A polar+equatorial wind model for broad absorption line quasars: I. Fitting the C IV BAL profiles
aa r X i v : . [ a s t r o - ph . C O ] M a r Astronomy&Astrophysicsmanuscript no. 13255tx c (cid:13)
ESO 2018November 1, 2018
A polar+equatorial wind model for broad absorption line quasars:I. Fitting the C iv BAL profiles
B. Borguet ,⋆ and D. Hutsem´ekers ,⋆⋆ Institut d’Astrophysique et de G´eophysique, University of Li`ege, All´ee du 6 Aoˆut 17, B-4000 Li`egee-mail: [email protected]
Received September 15, 1996; accepted March 16, 1997
ABSTRACT
Context.
Despite all the studies, the geometry of the wind at the origin of the blueshifted broad absorption lines (BAL) observed innearly 20% of quasars still remains a matter of debate.
Aims.
We want to see if a two-component polar + equatorial wind geometry can reproduce the typical BAL profiles observed in theseobjects. Methods.
We built a Monte Carlo radiative transfer code (called MCRT) to simulate the line profiles formed in a polar + equatorialwind in which the photons, emitted from a spherically symmetric core are resonantly scattered. Our goal is to reproduce typical C iv line profiles observed in BAL quasars and to identify the parameters governing the line profiles. Results.
The two-component wind model appears to be e ffi cient in reproducing the BAL profiles from the P Cygni-type profiles to themore complex ones. Some profiles can also be reproduced with a pole-on view. Our simulations provide evidence of a high-velocityrotation of the wind around the polar axis in BAL quasars with non P Cygni-type line profiles. Key words.
Quasars: absorption lines – radiative transfer – Methods: numerical
1. Introduction
Depending on the selection technique and the definition used,about 20% to 30% of the quasars detected in recent surveys showthe presence of the broad absorption line (BAL) troughs associ-ated with the emission lines in their rest frame UV spectrum (e.g.Knigge et al. 2008, Ganguly et al. 2008). These BALs, reminis-cent of the P Cygni-type profiles seen in the spectra of massivestars, are mainly observed in high ionization lines like C iv andSi iv and are sometimes detected in lower ionization species likeMg ii . They reveal strong outflows from quasars (Scargle 1972),which can reach velocities up to 0.2 c (Foltz et al. 1983).Despite the large number of observations, the physical andgeometrical properties of the wind at the origin of the BALsremain largely unknown (e.g. Brotherton 2007). Moreover, thedistance at which those objects are found ( z ≥ .
5, so that C iv isshifted in the optical domain) hampers direct observation of theregions at the origin of the BALs even with the best telescopespresently available. Thus, all the information we can get aboutthe inner regions of BAL quasars comes mainly from indirectobservations.The first attempts to model the BAL profiles considered theresonant scattering of photons emitted by a continuum sourcein a spherically symmetric stellar-like wind (e.g. Scargle et al.1972, Surdej & Hutsem´ekers 1987). However, the growing num-ber of observed spectra displaying a huge variety of line profiles(Korista et al. 1993) revealed the need for other wind models.Facing the diversity of line profiles, Turnshek (1984a) proposedthat BAL quasars could be broadly divided into two samples:those quasars that exhibit smooth P Cygni-type profiles, and ⋆ PhD. grant student of the Belgian National Fund for ScientificResearch (F.N.R.S.) ⋆⋆ Senior research associate F.N.R.S. other ones that display an absorption trough that is detached invelocity from the associated weaker and wider emission peak.These observations indicate that the properties of the wind aremore complex than the simple spherically symmetric outflowinferred for stellar winds (Lee & Blandford 1997). However, asemphasized by Turnshek (1984b), it is very likely that distincttypes of BAL QSOs do not exist but are instead di ff erent mani-festations of the same phenomenon.The similarities of the emission line, optical continuum, andinfrared properties of BAL and non-BAL QSOs (e.g. Weymannet al. 1991, Gallagher et al. 1999, Reichard et al. 2003, Gallagheret al. 2007), as well as the spectropolarimetric observations (e.g.Schmidt & Hines 1999, Ogle et al. 1999, Lamy & Hutsem´ekers2004), favor a unification by orientation scheme for the BALQSOs over the evolutionary scheme (Hazard et al. 1984, Beckeret al. 2000). In the unification by orientation scheme, only a frac-tion (roughly corresponding to the observed fraction of BALQSOs) of the continuum source is covered by optically thickmaterial producing the broad absorption lines, which suggests adisk-like equatorial geometry for the BAL region (e.g. Turnshek1984a, Hamann et al. 1993, Murray et al. 1995, Elvis et al.2000, Yamamoto 2002). Such a geometry is supported by the-oretical studies and commonly accepted, since the QSOs arethought to be powered by accretion of matter onto a supermas-sive black hole in the form of a disk, from which the wind couldbe launched. However, the recent discovery of radio loud BALQSOs (e.g. Becker et al. 2000) and subsequent radio variabilitystudies reveal polar outflows in at least some of them (Brothertonet al. 2006, Zhou et al. 2006, Ghosh & Punsly 2007). Modelscombining polar and equatorial components have also been sug-gested (e.g. Lamy & Hutsem´ekers 2004) and evaluated from atheoretical point of view (Pereyra et al. 2004, Proga et al. 2000,Proga 2003, Proga & Kallman 2004) B. Borguet & D. Hutsem´ekers: Fitting the C iv BAL profiles in quasars with a polar + equatorial wind model In this context and given the similarities between typicalBAL profiles (e.g. Korista et al. 1993) and the line profiles pro-duced by a two component polar + equatorial wind like the onepresented by Bjorkman et al. (1994), our goal in this first pa-per is to determine whether such a simple two-component windcan qualitatively reproduce the various types of line profiles ob-served among the BAL QSOs. We also try to identify the key in-gredients needed to reproduce BAL profiles. In a second paper,we will investigate the e ff ect of microlensing on these profiles,aiming at a realistic interpretation of the spectral di ff erences ob-served in gravitationally lensed BAL QSOs like H1413 +
117 (cf.Hutsem´ekers et al. 2009).In Sect.2, we present MCRT, the Monte Carlo radiative trans-fer code we implemented in order to simulate resonance lineprofiles in a two-component axisymmetric wind. In Sect.3 webriefly identify the influence of the wind model parameters onthe line profiles we computed. In Sect.4, we show how MCRTis able to reproduce typical C iv BAL QSOs line profiles. Wediscuss the results of the line profile fitting and summarize ourconclusions in the last two sections of the paper.
2. The MCRT code
MCRT is a Fortran77 fully 3D Monte Carlo (MC) radiativetransfer (RT) code that we built to compute the resonance lineprofiles produced in axisymmetric winds. The use of the MonteCarlo simulation technique allows the radiative transfer equationto be solved exactly (i.e. without making use of the Sobolev ap-proximation), as well as ensuring the self consistent treatment ofthe radiative coupling between distant regions in a wind subjectto more complex velocity fields than monotonic radial laws (e.g.Knigge et al. 1995).Monte Carlo RT code have been extensively described (e.g.Knigge et al. 1995, Wood et al. 2001, Dijkstra et al. 2006), so thatwe only recall here the fundamental principles of this techniqueand the particularities of the code we developed.As stated in the introduction, our main goal is to identifyof the key ingredients (geometry and overall kinematics) of thewind governing the typical profile of the BAL QSO UV reso-nance lines. Thus we do not consider negligible e ff ects, suchas the relativistic ones that remain small even for outflows withhigh (v max ≤ . max (e.g. Hewitt et al. 1974, Grinin 1984). When using the MC technique, the solution of the RT equa-tion is found by following a huge number of photons on theirway through the wind. Each step in the photon’s life (positionand direction of emission, position of interaction, etc) is deter-mined by the mean of random numbers distributed according tothe normalized probability density function (NPDF) of the cor-responding simulated physical process. Thus if one wishes thatthe frequency ν i of all of the emitted photons follows a givenlaw L ( ν ) over the frequency interval [ ν min , ν max ], then ν i will berandomly chosen by solving the transformation equation (Presset al. 1992): ξ = Z ν i ν min L ( ν ) d ν , (1)where ξ is a random number drawn from a uniform distributionin the interval [0 , ξ refers to the call of such a new random num-ber. In general, there is seldom an analytical solution to Eq.1 sowe implemented the “table lookup method” (see Avery & House1968), which allows us arbitrary NPDF’s.In MCRT the initial position of emission of the photons ischosen isotropically on the surface of the continuum emissionregion, which is modeled by a sphere of radius R in and of infi-nite optical depth ( τ C = ∞ ) located at the center of the wind.The direction of travel through the wind is then determined byrandomly sampling a half sphere taking into account that thephotons are forced to leave the continuum source upward. The wind is filled with 2-level atoms whose rest-frame normal-ized absorption profile φ abs is described by a Gaussian (Natta &Beckwith 1986, Knigge et al. 1995) such that φ abs ( ν − ν ) = ( φ abs ( ν − ν , σ turb ) if | ν − ν | ≤ | ∆ ν abs | , (2)where ν is the rest-frame frequency of the considered transition,and φ abs ( ν − ν , σ turb ) = H √ πσ turb exp − ( ν − ν ) σ turb + K , (3)in which K ensures a continuous transition between the absorp-tion profile and the zero intensity. Here, H is a constant allow-ing for the normalization of the line profile over the interval ν ± | ∆ ν abs | /
2, where ∆ ν abs is the full width at zero intensity(FWZI) of the absorption profile. We choose the value of ∆ ν abs toensure the continuity of the absorption profile at the border of theinterval ν ±| ∆ ν abs | /
2. The parameter σ turb = ∆ ν turb / (2 √ ∆ ν turb = ν (v turb / c) is the FWHM of the absorptionprofile. The velocity v turb includes the thermal and the macro-scopic turbulence components in the wind that broaden the ab-sorption profile. We assume v turb to be constant throughout thewind.Owing to the velocity field −→ v ( r , θ, φ ) present in the wind, theinitial frequency ν i of a photon flying in the direction −→ n is seenDoppler-shifted by an atom of the wind in such a way that its“local” frequency ν l in the atom rest-frame is given by ν l = ν i − −→ v −→ nc ! . (4)Thus a photon will enter in resonance with the surroundingatoms only if its local frequency fulfills the condition definingthe so-called “resonance zone”: ν − ∆ ν abs < ν l < ν + ∆ ν abs . (5)When the photon enters such a region, the opacity of the mediumbecomes nonzero as does the probability of being absorbed. If n resonance zones are found along the direction of propagation ofthe photon in the wind, the total optical depth τ tot seen by thephoton until it escapes the wind is simply computed as τ tot ( ν i ) = n X j = Z b j a j κ ν φ abs ( ν l − ν , σ turb ) ds , (6)where κ ν is the total absorption coe ffi cient of the considered res-onance transition, and a j and b j are respectively the coordinates . Borguet & D. Hutsem´ekers: Fitting the C iv BAL profiles in quasars with a polar + equatorial wind model 3 of the beginning and of the end of the j th resonance zone foundalong the line of flight of the photon.Given the probabilistic interpretation of the RT, a photonexperiencing a total optical depth of τ tot ( ν i ) has a probability p = e − τ tot ( ν i ) of escaping the medium without being absorbed.This interpretation is used in the MC code to identify the occur-rence and the position of the scattering sites along the path ofthe photon through the wind. Indeed by using the transformationequation (Eq.1) we can determine the random optical depth τ MC at which the photon interacts : τ MC = − ln(1 − ξ ) . (7)Because we stored the run of τ tot = τ tot ( s ) along the photonpath, it is easy to invert this relation and find the point s where τ tot = τ MC . At this location the photon is radiatively absorbedand then instantaneously re-emitted at a frequency and in a direc-tion chosen by assuming a complete redistribution in frequencyand direction (CRFD, Lucy 1971, Mihalas et al.1976). This pho-ton may then either be re-absorbed somewhere else in the windor leave it and be detected by one of the detector (spectrographs,imagers) located around the wind.To decrease the simulation time in the case of non-spherically symmetric winds we make an intense use of the ad-vanced concepts of “first forced interaction” (e.g. Cashwell &Everett 1959, Witt 1977) and “peeling o ff ” (e.g. Yusef-Zadeh etal. 1984, Wood & Reynolds 1999) where we follow a photonpacket rather than a single photon.We checked the validity of our MCRT code by compar-ing the line profiles we obtained to line profiles computed withtwo traditional methods for spherical winds that allow an ex-act integration of the transfer equation. These benchmarks arethe well-known SEI method of Lamers et al. (1987) and thecomoving frame method of Hamann et al. (1981). We notedgood agreement between the general shape of the computed pro-files, regardless of the considered turbulence ( ∆ F / F ≤
5% onthe normalized emission peak flux, as well as a good matchbetween the absorption profiles). We also tested MCRT in thecase of axi-symmetric winds by comparing the profiles obtainedwith MCRT to those produced by the SEI method adapted byBjorkman et al. (1994). Once again we observed good agree-ment between the line profiles produced by both methods (seeBorguet 2009 for details).
While the shape of the C iv line in BAL QSOs can be mostly gov-erned by resonance scattering (Scargle et al. 1972), the presenceof C iii ] emission constitutes evidence that part of the emissionis due to collisional excitation (Turnshek 1984a, Turnshek 1988,Hamann et al. 1993). To account for this second source of pho-tons, we allow the production directly in the wind of a fraction ofphotons f e = I pure emission / I continuum . The choice of the location ofthe emission ( r e , θ e , φ e ) of these photons is made using a randomsampling of the corresponding NPDF: ξ = p ( r e , θ e , φ e ) = Z φ e Z θ e Z r e R in η ( r , θ, φ ) r sin θ drd θ d φ , (8)where the η ( r , θ, φ ) is a function that describes the emissivitythroughout the wind. Once again, our goal here is not to providea detailed self-consistent model of the wind so we choose as afirst guess an emissivity function of the form η ( r , θ, φ ) = n ( r , θ, φ ) (cid:18) R in r (cid:19) γ , (9) where n ( r , θ, φ ) is the density of the ion through the wind andwhere the second term allows taking the temperature distribu-tion and the ionization fraction into account. In the following wesimply take γ = Introduction
As stated in the introduction, it is di ffi cult to give a simple ex-planation to the observed BAL profiles when using a sphericallysymmetric expanding wind. The obvious next type of geome-try that can then be considered is the axi-symmetric one. Thesimplest of these models would still consist in a wind origi-nating from the central core. Such a generic model, with polarand equatorial components like the one presented in details byBjorkman et al. (1994) produces line profiles remarkably simi-lar to those observed in some BAL QSOs. Although simple, thismodel is versatile enough to produce a variety of line profiles,as observed in BAL QSOs. It constitutes a first good approxima-tion to the more complex wind from disk models proposed forAGN outflows in which the BALR and the BELR are generallycospatial (Sect. 1).In our model, we adopt stellar wind laws to describe thekinematics of the winds observed in quasars. Indeed, quasarwinds are also supposed to be driven by radiation (Arav & Li1996, Murray et al. 1995) as suggested by the line-locking inthe spectra of some BAL QSOs (e.g. Weymann et al. 1991,Korista et al. 1993, Arav 1996, 1997). However, there are im-portant di ff erences between stars and quasars (e.g. Arav 1994).One of them is the so-called overionization problem caused bythe strong UV / X-ray central source in quasars (e.g. Proga et al.2000). Several scenarios have been suggested to solve this prob-lem: Murray et al. (1995), Murray & Chiang (1997), Risaliti &Elvis (2009), Punsly (1999) and Ghosh & Punsly (2007). In ourstudy we assume the existence of shielding material between theradiation source and the outflow that prevents the total ionizationof the outflow (see Krolik 1999).Another di ff erence between stellar objects and quasarscomes from a significant fraction of the radiation in quasars sup-posedly being emitted from an accretion disk rather than froma spherically symmetric photosphere (e.g. Proga et al. 2000).Outflows with axial geometries have been studied by several au-thors, who show that the flow can be launched vertically fromthe disk and then pushed away by the radiation from the centralsource (Murray et al. 1995, Proga et al. 2000) with the eleva-tion of the wind over the disk is still small when the flow startsto expand radially. Since the launching conditions are unclear(Risaliti & Elvis 2009) and since we assume the BALR and theBELR to be cospatial, we simplify the geometry by assumingthat the wind is purely radial, which is correct at some distancefrom the disk. We considered a wind launched from a spherewith a radius equal to the inner radius of a typical BELR (10 − pc). The outer radius of the BELR / BALR was chosen to be 1pc, the radius at which the wind reaches the terminal velocity. Ifneeded, the anisotropy of the radiation field from the continuumsource can be readily introduced into our model.
B. Borguet & D. Hutsem´ekers: Fitting the C iv BAL profiles in quasars with a polar + equatorial wind model Fig. 1.
Illustration in the x − z plane of the two-component windused in our MC simulations, the velocity field is pictured byarrows in the lower part of the picture. The equatorial wind isshown edge-on (in dark grey) so that the wind model is rotation-naly symmetric along the z axis. The viewing angle of the ob-server is i = ◦ , and the absorption profile is produced by bothcomponent, the polar one contributing only at low velocities (i.e.for x < r lim ) given the disk opening angle and the viewing angle.Inspired from Fig. 8 of Bjorkman et al. (1994). Velocity field and density law
Keeping in mind the aforementioned simplifications we thendecided to implement the model described by Bjorkman et al.(1994). We recall its basic characteristics here. The velocity field −→ v ( r , θ, φ ) considered here can be written in spherical coordi-nates: −→ v ( r , θ, φ ) = v r (r , θ ) −→ e r + v φ (r , θ ) −→ e φ + v θ (r , θ ) −→ e θ , (10)where for simplicity we assume, as in Bjorkman et al. (1994),that the streamlines lie on surfaces of constant polar angle sothat v θ =
0. The radial component of the velocity field has thetypical β − law shape:v r (r , θ ) = v min + (v max ( θ ) − v min ) − R in r ! β , (11)where v min is the wind speed at the surface of the source of thecontinuum. The variable terminal speed v max ( θ ) allows for theintroduction of a slow expanding equatorial wind in a faster polarwind:v max ( θ ) = v pomax + (v eqmax − v pomax )f( θ ) , (12)where v eqmax and v pomax are respectively the terminal velocity of theequatorial and the polar components. The function that allowsthe smooth transition between the two components of the windtakes the form f ( θ ) = . " + π arctan sin ∆ θ − cos θ ∆ θ t ! , (13)where ∆ θ is the equatorial wind half opening angle and where theparameter ∆ θ t controls the transition between the equatorial andthe polar component of the wind. We chose, as in to Bjorkman et al. (1994), a low value for ∆ θ t = .
001 in order to keep thisregion much thinner than the equatorial wind opening angle.The v φ component of the velocity field is simply given byassuming conservation of the angular momentum in the wind:v φ = V rot R in r sin θ , (14)where V rot is the rotational speed at the surface of the source ofthe continuum.The law governing the distribution of the ion density is de-rived from the equation of continuity of matter in a central windand is parameterized using n ( r , θ, φ ) = n ( θ ) rR in ! − α v r (r , θ )v min ! − , (15)with the parameter α implicitly including the radial variation ofthe ionization (i.e. α = n ( θ ) allowing the transition between the polarand the equatorial components: n ( θ ) = n po + ( n eq − n po ) f ( θ ) , (16)where n eq and n po are, respectively, the density of the consideredion at the base of the wind in the equatorial or in the polar com-ponent. The value of n po is computed by specifying the value τ tot p of the total optical depth of the wind along the polar axis(i.e. θ = ◦ ) integrated over frequency: τ tot p = Z ∆ ν l − ∆ ν l τ tot ( ν i ) d ν i , (17)with 2 ∆ ν l the measured width of the observed line profile. Thevalue of n eq is fixed by the free parameter k pm , which definesthe ratio of the ionic density between the two components at thebase of the wind: n eq = k pm n po . (18)
3. Parameter study
Here we concentrate on the main parameters a ff ecting the lineprofiles for a two-component wind where we suppose no pureemission (i.e. f e = ff ects of the pa-rameters governing the velocity and density laws or the e ff ectsof the turbulent component in the wind since they are similarto those observed in the well-understood spherically expand-ing wind case (Castor & Lamers 1979, Beckwith & Natta 1987,Hamman 1981, Lamers et al. 1987).The most important parameters we have to specify for com-puting a line profile are the frequency integrated polar opticaldepth τ tot p , the ratio between the equatorial and the polar ionicdensity k pm , the velocity ratio between the polar and the equa-torial terminal speed v eqmax / v pomax , the disk half-opening angle ∆ θ ,the viewing angle i , and the ratio V rot / v pomax between the rota-tional speed of the source of continuum and the polar termi-nal velocity. The parameters used for the reference line profileare summarized in Table 1. Such a parameter study was previ-ously carried out by Bjorkman et al. (1994) using an SEI-typemethod. Because their calculations agree with ours using an ex-act method, we only recall here the general e ff ects produced byeach parameter and refer the reader to the Bjorkman et al. pa-per for further details. We do, however, emphasize the e ff ect ofthe wind rotation given the important changes in the line profileproduced by the variation of this parameter, more particularly . Borguet & D. Hutsem´ekers: Fitting the C iv BAL profiles in quasars with a polar + equatorial wind model 5 Fig. 2.
Illustration of the e ff ects of the wind’s main parameter on the line profile (see text for details). Each spectrum is representedas a function of the normalized wavelength X = ( λ − λ ) / ( λ max − λ ) and is the result of the simulation of 2 10 photon paths throughthe wind ( S / N >
100 on the continuum level).
Table 1.
Wind parameter for the benchmark model
Parameter Value Parameter Valuev pomax − α . min
100 km s − β . eqmax − ∆ θ ◦ V rot − ∆ θ t . turb
500 km s − i ◦ τ tot p . f e . k pm . γ . when the equatorial disk is viewed near edge-on (Mazzali 1990,Petrenz & Puls 1996, Busche & Hillier 2005).The profiles illustrated in the panel A of Fig.2 are represen-tative of the profiles that can be produced in a two-componentwind when the equatorial component is seen near edge-on. Theshape of these profiles is constituted by typical P Cygni-typeprofile extending to the higher velocities coming from the polar component, but where a sharp absorption trough is produced atlower velocities by the slowly expanding equatorial wind. In thispanel we illustrate the evolution of the line profiles as a functionof the total polar optical depth integrated over frequencies τ tot p .Similar to the spherically symmetric expanding wind case (e.g.the atlas constructed by Castor & Lamers 1979), when τ tot p isincreased, we observe an increase in the emission peak and inthe equivalent width of both the emission and absorption partsof the line profile. No variations are observed in the equatorialabsorption since that part of the profile is already saturated forthe lower value of τ tot p .The e ff ect of the k pm ratio is illustrated in the panel B ofFig. 2. When k pm is decreased, the depth of the absorption pro-file of the equatorial component evolves in the same way. Asin Bjorkman et al. (1994), we observe that the equatorial com-ponent is still optically thicker to the radiation than the polarcomponent even for k pm = .
1, and this because of the narrowervelocity range of the equatorial component.
B. Borguet & D. Hutsem´ekers: Fitting the C iv BAL profiles in quasars with a polar + equatorial wind model The change in the ratio between the teminal speed v eqmax andv pomax of the two components essentially modifies the position ofthe edge of the low-velocity absorption component (see panelC of Fig. 2). We also observe that, when v eqmax is increased, theabsorption due to the presence of the disk no longer remainsblack near the line center. Indeed, to produce a black absorption,the disk has to cover the whole source of continuum. But for anequatorial wind with a half-opening angle ∆ θ , this only happensbeyond the radial coordinate r > r lim = R in cotan ∆ θ (see Fig. 1),which corresponds to the velocity v eqlim ∼ v r (r lim , ◦ ), the valueof which is sensitive to v max ( θ ) (cf. Eq. 11).In panel D of Fig. 2, we illustrate the evolution of the lineshape as a function of the half-opening angle of the equatorialwind ∆ θ . We observe the development of a broad high-velocityabsorption when ∆ θ is decreased. This observation is once moreexplained by considering the radial coordinate r lim at which thedisk completely covers the source of the continuum. As the high-velocity absorption (due to the polar component) occurs beforethe equatorial wind, the high absorption velocity range is limitedwithin the interval [0 , v polim ], where v polim ∼ v r (r lim , ◦ ). In contrast,when ∆ θ is increased, we observe the apparition of a secondaryblueshifted emission peak beyond v eqmax given that, for a su ffi -ciently wide disk, there is no remaining polar absorption of thecontinuum.The viewing angle i to the wind plays a critical role in theline profile (see panel E of Fig. 2). Indeed the equatorial ab-sorption component is only seen when the disk is viewed nearedge-on (i.e. i = ◦ ). Because i is decreased from an edge-on toa pole-on ( i = ◦ ) view of the disk, the low-velocity absorptionproduced by the disk decreases, since only the high-velocity endof this component covers the continuum.Finally, panel F of Fig. 2 illustrates the modifications ofthe line profile when varying the rotational speed of the wind.The major e ff ect of the rotation is observed on the emissionpeak, which decreases and is significantly redshifted when theV rot / v pomax ratio is increased. Indeed, when there is no rotation,the emission peak is relatively sharp because that part of the pro-file is produced in the inner, optically thicker regions of the wind,whose velocity range is narrow. When rotation is considered, theresonance zones become twisted in such a way that the inner re-gions are distributed over a wider range of projected velocity.This induces the smoothening of the emission peak since the ro-tation allows the absorption to occur in the redder part of thecontinuum at frequencies centered on the rest-frame frequencyof the line transition ν (e.g. X = .
0) (see Fig.3 and also Hallet al. 2002 for a detailed explanation). The bluer part of the ab-sorption profile is not significantly a ff ected by the rotation be-cause this part of the profile is produced in front of the contin-uum source, i.e. where the projected rotational velocity is nearlyzero.
4. Fitting BAL profiles with the polar+equatorialwind model
In this section we try to reproduce a representative sample ofC iv line profiles observed in BAL QSOs and extracted from thepaper of Korista et al. (1993), which provides homogeneous andhigh-quality spectroscopic data for a large sample of BAL QSOs.Our goal is to check that such profiles can be modeled using asimple two-component wind geometry for the BALR. Ten spec-tra were carefully selected out of the 72 BAL QSOs presented inthe Korista et al. paper on the basis of two criteria. Fig. 3.
Closer illustration of the e ff ect of the rotation of the windover the line profile, its part in emission, and its part in absorp-tion. The dotted line represents the profiles for which the rota-tional velocity is zero, while the straight line represents the pro-files with V rot = .
25 v eqmax , and the dashed line a wind whereV rot = .
50 v eqmax . The parameter used are those gathered inTable 1 (see text). – We retained as far as possible objects free of doublet e ff ects(i.e. v pomax ≫ C iv doublet separation), non-blended and withsmooth emission / absorption C iv line profiles (i.e those lessa ff ected by multiple absorption troughs). – We selected objects for which the continuum can be securelydefined on both sides of the C iv line profile, allowing for acorrect normalization of the spectra.The observed and the fitted spectra of each selected objectare illustrated, normalized to the continuum level, in Figs. 4 and5. We note good qualitative agreement between the observed lineprofile and the model. The parameters used in the fit of eachC iv line profile are collected in Table 2. While some parame-ters (v eqmax , v pomax , i , τ tot p , α , f e ...) were allowed to vary, we tried tokeep fixed the radial velocity gradient in the wind (the β param-eter), the emission parameter γ and the disk opening angle ∆ θ .The latter was chosen equal to the value generally adopted forthe opening angles of disk winds in AGN models (Murray et al.1995, Proga & Kallman 2004). However, even those parameterswere varied in a few cases to slightly modify the part of the pro-file in emission. In particular, we found that the opening angle . Borguet & D. Hutsem´ekers: Fitting the C iv BAL profiles in quasars with a polar + equatorial wind model 7 ∆ θ of the disk has to be decreased for fitting the high-velocity ab-sorption component (see Sect. 3) observed in the P Cygni-typeline profiles (Q1333 + + / detachedabsorption ones with a lower emission peak. However we triedto model all these line profiles using the same wind geometrysince, as suggested by Turnshek (1984b), it is likely that distincttypes of BAL profiles are the consequence of a unique mass-lossphenomenon.The empirical fitting procedure we adopted here makes thedistinction between three types of line profiles, each possessingits own set of spectral signatures. The first kind of line profile isthe P Cygni-type (Q1333 + +
117 see top pan-els of Fig.4). In this subsample, the absorption trough seemsconstituted of two subtroughs covering two overlapping veloc-ity ranges, i.e. an optically thick “narrow” ( ∼ − wide)absorption component superimposed on an optically thin absorp-tion trough extending up to velocities of 10000 km s − . Thesecharacteristics suggest that there is an equatorial denser disk-likeregion seen nearly edge-on and producing the narrow absorptionobserved. The necessity of considering such a more slowly ex-panding disk in a polar wind is illustrated particularly well whenobserving the C iv line profile of Q1413 + − ,which implies, through resonance scattering, the presence of anunderlying emission component extending from -10000 km s − to 10000 km s − . Since the flux is almost zero at slower veloc-ities (v ≥ − − ), a part of these photons has to be re-absorbed somewhere, suggesting there is an optically thicker re-gion on the line of sight to the observer. This observation fits theframework in which a part of the emission from the BELR isabsorbed in the BALR (e.g. Turnshek et al. 1988, Hamann et al.1993).The second type of line profile we considered is presentedin the lower panels of Fig. 4. These profiles are character-ized by an asymmetric emission peak whose intensity rela-tive to the continuum level is significantly lower than in theP Cygni-type ones. Some individuals of this subsample alsoshow, similar to the P Cygni-type ones, higher velocity ab-sorption through superimposed to a narrower component (bestseen in, e.g., Q0842 + + iv line profile of seven out of the ten objects in oursample (Q0019 + + + + + pomax ) and is approximatelyequal to the equatorial wind terminal velocity. For the P Cygni-type profiles (Q1333 + + χ type technique while searching for the best model. However, this is not a maindrawback since our main goal is to show that a simple windmodel is able to approximately reproduce a variety of resonanceline profiles observed in BAL QSOs. Moreover, given the degen-eracy between some of the model parameters ( k pm with i , v eqmax with i , β with α , etc), as well as the di ffi culty in some cases ofcorrectly evaluating v pomax or other model parameters, more thanone best fit is generally possible.The absence of the two-component wind signatures definedabove in the C iv line profile of some objects led us to define athird subsample of line profiles. These line profiles can be fittedby a two-component wind (see upper panel of Fig. 5). However,some profiles (the prototype being Q0019 + + iv line profile of Q0041-4023 canbe reproduced by a two-component wind seen nearly pole-on.This arises when a single deep absorption trough is associatedwith a quasi-symmetric emission profile. Once again, given theuncertainties on the wind parameters because of the lack of clearsignatures in the line shape, several wind models can be fitted tothe observed line profiles (here we chose as typical values formodel M2 v eqmax = V rot = . pomax ).From Figs. 4 and 5, we note that our simple model is ableto reproduce the diversity of the BAL profiles observed in a realsample of objects quite well. Interestingly enough, in order to beable to fit the C iv profiles with MCRT, we must shift the wholesimulated line profile with respect to the emission peak, usuallyused for redshift determination. This shift is needed to center theunderlying emission component of the profile on the zero veloc-ity. Indeed, when dealing with resonant scattering, an absorptiontrough extending over the velocity range [ − v max , 0] produces anemission feature extending from − v max to + v max . The redshiftof the quasar determined from the center of the underlying C iv emission line is given in the second column of Table 2.From the fitting procedure, one of the major parameters thatcontrol the line profile in this type of wind remains the viewingangle i , which plays a crucial role in the shape of the absorptionpart of the line by controlling the relative contribution of theequatorial and polar components (when both are required). Thuswhen a line profile exhibits a sharp, deep absorption trough su-perimposed on a shallower high-velocity absorption component,the quasar is probably viewed along a line of sight, such as thedense equatorial wind seen nearly edge-on (e.g. Q1413 + f e > B. Borguet & D. Hutsem´ekers: Fitting the C iv BAL profiles in quasars with a polar + equatorial wind model Table 2.
Parameter of the two-component wind model for the best fit of the C iv BALs in the selected quasar sample.
BAL QSO Name z τ tot p k pm v pomax (km s − ) v eqmax (km s − ) V rot (km s − ) α β ∆ θ ( ◦ ) i ( ◦ ) f e γ Q1333 + + + + + + + + a - 9000 8000 2.5 1.5 15 90 0.11 1.0Q0041-4023 M1 2.450 5.00 10.0 10000 5000 3000 2.0 1.5 15 90 0.18 1.0Q0041-4023 M2 2.450 15.0 5.0 6000 3000 3000 2.0 0.5 15 0 0.07 1.0 a k pm represents the total equatorial ( i = ◦ ) optical depth integrated over frequencies since τ tot p =
5. Discussion
We showed that a simple two-component equatorial + polar windmodel is able to reproduce a variety of BAL profiles, rangingfrom detached absorption troughs to P Cygni-type profiles. Thesolutions of the fits are not unique and several models with dif-ferent geometries and / or physical properties can equally repro-duce the observed spectra. In accordance with previous studies(e.g. Hamann et al. 1993), this demonstrates that a unique phys-ical characterization of the outflow cannot be derived from lineprofile fitting.While detailed information on the geometry of the outflowscannot be derived, we nevertheless reached some interestingconclusions. First, in some objects, it is necessary to includeboth the equatorial and the polar absorption regions. This is in-deed the case for objects like Q1413 + + + + + + iv line shape of the P Cygni-typequasar prototype PHL5200. This indicates that the model useddoes not include all the ingredients needed. Indeed, the modelcannot reproduce the very sharp transition observed between theabsorption and the emission components in the C iv profile ofPHL5200 (Turnshek et al. 1988). Such a sharp transition at zerovelocity could in turn be produced in a wind launched from thedisk itself. In that type of model, which exhibits large-scale prop-erties similar to those of the model considered in the presentstudy, the wind is launched from the disk and then radially ac-celerated by the radiation pressure (Murray et al. 1995, Proga& Kallman 2004). When observed nearly edge-on, it can pro-duce strong absorption at the center of the line as observed inPHL5200. Proga (2003) shows the capabilities of these winds toproduce a sharp transition between the absorption and emissionin the case of cataclysmic variable stars. Implementing that typeof wind is beyond the scope of this paper and has been left forfuture work.Furthermore, in a majority of objects we found it necessaryto use high values of the ratio of the rotational speed to the po-lar terminal speed of the wind V rot / v pomax to adequately reproducethe asymmetry of the emission line profiles. Such a high valueof the rotation accounts for the redshift and the faintness of theemission peak. These characteristics result from the continuumemitted on the red side of the line profile possibly being ab-sorbed by the optically thick material located between the sourceof continuum and the distant observer when rotation is present(see Fig. 3). The rotational velocity at the base of the wind canreach several thousand km s − , which is consistent with the ro-tational velocities inferred for gas orbiting in the vicinity of asupermassive black hole (e.g. Murray et al. 1995, Young et al.2007). Interestingly, we found that the rotational velocity must . Borguet & D. Hutsem´ekers: Fitting the C iv BAL profiles in quasars with a polar + equatorial wind model 9 Table 3.
Blueshift of the C iv line relative to the systemic redshift z sys for the three quasars from our sample with secured [O iii ] linemeasurement. BAL QSO Name z sys Ref. z sys ∆ v blueshift Q0019 + − Q0226-1024 2.268 McIntosh et al. 1999 9200 km s − Q1413 + − remain low in quasars with P Cygni-like line profiles. Indeed,to keep the emission intense, the redward absorption due to therotation must be small (cf. Fig. 3). As a consequence, the shal-low blue absorption wing only comes from the polar wind. Thismay indicate a possible dynamical di ff erence between the BALQSOs with detached profiles and those ones with P Cygni typeprofiles.The rotation of the wind naturally provides a simple andstraightforward interpretation of the correlation between theproperties of the broad emission lines (BELs) and those of thebroad absorption lines as reported by Turnshek (1984a). Indeed,as shown in that paper, BAL QSOs having complex absorptiongenerally have a weaker C iv emission peak relative to the con-tinuum than does BAL QSOs with smooth P Cygni absorption.This can be explained by the stronger / wider absorption on thered side of the line profile resulting from the rotation of opticallythick material in front of the continuum source. Combining theemission profile and the redshifted absorption of the continuumresults in profiles resembling the so-called detached troughs ob-served in several BAL QSO spectra (Korista et al. 1993, Arav& Begelman 1994, Hall et al. 2002, Proga & Kallman 2004).Recently, spectropolarimetry of the BAL QSO PG1700 + α BEL, which is interpreted as the typical sig-nature of a rotating wind (Young et al. 2007, Wang et al. 2007).When fitting the C iv line profiles, we found it necessary toadopt a systemic redshift for the wind lower than the redshiftgiven by the peak of the C iv emission line. This “wind redshift”corresponds to the centro¨ıd of the full emission component thatunderlies the observed absorption + emission profile and definesthe rest frame of the outflow model. It is interesting to comparethis redshift to the redshift determined from the narrow forbid-den lines usually thought to provide the true systemic redshift ofthe quasar and its host galaxy (e.g. McIntosh et al. 1999, VandenBerk et al. 2001). Unfortunately, only a few measurements areavailable because the [O iii ] lines are shifted in the near-infraredand are fainter in BAL QSOs than in non-BAL QSOs (Yuan etWills 2003). For the BAL QSOs of our sample, only three accu-rate determinations are available, as given in Table 3. For thesequasars, we find a net blueshift of the simulated C iv line pro-files by several thousand km s − with respect to the systemicredshift measured from [O iii ]. Such a blueshift of the highlyionized species relative to the narrow [O iii ] lines –or to the lowionization Mg ii line– is rather common and well known in thecase of both the BAL and non-BAL QSOs (e.g. Gaskell 1982,Corbin 1990, McIntosh et al. 1999), reaching up to 4000 km s − (Corbin 1990). BAL QSOs are among the QSOs with the high-est blueshifts (Richards et al. 2002, 2008), in agreement withour measurements. While the blueshift of the C iv emission withrespect to [O iii ] emission is well documented, its origin is stillunclear. Several mechanisms have been proposed to interpret it,including dust attenuation of the red emission component, scat-tering of the line profile, relativistic e ff ects, and black hole recoil(cf. Corbin 1990, Mc Intosh et al. 1999, Vanden Berk et al. 2001, Shields et al. 2009). Ultimately, it might be necessary to considerthese e ff ects for full self-consistent modeling of quasar outflows.In the particular case of Q0019 + iv absorp-tion lines are observed at -3000 and + − in the windrest frame (Fig. 4), i.e. at -8000 and -2000 km s − in the sys-temic quasar + host rest frame. These velocities suggest that theyoriginate in a large-scale outflow in the host galaxy rather thanin the BAL wind. Interestingly enough, the velocity di ff erencebetween these narrow absorption lines is close to the velocityseparation between the Ly α and NV resonance doublets ( ∼ − ), suggesting a possible line locking e ff ect (Korista et al.1993, Arav & Begelman 1994).
6. Conclusions
In this study, we used a combination of a Monte Carlo radia-tive transfer code and a simple two-component polar + equatorialwind model in which photons are emitted from a central spher-ically symmetric source and resonantly scattered in the wind toreproduce typical C iv resonance line profiles selected from ahomogeneous sample of BAL QSO spectra.Although the lack of uniqueness of the line profile fittingdoes not allow us to strongly constrain the geometry of the wind,we can summarize our main findings as follows1. The diversity of BAL profiles produced by the adopted po-lar + equatorial model ranges from the typical P Cygni-typeprofiles to the detached absorption ones, reproducing thoseobserved in a homogeneous sample of BAL QSOs.2. While in some cases the line profiles can be reproduced bya single equatorial wind, we find it necessary to use a two-component polar + equatorial wind in a majority of objects.3. The viewing angle to the wind is generally large (disk seennear edge-on); however in some cases, the line profiles canalso be reproduced when assuming a pole-on view, in accor-dance with the results of recent radio surveys of BAL QSOs.In this context, it would be interesting to obtain good qualityspectra of bona-fide polar BAL quasars and try to fit theirline profiles by assuming the pole-on view.4. The equatorial wind is rotating, and the rotational velocity atthe base of the wind can reach a significant fraction of thepolar terminal speed.A possible way to break the degeneracy between the variousparameter combinations of the two-component model that canreproduce the observed BAL profiles is to use gravitational mi-crolensing. Indeed, a microlens moving across the quasar innerregions can di ff erentially magnify the di ff erent line-forming re-gions, inducing line profile variations from which the geometryof the outflow can in principle be retrieved (e.g. Hutsem´ekers1993, Hutsem´ekers et al. 1994, Lewis & Belle 1998, Chelouche2003, 2005). Our code MCRT has been explicitly built to inte-grate these microlensing e ff ects. The e ff ect of microlensing onBAL profiles, their use for deriving the physical properties ofthe outflow, and application to a known lensed system will bepresented in a second paper. References
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Illustration of the best fit for eight out of the ten C iv line profile selected from the BAL quasar sample of Korista et al.(1993). The observed spectrum is represented by a full line and the two-component model profile by a dashed line. Each spectrumis normalized to the continuum level and represented as a function of the velocity. iv BAL profiles in quasars with a polar + equatorial wind model Fig. 5.
Illustration of the non-uniqueness of the fit for two particular objects of our sample. The upper panels (labelled M1) of thisfigure show that the C iv line profile of these two objects can be fitted in the framework of the two-component wind model. In thelower panels (labeled M2), we show that the lack of typical two-component wind signatures in the line profile allows alternative fitswith di ffff