Dark energy constraints from quasar observations
B. Czerny, M.L. Martínez-Aldama, G. Wojtkowska, M. Zajaček, P. Marziani, D. Dultzin, M. H. Naddaf, S. Panda, R. Prince, R. Przyluski, M. Ralowski, M. Śniegowska
DDark energy constraints from quasar observations
B. Czerny , M.L. Mart´ınez-Aldama , G. Wojtkowska , M. Zajaˇcek , P. Marziani , D.Dultzin , M. H. Naddaf , S. Panda , R. Prince , R. Przyluski , M. Ralowski , and M.´Sniegowska Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotnik´ow 32/46,02-668 Warsaw, Poland Warsaw University Observatory, Al. Ujazdowskie 4, 00-478 Warszawa, Poland INAF, Osservatorio Astronomico di Padova, Italy Instituto de Astronom´ıa, UNAM, Mexico Space Research Centre, Polish Academy of Sciences, Bartycka 18a, 00-716 Warsaw,Poland Astronomical Observatory of the Jagiellonian University, Orla 171, 30–001 Krakow,Poland * Corresponding author: B. Czerny, [email protected] words: cosmology, dark energy, quasars
Abstract
Recent measurements of the parameters of the Concordance Cosmology Model (ΛCDM) done inthe low-redshift Universe with Supernovae Ia/Cepheids, and in the distant Universe done with CosmicMicrowave Background (CMB) imply different values for the Hubble constant (67.4 ± − Mpc − ] from Planck vs 74.03 ± − Mpc − ] Riess et al. 2019). This Hubble constant tensionimplies that either the systematic errors are underestimated, or the ΛCDM does not represent well theobserved expansion of the Universe. Since quasars - active galactic nuclei - can be observed in thenearby Universe up to redshift z ∼ ∼ The cosmological parameters can be estimatedfrom different sets of data at various redshifts, butif the standard ΛCDM (Lambda-Cold Dark Matter)model is valid, they can always be represented bythe current (zero redshift) values. The final resultsfrom the Planck mission, based on the analysis ofthe Cosmic Microwave Background (CMB) do notindicate any tension with the standard model, andgive the value of the Ω m = 0 . ± .
007 [1] and theHubble constant H = 67 . ± . − Mpc − ].Many of the measurements done in the local Uni-verse ( z <
10) are in significant disagreement with these Ω m or H values (e.g. [2]) while other mea-surements, also local, are still roughly in agreementwith the results from Planck (e.g. the last resultsfrom gravitational waves [3]).Therefore various probes and methods are neededto confirm, or to reject, the hypothesis that theΛCDM model does not well describe the Universe,and the evolving dark energy is needed instead ofthe cosmological constant. Quasars (QSO) are veryattractive cosmological probes, since they cover abroad range of redshifts, from nearby sources (re-ferred to as Active Galactic Nuclei, AGN) to mostdistant objects at redshift above 7 [4, 5]. They also1 a r X i v : . [ a s t r o - ph . C O ] J a n o not show significant evolution with redshift [6]. We are currently using two methods of turn-ing quasars into standardizable candles. The firstmethod is based on the radius-luminosity relationand the second method is based on super-Eddingtonsources.
The reverberation mapping technique is basedon the long-term monitoring of a source in or-der to determine the time response ( τ BLR ) of theemission line to the continuum variations [7]. Themost important result from the reverberation map-ping studies is the correlation between the contin-uum luminosity ( L ) and the distance ( R BLR ) wherethe emission line is emitted in the broad line re-gion (BLR). This relation is known as the Radius-Luminosity relation (RL) and it is given approxi-mately by R BLR ∝ L . . The reverberation mappingstudies require extensive use of telescope time toachieve high quality results, thus only ∼
120 sourceshave been analyzed with this technique until date.Most of the monitoring are based on the opticalH β for low-redshift sources, while for high redshiftregimes, due to the Doppler shift, the monitoringare focused on the UV emission lines such as Mg ii λ iv λ iii] λ σ rms ∼ .
13 dex) [8], which ensured its usein the determination of the black hole mass ( M BH ).However, the inclusion of new sources, particularlythose radiating close to the Eddington limit (highaccretion rates), has led to a much larger scatter,clearly related with the accretion rate [9, 10]. Somecorrections based on the accretion rate [11] and in-dependent parameters such as the Fe ii strength orthe amplitude of variability [12, 13, 14] (in turn cor-related with the accretion rate) have been proposedto correct this effect, allowing to reduce the scatter. Figure 1: Top panel: Quasar Hubble diagram usingthe reverberation mapped sources. Blue circles andred diamonds correspond to the H β and Mg ii λ m = 0 . H = 67 . − Mpc − ]. Bottom subpanel shows the resid-uals. Bottom panel: Confidence contours at 68%(cyan) and 95% (blue) for Ω m and Ω Λ for generalΛCDM model based on χ fitting where the bestΩ m and Ω Λ are represented by the yellow symbol.Besides, the Radius-Luminosity relation offersthe possibility to determine the luminosity indepen-dently of the redshift [15, 16], and to estimate thecosmological parameters. However, in [11] the er-rors for Ω m and Ω Λ based on available H β were stillvery large, despite the corrections for the accretion2ate. In the present paper, we make the follow-ing important modifications. First, we combine theprevious sample with Mg ii λ χ statisticsto determine the cosmological parameters, we usethe method of [19] instead of a simple symmetriza-tion of the errors.We also modified the approach to the R-L rela-tion in case of the H β sample which is extremelyheterogeneous. We treated the coefficients of thisrelation as arbitrary, and minimized the total χ fit to a flat cosmological model, with Hubble con-stant fixed at 67.5 [km s − Mpc − ]. For Mg ii λ β sample: Mrk 493,J074352.02+271239.5, Mkn 509, MCG+08-11-011,J142103, J142043, J141123, and J142052. Thus ourtotal sample has now 120 objects. We then refittedthe Hubble diagram. The best-fit returned the bestR-L parametrization of H β sample as log L =1 .
489 log τ corr − . τ corr is the time de-lay corrected by the accretion rate effect [11]. Forthe flat cosmology, we obtained the best-fit valueΩ m = 0 . +0 . − . (see Fig. 1, top panel). This valueis fully consistent with the value 0 . ± . σ error, so we do not see any tension with theresults based on Cosmic Microwave Background. Quasars radiating close to the Eddington limitare known as xA-QSO or super–Eddington sources[20, 21]. This QSO population shows peculiar spec-tral and photometric properties, which differenti- ate them from the rest of the QSO population andmake them easy to identify in catalogs like SDSSor the upcoming Vera Rubin Observatory’s LegacySurvey of Space and Time (LSST). In the opticalrange, they are the strongest Fe ii emitters anddo not show a strong contribution of narrow emis-sion lines such as [O iii] λλ iv λ iv λ β or Al iii λ H = 10 − [cm − ]),low-ionization parameters (log U < −
2) and highmetallicities ( Z ∼ Z (cid:12) ) [24, 25, 26, 27]. In ad-dition, Super-Eddington sources also show remark-ably low optical variability and time delays shorterthan the predicted by the RL relation [28]. TheUV flux ratios Al iii λ iii] λ > iii] λ iii] λ < ii /H β> L / M BH ) does notchange and they can be considered as “Eddingtonstandard candles”. A similarity in the physical con-ditions (density, ionization parameter, metallicity)of the BLR is expected because them belonging tothe same population, therefore a generalization ofall of them can be considered [29]. Since the low-ionization lines are less affected by the strong radi-ation forces, emission lines like H β and Al iii λ ∼ z < . < log L < − ] at0 . < z < .
3, where ∼
20% show high accretionrates, so they can be considered as Super-Eddingtoncandidates. In the xA sources the Fe iii λ iii] λ iii λ iii in their multicomponent fittings, so not all thesources satisfy the selection criteria to identify themas the xA. So for the first test, we select the sourcesbased on the Eddington ratio (L/L Edd > .
2) es-timated from the Al iii λ AlIII values, our final sample includes 88 ob-jects at 1 < z < . β , while circles belong toUV Al iii λ H fromPlanck, and best fit Ω m = 0 . m and Ω Λ , we combine the previous xA sam-ples such as the super-Eddington sources fromthe super-Eddington accreting massive black holes(SEAMBHs) project with the most recent measure-ments from [25]. The quasar Hubble diagram withthe super-Eddington sources is shown in Fig. 2.We adopt the scaling of the virial estimator tobe consistent with Planck H value, and we as-sume the flat cosmology. In this case we obtainΩ m = 0 . +0 . − . , fully consistent with the Planckresults despite the fact that quasars cover the red-shift range from nearby sources to almost 4.5. Here we presented the most recent results basedon the two methods for applying quasars to con-strain the expansion rate of the Universe. Ourmethods, as for now, are not based on absolutescaling so they cannot predict the value of H . Inprinciple, such an absolute scaling can be achieved.For method (i) it would require an independentmeasurement of the dust temperature at the BLRonset, and the development of a 3-D BLR model,which is in progress (see e.g. [32]). For method (ii),we would need an absolute scaling of the radius-luminosity relation, also establishing the mean den-sity of the BLR (see e.g. [20, 29]). At this stage, wefixed the value of the Hubble constant at the Planckvalue and tested, whether the redshift dependenceof the luminosity distance is consistent with thestandard ΛCDM model, and whether the remainingcosmological parameters derived from quasar dataare consistent with Planck values.So far, within the available accuracy, our values ofΩ m are fully consistent with the Planck value for theflat Universe despite the fact that second methodextends up to the redshift 4.5. Thus we do notsupport the claim of the tension with the standardmodel based on Supernovae Ia with absolute scalingin turn predominantly based on Cepheid stars [33].Our results from method (i) are consistent with thetension found by [34] since they claim to see depar-tures only above the redshift 1.5 - 2, and method (i)does not go this far. As for the method (ii), we havemany sources up to redshift 2.5, but indeed veryfew above 2.5, and our method of analysis was notyet optimized by an outlier removal through sigma-clipping. Further studies are clearly needed for thismethod, both with the current data and eventuallyby increasing the number of high redshift quasars. Acknowledgement
The project is partially based on observa-tions made with the SALT under programs2012-2-POL-003, 2013-1-POL-RSA-002, 2013-2-POL-RSA-001, 2014-1-POL-RSA-001, 2014-2-SCI-004, 2015-1-SCI-006, 2015-2-SCI-017, 2016-1-SCI-011, 2016-2-SCI-024, 2017-1-SCI-009, 2017-2-SCI-033, 2018-1-MLT-004 (PI: B. Czerny). Theauthors acknowledge the financial support bythe National Science Centre, Poland, grantNo. 2017/26/A/ST9/00756 (Maestro 9), and bythe Ministry of Science and Higher Education(MNiSW) grant DIR/WK/2018/12. The Polish4articipation in SALT is funded by grant No.MNiSW DIR/WK/2016/07.
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