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Edited by: Paola Marziani, National Institute for Astrophysics (INAF), Italy

Reviewed by: Luigi Foschini, Brera Astronomical Observatory, Italy; Erika Maria Benitez, National Autonomous University of Mexico, Mexico

*Correspondence: Sladjana Marčeta-Mandić

Luka Č. Popović

This article was submitted to Milky Way and Galaxies, a section of the journal Frontiers in Astronomy and Space Sciences

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Here we investigate the Hβ and Mg II spectral line parameters used for the black hole mass (M_{BH}) estimation for a sample of Type 1 Active Galactic Nuclei (AGN) spectra selected from the Sloan Digital Sky Survey (SDSS) database. We have analyzed and compared the virialization of the Hβ and Mg II emission lines, and found that the Hβ line is more confident virial estimator than Mg II. We have investigated the influence of the Balmer continuum emission to the M_{BH} estimation from the UV parameters, and found that the Balmer continuum emission can contribute to the overestimation of the M_{BH} on average for ~5% (up to 10%).

Several methods are used to estimate central black hole (BH) mass M_{BH} in galaxies (for review see e.g., Marziani and Sulentic, _{BH} estimation are those using the strong broad emission lines (BELs), as the most prominent features in their spectra. The virial methods (see Peterson et al.,

One of these methods is based on the R–L relationship (see e.g., Bentz et al., _{BH} estimation using the BEL parameters is based on the gravitational redshift in the broad line profiles (see Zheng and Sulentic,

There are many unresolved questions relevant for the application of these methods. For example, since the BLR geometry could be complex (see e.g., Sulentic et al., _{BH} estimation and if the gravitational redshift could be measured from the BELs complex shapes, or if it may be suppressed by some other effects.

The most frequently used BELs as the virial estimators are the broad Hβ (in the optical) and Mg II (in the UV) lines (see Marziani and Sulentic, _{BH} estimation. Extracting refined Hβ and Mg II profiles is a difficult task and it is essential for an accurate M_{BH} estimation. Especially since the broad Hβ overlaps with a numerous optical Fe II lines, the [O III] doublet and the Hβ narrow line component, while the Mg II line overlaps with a numerous UV Fe II lines. Finally, the presence of the Balmer continuum for λ < 3,646Å, is contributing to the uncertainty of the M_{BH} estimation from the UV parameters and it has to be subtracted for obtaining the pure power law luminosity in the UV band.

In this paper we first present the models of the optical Fe II, UV Fe II emission and Balmer continuum, that could give more precise measurements of the optical and UV parameters [Hβ and Mg II broad line profiles, power law luminosity at λ = 3,000Å, as _{λ}(3,000Å)] used for the M_{BH} estimation. Then, we analyze the virialization assumption for the Hβ and Mg II broad lines, and the influence of the Balmer continuum to the M_{BH} estimation from the UV parameters.

The used sample consists of the 287 spectra of Type 1 AGN, obtained from the SDSS Data Release 7 (DR7). The sample is the same as in Kovačević-Dojčinović and Popović (_{BH}.

To obtain a pure broad Hβ component, the narrow Hβ and [O III] lines have to be carefully subtracted, as well as the optical Fe II lines. After correcting the spectra for the Galactic reddening and the cosmological redshift, and subtracting the underlying continuum, we applied the multi-Gaussian fitting procedure in 4,000–5,500Å range, described in details in Kovačević et al. (

We have made a Fe II template as a sum of the most prominent Fe II lines, described with Gaussian functions, with the same widths and shifts, since we assumed that all optical Fe II lines were originating from the same emission region. The number of free parameters was reduced by calculating the relative intensities for the Fe II lines with the same lower term of transition (see Kovačević et al.,

The example of the decomposition of the UV-optical pseudo-continuum (power law + Balmer continuum) and emission lines in ranges 2,650–3,050Å and 4,000–5,500Å for object SDSS J014942.50+001501.7. The observations are denoted with dots, the sum of pseudo-continuum and emission line model with solid line, and the power law continuum with dashed line. Bellow, the Balmer continuum is given with dotted line, and UV/optical Fe II templates with dotted-dashed line and all emission lines with solid line.

The UV pseudo-continuum consists of the power law, which represents the emission from the accretion disc and the bump at 3,000Å, which represents the sum of the blended, high-order broad Balmer lines, and the Balmer continuum (λ < 3,646Å). In order to measure the flux or luminosity of the power law at UV spectral range (e.g., 3,000Å), one needs to subtract the Balmer continuum emission first (see Figure

We performed the spectral decomposition in 2,650–3,050Å range in order to estimate the pure Mg II profile, which overlaps with the UV Fe II lines (Figure

From the pure broad profiles of the Hβ and Mg II lines, we measured the FWHM of these lines, as well as Full Width at 10% of the Maximum (FW10%M). The asymmetries of these lines (intrinsic shifts) were measured at different levels of the line maximal intensity (at 50%, z_{50} and at 10%, z_{10}), as the centroid shift with respect to the broad line peak (see Jonić et al., _{M} = 0.3, Ω_{Λ} = 0.7, Ω_{k} = 0, and Hubble constant H_{o} = 70 km s^{−1} Mpc^{−1}. The virial M_{BH} for the UV parameters [FWHM Mg II, _{λ}(3, 000)] was calculated using the formula given in Wang et al. (

If the emission gas in the BLR is virialized, one can expect to observe correlations between the widths and the gravitational redshifts of the BELs, which comes from the equations for the M_{BH} estimation by the virial method using the line width (see Zheng and Sulentic, _{G} ~ FWHM^{2}, i.e., log(z_{G}) ~ log(FWHM) (see Jonić et al.,

We investigated correlation between the intrinsic shifts, as indicators of the gravitational redshifts, and the widths of the Hβ or the Mg II lines, at different levels (50 and 10%) of their maximal intensity, for the sample of 123 Type 1 AGNs with the red asymmetry in BELs. We have found that the width of the Hβ line is well correlated with the line's intrinsic shift measured at the 50% and at the 10% of the maximal intensity. However, in the case of the Mg II line, the correlation between the Mg II width and intrinsic shift is detected only at the 50% of the line maximal intensity, whereas at the 10% of the line maximal intensity an anti-correlation is seen (for more detail see Jonić et al.,

Note here that the literature in the field presents comparisons on the use of the optical and the UV lines, like Hβ and Mg II, as virial estimators of the M_{BH} in AGN, pointing out that in some cases Mg II is more reliable as M_{BH} estimator then Hβ (e.g., Marziani et al.,

We calculated the luminosity at 3,000Å before [_{λ}(3,000Å)_{tot}] and after the Balmer continuum [_{λ}(3,000Å)_{pow}] contribution was subtracted. In the sample of 287 Type 1 AGN spectra, the Balmer continuum contributes to the continuum _{λ}(3,000Å) on average for ~10%, with the maximal value of 18%. The ratios of the _{λ}(3,000Å), with and without the Balmer continuum contribution, are shown on the histogram (Figure _{BH} estimation using the UV parameters neglect the contribution of the Balmer continuum (see e.g., McLure and Jarvis, _{BH} using the FWHM Mg II and _{λ}(3,000Å), assuming that after subtraction of the Balmer continuum, the _{λ}(3,000Å) is the pure power law continuum, therefore we then compared M_{BH} calculated with and without consideration of the Balmer continuum contribution. We got that the Balmer continuum increased M_{BH} on average for ~5% (0.02 dex), with the maximal value of the M_{BH} overestimation up to 10% (0.04 dex). The ratio of the M_{BH} estimates before and after the Balmer continuum subtraction is shown in Figure _{BH} values before (index “tot”) and after the Balmer continuum subtractions (index “pow”) are also given in Figure _{tot} = 0.783 and ρ_{pow} = 0.786), _{tot} = 0 and P_{pow} = 0) and linear best-fit (y = a^{*}x+b) coefficients are given: slope a, (a_{tot} = 0.85 and a_{pow} = 0.84) and y-intercept b, (b_{tot} = 1.36 and b_{pow} = 1.43). It can be seen that the influence of the Balmer continuum to the M_{BH} estimation is so small that it barely changes the correlation coefficient (ρ) or the coefficients of the linear best-fit (a, b) between the M_{BH} estimated with the optical and the one estimated with the UV parameters. Also, it seams that removing the Balmer continuum does not affect the outliers in this relationship.

_{λ}(3,000Å) before [_{tot})] and after [_{pow})] the Balmer continuum subtraction. _{BH} estimate before [M_{BH} (_{tot})] and after [M_{BH} (_{pow})] the Balmer continuum subtraction.

The relation of the M_{BH}[Hβ, _{λ}(5,100Å)] vs. M_{BH}[MgII, _{λ}(3,000Å)] before (index “tot,” open circles) and after the Balmer continuum subtraction (index “pow,” full circles). The corresponding correlation coefficients,

Here we have used the sample of the SDSS Type 1 AGN spectra to compare the most frequently used emission lines for the M_{BH} estimation, Hβ (in the optical band) and Mg II (in the UV band), in order to assess which line is better virial estimator and thus more convenient for that purpose. We investigated how the Balmer continuum affect the BH mass estimation using the UV parameters.

From our investigation we can outline the following conclusions:

The Hβ line is a more reliable virial estimator than the Mg II line, since the expected linear relationship between logarithms of the widths (influenced by the Keplerian motion) and red asymmetries (caused by the gravitational redshift) was evidenced for both lines when measured at the 50% of the line maximal intensities, but when measured in the line wings (at the 10% of the line maximal intensities) the expected relationship was present only for Hβ (see Jonić et al.,

The disregard of the Balmer continuum emission, in the case of the M_{BH} estimation using the UV parameters [Mg II, _{λ}(3,000Å)], causes the overestimation of the M_{BH} on average for ~5% (0.02 dex) and up to 10% (0.04 dex).

At the end, let us note that similar investigation should be performed on the sample where more reliable methods for mass measurements (as e.g., reverberation) should be applied to explore the influence of the Balmer continuum and this we postpone for our future work. Moreover, some additional effects (as e.g., relativistic jets) can significantly affect line profiles, i.e., the radio loudness which can indicate the presence of relativistic jets, therefore in the future work radio properties of the sample should also be explored.

JK, SM, and LP: Developing concept of the work; the acquisition, analysis and interpretation of data for the work; drafting the work and revising it critically for important intellectual content; final approval of the version to be published; being accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The work is a part of the project 176001 financed by the Ministry of Education, Science, Technology and Development, Republic of Serbia.