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SDSS J1058+5443: A blue quasar does not have optical/NUV broad emission lines

In the manuscript, the blue quasar SDSS J105816.19+544310.2 (=SDSS J1058+5443) at redshift 0.479 is reported as so-far the best candidate of true type-2 quasar with disappearance of central BLRs. There are so-far no definite conclusions on the very existence of true type-2 AGN, mainly due to detected optical broad emission lines in high quality spectra of some previously classified candidates of true type-2 AGN. Here, not similar as previous reported candidates for true type-2 AGN among narrow emission-line galaxies with weak AGN activities but strong stellar lights, the definite blue quasar SDSS J1058+5443 can be well confirmed as a true type-2 quasar due to apparent quasar-shape blue continuum emissions but apparent loss of both the optical broad Balmer emission lines and the NUV broad Mg~{\sc ii} emission line. Based on different model functions and F-test statistical technique, after considering blue-shifted optical and UV Fe~{\sc ii} emissions, there are no apparent broad optical Balmer emission lines and/or broad NUV Mg~{\sc ii} line, and the confidence level is smaller than 1sigma to support broad optical and NUV emission lines. Moreover, assumed the Virialization assumption to broad line emission clouds, the re-constructed broad emission lines strongly indicate that the probable intrinsic broad emission lines, if there were, cannot be hidden or overwhelmed in the noises of SDSS spectrum of SDSS J1058+5443. Therefore, SDSS J1058+5443, so-far the best and robust candidate of true type-2 quasar, leads to the further clear conclusion on the very existence of true type-2 AGN.


INTRODUCTION
Type-1 AGN (broad line Active Galactic Nuclei) and type-2 AGN (narrow line AGN) are the two main classes of AGN, due to quite different spectroscopic emission line features. The constantly being improved Unified Model (Antouncci 1993;Netzer 2015) has been widely accepted to explain the different observational phenomena between type-1 and type-2 AGN: central AGN continuum emissions and broad line emissions from central broad emission line regions (BLRs) are seriously obscured by central dust torus in type-2 AGN. And the well detected polarized broad emission lines in type-2 AGN, such as the results well discussed in Antonucci & Miller (1985); Tran (2001Tran ( , 2003; Savic et al. (2018), provide robust evidence to strongly support the Unified Model, indicating that type-1 and type-2 AGN have the same central geometric structures including similar BLRs, but central BLRs hidden in type-2 AGN.
Interestingly, based on the pioneer work on studying polarized broad emission lines in type-2 AGN in Antonucci & Miller (1985); Tran (2001Tran ( , 2003; Nagao et al. (2004); Cardamone et al. (2007) and then followed in Shi et al. (2010); Barth et al. (2014); Zhang (2014); Li et al. (2015); Pons & Watson (2016); Zhang et al. (2021c), there is one special kind of AGN: true type-2 AGN (or AGN with none hidden-BLRs, or BLRs-less AGN or unobscured type-2 AGN in the literature), which have no expected hidden central BLRs. There are about 30 Seyfert 2 galaxies with no hidden BLRs reported in Tran (2001Tran ( , 2003, due to lack of polarized broad emission lines. There are two strong candidates of true Type-2 AGN, NGC3147 and NGC4594, reported in Shi et al. (2010), due to their few X-ray extinctions and the upper limits on the broad emission line luminosities are two orders of magnitude lower than the average of typical Type-1 AGN. A small number of Type-2 quasar are reported in Barth et al. (2014) through their strong g-band variabilities. A sample of candidates of true Type-2 AGN are reported in Zhang (2014), through both their the long-term variability and the expected reliable power law components in their spectra in SDSS (Sloan Digital Sky Survey). A candidate of true Type-2 AGN, SDSS J0120, is reported in Li et al. (2015), through its long-term variability properties but none-detected broad emission lines. A small sample of candidates of true Type-2 AGN are reported in Pons & Watson (2016) based on their properties of unobscured X-ray emissions. More recently, Zhang et al. (2021c) reported the composite galaxy SDSS J1039 as a candidate of true type-2 AGN, based on its long-term variabilities and its apparent loss of broad optical Balmer emission lines. Meanwhile, there are different physical models proposed to explain the disappearance of central BLRs, such as the well reported models in Nicastro et al. (2003); Elitzur & Ho (2009);Cao (2010); Ichikawa et al. (2015); Elitzur & Netzer (2016), strongly indicating disappearance of central normal BLRs depending on physical properties of central AGN activities and/or depending on properties of central dust obscuration. Nicastro et al. (2003) have shown that absence or presence of central BLRs can be well regulated by accretion rate, assumed the BLRs formed by accretion disk instabilities. Elitzur & Ho (2009) have proposed a disk-wind scenario to predict the disappearance of the central BLRs at quite low luminosities. Cao (2010) has shown that disappearance of central BLRs associated with the outflows from the accretion disks can be expected in AGN with Eddington ratio smaller than 0.001. Elitzur & Netzer (2016) have shown that disappearance of central BLRs could be expected in AGN with higher luminosities than 4 × 10 46 erg s −1 considering mass conservations in the disk outflows.
However, detailed study on reported candidates of true type-2 AGN questions the very existence of true type-2 AGN, such as the detailed study in Mrk573 and NGC3147. Tran (2001) has classified Mrk573 as a candidate of true type-2 AGN, however Nagao et al. (2004) have shown the clearly detected polarized broad Balmer lines, leading Mrk573 as a normal type-2 AGN with central hidden BLRs. Similarly, Shi et al. (2010); Bianchi et al. (2012) have classified NGC3147 as a candidate of true type-2 AGN through both spectropolarimetric results and unobscured X-ray emission properties, however Bianchi et al. (2019) more recently have clearly detected double-peaked broad H in high quality HST spectrum. Furthermore, Ichikawa et al. (2015) have well discussed that none detected polarized broad emission lines in candidates of some true type-2 AGN may probably due to effects of less scattering medium and/or due to effects of the increased torus obscurations.
Besides true type-2 AGN with loss of central BLRs as a precious subclass of AGN, there is one another precious subclass of AGN: weal-line quasars which have quite weak broad emission lines in UV-optical band. Since the first sample of 74 high redshift ( > 3) weak-line quasars in SDSS reported in Diamond-Stanic et al. (2009), weak-line quasars are interesting targets to provide further clues on accretion disk formation and/or abnormal properties of central BLRs for high ionization emission lines, such as in Shemmer et al. (2010); Plotkin et al. (2015); Marlar et al. (2018); Paul et al. (2022). However, among the reported weak-line quasars identified by UV emission line properties, optical Balmer emission line (H and H ) properties have been checked and reported in dozens of weak-line quasars, such as the results in Plotkin et al. (2015) and the reported virial BH masses of weak-line quasars by properties of broad Balmer lines in Marculewicz & Nikolajuk (2020), indicating there are apparent broad Balmer emission lines (large rest-frame equivalent widths) in weak-line quasars. Therefore, weak-line quasars with quite weak UV emission lines (especially Ly and C IV) but apparent broad Balmer lines are not similar as true type-2 AGN with none-detected broad Balmer lines, and there are no further descriptions and discussions on weak-line quasars in the manuscript.
There is so-far no definite conclusion on the very existence of true type-2 AGN because of lower quality spectra with larger noises being applied to explain the undetected broad emission lines, but to detect true type-2 AGN in high luminous blue AGN would provide more clearer clues on the very existence of true type-2 AGN. Here, we report one candidate of true type-2 AGN in the blue quasar SDSS J1058+5443 with none detected broad emission lines, which will provide robust evidence to support the very existence of true type-2 AGN. And due to none-detected broad Balmer lines, there are no further discussions on the SDSS J1058+5443 as one weakline quasar in the manuscript. Section 2 presents our main results on spectroscopic properties of SDSS J1058+5443, to provide strong evidence to support disappearance of broad optical and NUV emission lines. Section 3 gives properties of BH mass of SDSS J1058+5443. Section 4 shows the necessary discussions. Section 5 gives our final summaries and conclusions. And we have adopted the cosmological parameters 0 = 70km · s −1 Mpc −1 , Ω Λ = 0.7 and Ω m = 0.3.

SPECTROSCOPIC PROPERTIES OF SDSS J1058+5443
SDSS J1058+5443 at redshift 0.479 is a well classified blue quasar in SDSS, with its spectrum shown in Fig. 1. The blue continuum emissions from NUV to NIR can be well described by a power law ∝ ( ) −1.65±0.01 with the continuum luminosity at rest wavelength 5100Å to be (about 5100 ∼ (5.74 ± 0.06) × 10 44 erg/s, leading SDSS J1058+5443 to be a definitely blue quasar. Meanwhile, the narrow emission lines, especially the apparent [O ] 4959, 5007Å doublet, can be well applied to totally confirm the redshift ∼ 0.479. Moreover, the composite spectrum of SDSS quasars reported in Vanden Berk et al. (2001) is also shown in Fig. 1, providing interesting clues on the apparent blue continuum emission features of SDSS J1058+5443. More interestingly, besides the quasar-shape power law continuum emissions, it looks T -2 3    Kovacevic et al. (2010). In order to show clearer results, the Y-axis is in logarithmic coordinate.  (Greene & Ho 2005a;Shen et al. 2011;Zhang 2021), considering probably spatially extended emission regions for the outflow-related extended [O ] components as discussed in Zakamska et al. (2016).
The model parameters of , and , are free model parameters, which will provide further clues to the origin of the very broad components around 4450Å, from Balmer emissions or from extended [O ] emissions or other physical origins. Then, through the Levenberg-Marquardt leastsquares minimization technique, the best-fitting results to the emission lines by the model A can be well determined, and shown in Fig. 2 with 2 / ∼ 0.88 (where 2 and are the summed squared residuals for the best-fitting results and the degree of freedom, respectively). Here, in order to show clearer results, left panel of Fig. 2 shows the best-fitting results to the emission lines around H with rest wavelength range from 4600 to 5400Å, and right panel of Fig. 2 shows the best-fitting results to the emission lines around H with rest wavelength range from 4200 to 4600Å.
Before proceeding further, one point is noted. Besides the two narrow Gaussian components for narrow H and narrow H and two broad Gaussian components for broad H and broad H discussed above, two Gaussian components are also considered in the Model A to describe probable 'outflow components' in narrow H and narrow H (the extended component for wings of narrow Balmer lines, such as the broad Gaussian components included in [O ] lines), and two additional Gaussian components are considered in Model A to describe probable 'outflow components' in broad H and broad H (or to describe probably complicated profiles of broad Balmer lines). However, for the model including the new four additional Gaussian components applied, the determined probable 'outflow components' in broad Balmer lines have fluxes to be zero, and the determined 'outflow components' in narrow Balmer lines have their line fluxes one times smaller than their corresponding uncertainties. Therefore, it is not necessary to consider the probable 'outflow components' in narrow Balmer line or in broad Balmer lines.
The determined parameters of emission lines are listed in Table 1 locities (relative to narrow Balmer lines) of the broad components of H and H ,  Kovacevic et al. (2010), which are mainly considered to explain the very broad component around 4450Å and around 4910Å. Considering the optical Fe emission templates in four groups (three groups related to the lower term of the transitions of 4 F, 6 S and 4 G terms, and the fourth group from the I Zw 1 Fe template) as discussed in Kovacevic et al. (2010), the Fe component is described by where ≥ 0 represents the intensity of Fe emission features in each group, , means the broadened and shifted Fe emission features in each group, and and means the same shift velocity and the same broadening velocity for the Fe emission features in the four groups. Then, the same restrictions applied in model A are accepted in model B on the Gaussian components of narrow Balmer emission components and the core and extended components from the [O ] emissions. Then, through the Levenberg-Marquardt leastsquares minimization technique, the best-fitting results to the emission lines by the model B can be well determined after considering the optical Fe emissions, and shown in Fig. 3 with 2 / ∼ 1330.88/1329. The determined parameters of emission lines are also listed in Table 1 Fig. 3, Fe emission features in the two groups related to the lower term of the transitions of 4 F, 6 S in Kovacevic et al. (2010) are strongly apparent, but there are quite weak Fe emission features related to the groups related to the lower term of the transition of 4 G in Kovacevic et al. (2010) Kovacevic et al. (2010) are strong enough, therefore, the other Fe templates, such as discussed in Boroson & Green (1992); Veron-Cetty et al. (2004); Tsuzuki et al. (2006), can not efficiently applied to describe the optical Features in SDSS J1058+5443, due to partly fixed intensity ratios of optical Fe features in their templates..
For the model C, based on the results determined by model B, there are two additional broad Gaussian components, and • Considering blue-shifted optical Fe emissions, optical spectroscopic emission features can be naturally described.
• The F-test technique can be well applied to confirm that it is not necessary to consider broad Balmer lines, once the optical Fe emissions are fully considered.

Properties of NUV Mg line
Besides properties of the optical Balmer emission lines, emission lines around Mg with rest wavelength range from 2600 to 3600Å can be well measured by two different models as follows. Here, the selected wavelength range extending to 3600Å can lead to well determined continuum emissions.
In model A, a broadened and shifted UV Fe template discussed in Kovacevic-Dojcinovic & Popovic (2015) plus a broad Gaussian function and a power law component are applied to describe the emissions. Here, considering the UV Fe templates in four groups (4 multiplets: 60 within Z X. G. & Z S. D. 2907 to 2979Å, 61 within 2861 to 2917Å, and 62 and 63 which overlap within 2709 to 2749Å) as discussed in Kovacevic-Dojcinovic & Popovic (2015), the UV Fe component is described by where ≥ 0 represents the intensity of UV Fe emission features in each group, , means the broadened and shifted UV Fe emission features in each group, and and means the same shifted velocity and the same broadening velocity for the UV Fe emission features in the four groups. The best-fitting results are shown in the left panel of Fig 4 with  Not only the large uncertainties of line flux and second moments as clues to rule out the expected broad Mg component, the F-test technique can be also applied to determine that the broad Gaussian component is not necessary to be considered. Based on the different 2 / values for the model A and Model B for emission lines around 2800Å, the calculated value is about Based on − and as number of dofs of the F distribution numerator and denominator, the expected value from the statistical F-test with confidence level about 40% will be near to . Therefore, the confidence level is only about 40%, smaller than 1sigma, to support the broad Mg component, indicating the determined broad Gaussian component by model A is not preferred. Certainly, the discussed results above are only based on different model functions and corresponding F-test technique, further efforts are necessary to totally confirm the discussed results above.
Furthermore, as discussed in Kovacevic-Dojcinovic & Popovic (2015) (see left panel in their Fig. 10), there is one positive broadening velocity correlation between optical Fe emission features and UV Fe features. Based on the determined broadening velocity about 6700km/s of UV Fe emission features and the determined broadening velocity about 6200km/s of optical Fe emission features in SDSS J1058+5443, there are clues to consider SDSS J1058+5443 to simply follow the broadening velocity correlation between UV and optical Fe emission features.

BH MASS OF SDSS J1058+5443
BH mass, one of fundamental parameters of AGN, is mainly estimated in the subsection. BH mass properties will be used in the following subsections to provide further clues to confirm probable loss of central BLRs in SDSS J1058+5443. Due to no apparent broad emission lines in SDSS J1058+5443, the reported virial BH mass is not considered in the manuscript based on the Virialization assumption applied to broad line emission clouds (Peterson et al. 2004;Shen et al. 2011). The following two methods are mainly considered.
First, based on the dependence of BH masses on continuum luminosity reported in Equation (9) in Peterson et al. (2004), BH mass of SDSS J1058+5443 can be estimated as with BH mass uncertainty determined by uncertainty of continuum luminosity and uncertainties of the factors in the equation. Second, the commonly accepted AGNSPEC code (Hubeny et al. 2000;Davis et al. 2007) is applied to roughly determine the central BH mass through properties of spectral energy distributions of SDSS J1058+5443, considering the non-LTE general relativistic accretion disk models. Fig. 5 shows the best descriptions to the SDSS spectrum of SDSS J1058+5443 with emission line features around 2800Å (from 2700Å to 2950Å) and around T -2 9  4900Å (from 4800Å to 5100Å) being masked out, with the BH mass ∼ (2.5 ± 1.1) × 10 8 M ⊙ , accretion rate ∼ 0.03 ± 0.01M ⊙ /year, BH spin * ∼ 0.91 ± 0.06, and inclination angle cos( ) ∼ 0.32 ± 0.11, through the AGN-SPEC code created templates applied through the Levenberg-Marquardt least-squares minimization technique.
The two different methods lead to similar BH mass, therefore the mean value ∼ (2.8 ± 1.4) × 10 8 M ⊙ is accepted as the BH mass of SDSS J1058+5443 in the manuscript .

Re-constructed probable intrinsic but hidden broad
Balmer lines? Based on the estimated BH mass, the intrinsic broad Balmer lines could be re-constructed. Then, it is interesting to check whether the expected intrinsic broad Balmer lines are actually overwhelmed in noises of SDSS spectrum of SDSS J1058+5443.
Not similar as the previous reported candidates of true type-2 AGN, weak broad emission components could lead to none detected broad emission lines in low quality spectra with large noises. In the blue quasar SDSS J1058+5443, strong power law AGN continuum emissions clearly indicate strong intrinsic broad Balmer emission lines, if there were broad line emissions. Based on the strong positive linear correlation (scatter of 0.2dex) between AGN continuum luminosity and total Balmer line luminosity from SDSS quasars in The virial BH mass about 3 × 10 9 M ⊙ is reported in Shen et al. (2011) in SDSS J1058+5443. However, as discussed above, the viral BH mass sensitively depending on broad line properties should be not reliable enough in SDSS J1058+5443. Therefore, rather than the virial BH mass 3 × 10 9 M ⊙ , the mass ∼ 2.8 × 10 8 M ⊙ is accepted in SDSS J1058+5443 in the manuscript. Moreover, after checked the results in Shen et al. (2011), there is weak correlation between virial BH mass and narrow line width in SDSS quasars, with Spearman rank correlation coefficient only about 0.07. Therefore, in the manuscript, we do not consider line width ( If the expected broad H with line luminosity of (9.84 ± 0.24) ×10 42 erg/s was intrinsically true in SDSS J1058+5443, there was only one point leading the expected strong broad H not to be detected in the SDSS spectrum: the strong broad H was extremely broad enough that the expected broad H with very lower heights are totally overwhelmed by the noises of SDSS spectrum. However, considering the estimated BH mass ∼ (2.8 ± 1.4) × 10 8 M ⊙ , line width of the expected intrinsic broad Balmer lines can be well estimated through the Virialization assumption (Peterson et al. 2004) combing with size-luminosity empirical relation (Bentz et al. 2013) (scatter of 0.13dex) to estimate distance of BLRs to central BH, where the factor 5.5 is the applied scale factor to estimate Virial BH mass used in Peterson et al. (2004), and uncertainty 28light-days of is determined by the scatter of 0.13dex of the size-luminosity empirical relation, and uncertainty 700km/s of ( ) is determined by the uncertainties of both BH mass and . Based on second moment ( ) = 1700 ± 700km/s and line flux ( ) = (1132 ± 550) × 10 −17 erg/s/cm 2 , the expected intrinsic Gaussianlike broad H , ( [ 0 , ( ), ( )]) with central wavelength 0 = 4862Å can be well re-constructed and shown in Fig. 6, after considering uncertainties of parameters of ( ) and ( ). It is clear that the expected intrinsic broad H is strong enough, if there was, the intrinsic broad H can not be overwhelmed by noises of SDSS spectrum.
can be hidden or overwhelmed in the noises of SDSS spectrum, if there was intrinsic broad Mg line.
First, based on the strong positive linear correlation (scatter of 0.15dex) between AGN continuum luminosity at 3000Å and Mg line luminosity from SDSS quasars in Shen et al. (2011) 1590+400, 1280-490], [2800, 1590-400, 1280+490], [2800,, respectively. expected intrinsic Gaussian-like broad Mg can be well reconstructed and shown in Fig. 7, after considering uncertainties of parameters of ( ) and ( ). It is clear that the expected intrinsic broad Mg is strong enough, if there was, the intrinsic broad Mg cannot be overwhelmed by noises of SDSS spectrum. Now, based on the re-constructed broad Balmer lines and Mg line, if there were intrinsic broad emission lines, it is interesting to compare the expected SDSS spectrum of SDSS J1058+5443 considering the probable intrinsic broad lines and the composite spectrum of SDSS quasars. The comparison is shown in Fig. 8. Here, the expected intrinsic broad H and H are re-constructed based on the re-constructed broad H with line flux ratios to be 4862 : 4341 : 4103 = 1 : 0.5 : 0.3 ( 4862 = 1132 × 10 −17 erg/s/cm 2 ) and with the same line width (1700km/s) in velocity space and with the same redshift. It is clear that the spectroscopic features with considering the expected intrinsic broad lines are totally similar as those of composite spectrum of SDSS quasars. In one word, if there were intrinsic broad lines, the broad lines cannot be hidden or overwhelmed in noises of SDSS spectrum in SDSS J1058+5443. Therefore, it can be clearly confirmed the loss of broad lines in the SDSS J1058+5443.

Further discussions
Besides the detailed discussions on emission lines, origin of blue continuum emissions is simply considered in the subsection, in order to confirm that SDSS J1058+5443 is truly an AGN.
There are two further points applied to confirm that the blue continuum emissions are not from younger stellar objects but from the central AGN activities in SDSS J1058+5443. On the one hand, long-term variabilities of SDSS J1058+5443 is well checked through the collected 8years-long light curve from the CSS (the Catalina Sky Survey) (Drake et al. 2009) shown in Fig. 9. The apparent variabilities can be well described by the Damped Random Walk (DRW) process (Kelly et al. 2009;Kozlowski et al. 2010;Zu et al. 2013) which has been proved to be the preferred process to describe intrinsic AGN variabilities. Through the public code of JAVELIN, the determined DRW process parameter of the characteristic variability timescale is about ln( / ) ∼ 4.95 ± 0.54 ( ∼ 140 ), similar as the mean value of in SDSS quasars well discussed in MacLeod et al. (2010). On the other hand, the determined flux ratio of the total [O ] 5007Å (both the core and broad component) to the narrow H is about 16.3 larger than 10, indicating strong central AGN activities in SDSS J1058+5443 by applications of BPT diagrams (Kewley et al. 2019;Zhang et al. 2020). Therefore, the apparently blue continuum emissions are confirmed to be from central AGN activities. And then, due to the strong blue continuum emissions from central AGN activities, there are no discussions on the loss of broad emission lines due to SDSS J1058+5443 classified as a changing-look AGN at dim state (Tohline & Osterbrock 1976;LaMassa et al. 2015;Yang et al. 2018;Zhang 2021b).
Moreover, the none detected broad emission lines are not due to SDSS J1058+5443 as a BL Lac (Plotkin et al. 2008). The radio properties of SDSS J1058+5443 is well checked through the Faint Images of the Radio Sky at Twentycm (FIRST) (Helfand et al. 2015). The radio intensity at 1.4GHz is about 17.7mJy in SDSS J1058+5443, leading SDSS J1058+5443 to be a radio loud AGN with radio loudness about 29. However, the [O ] 5007Å has rest equivalent width (EW) about 49Å very larger than 5Å, indicating SDSS J1058+5443 is not a BL Lac object but a normal radio loud quasar.

What should be done in the near future?
Actually, there is one surefire way to confirm the SDSS J1058+5443 as a true type-2 AGN. To get the spectroscopic observations around H will provide robust evidence to support the conclusions in the manuscript for SDSS J1058+5443. If there were no broad components of H , there will be no doubt to well identify the SDSS J1058+5443 as a true type-2 AGN. We wish there will be good chance to get NIR spectroscopic observations of the SDSS J1058+5443in the near future.   Once loss of broad emission lines can be confirmed, it is interesting to consider the potential physical origin of the loss of central normal BLRs. In SDSS J1058+5443 with bolometric luminosity about 6 − 9 × 10 45 erg/s (about 10 times of the continuum luminosity 5100 ) (Netzer 2019), both the steep bluer power law AGN continuum emissions and the strong bolometric luminosity indicate that the disk-wind scenario with luminosities higher than 10 46 erg/s as well discussed in Elitzur & Netzer (2016) can be well applied to explain the loss of broad emission lines in SDSS J1058+5443, rather than the accreting process with lower accretion rates as discussed in Cao (2010); Nicastro et al. (2003); Elitzur & Ho (2009), etc. And the apparent blue-shifted broad UV and OPT Fe emission lines and the AGNSPEC simply determined large * ∼ 0.91 can provide probable clues to support the expected disk-winds scenario in Elitzur & Netzer (2016).
Before the end of the subsection, one point should be noted. As discussed in Villar Martin et al. (2020), there is a special subclass of AGN, the called core-extremely red quasars (core-ERQs) previously defined in Hamann et al. (2017), representing an intermediate evolutionary phase in which a heavily obscured quasar is blowing out the circumnuclear interstellar medium, leading to commonly consequent extreme outflows in high luminosity core-ERQs. In other words, the conditions of the disk-wind scenario discussed in Elitzur & Netzer (2016) could be well satisfied in high luminosity core-ERQs, however, there are common BLRs in core-ERQs. Therefore, the proposed disk-wind scenario dis-T -2 13 cussed in Elitzur & Netzer (2016) can be applied to explain the disappearance of central BLRs, but cannot be accepted as a standard criterion leading to disappearance of central BLRs in AGN.

SUMMARIES AND CONCLUSIONS
Finally, the main conclusions are given as follows.
• SDSS J1058+5443 is a blue quasar with apparently blue continuum emissions coming from central AGN activities, based on DRW process well determined long-term variabilities and flux ratio larger than 10 of [O ] to narrow H of SDSS J1058+5443. Not similar as previous reported candidates of true type-2 AGN among emission-line objects with weak AGN activities but strong host galaxy contribution, properties of SDSS J1058+5443 could provide more robust evidence to support the very existence of true type-2 AGN.
• Considering different model functions applied to describe emission lines around H , rather than broad Balmer lines but blue-shifted optical Fe emissions can be preferred in SDSS J1058+5443, leading to the conclusion that there are no broad optical Balmer emission lines in SDSS J1058+5443. The confidence level is smaller than 1sigma to support probably existence of broad Balmer emission lines.
• Considering different model functions applied to describe emission lines around 2800Å in SDSS J1058+5443, the blue-shifted UV Fe emissions can be preferred in SDSS J1058+5443, leading to the conclusion that there are no broad NUV Mg line in SDSS J1058+5443. The confidence level is smaller than 1sigma to support probably existence of broad NUV Mg line.
• Considering Virialization assumption to broad emission clouds in SDSS J1058+5443, combining with estimated BH mass, the expected intrinsic broad opti-cal Balmer lines and NUV Mg line can be well reconstructed, if there were intrinsic broad emission lines in SDSS J1058+5443. The SDSS spectrum plus reconstructed broad lines are totally similar as the composite spectrum of SDSS quasars.
• The re-constructed intrinsic broad lines can not be hidden or overwhelmed in the noises of SDSS spectrum of SDSS J1058+5443, indicating the loss of broad emission lines are not due to spectral quality.
• The SDSS J1058+5443 is so far the best candidate of true type-2 quasar, leading to the clear answer to the very existence of true type-2 AGN. And the expected disk-winds scenario with high luminosity could be preferred to explain the loss of central BLRs in SDSS J1058+5443.