adsabs/FOCAL huggingface dataset:
As can be seen from Fig. 1, in both the optical and the NIR band, several predominant flares appearing in the whole period considered are usually surrounded by other smaller subflares. In addition, it seems that the NIR light curves follow a similar flaring activity, lasting for several days or weeks, to the optical bands, although the NIR flux is more variable compared than the optical one, increasing by about 7 times in the J band, from 9.68 to 67.85 mJy (for an example, see Table 1). An exponential rise/decay model can appropriately fit the blazar light curve, which generally consists of superpositions of a steady background flux density and a number of flare components caused by events in the jet or the accretion disc/corona region (e.g. Valtaoja et al. 1999; Chatterjee et al. 2008; Abdo et al. 2010b; Chatterjee et al. 2012; Guo et al. 2016; Li et al. 2017, 2018, and references therein). Following Abdo et al. (2010b), we define the multipeaked model to analyse the temporal flare profiles during the interval of interest:
(3)
\begin{eqnarray*}
F(t) = {F_{\rm c}} + \sum _{i}\left[{F_i}{\left({{{\rm e}^{\frac{{{T_{0,i}} - t}}{{{T_{r,i}}}}}} + {{\rm e}^{\frac{{{\rm t} - {T_{0,i}}}}{{{T_{{\rm d},i}}}}}}} \right)^{ - 1}}\right],
\end{eqnarray*}
where Fc is the assumed constant background flux level underlying the flare components and is constrained to be less than or equal to the lowest value of flux, and the sum runs over all of the individual flares being fitted. For any one of the individual flares, Fi is the variability amplitude, T0, i is the epoch of the peak, and Tr, i and Td, i are the time-scales of rise and decay, respectively. Equation (3) represents flares within a limited time interval, because the observational gaps exist regularly or occasionally. In order to ensure the accuracy of the fitting model, the divided observational segments in different bands mentioned in Section 2 were used to analyse the temporal flare profiles. Each segment of the light curves was first interpolated by means of cubic spline interpolations through the 1-d binned light curves, then smoothed by a five-point moving-average filter to reduce the impact of the short-term variabilities.
Citation: Chatterjee et al. 2008
Citation function: Uses
Outflows from the central regions of active galactic nuclei (AGNs) are thought to be the main agents that regulate the evolution of both the central supermassive black holes as well as the host galaxies (Silk & Rees 1998; Di Matteo, Springel & Hernquist 2005). The presence of high-velocity outflows from AGNs can be established from the evidence provided by the blueshifted broad absorption lines (BALs) seen in the spectra of 10–20 per cent of quasi-stellar objects (QSOs)1 (Weymann et al. 1991). BALQSOs are classified into three sub-classes based on the ionization state of the absorbing gas: (a) high-ionization BALQSOs (HiBALs) consist of absorption from high-ionization lines such as C iv, Si iv, and N v (Gibson et al. 2008; Filiz Ak et al. 2013; Vivek, Srianand & Gupta 2016; Vivek 2019; Mishra et al. 2021) (b) low-ionization BALQSOs (LoBALs) show absorption from low-ionization lines such as Mg ii and Al iii along with the high-ionization lines (Voit, Weymann & Korista 1993; Vivek et al. 2014; Vivek, Srianand & Dawson 2018; Yi et al. 2019), and (c) iron-LoBALs (FeLoBALs) are LoBALs with excited fine-structure Fe ii and/or Fe iii absorption lines (Vivek et al. 2012; McGraw et al. 2015). The observed BALQSO fraction is explained either by an orientation model, where the line of sight intersects with the BAL absorbing clouds in 10–20 per cent QSOs (Weymann et al. 1991; Elvis 2000), or an evolutionary model, where the QSO spends 10–20 per cent of its lifetime in the BALQSO phase (Farrah et al. 2007; Lipari et al. 2009). Although the similarity in the optical/NIR properties of BAL and non-BALQSOs, higher reddening and polarization features in BALQSOs support the orientation model, the observed radio spectral indices of BALQSOs and the discovery of polar winds in BALQSOs challenge this scenario (Reichard et al. 2003; Zhou et al. 2006; Wang, Wang & Wang 2007; Montenegro-Montes et al. 2008). On the other hand, the anticorrelation between the radio loudness parameter and balnicity index, Compact Steep Spectrum (CSS) nature of BALQSOs, and the redshift dependence of BALQSO fraction favour the evolutionary model (Gregg, Becker & de Vries 2006; Farrah et al. 2007; Allen et al. 2011).
Citation: Vivek, Srianand & Gupta 2016
Citation function: Background
In this paper, following the method proposed by Ofek et al. (2003), we use the differential optical depth to lensing with respect to the lens redshift zl as the probability density. For a statistical sample that contains Nl strong lensing systems, the log-likelihood of observing the lens at redshift zl is given by
(9)$$\begin{eqnarray*}
{\rm ln}\mathcal {L}({\bf p})=\sum _{i=1}^{N_l} {\rm ln} \delta p_i({\bf p}),
\end{eqnarray*}$$where p represents the set of the VDF parameters (α, β) and the galaxy evolution parameters (νn, νv). Now one can perform Monte Carlo simulations of the posterior likelihood ${\cal L} \sim \exp {(- \chi ^2 / 2)}$, where the χ2 function is defined as
(10)$$\begin{eqnarray*}
\chi ^2=-2{\rm ln}\mathcal {L}.
\end{eqnarray*}$$in our statistical analysis of lens redshift distribution. The sample used in this paper is primarily drawn from Sloan Lens ACS Survey (SLACS) and recent large-scale observations of galaxies, which is compiled and summarized in Cao et al. (2015) and Shu et al. (2017). The combined sample includes 91 lenses from SLACS (Bolton et al. 2008; Auger et al. 2009; Shu et al. 2017) and an extension of the SLACS survey known as ‘SLACS for the Masses’ (S4TM) (Shu et al. 2015, 2017), 35 lenses from the BOSS emission-line lens survey (BELLS) (Brownstein et al. 2012) and BELLS for GALaxy-Lyα EmitteR sYstemsGALLERY (BELLS GALLERY) (Shu et al. 2016a,b), 26 lenses from the Strong Lensing Legacy Survey (SL2S) (Sonnenfeld et al. 2013a,b), and five lenses from Lenses Structure and Dynamic (LSD) (Treu & Koopmans 2002; Koopmans & Treu 2003; Treu & Koopmans 2004). The advantage of this recently assembled lens sample, the detailed information of which is described and listed in Chen et al. (2019), lies in its well-defined observational selection criteria satisfying the assumption of spherical lens mass model. Fig. 1 shows the redshift distributions of the lensing systems used in our analysis. However, a statistical analysis requires a sample that is complete and has well-characterized, homogeneous selection criteria. Note that the lensing systems collected in this analysis are selected in very different manners. For instance, the SLACS, S4TM, and BELLS surveys, respectively, selected candidates from the spectroscopic observations of ETGs and look for the presence of higher redshift emission lines in Sloan Digital Sky Survey I (Eisenstein et al. 2001) and Sloan Digital Sky Survey-III (Eisenstein et al. 2011). These lens candidates were followed up with HST ACS snapshot imaging and after image processing. Therefore, in order to verify the completeness of the full early-type lens sample (hereafter Sample A), one additional subsample will also be applied to discuss its utility for the redshift test: 126 deflector-selected lenses from SLACS, S4TM, BELLS, and BELLS GALLERY (hereafter Sample B). Such choice is also motivated by the fact that the SLACS and BELLS lenses could be moderately suffered from the finite Sloan fibre size (Brownstein et al. 2012).
Citation: Bolton et al. 2008
Citation function: Uses; Uses
The formation of the approximately 40% of sdB stars that appear to be single has been a mystery for decades. In the absence of a companion, it is hard to explain how the star can expel most of its envelope on the RGB and still achieve core-He burning ignition. Recently, Pelisoli et al. (2020) suggested that all sdB stars might originate from binary evolution. Merger scenarios involving two low-mass white dwarfs have also been investigated (Webbink 1984; Han et al. 2002, 2003; Zhang & Jeffery 2012), but several facts challenge this hypothesis. First, compact low-mass white dwarf binaries are quite rare, even though some candidates are identified (Ratzloff et al. 2019). Second, the mass distributions of single and binary sdB stars are indistinguishable (Fontaine et al. 2012, Table 3 in particular). This mass distribution is mainly obtained from asteroseismology (some sdB stars exhibit oscillations, which allow the precise and accurate determination of the stellar parameters, including total mass; Van Grootel et al. 2013) and also from binary light-curve modeling for hot subdwarfs in eclipsing binary systems. Single and binary mass distributions peak at ~ 0.47 M⊙, which is the minimum core mass required to ignite He through a He-flash at the tip of RGB (stars of ≳ 2.3 M⊙ are able to ignite He quietly at lower core masses, down to ~0.33 M⊙, but the more massive the stars, the rarer they are). A mass distribution of single sdB stars from mergers, in contrast, would be much broader (0.4−0.7 M⊙; Han et al. 2002). With the DR2 release of Gaia (Gaia Collaboration 2018) and precise distances for many hot subdwarfs (Geier 2020), it is now also possible to build a spectrophotometric mass distribution for a much larger sample than what was achieved with the hot subdwarf pulsators or those in eclipsing binaries. Individual masses are much less precise than those obtained by asteroseismology or binary light-curve modeling (Schneider et al. 2019). However, single and binary spectrophotometric mass distributions share the same properties here as well, which tends to disprove the hypothesis of different origins for single and binary sdB stars. The third piece of evidence against merger scenarios (which would most likely result in fast-rotating objects) is the very slow rotation of almost all single sdB stars, as obtained through v sin i measurements (Geier & Heber 2012) or from asteroseismology (Charpinet et al. 2018). Moreover, their rotation rates are in direct line with the core rotation rates observed in RC stars (Mosser et al. 2012), which is another strong indication that these stars and the single sdB stars do share a same origin, that is, that they are post-RGB stars.
Citation: Fontaine et al. 2012
Citation function: Motivation; Motivation
The present HST-COS data were taken 20 days after the last XMM-Newton pointing (Kaastra et al. 2011) as the closing measurements of the campaign, which lasted in total about 100 days. Spectral coverage simultaneous to HST-COS was provided instead by both Chandra-LETGS (Ebrero et al. 2011) and Swift-XRT (Mehdipour et al. 2011). We used the average SED recorded by the XMM-Newton instruments 20–60 days before the HST-COS observation. The choice of SED is very important in the BLR modeling, as different lines respond to the continuum variations on different time scales (Korista & Goad 2000; Peterson et al. 2004). Reverberation mapping studies of Mrk 509 report that the delay of the Hβ with respect to the continuum is very long (about 80 days for Hβ, Carone et al. 1996; Peterson et al. 2004). However, higher ionization lines respond more quickly to the continuum variations. Taking as a reference the average Hβ/C iv delay ratio for NGC 5548 (Peterson et al. 2004), for which – contrary to Mrk 509 – a large set of line measurements is available, we obtain that the C iv line in Mrk 509 should respond in approximately 40 days. A similar (but shorter) time delay should apply to the Lyα line (Korista & Goad 2000). This delay falls in the time interval covered by the XMM-Newton data. Therefore, our choice of SED should be appropriate for the modeling of at least the main UV lines. Variability of the X-ray broad lines has been reported on time scales of years (Costantini et al. 2010); however, no short-term studies are available. We expect that the X-ray broad lines should respond promptly to the continuum variations, as they may be located up to three times closer to the black hole with respect to the UV lines (C07). During the XMM-Newton campaign the flux changed by 30% at most, with a minimal change in spectral shape (Sect. 3.1). The used SED should therefore represent what the BLR gas sees for the X-ray band. However, for the optical lines the used SED might be too luminous as we observed an increase in luminosity of about 30% during the XMM-Newton campaign and, as seen above, the time-delay of the optical lines may be large.
Citation: Korista & Goad 2000
Citation function: Motivation
We appear to live in a flat, homogeneous and isotropic expanding Universe (at scales >100 Mpc) well described by the Friedmann–Lemaître–Robertson–Walker (FLRW) metric where the scalefactor, a(t), describes the time dependence of the Universe geometry: a(t) ∝ t1/2 for radiation domination, a(t) ∝ t2/3 for matter domination, and $a(t)\propto \exp (\scriptstyle\sqrt{\frac{\Lambda }{3}}ct)$ for dark energy domination, where Λ = 3H0ΩΛc−2 is the cosmological constant (e.g. Beringer et al. 2012) – see Table 1. A common normalization of the FLRW metric defines the scalefactor equal to unity at the present time (a(t0) = 1; e.g. Liddle & Lyth 1993), yielding, for a Universe dominated by a positive cosmological constant (cf. Table 1)

(5)

\begin{eqnarray}
a_{\Lambda }(t)=\exp \left(c\sqrt{\frac{\Lambda }{3}}(t-t_{0})\right),&amp; t_{\Lambda }\le t\le t_{0} \:.
\end{eqnarray}

For the matter-dominated Universe, we have

(6)

\begin{eqnarray}
a_{\text{m}}(t)=a_{\Lambda }(t_{\Lambda })\left(\frac{t}{t_{\Lambda }}\right)^{2/3}, \:\: t_{\text{eq}}\le t\le t_{\Lambda } \:.
\end{eqnarray}

Between the end of inflation at t = te ∼ 10−33 s; (e.g. Narlikar & Padmanabhan 1991) and t = teq = 2.37 × 1012 s, the Universe was radiation-dominated since at the latter instant a radiation-matter equality is reached (Table 1). Exceptions to radiation-domination in the te ≤ t ≤ teq time interval might have taken place during cosmological phase transitions such as the QCD (when the Universe might have been dust-like). We, then, split the radiation-domination epoch into three parts. For the interval between the end of the QCD phase transition (t+) and teq, we define

(7)

\begin{equation}
a_{\text{rl}}(t)=a_{\text{m}}(t_{\text{eq}})\left(\frac{t}{t_{\text{eq}}}\right)^{1/2}, \:\: t_{+}\le t\le t_{\text{eq}} \:.
\end{equation}

During the QCD phase transition, we define

(8)

\begin{eqnarray}
a_{\text{QCD}}(t)=a_{\text{rl}}(t_{+})\left(\frac{t}{t_{+}}\right)^{n_{\text{QCD}}}, \:\: t_{-}\le t\le t_{+},
\end{eqnarray}

where nQCD = 2/3 if the Universe experiences a QCD dust-like phase or nQCD = 1/2 if the Universe continues to be radiation-dominated during that epoch. Finally, between the end of inflation (te) and the beginning of the QCD phase transition (t−), we define

(9)

\begin{equation}
a_{\text{rm}}(t)=a_{\text{QCD}}(t_{-})\left(\frac{t}{t_{-}}\right)^{1/2}, \:\: t_{\text{e}}\le t\le t_{-} \:.
\end{equation}
Citation: Narlikar & Padmanabhan 1991
Citation function: Background; Background
Observations of the polarized dust emission of nine low-mass protostars at 0.87 mm were obtained using the SMA (Projects 2013A-S034 and 2013B-S027, PI: A. Maury) in the compact and subcompact configuration. To increase our statistics, we also included SMA observations from three additional sources from Perseus (NGC 1333 IRAS4A and IRAS4B) and Ophiuchus (IRAS16293) observed in 2004 and 2006 (Projects 2004-142 and 2006-09-A026, PI: R. Rao; Project 2005-09-S061, PI: D.P. Marrone). The observations of NGC 1333 IRAS4A and IRAS16293 are presented in Girart et al. (2006) and Rao et al. (2009), respectively. Marrone (2006) and Marrone & Rao (2008) provide a detailed description of the SMA polarimeter system, but we provide a few details on the SMA and the polarization design below. The SMA has eight antennas. Each optical path is equipped with a quarter-wave plate (QWP), an optical element that adds a 90° phase delay between orthogonal linear polarizations and is used to convert the linear into circular polarization. The antennas are switched between polarizations (QWP are rotated at various angles) in a coordinated temporal sequence to sample the various combinations of circular polarizations on each baseline. The 230, 345, and 400 band receivers are installed in all eight SMA antennas. Polarization can be measured in single-receiver polarization mode and in dual-receiver mode when two receivers with orthogonal linear polarizations are tuned simultaneously. In this dual-receiver mode, all correlations (the parallel-polarized RR and LL and the cross-polarized RL and LR; with R and L for right circular and left circular, respectively) are measured at the same time. Both polarization modes were used in our observations. This campaign was used to partly commission the dual-receiver full polarization mode for the SMA. A fraction of the data was lost during this period owing to issues with the correlator software. Frequent observations of various calibrators were interspersed to ensure that such issues were detected as early as possible to minimize data loss.
Citation: Rao et al. (2009)
Citation function: Background; Background
Magnetic flux ropes are frequently observed magnetic structures with helical magnetic field lines and a strong core field. In spacecraft observations, flux ropes are often identified from bipolar variations in one magnetic field component and the enhancement of magnetic strength at the center. There are various observations of flux ropes in the magnetosphere (e.g., Khurana et al. 1995; Slavin 2003; Yang et al. 2013; Poh et al. 2019; Sun et al. 2019), boundary of magnetosphere (e.g., Rijnbeek et al. 1984; Kawano & Russell 1997; Fear et al. 2008, 2009; Akhavan-Tafti et al. 2018; Hwang et al. 2018; Yao et al. 2020), and solar wind (e.g., Zheng & Hu 2018; Blanco-Cano et al. 2019; Bai et al. 2020). Flux ropes are also observed in the magnetospheres of Mercury (Zhong et al. 2020a), Mars (Briggs et al. 2011), Jupiter (Sarkango et al. 2021), and Saturn (Jasinski et al. 2016). Flux ropes are widely believed to result from magnetic reconnection. In earlier studies, some flux ropes near the magnetopause are referred to as flux transfer events (FTEs; Russell & Elphic 1978), which allow plasma transportation across the magnetopause. Various mechanisms for FTE generation have been proposed, such as single X-line reconnection (Scholer 1988; Southwood et al. 1988) and multiple X-line reconnection (Lee & Fu 1985). Recent simulations show that reconnection can generate not only fluid-scale flux ropes but also those with ion or even electron scales (Daughton et al. 2011; Hoilijoki et al. 2019; Lu et al. 2020). These kinetic-scale flux ropes may interact with one another to form larger-scale flux ropes (Daughton et al. 2011), which could be manifested in spacecraft observations as entangled flux ropes (Wang et al. 2017; Øieroset et al. 2019; Qi et al. 2020). There are also observations of ion-scale flux ropes near the ion/electron diffusion region (Wang et al. 2016; Hwang et al. 2018; Poh et al. 2019; Dong et al. 2020). The flux ropes can change in size while moving through convection, often expanding (Dong et al. 2017; Akhavan-Tafti et al. 2018, 2019) and sometimes contracting (Hasegawa et al. 2016). Eastwood et al. (2012) investigated that the flux ropes in the day side and in the distant-tail magnetopause have similar orientations and comparable magnetic flux content, indicating that the flux ropes may be in quasi-equilibrium as they are convected tailwards along the magnetopause. Moreover, ion-scale flux ropes are believed to be responsible for exciting waves (Huang et al. 2016; Wang et al. 2019) or accelerating particles (Zhu et al. 2019; Zhong et al. 2020b), implying that they are actively involved in magnetospheric physics.
Citation: Zheng & Hu 2018
Citation function: Background; Background
The projected position angle (PA) of the jet gradually rotates counterclockwise with increasing distance from the jet base. In the 2.3 GHz VLBA image the PA is 50° ± 5° east of north at about 20 mas from the core and the jet bends toward the north–south direction closer to the core, consistently with the jet orientation in the nonsimultaneous 1.6 GHz image at 5–10 mas from the core (Shen et al. 1999). At 8.7 GHz we find a PA of 25° ± 5° at about 5 mas from the core, consistent with the archival VLBA monitoring results at 15 GHz, showing a persistent jet orientation at a PA of about 30° in the epochs from 1995 to 2013 at angular scales ∼5 mas (Kellermann et al. 1998; Pushkarev et al. 2017). The same MOJAVE observations hint at more variability of the jet PA on the smallest resolved scales ∼1 mas. Observations by Shen et al. (2002) with the VLBA between 1994 and 2000 across four frequencies (5, 12, 15, and 43 GHz) showed a consistent PA orientation of 30° at 5 GHz with a clockwise shift of about 51°–67° at 43 GHz. At 86 GHz a possible bent jet structure is seen, with the inner jet oriented with a PA of about −40° less than 0.3 mas from the core, and an apparent transition to a northeast direction further out. The −40° PA with respect to the core is consistent with the PA of the single jet component located ∼400 μas from the core, imaged from 2018 April GMVA observations (see Figure 4 of Issaoun et al. 2021). 2018 images at 86 GHz do not indicate jet bending. At 230 GHz, the component C1 is located at a PA of −45° and C2 at a PA of −35° with respect to the core C0. This morphology can potentially be explained by a helical structure in the jet (Conway & Murphy 1993; Steffen et al. 1995). Such a helical jet structure can be caused by an orbiting lower-mass secondary black hole around a stable primary central black hole, as also proposed for 4C 73.18 (Roos et al. 1993) and OJ 287 (e.g., Dey et al. 2021; Gómez et al. 2022), precession caused by a wobbling disk (Britzen et al. 2018), or a large-scale accretion flow that is tilted with respect to the black hole spin axis (e.g., as in M81; Martí-Vidal et al. 2011).
Citation: Kellermann et al. 1998
Citation function: Compare/Contrast