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REVIEW 3 major objections 4 minor 11 references

Insight into the origin of multiwavelength emissions of PKS 1510-089 through modeling 12 SEDs from 2008 to 2015

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read For the quasar PKS 1510-089, the accretion disk's innermost edge is not fixed but moves outward from 3 to 18 Schwarzschild radii across flares, linking the central engine to the jet.

desk verdict Solid multi-epoch SED modeling of PKS 1510-089, but the claimed variable inner disk radius is a degeneracy with the fixed black hole mass, not a robust result. read the letter →

arxiv 2506.02500 v1 pith:ZJ4DQC2X submitted 2025-06-03 astro-ph.HE

Maichang Lei , Yuan Zheng , Jianfu Zhang , Yuhai Yuan , Jiancheng Wang This is my paper
classification astro-ph.HE
keywords PKS1510-089flat-spectrumradioquasarsspectralenergydistributionbigbluebumpaccretiondiskinnerradiusexternalComptonscatteringBlandford-Znajekmechanismblazarjetpower
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper sets out to show that the accretion disk of the flat-spectrum radio quasar PKS 1510-089 does not have a fixed inner edge. Fitting twelve spectral energy distributions (SEDs) from 2008 to 2015 requires the innermost stable orbit $R_{\rm ISO}$ to swing between $3\,R_{\rm S}$ and $18\,R_{\rm S}$. The changing peak of the optical/ultraviolet big blue bump is read as a changing inner disk radius rather than a changing black hole mass, which is held fixed at $5.4\times10^8\,M_\odot$. If this is correct, the inner disk edge is coupled to jet activity, so the state of the accreting black hole and the state of the relativistic jet are connected. The same modeling attributes the high-energy hump to inverse Compton scattering of broad-line-region photons, places the gamma-ray emission zone beyond the broad-line region but inside the dusty torus, and concludes that the jet is powered by the Blandford-Znajek mechanism rather than the Blandford-Payne mechanism.

What carries the argument

The machinery is a one-zone homogeneous leptonic emission model built around a Shakura-Sunyaev accretion disk with a movable inner edge. The disk is a multichromatic blackbody with inner radius $R_{\rm in}=f_{\rm dic}(3R_{\rm S})$, and the dimensionless factor $f_{\rm dic}$ is the control knob that shifts the big blue bump peak to fit the optical/UV data. External radiation fields from a spherical broad-line region and a thin dusty torus supply seed photons for external Compton scattering, while a corona contributes to the X-ray band. Jet powers from the Blandford-Znajek and Blandford-Payne mechanisms are computed from the best-fit accretion luminosity and compared with the inferred total jet power to decide which mechanism can energize the jet.

What would settle it

Measure the big blue bump peak frequency across several epochs with simultaneous high-precision optical/UV spectroscopy and an independent reverberation-mapping black hole mass; if a canonical disk with a fixed inner edge and a single mass reproduces all epochs, the claimed $R_{\rm ISO}$ variation collapses.

Watch

Extended reading notes

Core claim

The central claim is that the innermost stable orbit of the accretion disk is not stable in time. For each of the 12 SEDs, the authors model the big blue bump as a multicolor blackbody from a Shakura-Sunyaev disk whose inner radius is parameterized as $R_{\rm in}=f_{\rm dic}(3R_{\rm S})$, with the fitted factor $f_{\rm dic}$ ranging from 1.0 to 6.0, giving $R_{\rm ISO}=3$ to $18\,R_{\rm S}$ across the epochs. The authors argue that a black hole cannot change its mass on a seven-year timescale, so the observed drift of the big blue bump peak frequency must come from a moving inner disk edge, and they connect that motion to energy extraction by the jet. In the same fits, the gamma-ray hump is dominated by Compton scattering of broad-line-region photons, the X-ray band is a superposition of several radiation components, and the derived jet powers favor the Blandford-Znajek mechanism over the Blandford-Payne mechanism.

Load-bearing premise

The argument assumes the black hole mass is fixed at $5.4\times10^8\,M_\odot$ and that the optical/UV big blue bump is pure thermal emission from a thin accretion disk with a sharp inner edge; if the mass is different, or if non-thermal jet emission shifts the bump peak, the inferred variation of the innermost stable orbit does not follow.

Editorial extensions

If this is right

  • If the inner disk edge really moves, the canonical picture of a fixed innermost stable orbit must be replaced by a time-dependent truncation tied to the central engine's activity state.
  • The location of the gamma-ray zone beyond the broad-line region but within the dusty torus, together with low magnetization, points to diffusive shock acceleration rather than magnetic reconnection as the particle energization process during these flares.
  • The Blandford-Znajek mechanism with a rapidly spinning black hole (spin parameter $a=0.95$) can supply the required jet power, while the Blandford-Payne mechanism falls short by one to two orders of magnitude.
  • Correlated variability follows: synchrotron and gamma-ray fluxes should track each other because both scale linearly with the electron density, whereas low-energy X-rays, containing an SSC component, should show more complex behavior.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A testable alternative is that the apparent $f_{\rm dic}$ variation could come from non-thermal synchrotron contamination shifting the apparent peak of the big blue bump; simultaneous polarimetry that measures the wavelength dependence of polarization dilution could separate these two explanations.
  • If the variable inner-disk truncation is real, it may be a general marker of magnetic-flux buildup and release in radio-loud AGNs rather than a peculiarity of PKS 1510-089; applying the same SED-fitting procedure to other flat-spectrum radio quasars with prominent big blue bumps would show whether this behavior is common.
  • The quasi-periodic oscillations reported for this source in radio and gamma-ray light curves could be dynamical signatures of the moving inner disk edge, since the paper provides an explicit formula for QPO timescales driven by disk motion at the inner radius.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The manuscript presents one-zone homogeneous leptonic SED modeling of 12 multi-epoch SEDs of the flat-spectrum radio quasar PKS 1510-089, covering 2008-2015. A multicolor Shakura-Sunyaev disk is used to fit the optical/UV big blue bump, while BLR and dusty-torus radiation fields, plus a corona component, are used to model the X-ray and gamma-ray bands. The authors report four principal findings: (i) the inferred innermost stable orbit radius R_ISO varies between 3 R_S and 18 R_S across epochs; (ii) the GeV hump is dominated by ERC of BLR photons, with the X-ray band containing multiple components; (iii) the gamma-ray emission region lies near or beyond the BLR but within the dusty torus, favoring shock acceleration; and (iv) the Blandford-Znajek mechanism can power the jet while the Blandford-Payne mechanism cannot. The paper also uses optical spectropolarimetric data from the Steward Observatory to break some jet-model degeneracies and to test the thermal-versus-nonthermal decomposition in the optical band.

Significance. If the central claim were established, the reported variability of R_ISO between 3 and 18 R_S would be an interesting and unusual result with implications for disk-jet coupling in FSRQs. The paper has several strengths: it applies a consistent multi-component model to a rather large sample of 12 quasi-simultaneous SEDs; it includes BLR, dusty torus, and corona contributions; it brings independent spectropolarimetric data to bear on the optical decomposition; it explicitly shows an alternative jet-parameter fit in Figure 5; and it provides quantitative estimates of BZ and BP jet powers. These are useful contributions. However, the headline claim is not robust as presented: it rests on fixing the black hole mass at a single value from a poorly constrained range, on a disk inner radius parametrization that is inconsistent with the assumed spin, and on a manual fitting procedure without reported uncertainties. The paper therefore contains valuable modeling work, but the main physical conclusion requires substantial additional analysis before it can be accepted.

major comments (3)
  1. [Section 2 and Section 4] The disk is defined with Rin = f_dic (3 R_S) (Section 2), and the text identifies this radius with R_ISO. However, Section 4 fixes the black hole spin at a = 0.95 for the BZ/BP calculations. For a Schwarzschild black hole R_ISO = 3 R_S, but for a = 0.95 the prograde ISCO is about 1.4 R_g = 0.7 R_S, and even a retrograde ISCO is about 9 R_g = 4.5 R_S. Thus f_dic = 1 does not correspond to the ISCO of the assumed highly spinning black hole, and the reported range 3-18 R_S is not a range of ISCO values in the adopted spacetime. The authors should either compute R_ISO(a) consistently in the disk model or refrain from identifying f_dic(3 R_S) with R_ISO.
  2. [Section 6.1, Eq. (25)] The central claim of variable R_ISO is degenerate with the black hole mass. The BBB peak frequency scales approximately as nu_p,AD ~ M_BH^{-1/2} L_d^{1/4} r_in^{-3/4} (see Eq. 25 and the temperature profile in Eq. 5). With M_BH fixed at 5.4e8 M_sun, the fitted f_dic values simply absorb the product M_BH^{-1/2} f_dic^{-3/4}. The paper itself lists literature mass estimates spanning 4.19e7 to 8.2e10 M_sun and reports that freeing M_BH leads to epoch-dependent masses. A constant f_dic with a mass within the allowed range can reproduce the same peak shifts; for example, changing M_BH from 5.4e8 to 5.7e7 shifts the BBB peak by roughly a factor of three, comparable to the effect attributed to the full f_dic = 1-6 range. The conclusion therefore requires a quantitative treatment of the M_BH-f_dic degeneracy, such as confidence contours in the M_BH-f_dic plane or a marginalization over M_BH. As written, the variable R_ISO is a direct consequence of the adopted mass normalization rather than a quantity demanded by the data.
  3. [Section 4, Table 2] The best-fit parameters are obtained by visual inspection, with no reported uncertainties, no goodness-of-fit statistic, and no quantitative exploration of the disk parameter space. The authors acknowledge degeneracy and demonstrate an alternative jet-parameter fit in Figure 5, but they do not explore the corresponding degeneracy in the disk parameters (f_dic, L_d, M_BH). Without error bars on f_dic, or a demonstration that, for example, f_dic = 2 cannot fit the Pr-19(C) optical/UV data within the photometric uncertainties, the claim that R_ISO varies between 3 and 18 R_S is not supported. The same absence of uncertainties propagates into P_jet, PBZ, and PBP, weakening the BZ/BP conclusion as well.
minor comments (4)
  1. [Abstract] The phrase 'the innermost stable orbit (R_ISO) is not stable' is confusing because the ISCO is by definition stable; the intended meaning is that the inferred inner edge radius varies with epoch. Please rephrase.
  2. [Throughout] There are numerous typographical and grammatical errors, including 'an unique opportunity', 'dabate', 'mutifrequency', 'writtten', 'protrons', 'negitive', and 'emssions'. The manuscript would benefit from a careful language edit.
  3. [Section 4] The description of the fitting procedure is brief: 'through the visual inspection, further fine tuning the model parameters' does not explain how the 12-parameter model was navigated, how many trials were performed, or how the final solution was selected. A concise description of the fitting strategy and a reproducibility statement would be helpful.
  4. [Section 6.1] The list of mass estimates obtained when M_BH is left free (8.0e8, 5.4e8, 1.6e9, 2.7e9, 2.2e9, 3.3e9 M_sun) is presented as the motivation for fixing M_BH, but this is precisely the degeneracy that needs to be quantified rather than removed by assumption. Consider presenting the same exercise as a two-dimensional constraint in M_BH and f_dic.

Circularity Check

2 steps flagged · score 6.0 of 10

Headline R_ISO variability (3–18 R_S) is the fitted fdic read back out: with MBH fixed at 5.4e8 Msun, the BBB-peak fit constrains only MBH^{-1/2} fdic^{-3/4}, so the claimed 'moving inner edge' is a normalization artifact, not a data-forced prediction.

  1. fitted input called prediction [Section 6.1, Section 2 (definition Rin = fdic(3RS)), Table 2, and Abstract result (i)]
    "we treat Rin as an adjustable quantity (via changing the parameter fdic) to well pin down the peak location of the big blue bump ... The resulting fdic values, ranging between 1.0 and 6.0, are listed in Table 2. Therefore, the RISO of the AD of PKS 1510−089 fluctuates within 3 RS and 18RS, rather than being fixed at 3 RS."

    By construction Rin = fdic·(3RS) (Section 2), so the claimed variability range 3–18 RS is exactly the Table 2 range of the fitted fdic values (1.0–6.0) expressed in Schwarzschild radii. The Abstract presents this as the derived result (i), but it is the fit parameter read back out: no observable independent of the fitted BBB peak constrains R_ISO. The paper states that fdic is fine-tuned to match each SED; reporting its fitted range as a physical discovery about the inner disk edge is statistically forced by the modeling choice, not required by the data.

  2. fitted input called prediction [Section 6.1, Eq. (25) and the discussion of BH-mass estimates]
    "if there are multiple SED observations spanning several years and their optical/UV data sets clearly demonstrate that νobs_p,AD is not constant. According to Equation (25), this would lead to a series of distinct BH masses. Given that a BH cannot change its mass within such a short period, then the peak shift of the BBB likely stems from the variation of RISO, instead of the BH itself."

    Eq. (25) is written for Rin = 3RS (fdic = 1), and the same section gives νobs_p,AD ∝ rin^{-3/4}·M_BH^{-1/4}·(mdot)^{1/4}, jointly fixing the BBB peak to the combination MBH^{-1/2}·fdic^{-3/4}·Ld^{1/4}. The 'series of distinct BH masses' and the 'fluctuating RISO' are the same algebraic relation solved for different unknowns. Fixing MBH at 5.4×10^8 Msun (itself a UV-photometry/BBB-based value from Abdo et al. 2010b) forces all epoch-to-epoch peak shifts into fdic, while the paper lists published masses spanning 4.19×10^7 to 8.2×10^10 Msun, a range that alone absorbs the reported shifts. The conclusion that the shift 'stems from the variation of RISO' is therefore a normalization choice built into the fit, not an inference the data force.

full rationale

The central circular step is the headline claim (i): R_ISO of the AD 'is not stable but varies between 3 R_S and 18 R_S.' This reduces by construction to the fitted parameter fdic: Section 2 defines Rin = fdic(3RS) as the knob 'for adjusting the peak location of the AD spectrum,' Table 2 lists the fitted fdic = 1.0–6.0, and Section 6.1 concludes 'Therefore, the RISO of the AD of PKS 1510−089 fluctuates within 3 RS and 18RS.' The prediction is the fit read back out. The deeper reason is the degeneracy exhibited by Eq. (25) and the rin^{-3/4} scaling: the BBB peak fixes only MBH^{-1/2} fdic^{-3/4} Ld^{1/4}. Fixing MBH = 5.4×10^8 Msun (itself a BBB/UV-photometry estimate from Abdo et al. 2010b and Oshlack et al. 2002) forces all epoch-to-epoch peak shifts into fdic; the paper's own free-mass fit instead yields masses from 8.0×10^8 to 3.3×10^9 Msun, and the cited literature range (4.19×10^7–8.2×10^10 Msun) can absorb the same effect. The paper discusses this degeneracy qualitatively and rejects a varying MBH on physical grounds, but does not quantify it, so the '3–18 R_S' range is the chosen parameterization, not a quantity the data require. This is the fitted_input_called_prediction pattern, affecting the central claim. Mitigating factors: (i) the BBB peak shift itself is empirical; (ii) the paper is otherwise self-contained against external benchmarks: the spectropolarimetric data independently discriminate the degenerate jet fits (Figure 2 vs 5), the ERC-BLR dominance and γ-ray-region locations are tested against MAGIC data and γγ optical-depth computations, and the BZ-vs-BP conclusion is an inference from assumed spin a = 0.95 and φBH = 50 rather than a circular step; (iii) the only self-citation (Lei & Wang 2014) is non-load-bearing; (iv) the authors explicitly concede 'we here cannot claim that the model parameters presented in Table 2 are exclusive, but only claim that they are relatively reasonable.' These concessions reduce but do not eliminate the circularity, since the Abstract still asserts the R_ISO range as a primary result. Score 6: partial circularity; the central prediction reduces by construction while the rest of the analysis has independent content.

Assumptions & free parameters 11 free parameters · 11 assumptions · 0 invented entities

The paper's central claims rest on a standard one-zone leptonic model with many user-set parameters. The key physical result, variable R_ISO, is a direct function of the fitted parameter f_dic, not an independent observable. The BZ/BP conclusion depends on additional fixed assumptions (spin 0.95, gamma_min=1, proton content). The ledger makes explicit that the paper adds a re-parameterized fit rather than a new physical mechanism.

free parameters (11)
  • f_dic (inner radius scalefactor) = 1.0 to 6.0 across 12 SEDs
    Tuned to match the BBB peak; the variation drives the central R_ISO claim.
  • L_d (disk luminosity) = 0.87e45 to 7.2e45 erg/s
    Fitted to the amplitude of the optical/UV excess; enters BLR and DT energy densities.
  • B' (magnetic field) = 0.36 to 1.6 G
    Fitted to the synchrotron peak and used for jet power and magnetization.
  • gamma_max = 1.4e4 to 3.3e4
    Fitted to extend the high-energy tail.
  • gamma_br = 130 to 210
    Fitted break Lorentz factor.
  • n0 (electron normalization) = 1.6e3 to 11e3 cm^-3
    Fitted normalization of electron distribution.
  • s1, s2 (spectral indices) = s1 ~ 1.9, s2 2.8 to 3.2
    Fitted spectral slopes.
  • R_b (blob radius) = 2.1e16 to 3.2e16 cm
    Adopted from variability timescales in the original papers.
  • delta_D (Doppler factor) = 21 to 25
    Fitted; correlated with the Compton peak.
  • R_H (distance of emission region) = 1.92e17 to 5.37e17 cm
    Fitted; determines BLR/DT photon densities.
  • xi_Corona = 0.06 (fixed)
    Fixed at 0.06, adopted from Ghisellini & Tavecchio (2009).
assumptions (11)
  • domain assumption The emission region is a single homogeneous spherical blob moving down the jet.
    Standard one-zone approximation invoked in Section 2.
  • domain assumption Electron distribution is a broken power law.
    Equation (1) in Section 2; no microphysical derivation.
  • domain assumption The accretion disk is a Shakura-Sunyaev thin disk with temperature profile of Equation (5).
    Section 2, used to fit the BBB.
  • ad hoc to paper The inner disk radius scales as Rin = f_dic * 3 R_S.
    Section 2 and 6.1; this scaling is the paper's device to shift the BBB peak.
  • domain assumption BLR is a spherical shell with inner radius from Equation (7), outer radius 2 R_BLR,in, and covering factor 0.1.
    Section 2; adopted from Ghisellini et al. (2010) and Donea & Protheroe (2003).
  • domain assumption Dusty torus is a thin spherical shell with covering factor 0.6 and temperature prefactor 100 K.
    Equations (13)-(15); the 100 K prefactor differs from Ghisellini & Tavecchio's 370 K.
  • domain assumption Black hole spin is fixed at a=0.95.
    Section 2; justified by radio-loudness, but not measured.
  • ad hoc to paper Minimum electron Lorentz factor gamma_min=1.
    Section 2; maximizes jet power and improves X-ray fit.
  • domain assumption One cold proton per ten electrons provides proton energy density.
    Section 6.5, following Ghisellini et al. (2014).
  • standard math BZ and BP power formulas (Equations 16 and 17) are the correct maximal jet-power estimates.
    Section 3, from Tchekhovskoy et al. (2010) and Cao (2003).
  • ad hoc to paper Black hole mass fixed at 5.4e8 M_sun.
    Section 6.1; chosen from a literature range spanning three orders of magnitude.

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Pith. "Pith review of Insight into the origin of multiwavelength emissions of PKS 1510-089 through modeling 12 SEDs from 2008 to 2015." pith.science (2026). https://pith.science/paper/ZJ4DQC2X

@misc{pith2026250602500,
  author       = {Pith},
  title        = {Pith review of: Insight into the origin of multiwavelength emissions of PKS 1510-089 through modeling 12 SEDs from 2008 to 2015},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZJ4DQC2X}},
  note         = {Machine review of arXiv:2506.02500}
}
abstract

PKS\,1510$-$089 is one of the most peculiar sources among the FSRQs, exhibiting a notable big blue bump (BBB). This provides an unique opportunity to explore the coupling between the activity of the central engine and the relativistic jet, offering further insight into the origin of the multiwavelength emissions. To this end, we collected multiwavelength data spanning four periods from 2008 to 2015 and performed the spectral energy distribution (SED) modeling using a one-zone homogeneous leptonic model. In the model, a multichromatic accretion disk (AD) is used to fit the optical/UV data sets, while the external radiation fields from the broad-line region (BLR) and dusty torus (DT) are properly considered to produce the high-energy $\gamma$-ray emissions. Our best fit to 12 SEDs yields the following results: (i) The innermost stable orbit ($R_{\rm ISO}$) of the AD is not stable but varies between $3\,R_{\rm S}$ and $18\,R_{\rm S}$ during these observations. (ii) The high-energy hump of the SED is well dominated by Compton scattering of the BLR photons, while the X-ray flux may be comprised of multiple radiation components. (iii) The $\gamma$-ray emitting regions are generally matter-dominated, with low magnetization, and are located beyond the BLR but within the DT. At such distance, the multiwavelength emissions are likely to originate from shock accelerations; (iv) For the energization of the relativistic jet, our study supports the Blandford$-$Znajek (BZ) mechanism, instead of the Blandford$-$Payne (BP) mechanism, as the latter fails to power the jet.

Figures

Figures reproduced from arXiv: 2506.02500 by the authors.

Figure 1
Figure 1. SED modelings of the quasi-simultaneous data sets for the low-, high- and mediate-active states, labeled respectively as Ab-10(A), Ab-10(B) and Ab-10(C). These states occurred during the high-activity period from 2008 September to 2009 June. The black dot-dashed, magenta dashed, darkcyan dot-dashed, brown dotted lines indicate emissions from the DT, AD, ERC-DT, ERC-BLR, respectively. The red, olive, green, blue soli… view at source ↗
Figure 2
Figure 2. SED modelings of the quasi-simultaneous data sets for high- and low-active states, labelled respectively as Na-12(A) and Na-12(B), the SED data are collected during a γ-ray flare and the Herschel observation, respectively. At radio/optical band in both panels, the Planck and Spizer data are added and indicated in gray as a reference to the current flux level (Planck Collaboration et al. 2011; Malmrose et al. 2011). … view at source ↗
Figure 3
Figure 3. SED modelings of the quasi-simultaneous data sets for high- and low-active states, labelled respectively as Ah-17(A) and Ah-17(B), which occurred during a long, high γ-ray state in May 2015. At radio/optical band in both panels, the Planck and Spizer data are added and indicated in gray as a reference to the current flux level (Planck Collaboration et al. 2011; Malmrose et al. 2011). The black dot-dashed, magenta da… view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: SED modelings of the quasi-simultaneous data for four flaring episodes and a quiescent state in 2015, labeled re￾spectively as Pr-19(A), Pr-19(B), Pr-19(Q2), Pr-19(C) and Pr-19(D). In Pr-19(B), the contemporaneous MAGIC observations, presented in Ahnen et al. (2017), a…
Figure 5
Figure 5. Figure 5: Similar to [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: The polarization degree Q varies with the ob￾servation time during three periods, which well encompass 12 SED observations. The vertical dotted line corresponds to the flaring time with the highest polarization degree, and the corresponding time and polarization degree…
Figure 7
Figure 7. Figure 7: Distribution of full-resolution optical flux with the frequency. Two notable spikes are marked by two red￾dotted lines, which are presumably the emission lines Hβ and Hγ. The black dashed-line represents the linear fitting using a linear function, f(x)=bx+k, where the …
Figure 8
Figure 8. Figure 8: Distribution of full-resolution optical flux with the frequency. Two notable spikes are marked by two red-dotted lines, which are presumably the emission lines Hβ and Hγ. The black dashed-line represents the linear fitting using a linear function, f(x)=bx+k, where the …
Figure 9
Figure 9. Figure 9: Dependence of polarization degree on the wave￾lengths covered by optical spectropolarimetric observations. A linear fitting of form p(λ) = bλ + k is applied to three wavelength ranges, [4000−7550] ˚A , [4300−7500] ˚A and [5000−7000] ˚A , shown as the red dotted, black …
Figure 10
Figure 10. Figure 10: Dependence of polarization degree on the wavelengths covered by optical spectropolarimetric observations. A linear fitting of form p(λ) = bλ + k is applied to three wavelength ranges, [4000−7550] ˚A , [4300−7500] ˚A and [5000−7000] ˚A , shown as the red dotted, black …
Figure 11
Figure 11. Figure 11: Left panel: Dependence of uBLR on Rz, The solid lines of different colors represent accurate calculations (acc.) for three cases: Ab-10(A), Pr-19(B) and Pr-19(C). The dashed lines are approximate representations (app.) using Equation (28). The shaded region indicates …
Figure 12
Figure 12. Figure 12: Distribution plane of normalized Stokes parameters u and q, in which the red star represents the median point of u and q distributions, and the red cross corresponds to u=0 and q =0. For the 12 SEDs studied in this paper, nine of them have corresponding spectropolarim…
Figure 13
Figure 13. Figure 13: Distribution plane of normalized Stokes param￾eters u and q, in which the red star represents the median point of u and q distributions, and the red cross corresponds to u=0 and q =0. larization data, this will be addressed in forthcoming work. In Section 5, we have c…

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