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Edited by: Gianluca Calcagni, Consejo Superior de Investigaciones Científicas (CSIC), Spain

Reviewed by: Øyvind Geelmuyden Grøn, Oslo and Akershus University College, Norway; Zdenek Stuchlik, Silesian University in Opava, Czechia

*Correspondence: C. Alenka Negrete

This article was submitted to Cosmology, 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.

We propose the use of quasars with accretion rate near the Eddington ratio (extreme quasars) as standard candles. The selection criteria are based on the Eigenvector 1 (E1) formalism. Our first sample is a selection of 334 optical quasar spectra from the SDSS DR7 database with a S/N > 20. Using the E1, we define primary and secondary selection criteria in the optical spectral range. We show that it is possible to derive a redshift-independent estimate of luminosity for extreme Eddington ratio sources. Our results are consistent with concordance cosmology but we need to work with other spectral ranges to take into account the quasar orientation, among other constrains.

Active Galactic Nuclei (AGN or quasars) are among the most powerful objects in the Universe. They have been studied for more than 50 years. Their spectra and intrinsic properties, indicating intense nuclear activity, are widely diverse. In order to organize this diversity, Sulentic et al. (_{BC}), (2) the ratio of the equivalent widths of Fe_{BC}, _{FeII} = EW(Fe_{BC}), and (3) the photon index of the soft X-rays, Γ_{soft}. Subsequently, Sulentic et al. (_{Edd}) and also by the BH mass (e.g., Marziani et al.,

Sulentic et al. (_{BC}) vs _{FeII}): Population A for quasars with FWHM(_{BC}) < 4,000 km s^{−1} and Population B for those with FWHM(_{BC}) > 4,000 km s^{−1} (Figure 1 of Sulentic et al., _{BC}) = 4,000 km s^{−1} and Δ _{FeII} = 0.5. This created the bins A1, A2, A3, A4 defined as the _{FeII} increases (Figure 1 of Sulentic et al.,

In this article we will briefly illustrate how the scheme of Sulentic et al. (_{0}, the Hubble constant (e.g., Perlmutter et al., _{M} + Ω_{Λ}, where Ω_{M} is the density of matter and Ω_{Λ} is the energy density. So it is important to measure the cosmic matter density Ω_{M} in the distance range 1 < z < 4. In this range, the effect of the cosmic matter density is believed to dominate over the repulsive effect of the cosmological constant.

There have been several works focused on measuring cosmological distances using different objects as standard candles. For example, cepheids, supernovae, extragalactic HII regions and clusters of galaxies (e.g., Perlmutter et al., _{M} + Ω_{Λ} = 1). At intermediate z, Terlevich et al. (_{M}, however the dispersion obtained is larger than the one using supernovae. Another method to reach higher z (~3.5) involves the use of baryonic acoustic oscillations (BAOs) obtained from the database BigBOSS/DESI (Schlegel et al.,

In 2014, Marziani and Sulentic (_{Λ} = 0.72 and Ω_{M} = 0.28.

For our study, we used a sample of quasars chosen from the Sloan Digital Sky Survey Data Release 7 Shen et al. (_{FeII} > 1, belonging to Pops. A3, A4 and also some very extreme objects of Pop. A5 (with _{FeII} > 2).

We imposed the following filters to select only the objects with quality good enough to carry out our analysis:

z < 0.8 to cover the

S/N > 20 in the continuum at 5,100 Å.

_{FeII} > 1. To select objects with this condition, we performed automatic measurements using the IRAF task

No host galaxy contribution. The objects showing a strong contribution of the underlying galaxy were rejected.

This four criteria gave us a sample of 302 spectra.

In order to isolate the “true” extreme accreting quasars, we made individual fits on the selected spectra using the ^{2} to find the best fit. The steps followed to accomplish identification, deblending, and measurement of the emission lines in each object are the following:

The continuum. We adopted a single power-law to describe the quasar continuum using the continuum windows around 4,430, 4,760, and 5,100 Å (see, e.g., Francis et al.,

Fe

Apart from these four parameters, in some cases it was necessary to add other emission lines. These extra emission lines could be strong and therefore obvious. In other cases, the emission lines are weak, but we can find and identify them in the residuals of the fit. These emission lines are:

An example of the line fitting is shown in Figure _{BC} and _{BC}. Grey lines are the

Example of line decomposition for the quasar J134704.91+144137.6 using

In order to isolate “true” extreme accreting quasars and avoid borderline/noisy objects, we impose tighter restrictions on the selected sample. On the one hand, we choose quasars with _{FeII} > 1.2, based on the typical _{FeII} error at two sigma (one sigma is 0.1). On the other hand, we isolate only Pop. A objects, i.e., those ones with FWHM(_{BC}) < 4,000 km s^{−1}. Finally, we selected objects with S/N strictly larger than 20.0 in the continuum. These restrictions, gave us an “extreme sample” of 117 objects. It is important to mention that in the beginning we were not able to impose these two conditions using the automatic measurements. The reason is that we would have introduced objects that are not extreme accretors, or reject some that really are extreme quasars.

As pointed out previously, the main hypothesis of Marziani and Sulentic (_{Edd} = _{Edd} is proportional to the product λ_{Edd} times its black hole mass (_{BH}). If we consider virial motions,

where cte = 10^{4.81}, _{s} is the structure factor, _{BLR} is the the broad line region radius, δ_{BLR} independently of the quasar luminosity, based on the definition of the ionization parameter U and described in detail in Negrete et al. (

where _{H} is the density, _{i}, with _{i} the average frequency of the ionizing photons, and _{BLR} can be derived if we know the product of the ionization parameter times density

In Negrete et al. (_{H} and U, can be derived for individual objects using specific line ratios and CLOUDY photoionization models. In the case of the extreme accretors, we found a “typical” value of the product _{H} U = 10^{9.6} (see also Padovani and Rafanelli,

In order to prove the consistency of our luminosity z-independent estimates we calculate how the distance modulus depends on the redshift. The distance modulus is μ = 5log(_{L}/10pc). The luminous distance is

Figure _{BC}) are above the solid curve, while the narrower objects are placed below. This figure shows that the so called “virial luminosity” is in agreement with the concordance cosmology.

Distance modulus of the “extreme sample” (black dots) and the Kessler et al. (

We have shown that the 4DE1 proposed by Sulentic et al. (_{BC}) Vs. _{FeII}, to isolate the most extreme accreting quasars. The principal characteristics of these objects is that they are strong Fe_{FeII} > 1, and they have relatively narrow lines, with a FWHM(_{BC}) < 4,000 km s^{−1}.

Based on the hypothesis that extreme accreting quasars should have the same intrinsic luminosity per unit mass, we test them as cosmological standard candles. Under several assumptions related to highly accreting objects, such as the physical conditions of the region close to the black hole, we computed a “virial luminosity” independent of z. With this luminosity we build the Hubble diagram which shows that the majority of the selected extreme quasars follow the trend of the distance modulus diagram.

In a forthcoming paper (Negrete et al., Submitted), we will give a detailed description of the selection of this sample, the methodology applied, a statistical analysis that includes the high-z sample, and the cosmological application to constrain Ω_{M} and Ω_{Λ}.

CN and DD wrote the paper. PM and JS contributed to the main idea of the paper. CN and DE-A made the fits and analyzed the sample. All the authors contributed to the discussion and revision of the paper.

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.

CN and DD acknowledge support from grants IN107313 PAPIIT, DGAPA UNAM and CONACYT project 221398. CN acknowledge support from DGAPA-UNAM grants IN111514 and IN113417. DE-A and MM-A acknowledges the doctoral and postdoctoral grant from the CONACyT, respectively. MM-A and AD acknowledge financial support from Spanish Ministry for Economy and Competitiveness through grants AYA2013-42227-P and AYA2016-76682- C3-3-1-P.