Relation between the variations in the MgII $\lambda2798$ emission-line and the 3000 {\AA} continuum

TL;DR

This study examines how the MgII emission line varies in response to continuum changes in quasars, revealing a small, luminosity-dependent responsivity using multi-epoch spectroscopic data.

Contribution

It provides the first statistical constraints on MgII line responsivity to continuum variations across different luminosities in intermediate-redshift quasars.

Findings

MgII line variations closely correlate with continuum changes.

The responsivity of MgII is small, averaging around 0.464.

MgII responsivity decreases with increasing quasar luminosity.

Abstract

We investigate the relationship between the MgII $\lambda2798$ emission-line and the 3000 {\AA} continuum variations using a sample of 68 intermediate-redshift ($z\sim$ 0.65$-$1.50) broad-line quasars spanning a bolometric luminosity range of 44.49 erg s$^{-1} \leq \rm{log}$$L_{\rm{bol}} \leq 46.31$ erg s$^{-1}$ (Eddington ratio from $\sim$ 0.026 to 0.862). This sample is constructed from SDSS-DR7Q and BOSS-DR12Q, each with at least 2 spectroscopic epochs in SDSS-I/II/III surveys. Additionally, we adopt the following signal-to-noise ratio (S/N) selection criteria: a) for MgII and the 3000 {\AA} continuum, S/N $\geq$ 10; b) for narrow lines, S/N $\geq$ 5. All our quasar spectra are recalibrated based on the assumption of constant narrow emission-line fluxes. In an analysis of spectrum-to-spectrum variations, we find a fairly close correlation (Spearman $\rho = 0.593$) between the variations in broad MgII and in the continuum. This is consistent with the idea that MgII is varying in response to the continuum emission variations. Adopting the modified weighted least squares regression method, we statistically constrain the slopes (i.e., the responsivity $\alpha$ of the broad MgII) between the variations in both components for the sources in different luminosity bins after eliminating intrinsic biases introduced by the rescaling process itself. It is shown that the responsivity is quite small (average $\bar{\alpha} \approx$ 0.464) and anti-correlates with the quasar luminosity. Our results indicate that high signal-to-noise flux measurements are required to robustly detect the intrinsic variability and the time lag of MgII line.

Tables

Table 1. Table 1: Sample Summary

ID	Object Name	Plate	Fiber	MJD	$E{W}_{{}_{\mathrm{mgii}}}$	$\log$$L_{{}_{\mathrm{mgii}}}$	$\log$$L_{{}_{\mathrm{nev2}}}$	$\log$$L_{{}_{\mathrm{oii}}}$	$\log$$L_{{}_{\mathrm{neiii1}}}$	$\log$$L_{{}_{\mathrm{oiii2}}}$	$z_{{}_{\mathrm{vi}}}$	$\log$$L_{{}_{3000}}$	Catalog	$N_r$
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)	(14)	(15)
1	J002303.15+011533.6	0390	562	51816	37.97	41.26	41.26	41.20	41.35	42.28	0.73	45.02	DR07Q	2
1	J002303.15+011533.6	0390	567	51900	37.69	41.09	41.38	41.24	41.41	42.31	0.73	45.09	DR07Q	2
2	J002303.15+011533.6	0390	567	51900	37.69	41.09	41.38	41.24	41.41	42.31	0.73	45.09	DR07Q	3
2	J002303.15+011533.6	4300	181	55528	39.33	40.99	41.53	41.33	41.42	42.44	0.73	45.10	DR07Q	3
3	J004212.19+173135.4	6198	799	56211	59.87	41.05	41.23	42.08	41.39	42.47	0.90	44.63	DR12Q	3
3	J004212.19+173135.4	6193	050	56237	68.00	41.06	41.22	41.98	41.33	42.36	0.90	44.61	DR12Q	3
4	J010033.49+002200.3	0396	342	51816	64.69	42.04	41.86	42.00	41.97	42.94	0.75	45.27	DR07Q	3
4	J010033.49+002200.3	0693	466	52254	49.07	41.50	41.65	41.96	41.66	42.89	0.75	45.33	DR07Q	3
5	J013053.43$-$095710.2	0662	276	52147	32.17	41.65	41.88	41.82	41.71	42.75	0.73	45.31	DR07Q	3
5	J013053.43$-$095710.2	0662	273	52178	30.19	41.64	41.77	41.77	41.86	42.82	0.73	45.32	DR07Q	3
6	J013053.43$-$095710.2	0662	276	52147	32.17	41.65	41.88	41.82	41.71	42.75	0.73	45.31	DR07Q	3
6	J013053.43$-$095710.2	2878	118	54465	53.63	41.20	41.75	41.65	41.72	42.70	0.73	45.03	DR07Q	3
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮

Table 2. Table 2: Relation Parameter Measurements

ID	Luminosity Bin	Spearman’s $\rho$	Fitted Slope	$\Delta t$ Range	Median $M_{\bullet }$	$N_{\mathrm{obj}}$	Slope Bias	Corrected Slope
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
1	44.49 $\le$ log 44.95	0.485	0.556 $\pm$ 0.026	$\le$727	7.6x${10}^7$	8	0.036	0.520 $\pm$ 0.026
2	44.95 $\le$ log 45.40	0.658	0.639 $\pm$ 0.031	$\le$4035	1.3x${10}^8$	21	0.072	0.567 $\pm$ 0.031
3	45.40 $\le$ log 45.85	0.697	0.467 $\pm$ 0.025	$\le$4781	2.8x${10}^8$	21	0.012	0.455 $\pm$ 0.025
4	45.85 $\le$ log 46.31	0.526	0.373 $\pm$ 0.050	$\le$3880	3.7x${10}^8$	18	0.033	0.340 $\pm$ 0.050
†	44.49 $\le$ log 46.31	0.593	0.513 $\pm$ 0.013	$\le$4781	2.3x${10}^8$	68	0.049	0.464 $\pm$ 0.013

Equations

$$f_{BC}(\lambda )=f_{3646}{B}_{\lambda }(T_e)(1-e^{-{\tau }_{\lambda }});\mathrm{if}\lambda ⩽{\lambda }_{\mathrm{BE}}$$

$$\Delta m=-2.5\log (f_2/f_1)+\Delta m_{\overline{r}}$$

$$\Delta m_{line0}+\Delta m_{\overline{r}}=\Delta m_{\mathrm{line}}=a+b\ast \Delta m_{\mathrm{cont}}$$

$$=a+b\ast (\Delta m_{cont0}+\Delta m_{\overline{r}})$$

$${\sigma }_{tol}=\sqrt{{\sigma }_{\Delta m_{\mathrm{line}}}^2+b^2\ast {\sigma }_{\Delta m_{\mathrm{cont}}}^2-2\ast b\ast {\sigma }_{\Delta m_{\mathrm{line}}\Delta m_{\mathrm{cont}}}^2}$$

Full text

black hole physics-galaxies: active-quasars: emission lines-quasars: general-surveys

\AuthorCallLimit

=1 \fullcollaborationNameThe Friends of AASTeX Collaboration

1 Introduction

It is now widely accepted that quasars are powered by accretion of material onto supermassive black holes (SMBHs). The continuum emission and the broad emission lines (BELs) often show aperiodic variations (e.g., Fitch et al. 1967; Andrillat & Souffrin 1968). Theoretically, the BEL fluxes are supposed to vary in response to the variations of the ionizing continuum with a lag of about light travelling time. Hence, via the cross correlation analysis of the BELs and the continuum, we are able to constrain the geometry of the spatially unresolved broad emission-line region (BLR) in active galactic nucleus (AGN). Notably, with the light-travel time delay, the distance of the BLR to the ionizing source is directly determined (e.g., Peterson 1993). By an attempt to model that the BLR is virialized, the central SMBH mass then can be estimated (e.g., Wandel et al. 1999).

So far emission-line reverberation mapping (RM; e.g., Blandford & McKee 1982) experiments have succeeded in measuring emission line lags in $\geq$ 60 AGNs; (e.g., Peterson et al. 1998, 2002, 2004; Wandel et al. 1999; Kaspi et al. 2000, 2005; Vestergaard & Peterson 2006; Bentz et al. 2009, 2013; Denney et al. 2010; Barth et al. 2011a, b; Grier et al. 2012; Hu et al. 2015; Goad et al. 2016; Jiang et al. 2016; Shen et al. 2016). It is revealed that, the BLR size as measured for a particular emission line such as \hbox{H\beta}\ \lambda 4861, is closely related to the AGN luminosity in the approximate form $R\propto L^{1/2}$ (the $R$-$L$ relation; e.g., Kaspi et al. 2000; Bentz et al. 2006; Shen & Liu 2012). This relation offers the possibility of taking advantage of single-epoch (SE) spectra to determine the SMBH masses (e.g., Vestergaard 2002; McLure & Jarvis 2002; Vestergaard & Peterson 2006). Over the past decade, several editions of these estimations have been developed (see, e.g., McGill et al. 2008; Wang et al. 2009). Resulted from the economical efficiency and operability, the SE virial SMBH mass estimation is a sort of praticable method on the determination of AGN SMBH masses compared to RM technique (e.g., Woo & Urry 2002; McLure & Dunlop 2004).

RM studies, as they are known, have been traditionally performed mostly on low-luminosity AGNs at low redshift ($z<$ 0.3) using the H$\beta$ emission-line to measure SMBH masses. For AGNs at redshifts beyond 1, rest-frame ultraviolet (UV) BELs are required, such as Mg ii, a crucial emission line of RM interest that can be presented in quasar spectra having redshifts between 0.3 and 2. However, RM results of Mg ii line (i.e., reliable detection of Mg ii lag) are quite scarce. This is initially interpreted that the Mg ii emission-line varies more slowly in response to continuum changes than H$\beta$ emission line, suggesting that the Mg ii-emitting region may have larger-scale structure than that of H$\beta$ (e.g., Corbett et al. 2003).

The relationship between the BEL flux ($F_{line}$) and the continuum flux ($F_{cont}$) within an individual source is often expressed by $F_{line}$ $\propto$ $F_{cont}^{\alpha}$, where $\alpha$ is traditionally measured from emission line and continuum flux light curves from AGN monitoring campaigns. This is related to the so-called intrinsic “Baldwin Effect” (see, e.g., Kinney et al. 1990; Pogge & Peterson 1992; Goad et al. 2004; Korista & Goad 2004). In fact, $\alpha$ is commonly referred to as the response of the BEL to variations in the ionizing continuum flux. Formally, we can parameterize the correlation between the variations in the $\hbox{Mg\,{\sc ii}}\ \lambda 2798$ line (\rm{dlog}$$F_{line}) and in the 3000 Å continuum (\rm{dlog}$$F_{cont}) with a simple linear function of the form \rm{dlog}$$F_{line}\propto \rm{dlog}$$F_{cont}. Given that the ratio in magnitude changes ought to be equivalent to $\alpha$, the value of Mg ii responsivity can be calculated by analysing spectroscopic monitoring data.

When determining the emission line responsivity parameter $\alpha$ = \rm{dlog}$$F_{line}/\rm{dlog}$$F_{cont}, it is of great importance to ensure that the emission-line flux is referenced to the correct (in time) continuum value (e.g., Goad et al. 2004; Goad & Korista 2014). Generally, this parameter is determined from temporally well-sampled continuum and emission line light curves, and the correct reference continuum is determined by shifting the emission line light curve backward in time by the emission line lag. In practice, the Mg ii lag is not well-constrained in prior RM campaigns (e.g., Clavel et al. 1991; Cackett et al. 2015, but see, Reichert et al. 1994; Metzroth et al. 2006), and few robust measurements of its responsivity have been measured. Instead of temporally well-sampled light curves of a single AGN, in this study, we use 1210 data pairs of spectroscopic observations of 68 AGNs to statistically estimate the responsivity of the broad Mg ii emission line. Here, we posit that our ignorance of the emission line lag corrections averages out statistically, and an ensemble responsivity of Mg ii may be determined from many pairs of measurements from an amount of AGNs.

Reliable flux calibration is of significance to accurately determine the observed emission-line and continuum flux. The Sloan Digital Sky Survey (SDSSS; York et al. 2000) spectroscopy is routinely calibrated using a series of standard stars, particularly main sequence F stars. For a single observation, it is assumed that the uncertainty of SDSS-I/II spectroscopic data is $\sim$ 0.04 mag (Adelman-McCarthy et al. 2008). With the smaller fibers, SDSS-III BOSS (e.g., Margala et al. 2015; Harris et al. 2016) spectroscopy is usually not as accurate as that of SDSS-I/II. In this work, we assume that the fluxes of narrow emission line have no variations during the spectroscopic monitoring due to the much large narrow-line region (NLR). Therefore, we attempt to use narrow-line fluxes to recalibrate SDSS quasar spectra. All the flux variations are measured using ground-based optical monitoring data from the observed flux of emission-lines and continuum in any two epochs during SDSS-I/II/III surveys.

The structure of this paper is as follows. In Section 2 we describe our quasar sample selection. In Section 3 we introduce the details of our spectral measurements. We derive the correlation between the variations of $\hbox{Mg\,{\sc ii}}\ \lambda$2798 and of the 3000 Å continuum in the SDSS quasars in Section 4. We discuss the related results in Section 5, and a summary of our conclusions in Section 6. Throughout this paper, we adopt a flat cosmology with $\Omega_{m}$ = 0.3, $\Omega_{\Lambda}$ = 0.7, and $H_{0}$ = 70 km s*-1* Mpc*-1*, and use magnitude (rather than flux or luminosity) differences to characterize variations. Unless otherwise specified, the reported wavelengths (taken from Berk et al. 2001) and timescales are in the quasar rest-frame.

2 THE Sample

In this work, we use the quasar data from the compilation of the SDSS Data Release 7 Quasar catalog (DR7Q; e.g., Schneider et al. 2010; Shen et al. 2011) and Data Release 12 Quasar catalog (DR12Q; e.g., Pâris et al. 2014; Pâris et al. 2017). All the spectra were taken by the Apache Point 2.5 m wide-field telescope (Gunn et al. 2006) during SDSS-I/II/III surveys (2000-2014). Each spectrum is stored in vacuum wavelength with a resolution of $R\sim 1500-2500$.

Our parent sample was compiled from the following 2 sub-samples: the DR7Q consisted of 105,783 objects that are brighter than $M_{i}=-22.0$, and the DR12Q including 297,301 quasars. There are 7,063 quasars from DR7Q and 28,105 quasars from DR12Q, each with multiple ($\geq$ 2) spectroscopic epochs, respectively. After confirming the quasar as a point-source in the SDSS image and rejecting the epoch with low-quality spectrum, we selected a sample of 2,374 quasars with Mg ii broad-line by requiring $0.65\leq z\leq 1.50$. This requirement ensures that broad Mg ii, narrow-lines (e.g., $[\hbox{O\,{\sc iii}}]\ \lambda\lambda 4960,5008$) and the 3000 Å continuum region are presented in the SDSS spectra.

We notice that additional flux deficit is confirmed in the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS; e.g., Eisenstein et al. 2011; Bolton et al. 2012; Dawson et al. 2013; Smee et al. 2013) relative to SDSS-I/II due to the difference in flux calibration from SDSS-I/II to BOSS. To obtain an accurate and reliable measurement of the intrinsic variations in $\hbox{Mg\,{\sc ii}}\ \lambda 2798$ and in the 3000 Å continuum for each quasar, we develop an independent correction to the flux variations, which is called narrow-line flux-recalibration (see Section 4.1). This requires that every quasar in our sample not only has repeated observations but also contains a minimum signal-to-noise ratio (S/N; defined as the ratio between the emission-line flux and its error) of 5 for narrow-line(s). In addition, we rejected objects with unusual emission line profiles and/or continuum shapes (i.e., BALQSOs) from our final sample. The reduced $\chi^{2}$ values ($\chi^{2}$/dof) of our best-fit model for these sources are often fairly large during emission-line fitting (see Section 3.6). More details about the sample-selection criteria include the following.

Multiple ($\geq$ 2) spectroscopic epochs/observations are included for each quasar in the SDSS-I/II/III surveys. 2. 2.

Quasar is confirmed to be a point-source in the SDSS image (take example for DR7Q, sdss_morpho = 0). 3. 3.

A minimum S/N ratio of 10 for quasar spectrum covering Mg ii through the 3000 Å continuum is preferred. 4. 4.

A redshift between 0.65 and 1.50 should be possessed for each object. 5. 5.

A minimum S/N ratio of 5 for narrow-line(s) are required in the SDSS quasar spectra. 6. 6.

Quasar with peculiar Mg ii emission-line and continuum property is rejected.

Table 2 summarizes part of the final 1210 data pairs consisting of 68 quasars that passed all the selection criteria and will be used for subsequent relation analysis of the spectroscopic variations in the $\hbox{Mg\,{\sc ii}}\ \lambda 2798$ emission-line and in the 3000 Å continuum.