On Si iv and C iv broad absorption line variability in the UV spectra of 10 BALQSOs

Abstract

In this article, we study the variability of Si iv and C iv broad absorption lines (BALs) between two different epochs in the case of 10 broad absorption-line quasi-stellar objects (BALQSOs). By performing multicomponent analysis of Si iv and C iv broad absorption troughs, we analyse each BAL trough to find the individual and uniquely determined number of components it consists of. By measuring the radial velocity, full width at half-maximum (FWHM) and optical depth of each component, we study the kinematics, physical conditions and variability of each absorber in the line of sight. Our results suggest that Si iv and C iv BAL troughs arise from clumpy gas clouds that have similar locations, kinematic structure and physical conditions and that both ions originate in the same gas clouds. Our findings favour ionization changes over the moving-cloud scenario as the main driver of BAL variability. However, the possible contribution of other mechanisms cannot be ruled out, given our small quasar sample. Finally, we find strong evidence indicative of density stratification within the absorbing gas, suggesting that quasar outflows are far from being smooth and homogeneous.

1 INTRODUCTION

About 20–30 per cent of the detected quasar population exhibits broad absorption line (BAL) troughs blueshifted with respect to the corresponding emission lines in their rest-frame UV spectra (Ganguly & Brotherton 2008; Knigge et al. 2008). BALs are usually observed in high-ionization species such as N v, Lyα, C iv and Si iv and are sometimes detected in lower ionization species like Mg ii or Al iii.

BALs exhibit a wide range of characteristics in terms of width, velocity shift, strength of absorption, level of ionization and structure of absorption profile (Turnshek 1988). An absorption line can be considered a BAL when it is characterized by velocity width > 2000 km s⁻¹ at depths > 10 per cent below the continuum (Weymann et al. 1991). For BALs, a representative line width is ∼10 000 km s⁻¹ (Weymann, Turnshek & Christiansen 1985; Narayanan et al. 2004). Maximum outflow velocities normally lie in the range 10 000–30 000 km s⁻¹ (Turnshek 1988) or more (Foltz et al. 1983).

In terms of structure, BAL troughs display great diversity (see Turnshek 1988; Korista et al. 1993). On the one hand, we encounter smooth absorption troughs that exhibit P Cygni type profiles, which sit in near-zero velocity. On the other hand, there are cases where the absorption is very broken up. There are also cases in which multiple troughs, which form near zero velocity, have been observed. Finally, there are broad absorption-line quasi-stellar objects (BALQSOs), which exhibit troughs detached from the corresponding emission. These troughs do not begin to form until the outflow velocity reaches a value of 3000–5000 km s⁻¹ (Turnshek 1988).

BALs identify high-velocity outflows launched from a rotating accretion disc that surrounds and feeds a central supermassive black hole. The properties of BAL material in phase space are uncertain and their origin remains an open question. On the one hand, we have smooth wind models (Scargle, Caroff & Noerdlinger 1970; Shlosman & Vitello 1993; Murray et al. 1995; Fukumura et al. 2018), according to which BAL troughs are the product of smooth continuous flow. On the other hand, we encounter models that assume that BALs are due to the flow of many individual substructures in the wind, called density enhancements or clumps or clouds, indicating that accretion-disc outflows are clumpy (McKee & Tarter 1975; Turnshek 1984; Lyratzi et al. 2009, 2010, 2011; Capellupo et al. 2012; Hamann et al. 2013; Takeuchi, Ohsuga & Mineshige 2013; Capellupo, Hamann & Barlow 2014; Misawa et al. 2014, 2016; Stathopoulos et al. 2015; Waters & Proga 2016).

The first attempts to model quasar winds and BAL profiles were motivated by analogy with winds from hot stars (Proga 2007). The so-called standard model of hot star winds (see Lucy & Solomon 1970; Castor, Abbott & Klein 1975; Friend & Castor 1983; Abbott & Lucy 1985; Friend & Abbott 1986; Pauldrach, Puls & Kudritzki 1986; Puls 1987; Lucy & Abbott 1993) assumes that the wind is stationary, homogeneous (e.g. no shocks or clumps), spherically symmetric and driven by radiation pressure acting on resonance lines. As in the case of hot stars, the first wind models of quasars assumed that the powerful outflows were smooth and homogeneous (e.g. Scargle et al. 1970; Drew & Boksenberg 1983; Shlosman & Vitello 1993; Murray et al. 1995; Higginbottom et al. 2013; Matthews et al. 2016). However, there is strong observational and theoretical evidence indicating that the outflows of hot stars (see Hamann, Feldmeier & Oskinova 2008, and references therein) and quasars are far from being smooth and homogeneous.

An alternative to a smooth and homogeneous quasar wind is the clumpy wind model. There are several arguments favouring the clumpy wind model over a smooth outflow. The diversity and complexity of BAL profiles, as well as their variability, imply that BALQSO winds are far from being smooth and homogeneous. The main idea is that quasar winds are pervaded by a large number of multiscale structures (clumps, clouds), the origin of which is probably some kind of radiative instability (Moscibrodzka & Proga 2013; Takeuchi, Ohsuga & Mineshige 2013, 2014; Proga et al. 2014; Proga & Waters 2015; Waters & Proga 2016; Kobayashi et al. 2018). From an observational point of view, Misawa et al. (2014, 2016), by observing multiple sight lines with the aid of strong gravitational lensing, managed to resolve the clumpy structure of the outflow winds in individual quasars. Hamann et al. (2011) identified five high-velocity outflow narrow absorption lines (NALs) in SDSS J212329.46–005052.9, which require five distinct clumpy outflow structures with similar physical conditions, characteristic sizes and kinematics. Lu & Lin (2018) managed to resolve the Si iv BAL of J002710.06–094435.3 into multiple (at least four) NALs and to identify the same number of NALs in the corresponding C iv BAL. They concluded that both the C iv and Si iv BALs originate from the same clumpy substructures of the outflow. The clumpy outflow scenario is also strengthened by variability studies of BAL profiles (see e.g. Misawa et al. 2007a; Gibson et al. 2008; Hamann 2008; Capellupo et al. 2011, 2012, 2014; Hall et al. 2011; Stathopoulos et al. 2017). Finally, clumpy outflows offer a possible solution to the so-called ‘overionization problem’ in quasar outflows (e.g. Junkkarinen, Burbidge & Smith 1983; Weymann, Turnshek & Christiansen 1985; Hamann et al. 2013).

1.1 Broad absorption line variability

Quasar outflows exhibit variability on short time-scales (days) as well as on longer time-scales (years to decades). The mechanisms invoked to explain BAL variability are the following: (1a) changes in the ionization state of the outflowing gas caused by fluctuations in the far-UV continuum flux (Hamann et al. 2011; He et al. 2017; Lu, Lin & Qin 2018), (1b) changes of gas ionization caused by the evolving gas density due to e.g. thermal instability (Waters et al. 2017) and (2) transverse motion of the absorbing cloud(s) relative to the line of sight (Gabel et al. 2003; Lundgren et al. 2007; Hall et al. 2007; Capellupo et al. 2011, 2012; Vivek et al. 2012).

The relation between continuum and BAL variability is different for each case. For example, in case (1a), continuum and BAL variability are highly correlated. As different parts of the outflowing gas face the same ionizing continuum, different absorption components exhibit coordinated variability. Filiz Ak et al. (2012, 2013) and Wildy, Goad & Allen (2014) found that different components of the same BAL or Si iv and C iv BAL troughs in one object vary in concert (all strengthening or weakening). This behaviour indicates that ionization change due to a variable ionizing continuum is important. On the other hand, in cases (1b) and (2), continuum and BAL variability are independent. In case (1b), ionization level changes can create non-coordinated variations between absorption components (see Waters et al. 2017 for the thermal instability case) within the same trough or between the troughs of different ions. Finally, in case (2), the transverse motion of clouds across the line of sight can cause non-coordinated variability (i) between absorption components within the same BAL (Capellupo et al. 2012) or (ii) between Si iv and C iv absorption components over corresponding velocities, within the same object.

Usually BAL variability studies are performed through equivalent width (EW) measurements of the whole BAL trough (e.g. Lundgren et al. 2007; Gibson et al. 2010; He et al. 2014; Welling et al. 2014; Wildy et al. 2014) or by measuring the variability of selected portions of BAL troughs (e.g. Gibson et al. 2008; Capellupo et al. 2011, 2012, 2013; Filiz Ak et al. 2013; He et al. 2015). However, various studies define variable regions in different ways. For example, Filiz Ak et al. (2013) detect variable regions wider than ≈275 km s⁻¹ and He et al. (2015) detect variable regions wider than ≈774 km s⁻¹, while Gibson et al. (2008) and Capellupo et al. (2011, 2012, 2013) detect variable regions wider than ≈1200 km s⁻¹.

BAL variability studies concentrating on the variations of individual components were carried out by Vilkoviskij & Irwin (2001) and Lu & Lin (2018). Vilkoviskij & Irwin (2001) observed a rise in the depths of absorption features in the BALQSO Q13031308. They attributed the depth variability in increasing amounts of absorbing matter and/or absorbing ions along the line of sight as probably due to spectral luminosity variations of the central object. Lu & Lin (2018) observed coordinated variability of all four Si iv narrow components of the Si iv BAL in the BALQSO J002710.06–094435.3. They attributed this variability to global changes in the ionization condition of the absorbing gas.

Studying the variability of individual substructures (clouds) within the outflow requires resolving and decomposing BALs into the components they consist of and measuring the variability of each individual component. In the case of resonance doublets, such as Si iv and C iv, a variability study requires measuring changes in both members of a doublet. In this article, we use (a) the model of Danezis et al. (2003, 2007) and Lyratzi et al. (2007) (Section 2), which can analyse BALs to determine individual components, (b) the fitting criteria and physical model of Stathopoulos et al. (2015) (Section 2), which guarantees that the number of components each Si iv and C iv BAL is split into is uniquely determined, and (c) the asta software (Tzimeas 2019), which is based on the model of Danezis et al. (2003, 2007) and Lyratzi et al. (2007) and the fitting criteria of Stathopoulos et al. (2015), in order to find the unique number of clouds forming Si iv and C iv BALs in 10 selected quasars (Section 3). In order to test the distinction and independence of the absorption components, in Section 4 we investigate the time variability of radial velocities (V_rad), full widths at half-maximum (FWHMs) and optical depths (τ₀) of each individual component between two different epochs. Finally, in Section 5 we discuss the findings derived from our analysis, while in Section 6 we provide our conclusions concerning the study of our sample of 10 quasars.

2 METHOD OF ANALYSIS

2.1 Physical model

In a series of articles, Bottorff et al. (2000) and Bottorff & Ferland (2000, 2002) proposed that the line widths produced by broad emission-line region (BELR) clouds are wider than their thermal widths (for Si iv, the thermal width in a 10⁴-K gas is FWHM ∼ 4 km s⁻¹ and in a gas of 10⁵ K, FWHM ∼ 12 km s⁻¹; for C iv, these values are about 6 and 20 km s⁻¹, respectively), due to the effects of microturbulence. They showed that microturbulent velocities can range from 200 km s⁻¹ up to 10³ km s⁻¹. Furthermore, Bottorff & Ferland (2001) proposed that each BELR cloud is a collection of overlapping constant density clumps. Finally, Lyratzi et al. (2009), using the model of Danezis et al. (2003, 2007) and Lyratzi et al. (2007), showed that, in individual quasars, Lyα and C iv BALs are the product of discrete components that are very close in velocity space and overlap.

Based on the previous studies, in Stathopoulos et al. (2015) we proposed a physical structure for the BAL region of quasars as well as a mechanism for the formation of Si iv and C iv BALs. According to the proposed physical model, BALs are complexes of absorption components produced by density enhancements within the outflow, which we call clouds. We note that the use of the ‘cloud’ terminology is a shorthand for some form of modulation in density within the flow along the line of sight to the continuum source. Clouds are considered as clusters of subunits called clumps or cloudlets (cloudlet regions II, figure 1 in Stathopoulos et al. 2015). From this point forward, we will always refer to the larger and more distinct structures as ‘clouds’ (regions I, figure 1, in Stathopoulos et al. 2015), while we will refer to the smaller structures as ‘clumps’. According to Stathopoulos et al. (2015), each ‘clump’ is responsible for the formation of absorption lines, the widths of which depend on the thermal and microturbulent motions of ions inside the clump. The synthesis of all these narrow lines produced by clumps, which are very close in velocity space and overlap, produce a broad component corresponding to a cloud. As a result, the relatively broad (broader than the the thermal and microturbulent width) components we use in our fits correspond to clouds. Synthesis of the lines produced by clouds forms the broad absorption troughs known as BALs.

In Stathopoulos et al. (2015), we also proposed that, in quasars exhibiting Si iv and C iv BALs, for corresponding velocities, both BALs originate in the same clumpy clouds, which have similar locations, kinematic structure and physical conditions. As a result, in Stathopoulos et al. (2015) we proposed that Si iv and C iv BALs consist of the same number of components and we set a series of fitting criteria which guarantees that the number of components each BAL is analysed into is uniquely determined (see Section 2.3). Furthermore, in Stathopoulos et al. (2015, 2017) we succeeded in fitting Si iv and C iv BALs with the same number of components in the case of four different BALQSOs.

2.2 Mathematical expression of the model

In order to study broad spectral lines in the context of the aforementioned physical model, we need a mathematical formulation of the physical model, which is capable of analysing BALs and broad emission lines (BELs) to determine the individual components they consist of. Below we describe the main idea behind the construction of such a model (for more details, see Danezis et al. 2003, 2007; Lyratzi et al. 2007).

A spectrum is a set of data points where each point is an ordered pair with coordinates of wavelength (Å) and flux (erg s⁻¹ cm⁻² Å⁻¹). Sloan Digital Sky Survey (SDSS) spectra are binned log-linearly for constant log(λ) and the pixel size is fixed in velocity space at 69 km s⁻¹. As a result, the problem of fitting a spectral line falls within the scope of numerical analysis. The method used in order to fit a spectral line, namely a set of data points, is interpolation. Interpolation is the process of constructing a mathematical function that has the best fit to a series of data points, such as a spectral line, possibly subject to constraints. Measures of goodness of fit typically summarize the discrepancy between observed values and the values expected under the model in question. One of the tests used in assessing whether a given distribution is suited to a data set is the reduced chi-squared test, which is the one used in our study.

The problem of constructing a function that provides the best fit of a complex spectral line of multicomponent nature is twofold: (a) finding the function that describes each one of the individual components composing the complex profile and (b) constructing the final function which, when interpolated, provides the best fit to the complex spectral line.

We note that Danezis et al. (2003, 2007) and Lyratzi et al. (2007) parametrized the optical depth profile (⁠|$\tau \equiv L\rm {\xi }$|⁠) of an absorption/emission component with the following distributions: Lorentz, Gauss, Voigt, rotation (Danezis et al. 2003) and Gauss–rotation (Danezis et al. 2007; Lyratzi et al. 2007). They also showed that if, for example, the optical depth profile follows a Gaussian distribution, then the line profile e^−τ is also Gaussian.

2.3 Fitting criteria

Previous studies (Gibson et al. 2009, 2010; Capellupo et al. 2011, 2012; Filiz Ak et al. 2014) have shown that C iv BALs are not always accompanied by Si iv BALs. Due to different ionization energy levels of Si iv and C iv, an absorbing gas may not have dense enough regions to produce Si iv absorption lines. Therefore, our study focuses on BAL quasars that present both C iv and Si iv BALs over corresponding velocity ranges.

In the case of quasars, we assume that the components of Si iv and C iv BALs follow Gaussian profiles, while the components of the corresponding BELs follow Voigt profiles. We reached this conclusion after testing all available distributions, namely Lorentz, Gauss, Voigt, rotation (Danezis et al. 2003) and Gauss–rotation (Danezis et al. 2007; Lyratzi et al. 2007). Our tests showed that, for Si iv and C iv BALs, the best fit is obtained if components follow Gaussian profiles, while for BELs Voigt profiles should be followed.

Thus, spectral fitting of BALs requires three free parameters for each Gaussian component, namely the radial velocity (V_rad), which is measured at the line centre, the optical depth at the line centre (τ₀) and the Gaussian standard deviation (σ). Therefore, a multicomponent fit, especially in the case of resonance doublets such as Si iv and C iv, requires a large parameter space. As a result, the problem of fitting Si iv and C iv BAL troughs is twofold: (a) achieve the best fit and (b) guarantee the uniqueness of the best fit. To conclude, we are interested not only in achieving the best fit of Si iv and C iv BALs but also in ensuring that the number of Gaussian components and the values of the measured parameters are uniquely determined.

The two problems mentioned above led us to introduce a series of fitting criteria, which guarantee not only the best fit of Si iv and C iv BALs but also the uniqueness of this fit. Before moving to the fitting criteria, we point out the following.

• We choose to fit and study resonance lines and not singlets. In the case of singlets, it is very difficult, if not impossible, to constrain the number of components required to fit the complex and broad absorption/emission profiles. In the case of singlets, the more components used during the fitting process, the better the fit becomes. We note that we do not treat resonance lines as singlets, but instead we take into account the fact that Si iv and C iv absorption/emission lines are resonance doublets. Therefore we model one blue and one red component for each line of a given absorption/emission doublet independently (taking into account their relations originating in atomic physics). Treating doublets as singlets is an oversimplification, which can cause incorrect measurements in physical parameter values. This is highly expected, especially in the case of Si iv, in which the wavelength separation between the members of the doublet is large (∼1930 km s⁻¹).

• Multicomponent analysis of BAL troughs is controversial. According to Laor et al. (1994), the major problem of multicomponent fits is that the best-fitting solution is not unique. Thus, the degeneracy of a multicomponent fit will be high unless both ions are fitted simultaneously. In order to overcome this problem and find a unique final solution that is also independent of initial parameter values, we fit the BALs of both ions simultaneously with parameters tied. During the fitting process, we assume that both ions follow the same kinematic structure. Finally, we consider doublets of both ions that are smooth and broad compared with the thermal line widths and show optical depth ratios inconsistent with 2:1. In that way, we ensure that these lines are intrinsic to the quasar (Hamann et al. 1997; Misawa et al. 2007b).

• We take into account objects that have at least moderately strong absorption in one of their BAL troughs (with a ‘balnicity index’ BI₀ > 100 km s⁻¹, as measured by Gibson et al. 2009).

As a result, in a previous article (Stathopoulos et al. 2015) we introduced two sets of fitting criteria. The first one sets the appropriate restrictions that apply to the fitting parameters (V_rad, τ₀, σ) between the blue and red members of a doublet. These restrictions stem from atomic physics. The second set provides the restrictions applied between two different ions, such as Si iv and C iv.

1. Criteria between the blue and red components of a doublet (C ivλλ 1548.187, 1550.772 Å and Si ivλλ 1393.755, 1402.77 Å).

   • A doublet must have exactly the same number of blue and red components. Thus, each C iv 1548.187-Å (blue) component has its corresponding C iv 1550.772-Å (red) component. The same applies to the Si iv doublet.

   • Each C iv 1548.187-Å (blue) component, at a specific velocity shift, has its corresponding C iv 1550.772-Å (red) component at the same velocity shift. The same applies to the Si iv doublet. However, we require that the difference in velocities at the line centres must not deviate from the theoretical doublet separation by more than two velocity bins (we adopt this condition from Wildy, Goad & Allen 2015). In SDSS spectra, one velocity bin corresponds to ∼69 km s⁻¹.

   • Both C iv 1548.187-Å and C iv 1550.772-Å components, at the same velocity shift, must have the same FWHM. The same applies to the Si iv doublet. Furthermore, the FWHMs of the components should not be smaller than the spectrograph’s FWHM. This constraint sets an upper limit on the number of components needed to achieve the best fit of a BAL.

   • For emission lines, we require the ratio of optical depths between the blue and red members of a doublet to be τ_b/τ_r = 2, as dictated by atomic physics (Savage & Sembach 1991).

   • For absorption lines, the ratio of optical depths between the blue and the red members of a doublet is free to vary in the range 1: 1 ≤ τ_b/τ_r ≤ 2: 1 (Wildy et al. 2015). This requirement is set in order to account for non-black saturation.

   As previously mentioned, the first four restrictions (a–d) are a consequence of atomic physics. In the case of Si iv and C iv, there are two fine-structure sublevels, which means that the observed spectral lines are resonance doublets. Both members of a doublet are characterized by the same width, the wavelength separation between the members of a doublet is fixed and the ratio of optical depths is determined by the ratio of oscillator strengths (Savage & Sembach 1991).

   The last restriction deviates from atomic theory. However, there are physical mechanisms that can produce discrepant optical depth ratios for doublet or multiplet transitions: (a) photons from the background emission source that are not absorbed and/or are scattered into the observer’s line of sight (Ganguly et al. 1999), (b) local emission by absorbers (Wampler, Chugai & Petitjean 1995) and (c) geometric partial coverage of the continuum and/or BEL source by the absorbing medium. According to the last scenario, the unabsorbed flux changes the relative depth of the lines (Wampler et al. 1995; Arav et al. 1999a,b).

2. Criteria between C iv and Si iv components at the same outflow velocity from the corresponding emission redshift.

   • Within the same quasar, both C iv and Si iv BALs consist of the same number of components.

   • Each C iv 1548.187-Å (blue) component at a specific velocity shift has its corresponding Si iv 1393.755-Å (blue) component at the same velocity shift. The difference in velocities between corresponding Si iv blue and C iv blue components must not exceed ∼200 km s⁻¹, which is the error in velocity measurements. The same applies between C iv 1550.772-Å (red) components and Si iv 1402.77-Å (red) components.

   • (τ_b/τ_r)_CIV at a specific velocity shift should be equal to (τ_b/τ_r)_SiIV at the same velocity shift. However, in this study, during the fitting process we relax criterion (2c) by letting the ratios (τ_b/τ_r)_CIV and (τ_b/τ_r)_SiIV take different values.

This set of criteria is based on the assumption that Si iv and C iv belong to the same cloud (Hamann et al. 2001; Hamann & Sabra 2004; Capellupo et al. 2012) and follow the same kinematic structure. Furthermore, both ions are assumed to have the same temperature (Rauch et al. 1996), in spite of their different ionization potentials. In fact, Si iv and C iv are high-ionization lines formed in regions of temperature 10⁴–10⁵ K.

It should be noted that during the fitting process the fitting code is forced to fulfil all the criteria mentioned above. These criteria are not set in order to verify our results after the fitting process, but are the constraints we follow with consistency while performing multicomponent fits.

3 OBSERVATIONS AND SPECTRAL FITTING

3.1 Quasar sample

In this work we use a sample of 10 known variable BALQSOs, presented in Table 1. The BALQSOs under study are chosen from the SDSS Data Release 9 Ahn et al. (2012) Broad Absorption Line (BAL) Quasar Variability Survey.¹ The main sample of BAL quasars contains 2005 objects assigned the ancillary target flag VARBAL. These 2005 objects were selected to be optically bright and to have at least moderately strong absorption in one of their BAL troughs (with a balnicity index of BI₀ > 100 km s⁻¹ as measured by Gibson et al. 2009). From this sample, we selected BALQSOs that meet the following criteria: (a) spectra with zWarning equal to zero, which means that they have no known problems, (b) 1.98 < z < 3.2, where the lower limit is set in order to ensure good coverage of both Si iv and C iv regions, (c) quasars that present both Si iv and C iv BALs, (d) at least one of the two epoch spectra should have signal-to-noise ratio (S/N) larger than 10. In the redshift range 1.98 < z < 3.2, we found 618 objects exhibiting Si iv and/or C iv BALs. From these objects, we rejected 161 exhibiting C iv BALs without Si iv BALs over corresponding velocities. Thus, our main sample includes 461 objects. In the current pilot work, we study 10 of the 461 BALQSOs, which (a) present |${V_{\rm outflow}^{\rm max}\lt 20\, 000}$| km s⁻¹ in order to avoid overlapping between the broad absorption of Si iv and the emission of O iλ1306 Å and (b) exhibit different types of profiles in terms of structure. We note that the time intervals of our sample of 10 BALQSOs present a ∼6–13 year time span.

3.2 Spectra preparation

Before proceeding to the fitting process, we correct all spectra for galactic extinction using the reddening curve of Fitzpatrick & Massa (1999) with R_V = 3.1. We obtain E(B−V) from the NASA Extragalactic Database (NED), which uses the dust maps of Schlegel, Finkbeiner & Davis (1998). We converted the observed wavelengths of the spectra to the rest frame using redshifts from the catalogues of Filiz Ak et al. (2013) and Shen et al. (2011). We smoothed the spectra and error arrays using an average filter of different width for each quasar, depending on the S/N of the spectrum.

3.3 Continuum, line fitting and goodness of fit

When performing multicomponent fits to Si iv and C iv BALs, as previously mentioned, we use equation (1) twice: once in order to synthesize all the blue components of a BAL and once in order to synthesize all the red components of the same BAL. We then synthesize these two sets of profiles in order to fit the complex BAL profile.

Based on the proposed fitting criteria, spectral fitting is performed as follows: for example, each time a new Si iv blue component is inserted, with initial parameter (V_rad,  τ₀,  σ) values, then the values of the parameters of the corresponding Si iv red component and the corresponding C iv blue component, at the same velocity shift, are determined automatically, according to the aforementioned fitting criteria. Furthermore, from the values of the C iv blue component, the values of the parameters of the corresponding C iv red component are determined automatically. The same applies in the case in which we change the value of one or more fitting parameters of the blue/red component of an ion. Then the values of the parameters of the corresponding red/blue component of the same ion, as well as the parameter values of the components of the other ion, are changed automatically according to the fitting criteria.

Each time we increase the number of components (preserving an equal number of components between Si iv and C iv), we iterate and test the goodness of fit using the reduced chi-squared parameter. The iterative process continues until the operator is satisfied that the data are modelled satisfactorily. Data are assumed to be modelled satisfactorily when we obtain a reduced χ² ≤ 2 (Laor et al. 1994). We note that we are looking for the minimum, as well as the same number of Si iv and C iv components that meet the |$\mathrm{\chi _{reduced}^{2} \le 2}$| criterion.

Through this process, we ensure that the best fit is determined uniquely. As a result, the number of components used to achieve the best fit of Si iv and C iv BALs and the values of the calculated parameters are also determined uniquely.

We use the same process when fitting both epoch spectra. However, it should be noted that the two epoch spectra are modelled independently, i.e. the fitting process is applied independently for the first and second epoch spectra.

We estimate the uncertainties of the absorption-line fitting parameters by adding Gaussian noise to the best fits. The width of the Gaussian at each pixel equals the flux uncertainty at that pixel. For each best fit, we produce 60 noisy spectra and then we fit each one in the same manner we fit the original spectrum. We measure the uncertainty of each parameter from its distribution.

4 RESULTS

4.1 Fitting results

In this section we provide the results obtained from the fitting process of Si iv and C iv BALs in two-epoch spectra of 10 BALQSOs. First and foremost, from the values of the calculated parameters V_rad,  τ₀ and  FWHM (where |$\mathrm{FWHM=\sigma \sqrt{8ln2}=2.355\sigma }$|⁠) in Tables A1, A2 and A3, one can observe that all the fitting criteria are applied with consistency and accuracy during the fitting process. In Fig. 1we give, as an example, the best fits of the Si iv and C iv spectral regions of J155335.78 + 324308.1 (spec-4966-55712-0266) for the second epoch spectrum. The observed spectrum is denoted with a black dotted line, while the thick black solid line corresponds to the best fit. In each best fit, we provide the reduced χ², which serves only as a measure of the quality of the fit. In Fig. 2 we give the best fits of both epochs for the whole quasar sample.

More specifically, in Table A1 in the first column we give the number of components each broad trough is analysed into. In columns 2–5, we give the radial velocities of the blue and red C iv components for both epochs. In columns 6–9, we give the radial velocities of the blue and red Si iv components for both epochs. Finally, in column 10 we give the mean value of radial velocity between C iv_b,  C iv_r,  Si iv_b and  Si iv_r of the measurements from the two epochs. In Table A2 we give the FWHMs of blue and red C iv and Si iv components for both epochs. In Table A3 we provide the optical depths of blue and red C iv and Si iv components for the two epoch spectra.

4.2 Variability in Si iv and C iv absorption components

4.2.1 Variations in radial velocities of components

We do not find variations in the velocity shifts of components between the two epochs in any of the QSOs studied. This result is evident in Fig. 3, where we plot (a) the radial velocities of C iv blue components (C iv_b: λ 1548.187 Å) of the second-epoch spectra with respect to the radial velocities of C iv blue components of the first-epoch spectra and (b) the radial velocities of C iv red components (C iv_r : λ 1550.772 A) of the second-epoch spectra with respect to the radial velocities of C iv red components of the first-epoch spectra. In panels (c) and (d) we do the same as in panels (a) and (b), but for Si iv blue and red components (Si iv_b: λ 1393.755 Å, Si iv_r: λ 1402.77 Å) respectively. From the graphs, it is obvious that C iv and Si iv blue and red components do not exhibit variations in their velocity shifts between the two different epochs. However, a more careful look at Table A1 indicates components that exhibit small variations in their radial velocities. These variations are ∼200–300 km s⁻¹, a value within the error of the radial velocity measurements. Consequently, we do not consider those components as variable.

4.2.2 Variations in FWHMs of components

In Fig. 4, we plot (a) the FWHMs of C iv blue components of the second-epoch spectra with respect to the FWHMs of C iv blue components of the first-epoch spectra and (b) the FWHMs of C iv red components of the second-epoch spectra with respect to the FWHMs of C iv red components of the first-epoch spectra. In panels (c) and (d) we do the same as in panels (a) and (b), but for Si iv blue and red components. In the majority of cases, C iv and Si iv absorption components do not exhibit variations in their widths between the two different epochs. However, in the case of C iv we observe that 5 out of 118 (∼4 per cent) absorption doublets show changes in their widths. In the case of Si iv, we observe that 12 out of 118 (∼10 per cent) absorption doublets show changes in their widths.

4.2.3 Variations in optical depths of components

In Table A4, we provide for each BALQSO the value of the variability measure N_σ(τ₀) for the optical depths of the C iv and Si iv blue and red absorption components. The sample of 10 BALQSOs exhibits 118 Si iv doublets and 118 C iv doublets over the corresponding velocities. As one can observe, Si iv and C iv BALs exhibit optical depth variations only in individual components. None of the 10 BALQSOs exhibits variability in its entire BAL trough. We observe three cases (J114548.38+393746.6, J155335.78+324308.1, J023252.80–001351.1) in which, within individual troughs, all variable components exhibit coordinated variability (within an individual absorption trough of Si iv or C iv, all variable components become stronger or weaker). The remaining seven quasars exhibit non-coordinated variability between individual components within their absorption troughs. We also observe one case (J114704.46+153243.3) in which a weak doublet has disappeared between the two observations. Finally, we observe one case (J101056.69 + 355833.3) in which two high-velocity broad and shallow components have emerged between the two epochs.

In Fig. 5, we examine the dependence of variability of Si iv and C iv absorption components on velocity. We split the velocity range into bins of 1000 km s⁻¹ width. In each bin, we count the number of observed absorption components and the number of variable absorption components. In Fig. 5(a), we plot the number of observed Si iv and C iv blue absorption components (dashed line) and the number of variable Si iv blue (shaded bars) and variable C iv blue (bars with pattern) components in each velocity bin. In Fig. 5(b), we do the same, but for Si iv and C iv red absorption components. We find that, in a number of the 118 Si iv doublets and 118 C iv doublets over the corresponding velocities, Si iv exhibits a higher incidence of variability. More specifically, 68 out of 118 (∼58 per cent) Si iv blue components exhibit variability in optical depth, while 44 out of 118 (∼37 per cent) Si iv red components show variable optical depth. On the other hand, 52 out of 118 (∼44 per cent) C iv blue components exhibit variability in optical depth, while 45 out of 118 (∼38 per cent) C iv red components show variable optical depth. If we consider a doublet variable as long as one of its members (blue or red) exhibits variability, then we have 75 out of 118 (∼64 per cent) Si iv doublets that show optical depth variations, while we find 63 out of 118 (∼53 per cent) C iv doublets exhibiting changes in their optical depths. The comparison between the number of variable Si iv and C iv absorption doublets in each velocity bin is shown in Fig. 5(c). Shaded bars denote the number of variable Si iv doublets in each velocity bin, while hatched bars denote the number of C iv variable doublets in each velocity bin.

Furthermore, C iv and Si iv absorption components exhibit variability over a wide range of velocities (see Fig. 5). The number of observed Si iv and C iv absorption components peaks in the range between −2000 and −9000 km s⁻¹. The number of variable Si iv and C iv blue components, as well as Si iv red components, also peaks in the same range of velocities (between −2000 and −9000 km s⁻¹). However, the number of variable C iv red components peaks at about −6000 and −9000 km s⁻¹. In the majority of velocity bins, Si iv exhibits a higher incidence of variability. In both panels, C iv shows a higher incidence of variability in the range −7000 to −8000 km s⁻¹.

Finally, we examine the occurrence of variability in Si iv doublets without corresponding changes in C iv doublets at the same velocities and vice versa. We find that, from 75 variable Si iv doublets, there are 38 that show changes in the corresponding C iv doublet at the same velocity (∼51 per cent). On the other hand, from 63 variable C iv doublets, there are 38 that present changes in the corresponding Si iv doublets at the same velocity (∼60 per cent). As a result, it is more possible to find variable Si iv components when C iv exhibits variability at the same velocity and not the opposite.

4.2.4 Coordinated and non-coordinated variations

In this section, we examine the variability behaviour between the members of Si iv and C iv doublets. More specifically, we examine coordination between (a) Si iv_b − Si iv_r, (b) C iv_b − C iv_r, (c) Si iv_b − C iv_b and (d) Si iv_r − C iv_r.

In the case of Si iv, we find that 36 out of 75 (∼48 per cent) variable doublets exhibit coordinated variations between their members, i.e. both members of a doublet strengthen or weaken. On the other hand, we find only 1 doublet out of 75 (∼1 per cent) in which one member of the doublet strengthens while the other weakens over time. Finally, we find 38 out of 75 (∼51 per cent) variable doublets in which only one member of the doublet varies, while the other does not change at all.

In the case of C iv, 32 out 63 (∼51 per cent) variable doublets exhibit coordinated variations between their members. In contrast, we find 2 out of 63 (∼3 per cent) doublets in which one member of the doublet strengthens while the other weakens over time. Finally, there are 29 out of 63 (∼46 per cent) variable doublets in which only one member of the doublet varies, while the other remains constant.

From 118 Si iv_b and 118 C iv_b components, there are 28 (∼24 per cent) that vary over the corresponding velocities. 23 out of 28 (∼82 per cent) components vary in concert (both strengthening or weakening), while the remaining five show non-coordinated variations (one strengthens while the other weakens). From 118 Si iv_r and 118 C iv_r components, 17 (∼14 per cent) vary over the corresponding velocities. 15 out of 17 (∼88 per cent) components vary in concert, while the remaining two show non-coordinated variations.

5 DISCUSSION

In this section, we discuss the implications of the results derived from our analysis. In view of these results, we also discuss different scenarios for the origin of Si iv and C iv broad absorption line variability.

5.1 Radial velocity and FWHM variations

As is evident in Fig. 3, Si iv and C iv doublets do not change their radial velocities between the two different epochs. Therefore, we do not observe any evidence indicating acceleration or deceleration of the BAL material in the line of sight. Given the statistics in Grier et al. (2016), this is expected due to the small sample size of this study.

In Fig. 4, one can observe that in the majority of cases the widths of Si iv and C iv absorption components do not change over time. In the case of C iv, we find that 5 out of 118 (∼4 per cent) doublets exhibit variation in their FWHMs. In the case of Si iv, we find that 12 out of 118 (∼10 per cent) doublets exhibit variation in their FWHMs. According to our physical model, the broad components used in the fits correspond to clouds that are clusters of subunits called clumps (see Section 2.1). The fact that individual components show changes in their widths may be interpreted in terms of changes in the internal structure of clouds or variations in the turbulent velocity field or both. In fact, Faucher-Giguére (2012) describes a mechanism for the formation of FeLoBALs (Low-ionization BAL quasars exhibiting absorption from Fe II and Fe III) in which a radiative shock wave propagating in a cloud shreds the cloud into cloudlets.

5.2 Optical depth variations

Optical depth variability occurs only in individual components of Si iv and C iv BAL troughs. None of the 10 quasars exhibits variability in all of its components, i.e. in its entire trough. Over corresponding velocities, Si iv exhibits a higher incidence of variability, which probably relates to different line strengths between the two ions. In particular, within the same object, C iv lines tend to be stronger than the corresponding Si iv lines at the same velocity shift. According to Capellupo et al. (2012), weaker lines are found to be more variable. Furthermore, C iv is usually saturated, thus small changes in the ionizing flux or small changes in column densities are not observable.

In J114704.46 + 153243.3, a high-velocity doublet has disappeared from the second-epoch spectra of both Si iv and C iv. On the other hand, J101056.69 + 355833.3 exhibits the emergence of two high-velocity broad and shallow doublets, evident in both Si iv and C iv. The disappearance/emergence of absorption components can be due to clouds moving into or out of our line of sight or ionization changes. However, in both quasars, none of the remaining doublets composing the Si iv and C iv BALs exhibits variations in each radial velocity, which weakens the moving-cloud scenario.

As mentioned above, none of the 10 quasars exhibits variability in all of its components, i.e. in its entire trough. Capellupo et al. (2012) argue that when variability occurs in selected portions (a few km s⁻¹ wide) of absorption troughs, the mechanism responsible is the transverse motion of clouds in the line of sight. They also argue that changes in ionization should cause more global variations and not changes in small and discrete velocity intervals of BALs. According to these arguments, the variability of individual components of BALs presented by our sample seems to fit well in the moving-cloud scenario.

However, there is a possibility that ionization changes can cause an effect where we observe only individual components varying. Let us consider a scenario in which BAL clouds are clumpy, they do not have the same density and the mechanism that causes the observed variations is the change in incident ionizing photons. The ionization parameter of each cloud depends on the fraction of incident photons relative to density and squared radius. Therefore, the densest regions will have a smaller ionization parameter and their response to increased/decreased photon energy will be less detectable or not detectable at all. Furthermore, absorption lines that are heavily saturated are less susceptible to small changes in ionization. Another simple case that can explain distinctive variations is the scenario in which there are clumps that may cover other clumps. The latter class of clumps would be shielded by closer-in clumps. Therefore, those shielded clumps will have relatively small effects of continuum variations and hence clumps at different radial velocities will show distinctive variations. As a result, variability of individual components of absorption troughs cannot provide a definitive answer as to whether variability is due to ionization changes or transverse motions of clouds in and out of the line of sight. At this point, we need to mention that we did not observe any changes in the radial velocities of components. If the transverse motion of clouds were responsible for the observed variability, we would expect to observe changes in the radial velocities of clouds. Thus, the moving-cloud scenario seems less possible.

5.2.1 Coordinated variations

We observed three types of coordinated variability: (1) all variable components within a BAL trough vary in concert (all strengthening or all weakening); (2) within the same object, Si iv and C iv components, over corresponding velocities, vary in concert; (3) both members of a doublet (Si iv_b − Si iv_r, C iv_b − C iv_r) vary in concert. The most likely explanation for (1) and (2) is global changes in ionization caused by fluctuations in quasar continuum flux (Hamann et al. 2011; Wang et al. 2015; He et al. 2017). For the third case, regardless of the variability mechanism involved, it is reasonable to expect coordinated variations between members of a doublet. Indeed, if the number of photons incident on a cloud changes, we would expect to observe coordinated changes between the members of a doublet. Also, if a cloud is moving into/out of our line of sight, it is possible to observe coordinated variations.

5.2.2 Non-coordinated variations

We observed three types of non-coordinated variability: (1) non-coordinated variations between components within a BAL (some components strengthen while others, at different velocities, weaken over time); (2) non-coordinated variations between Si iv and C iv components, at the same velocity, within the same quasar; (3) non-coordinated variations between the members of a doublet (Si iv_b − Si iv_r, C iv_b − C iv_r). Cases (1) and (2) can be interpreted in two ways. Non-coordinated variability can be caused by clouds moving in and out our line of sight. However, the lack of radial velocity variations observed in our sample weakens the moving-cloud scenario. On the other hand, non-coordinated variations can be caused by changes in the ionization state of the gas, e.g. evolving gas density due to thermal instability (see Waters et al. 2017).

The most unexpected finding is non-coordinated variability between the members of a doublet. Our physical model could provide a possible explanation for this finding. We proposed that clouds are clusters of overlapping subunits called clumps (see Section 2.1). Thus, each cloud component is the superposition of narrow components produced by clumps. We suggest that non-coordinated variability between the members of a doublet may be due to variations exhibited by clumps, i.e. variations in the internal structure of clouds. Since our model is able to study clouds and not their internal structure, we are not able to probe the physical conditions of clumps, so our explanation is only a suggestion. Finally, it should be noted that discrepancies between the two members of a doublet can be caused due to (a) photons from the background emission source that are not absorbed and/or are scattered into the observer’s line of sight, (b) local emission by absorbers and (c) geometric partial coverage of a continuum and/or BEL source by absorbing clouds. To conclude, non-coordinated variations between the members of a doublet could be caused by a mixed scenario involving a combination of the above mechanisms.

5.3 Clumpy versus smooth and homogeneous outflow

Finally, we would like to comment on the structure of the outflows. BALs consisting of complexes of narrow components motivate the idea that broad absorption troughs are the product of clumpy gas clouds with similar kinematics, locations and physical conditions. All BALs in our sample exhibit independent variations of absorption components. Thus absorbing clouds vary independently. This is an indication of the distinction and independence of the clumps from each other. Concerning our sample, evidence favours a clumpy structure of the outflow over a smooth and homogeneous wind.

6 CONCLUSIONS

Using the model of Danezis et al. (2003, 2007) and Lyratzi et al. (2007) and applying the fitting criteria of Stathopoulos et al. (2015), in two-epoch spectra of 10 BALQSOs, we succeeded in decomposing the Si iv and C iv BALs into the individual components they consist of. By measuring the radial velocity, FWHM and optical depth of each component, we are able to study the kinematics, physical conditions and variability of each absorbing cloud in the line of sight. The main results are the following.

In each quasar, Si iv and C iv BALs, over corresponding velocities, consist of the same number of absorption components. Each BAL trough arises from clumpy gas clouds that have similar locations, kinematic structure and physical conditions. Furthermore, both ions originate in the same gas clouds. The main cause of BAL variability is changes in the optical depths of individual Si iv and C iv components. Si iv and C iv absorption components present independent variations, which is an indication of the distinction and independence of the clouds from each other. All the above are indicative of density stratification within the absorbing gas, suggesting that quasar outflows are far from being smooth and homogeneous.

Concerning the mechanism responsible for the observed variability, our results favour the ionization change scenario as being more dominant, as we did not observe any changes in the radial velocities of clouds. However, the possible contribution of other mechanisms cannot be ruled out, given the small size of our sample.

We also found that the number of variable Si iv and C iv doublets peaks at the same range of velocities. However, Si iv exhibits a higher incidence of variability than C iv. Furthermore, within the same object, a variable Si iv component is more likely when the C iv component at the same velocity exhibits variability and not the opposite.

SUPPORTING INFORMATION

Figure 2. Best fits of Si iv and C iv BELs and BALs, complete set. The black dotted line denotes the observed spectrum, while the black, thick solid line corresponds to the best fit. For each fit we provide the reduced χ². Below each fit we present a panel with the residual, which appears as a green thin line. Panels (I) denote the first epoch spectrum, while panels (II) denote the second epoch spectrum. We note that, in all studied spectra, the distinction between the observed spectrum and the best fit is not obvious, due to the high accuracy of the fit.

Please note: Oxford University Press is not responsible for the content or functionality of any supporting materials supplied by the authors. Any queries (other than missing material) should be directed to the corresponding author for the article.

ACKNOWLEDGEMENTS

This research project is progressing under the financial support of the Ted and Erica Spyropoulos Foundation and the Special Account for Research Grants of the National and Kapodistrian University of Athens, to which we are very grateful. Finally, we thank the anonymous referee for valuable comments that greatly improved the manuscript.

Footnotes

REFERENCES

APPENDIX A