiation-driven scenario offers a possible explanation for the rarity of BAL acceleration as reported in Grier et al. (2016), it appears difficult to explain the large BAL-acceleration magnitudes seen in the group-1 quasars.While the large BAL acceleration from group-1 is likely driven by UV radiation pressure at relatively small radii (e.g., R < 1 pc), the dust responsible for UV extinction/suppression may not be necessarily related to the presumably traditional torus with R < 10 pc; instead, dust could reside in a broad range of regions (e.g., Hamann et al. 2017;Temple et al. 2019;Calistro Rivera et al. 2021).Thus, whether a BAL wind, which is launched from its accretion disk, has reached a circumnuclear region or beyond is crucial for the discussion.A combined analysis of the BAL, BEL, and continuum time-variability behaviors can provide valuable diagnostics, which are discussed below.
One of the most striking differences between the two group-1 quasars is the opposite time-variability pattern in UV continuum flux, such that J0136/J1344 become brighter/fainter in later epochs.If UV radiation is the dominant driver for the observed BAL acceleration, one may expect to see a strong correlation between the continuum flux and BAL-velocity shift.Indeed, the largest velocity shift (acceleration) occurs in the time interval along with a decrease of UV continuum for both quasars (see Fig. 3 and Fig. 4); thus, the two quantities may always exhibit an opposite time-variability pattern during an acceleration phase or the variability in UV continuum may be only loosely coupled to the variability in the incident ionizing continuum seen by the BAL gas.In contrast, the two quantities appear to display an opposite variability behavior for J1259 in the interval from MJD=55983 to 58216 but a similar variability behavior in the interval from MJD=58216 to 58601.On the other hand, a much redder color in group-2 than in group-1, again, supports a different acceleration mechanism, such as radiation pressure on dust from a large-scale region.
For the group-2 quasar J1259, Shi et al. (2016) inferred from the two SDSS spectra that a BAL absorber is likely located at a distance of R ∼1 pc, on the basis of transverse motion as the cause of its BAL variability.This is also another reason for our caution in identifying any BAL acceleration based on only one spectroscopic pair.Suppose the same BAL absorber is persistent after the second epoch, one can see from the MJD vs. Mag panel of Fig. 6 that the ZTF-g band monotonically brightens while the ZTF-r band remains generally unchanged over the last four spectroscopic epochs.This result, at first glance, appears to be caused by the weakening Hγ trough after MJD=58216; however, it is difficult to explain the lack of significant variability in H9 (Fig. 6).We suspect that it may signal a substantial decrease of dust or a change of dust distribution/composition along our LOS, because it is possible that the kinematic sig-natures of BAL acceleration/deceleration in J1259 trace the coupling process between dust and gas, i.e., radiation pressure on dust as a driver for launching outflows and interacting with outer ISM.For the other group-2 quasar J1238, the ZTF-g/r bands show a similar light curve characterized by an increasing brightness over the last two spectroscopic epochs.
Interestingly, J1238 and Mrk 231 have many common features, such as the spectral shape, strong LoBAL (Mg ii) and weak HiBAL (He i*) troughs, strong Fe ii and weak [O iii] emission, potentially inner decelerated winds and outer accelerated outflows (the decreased portion of the BAL subflow at −12500 < v LOS < −10000 km s −1 is comparable to the increased portion of the BAL subflow at −7000 < v LOS < −5000 km s −1 from MJD=54234 to 56035; see Fig. 9), and moderately weak radio emission.Therefore, like Mrk 231 having BAL distances at R ∼2-100 pc, BAL distance in J1238 may also cover a wide range (see Leighly et al. 2014;Veilleux et al. 2016).If this speculation is true, the mild acceleration seen in J1238 is also likely, at least partly, due to IR radiation pressure on dust, although we cannot exclude the possibility that UV radiation on ionized gas is the dominant driver for the initial BAL acceleration in both quasars, particularly in cases where the dust and gas are not efficiently coupled.
For the group-1 quasar J1344, an intriguing result is the progressively broadening BAL-2 as opposed to narrowing BAL-1, such that the width increment of BAL-2 is almost equal to the width decrement of BAL-1 from MJD=53503 to 59384 in both Al iii and Mg ii (see the MJD vs. w 95 panel in Fig. 3), possibly indicative of a new BAL-acceleration event characterized by a high-velocity inner wind (BAL-1 subflow) overtaking a low-velocity outer wind.This scenario is supported by the disappearance of both the Al iii BAL (at v LOS ∼ −11000 km s −1 ) and the Al iii BEL peak, as well as the rapid drop of the C iv BEL strength after MJD = 58224, an epoch when the BAL-1 started to level off or perhaps decelerate.For the other group-1 quasar J0136, the disappearance of LoBAL ions that are associated with a decrease of dust, could be the main cause for the brightening UV continuum; hence, its largest BAL acceleration magnitude detected between MJD=52203 and 55444, could be dominated by UV-radiation-pressure on dusty gas.This interpretation is further supported by a decline of the acceleration magnitude after MJD=55444 (see Fig. 4), an epoch when LoBALs and dust started to disappear along our LOS.It is worth noting that the time-resolved evidence for large-magnitude BAL acceleration along with line-locking, associated absorption lines (AALs; see Weymann et al. 1991 and references therein) seen in group-1 quasars, offers a plausible interpretation to link nuclear BAL winds and galactic AAL outflows, despite the huge difference in distance (< 1 pc vs. >1,000 pc).As a comparison, spatially resolved evidence for small-magnitude acceleration/deceleration traced by the positive/negative correlations between [O iii] emission-line width and velocity has been reported in the literature (e.g., FWHM increasing due to turbulence from acceleration or deceleration; see Fig. 5 in Nesvadba et al. 2006).Therefore, spatially resolved spectroscopy of the BAL-acceleration quasars in the future may provide unique and valuable information to bridge the huge gap of distance.
A joint analysis of variability in both absorption and emission may offer additional diagnostics to further advance our understanding of BAL acceleration.It is clear that the BALs and BELs vary dramatically in J1344, while the Mg ii/Al iii BELs in J0136 remain generally unchanged as opposed to complete disappearance of the Mg ii/Al iii BALs.In particular, the Al iii BEL peak in J1344 exhibited a velocity shift comparable to that of the Al iii BAL-1 in the interval from MJD=53503 to 58224, despite the different acceleration magnitudes measured in between.Such a difference can be explained by the complex structures and inner physics of the BEL outflows.Moreover, the Al iii BEL in J1344 became progressively weak after MJD=56363 (its peak nearly disappeared at MJD=59384; see Fig. 3), again, supportive of UV-radiation pressure as a common driving force to accelerate both the BAL-1 and Al iii BEL outflows.Given the brightening/dimming UV continuum detected in J0136/J1344, we argue that the absorption/emissionline variability behaviors, such as the monolithic BAL shifts and large REW drops of the C iv BEL, are loosely linked to UV continuum variability.
In addition, the BAL/BEL signal the LOS/bulk effects, respectively, which may also contribute to the differences of variability behaviors between J0136 and J1344.However, it remains difficult to explain (1) the opposite timevariability pattern in REW between BAL-1 and BAL-2 for J1344, and (2) the rapidly disappeared Al iii BEL as opposed to the generally unchanged Mg ii BEL for J1344 after MJD=58224.The second phenomenon may be linked to the third Al iii BAL at v LOS ∼ −11000 km s −1 , whose variability behavior cannot be assessed in detail given its presence only at MJD=56363.Interestingly, both quasars show a common variability pattern that the C iv BEL strength decreased by a factor of ∼2 near the point where the BAL velocity starts to level off, again, supporting a connection between the BAL and BEL outflows; furthermore, both quasars exhibit slightly blueshifted, line-locking C iv signatures, indicative of quasar radiation-driven outflows coupled to large-scale ISM.
It is worth noting again that the smaller the BALvelocity shift between two epochs, the greater the chance that the shift could be due to velocity-dependent variability caused by ionization changes and/or transverse motions.Therefore, it is possible that another agent comes into play at some point in term of curtailing acceleration, particularly when noticing the plateau-like trend among them in later epochs (see Fig. 7).

BAL deceleration as an origin of weak radio emission and large-scale AALs
The presence of radio emission in BAL quasars remains unknown since BAL winds are thought to be launched from a viewing angle closer to the equatorial plane of accretion disk than the jet (e.g., Becker et al. 2000;Yi et al. 2019;Nair & Vivek 2022).However, both theoretical and observational studies of the wind-ISM interactions predict the production of weak radio emission (e.g., Faucher-Giguère & Quataert 2012; Zakamska & Greene 2014), which were indeed detected in the group-2 quasars (J1238 with a flux density of 2.5/5.84mJy and J1259 with a flux density of 0.8/2.0mJy at 3.0/1.4GHz, respectively).In-terestingly, the two radio-band observations yield a spectrum index of α ∼ −1.1 for both quasars, reinforcing the argument for the wind-ISM interaction as an origin of weak radio emission (Panessa et al. 2019).Moreover, all but J1344 were also detected by RACS at ∼800 MHz (∼8.3/2.2/1.7 mJy for J1238/J1259/J0136, respectively, while out of the survey range for J1344; McConnell et al. 2020), consistent with a higher radio-detection rate at a lower frequency in the LoBAL population (Morabito et al. 2019).Given that the LoBAL quasar Mrk 231 also has moderately weak radio emission along with evidence for BAL deceleration/acceleration and radio flares, we propose an underlying link between the two phenomena, which can be tested with follow-up observations in the future.
As a comparison, Shi et al. (2016) speculated that the Balmer absorber in J1259 experienced deceleration due to the collision with surrounding medium, based on an analysis of the two SDSS spectra.In combination with the observational results from six optical spectra and multi-wavelength data, we did find additional evidence in support of wind deceleration for J1259.Furthermore, such deceleration events can explain the high incidence of weak radio emission among red quasars that appears to peak around the radio-quiet and radio-loud threshold (Klindt et al. 2019), given an anomalously high fraction of BALs seen in red quasars (e.g., Urrutia et al. 2009;Fynbo et al. 2013;Hamann et al. 2017) and a high radiodetection rate found in the BAL population (e.g., Yi et al. 2019;Morabito et al. 2019).
Like the group-1 quasars, three X-ray bright BAL quasars from Joshi et al. (2014Joshi et al. ( , 2019) also possess AALs and kinematic signatures of BAL deceleration.The lack of significant velocity shifts in AAL as opposed to large BAL-velocity shifts found both in this work and Joshi et al. (2014Joshi et al. ( , 2019)), suggests that large-magnitude, identifiable acceleration events mostly occur in BALs rather than AALs, consistent with the latter being located at a large-scale region, i.e., the quasar host galaxy or a cluster near the quasar (e.g., Weymann et al. 1991); furthermore, a complex AAL without significant variability over decades may trace an outermost remnant of BAL winds fully coupled to ISM, given the presence of wide-spread, line-locking signatures in the group-1 quasars.The group-2 quasars, however, have lower systemic redshifts than group-1 quasars, making an identification of C iv AALs impossible from optical spectroscopy.These BAL-acceleration candidates lack or possess shallow Mg ii AALs, indicating that AALs tend to be in a relatively high-ionization state, although it is difficult to identify shallow Mg ii AAL features from group-2 due to overlapping absorption.Additional insights of BAL-acceleration/deceleration and their effects may be gained from X-ray observations, particularly in the context that BAL wind is thought to be associated with the shielding gas.

Implications from quasar color
All four quasars have a SED shape consistent with that of red quasars (see Calistro Rivera et al. 2021); however, the group-2 quasars exhibit weak radio emission and are much redder than the group-1 quasars (see Fig. 8).If radio emission in group-2 signals a small viewing angle to the jet axis and the group-1 LOS is seen through the edge of a traditional torus, then the group-2 quasars are expected to be bluer than group-1, which is opposite to the observations.As discussed above, the weak radio emission in group-2 is likely a byproduct from BAL-ISM interactions rather than a tracer of low-power jets.
Here, we explore whether the redder color in group-2 is also a consequence of the BAL-ISM interaction.In stark contrast with the rest-frame UV continuum variability detected in the four quasars, none showed significant variability in the W1 and W2 bands.This difference, along with the partial LOS covering for BAL winds, suggests that the UV continuum variability is likely due to a patchy effect caused by rapid changes in dust composition, distribution, and/or transverse motions during the BAL-acceleration phase.Indeed, the dimming Vband brightness in J1259 (see Fig. 6) is at least partly caused by the BAL-ISM coupling, a process that can produce rapid changes of the dust/gas in distribution and composition, making in situ dust formation and patchy obscuration possible.
All the four quasars have a SED bump at λ rest ∼ 3 µm, in agreement with the prediction of dusty winds (e.g., Zhang et al. 2014;Gallagher et al. 2015;Calistro Rivera et al. 2021).Importantly, the group-2 quasars have a steeper SED rise at 1 < λ rest < 3 µm than group-1 quasars, providing further evidence for the correlation between near-IR slope and BAL properties as reported in Zhang et al. (2014), where they speculated that BAL winds are strongly decelerated by interacting with ISM.Our observations suggest that BAL deceleration may play a more important role than BAL acceleration with respect to controlling the SED shape, perhaps due to stronger in situ dust formation and/or entrainments from an inhomogeneous/clumpy/patchy environment.This result is intriguing and sheds light on the nature of red and blue quasars, especially those with outflows undergoing actual acceleration, as the W3/SDSS-i ratio may change dramatically on short timescales due to changes solely by dust variability along our LOS.Likewise, the conventional classification of radio-loud and radio-quiet quasars would be problematic in such cases (see an alternative tracer of radio loudness proposed by Klindt et al. 2019).However, the relations between BAL acceleration and UV reddening or brightness are unclear, given that J0136/J1259 become brighter/dimmer in the UV band while both show an increase in UV reddening over the epochs, and that J1238/J1344 become brighter/dimmer in the UV band while both remain generally unchanged in UV reddening.Apart from the inhomogeneous/clumpy/patchy environment, different dust variability behaviors at different wavelengths may be also related to dust composition or in situ dust formation, i.e., the wind-ISM interaction can break dense clouds into diffuse filaments, making more dust exposed to quasar UV radiation and hence enhancing IR emission (e.g., Wagner, Umemura, & Bicknell 2013;Hamann et al. 2017).

SUMMARY
In this work, we select from our sample four LoBALacceleration candidates and investigate their physical properties based on multi-wavelength, multi-epoch observations, aiming to bridge the gap over HiBAL acceleration and gain unique insights into actual quasar feedback.The main observational results and conclusions are summarized below.
1. We identified one compelling (J1344), one strong (J0136), and two tentative cases of LoBAL acceleration, among which J0136 exhibited BAL disappearance in Al iii and Mg ii (see Section. 3).
2. The group-1 (J1344 and J0136) are radio quiet and exhibit line-locking signatures in C iv AALs, while the group-2 (J1238 and J1259) have red SEDs and weak radio emission with a steep spectral index (α ∼ −1.1) (see Section. 4.1 and 5.1.2).
3. The BAL-ISM coupling is one of the major avenues for the origin of quasar reddening, patchy obscuration, large-scale AALs, and perhaps weak radio emission (see Section. 5.2).
All the four quasars exhibit BAL-acceleration magnitudes larger than the detection upper limits of BAL acceleration derived from Grier et al. (2016), which deserve multi-wavelength, follow-up observations, particularly J1259 with one-sided, off-nuclear [O ii] emission nebula.They may provide an ideal laboratory to study the actual feedback processes, such as strong deceleration of BAL winds before traveling out to large scales, the process of BAL winds breaking out a circumnuclear dust cocoon (e.g., Zhang et al. 2014;Shi et al. 2016;Temple et al. 2019), the origin of giant nebulae from a non-galaxycluster environment, the relation between mergers and star-formation/quasar activities, and gravitational-wave recoiling SMBHs etc, in the context that LoBALs are representative of young quasars from gas-rich mergers (e.g., Urrutia et al. 2009;Yi et al. 2022).

Figure 3 .
Figure3.Left: Zoom-in profiles of the BAL-1 in Al iii and Mg ii, in which a set of three blueward components of the Al iii and Mg ii doublets (gray/green/red vertical dotted lines) with two fixed velocity separations is identified in each of the three spectra with relatively high S/N, indicative of the same BAL-1 subflow persisting over the epochs.Middle: Continuum normalized spectra of the group-1 quasar J1344, in which two distinct BALs are labeled with BAL-1 and BAL-2.The comb-like symbols in the middle subpanel indicate radiativeacceleration, line-locking signatures of C iv.The Earth symbol in the bottom-left subpanel indicates telluric absorption.The three bell-like profiles depict the one-Gaussian fits to the apparent Al iii BEL peaks.Right: MJD vs. velocity shifts (relative to the first epoch), trough widths (w 95 ; trough width at the 95% continuum level), REWs (the Al iii emission peak nearly disappeared at MJD=59384), and continuum flux at λrest = 1700 Å, respectively.

Figure 6 .
Figure6.Left: Continuum normalized spectra of the group-2 quasar J1259 over six epochs.The vertical red/blue dashed lines refer to the peak absorption at the first/other epochs, from which one can directly see how the velocity shift varies with time using the first epoch as a benchmark (the first spectrum is superimposed on all successive epochs and the positions of the red and blue dashed lines in H9 are fixed by those of Hγ).Apparently, the H9 remains generally unchanged in REW while the Hγ BAL appears to vary from epoch to epoch.Right: MJD vs. velocity shift of the Hγ BAL relative to MJD=55983, REWs of different ions, and photometric magnitudes, respectively.The apparent disappearance in [O ii] emission at MJD=58894 (highlighted by the red circle) is due to a rotation (marked by position angle (PA) from the left panels) between the two long-slit spectroscopic observations targeting the quasar core with a one-sided, off-nuclear [O ii] emission nebula(Yi et al. in prep).

Figure 8 .
Figure8.SEDs of the four quasars, which incorporate data from GALEX (diamond), SDSS (triangle), 2MASS (square), WISE (circle), VLASS and FIRST (star).The early/late epoch spectra are shown in red/blue for each quasar, complemented with a near-IR (cyan) spectrum if it exists.J0136 and J1344 (group-1) have BAL-acceleration signatures and are radio quiet; in addition, J0136 is undergoing a LoBAL→HiBAL transformation along with an increase of brightness over the epochs, while J1344 remains to be in a LoBAL state along with a decrease of brightness.J1238 and J1259 (group-2) exhibit BAL-acceleration/-deceleration signatures and weak radio emission, with f 3GHz /f 1.4GHz = 2.5/5.84mJy and 0.8/2.0mJy for the former and latter, respectively.The GALEX photometry for J1259 should be treated with caution given its large flag values.The median SED of red quasars from CalistroRivera et al. (2021) is scaled to the W3-band.
named in honour of its principal benefactors, William P. Hobby and Robert E. Eberly.The Low-Resolution Spectrograph 2 (LRS2) was developed and funded by the University of Texas at Austin McDonald Observatory and Department of Astronomy, and by the Pennsylvania State University.We thank the Leibniz-Institut für Astrophysik Potsdam and the Institut für Astrophysik Göttingen for their contributions to the construction of the integral field units.The LBT is an international collaboration among institutions in the United States, Italy and Germany.LBT Corporation partners are: The University of Arizona on behalf of the Arizona Board of Regents; Istituto Nazionale di Astrofisica, Italy; LBT Beteiligungsgesellschaft, Germany, representing the Max-Planck Society, The Leibniz Institute for Astrophysics Potsdam, and Heidelberg University; The Ohio State University, representing OSU, University of Notre Dame, University of Minnesota and University of Virginia.We acknowledge the support of the staff of the Lijiang 2.4 m telescope (LJT).Funding for the telescope has been provided by CAS and the People's Government of Yunnan Province.

Table 1
Spectroscopic observations of the four BAL-acceleration quasar candidates Left: Continuum normalized spectra of the group-2 quasar J1238 for the Mg ii BAL/BEL over four epochs.Right: MJD vs. velocity shift of the Mg ii BAL, REW for the BALs and BELs, and photometric magnitudes, respectively, which depict the time-variability patterns of these quantities.Unlike the Mg ii BAL which has at least three subflows, the He i* BAL is detected only at v LOS ∼ 6000 km s −1 (see Section 4.2) and offset above by 37 Å for clarity.The positive/negative velocity shifts detected over the epochs may be linked to BAL acceleration/deceleration events for this quasar.
Hγ BAL spectral region has the highest S/N Grier et al. 2016)016)Comparison between the LoBAL (color) and Hi-BAL (gray; from Table4ofGrier et al. 2016)samples.The two horizontal dotted lines are the upper limits of BAL acceleration/deceleration inGrier et al. (

Table 2
Measurements of the rest equivalent widths, trough widths, trough-velocity shifts, and acceleration magnitudes The square represents the benchmark spectrum used for the CCF analysis for each quasar.(2) w 95 is the trough width at the 95% continuum level.(3) a 34 and a 45 are the deceleration rates derived from the 3rd/4th and 4th/5th epoch pairs, respectively.

Table 3
Spectral fitting results of the BELs for J0136