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Time lag in transient galactic and extragalactic accreting sources

T0 review · 4 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

Pith's one-line read The paper claims that one viscous-disk formula reproduces the observed optical-to-X-ray delays in four galactic accreting sources, and that in AGNs the same delay measures the free-fall time of tidally disrupted stellar debris from the…

desk verdict A conference-proceedings narrative that honestly summarizes prior work; as a research preprint it lacks derivations, and the four-source 'excellent agreement' is not independently supported because input parameters are not given. read the letter →

arxiv 1908.09667 v1 pith:GYGDIWJW submitted 2019-08-26 astro-ph.HE

classification astro-ph.HE
keywords timedelayX-raybinariesaccretiondisksviscositytidaldisruptioneventsactivegalacticnucleimultifrequencyobservationsoptical-X-ray
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 tries to show that the delay between an optical flare and the later X-ray flare in transient accreting sources is a physical clock rather than an accident. For galactic binaries the delay is the time a viscosity-driven surge of matter takes to cross the accretion disk from its outer edge to the compact star, and a single formula (Eq. 6.1) is claimed to match observed delays in A0535+26, SS Cygni, Aql X-1, and GRO J1655-40. For AGNs, the same delay is claimed to be the free-fall time of matter from a tidally disrupted star down to the black hole, so the observed lag directly gives the radius of the disrupted star. A sympathetic reader would care because if true, simultaneous optical and X-ray monitoring becomes a measurement tool for disk viscosity and for the sizes of stars destroyed by supermassive black holes. The paper presents the formulas and the comparisons but does not re-derive Eq. 6.1 here.

What carries the argument

The load-bearing objects are two analytic formulas. Eq. 6.1, $\tau = 6.9\, m^{2/3} \dot{m}^{1/15} \alpha^{-4/5} (T_4)^{28/15}$, is the viscous propagation time of a mass-flow surge through a standard $\alpha$ disk; it encodes the compact-object mass $m$, accretion rate $\dot{m}$, viscosity parameter $\alpha$, and disk optical temperature $T_4$, and it is what converts an observed delay into a physical quantity. Eq. 6.3, $r_{\mathrm{opt}} = 1.65 \times 10^{12} \tau_{\mathrm{obs}} m^{1/3}$ cm, comes from integrating the free-fall velocity and converts an AGN delay into the radius where the optical flash originates, identified with the tidal radius. The argument rides on these two identities: measured delays are plugged into them to recover viscosity or disrupted-star radius.

What would settle it

Measure the delay in a transient whose disk mass, temperature, and viscosity are independently constrained, and compare with Eq. 6.1; a discrepancy of more than a factor of two would falsify the formula's universal form. For an AGN tidal disruption event with a well-measured black hole mass, check whether the delay implies a disrupted-star radius in the giant range; a radius far outside the giant branch, or a light curve showing a slow viscous disk-rise, would refute the free-fall identification.

Watch

Extended reading notes

Core claim

The central claim is that in disk-accreting close binaries an outburst begins at the disk periphery, seen as an optical brightening, and the increased mass flow then propagates inward under turbulent viscosity, producing the X-ray flash only after a delay $\tau$. The paper states that Eq. 6.1, $\tau = 6.9\, m^{2/3} \dot{m}^{1/15} \alpha^{-4/5} (T_4)^{28/15}$ days, gives excellent agreement with four measured delays: about 8 days for A0535+26, 0.9\textendash 1.4 days for SS Cygni, about 3 days for Aql X-1, and about 6 days for GRO J1655-40. For AGNs the paper claims that the debris from a star disrupted at the tidal radius falls almost radially at free-fall speed, so the observed optical-to-X-ray delay equals the free-fall time; inverting that gives the radius of the optical flash, which for the six listed AGNs implies disrupted stars with radii of tens to hundreds of solar radii, characteristic of giants. The paper also expects that debris with larger angular momentum will later form a disk and produce long-lived multiwavelength variability.

Load-bearing premise

For the AGN part, the load-bearing premise is that the shredded star's debris falls almost straight inward with very little angular momentum, so the observed optical-to-X-ray delay equals the free-fall time from the tidal radius; if angular momentum is substantial, a disk forms and the inflow is viscous and much slower.

Editorial extensions

If this is right

  • If the formula holds, a measured optical-to-X-ray delay in a transient with known companion mass and accretion rate yields the disk viscosity parameter $\alpha$, which is otherwise very hard to measure.
  • The scaling $\tau \propto (T_4)^{28/15} \alpha^{-4/5} \dot{m}^{1/15} m^{2/3}$ predicts that the delay is almost insensitive to accretion rate but very sensitive to the disk's optical temperature, a directly testable trend across a sample of transients.
  • In AGNs, measuring a delay and knowing the black hole mass gives the radius of the disrupted star; the values recovered in this paper indicate giant-branch stars, linking optical-X-ray delays to stellar evolution.
  • After an AGN tidal-disruption flash, matter with appreciable angular momentum should form an accretion disk and produce long-duration, irregular variability across the electromagnetic spectrum.
  • The periodic ephemeris approach for A0535+26 lets observers predict the arrival of X-ray outbursts from observed optical brightenings around periastron.

Reading between the lines

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

  • Inference beyond the paper: if Eq. 6.1 is robust, the delay can be used as an independent estimator of disk temperature, since the delay depends so steeply on $T_4$; multi-band optical monitoring timed against X-ray flares would test this.
  • Inference beyond the paper: the galactic and AGN models predict opposite scalings with angular momentum, so a tidal disruption event with a slow, viscous rise should show a much longer delay than the free-fall value; distinguishing the two regimes is an observational handle on the debris angular-momentum distribution.
  • Inference beyond the paper: the reported roughly 5-day lag between the H-beta and H-alpha equivalent-width jumps, if real, may trace the radial propagation of the same viscosity wave through different line-forming disk zones; simultaneous time-resolved spectroscopy of future outbursts could map that propagation directly.
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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

4 major / 5 minor

Summary. This paper reviews the evidence for optical–X-ray time delays in transient accreting sources and summarizes a model for the delay in galactic X-ray binaries, cataclysmic variables, and AGNs. For galactic sources, the delay is attributed to viscous propagation of an accretion wave through a disk, and the paper quotes Eq. (6.1), which is said to reproduce the observed delays of four systems to within about ten percent. For AGNs, the delay is interpreted as the free-fall time from the tidal radius of a disrupted star, leading to Eq. (6.3), and a table of six sources is presented. The paper also contains a historical account of the A0535+26/HDE245770 system and its multifrequency behaviour.

Significance. If the quantitative claims were fully supported, the paper would offer a simple unified formula connecting the optical–X-ray delay to stellar mass, accretion rate, disk viscosity, and disk temperature for galactic sources, and to the SMBH mass and stellar radius for TDE-like AGN flares. The empirical synthesis of A0535+26 observations and the proposed extension to AGNs are suggestive. However, the central equations are not derived in this manuscript, the input parameters are not given, and the AGN comparison is constructed from the observed delays. As it stands, the paper is better read as a conference summary of earlier work (GBK13, BKG17) than as a self-contained validation of the delay model.

major comments (4)
  1. [Section 6, Eq. (6.1)] The central quantitative claim of the paper — that Eq. (6.1) reproduces the observed optical–X-ray delays in A0535+26, SS Cygni, Aql X-1, and GRO J1655-40 — is not testable from the manuscript because no derivation of Eq. (6.1) is given and the input parameters (m, \dot{m}, T0, and especially α) for each of the four systems are not reported. The text immediately after the list states that Eq. (6.1) can be used to determine α from the experimental delay; if α is adjusted to match τ_exp, the claimed “excellent agreement” is by construction rather than a validation. Please provide either the derivation or a table of independently constrained input parameters and the resulting α for each source.
  2. [Section 6, Eq. (6.1)] The printed formula has τ ∝ α^{4/5}, i.e., a positive power of α. For a delay produced by outward transport of a viscosity wave, one expects the viscous time to decrease with increasing α, since larger α means faster angular momentum transport. As written, the formula implies that higher viscosity produces longer delays, which is opposite to the physical mechanism described in the text and sketched in Fig. 7. This sign (or exponent) needs to be corrected or physically justified.
  3. [Section 7, Eq. (6.3) and Table 2] The AGN test is circular. Eq. (6.3) is obtained by setting τ_ff = τ_obs and solving for r_opt, and Table 2 then lists r_opt = r_t and computes the implied stellar radius R_s = ... × m_s^{1/3} R_⊙. Since r_opt is constructed from τ_obs, the agreement between r_opt and r_t is a consequence of the construction, not an independent confirmation of the model. A genuine test would require computing τ_ff from independently measured stellar and SMBH parameters and comparing it with τ_obs.
  4. [Section 7 and Section 8] The model's applicability to the AGN sources in Table 2 rests on the assumption that the debris from the disrupted star falls quasi-spherically at near free-fall velocity with low angular momentum. This assumption is not justified for any of the listed sources. Standard TDE scenarios from Rees (1988) and later work generally involve debris with significant angular momentum that forms an accretion disk, in which the inflow time is the much longer viscous time; the paper itself acknowledges in Section 8 that higher-angular-momentum matter forms a disk. Please provide a quantitative argument or observational evidence that the debris in these specific objects has low angular momentum.
minor comments (5)
  1. [Abstract] The text cites “Rees (1998)”, but the body and reference list give Rees (1988); the year should be corrected.
  2. [Section 6, Eq. (6.1)] The equation is not clearly typeset: multiplication symbols between m, \dot{m}, α, and T4 are missing, and it is unclear whether the exponent of T4 is positive or negative; please check the original expression and reproduce it unambiguously.
  3. [Table 2] The entry for 3C 120 lists “3.9-6.2? (10)”, which is ambiguous and should be clarified with a reference or an explanation of the uncertainty.
  4. [Section 4, Table 1] The phrase “The mass are expressed in unit of SMC” should be “The masses are expressed in units of the SMC mass.”
  5. [Section 1] The philosophical preamble and the explanation that the talk was not originally scheduled are unusual in a research paper; consider condensing this material into a footnote or deleting it.

Circularity Check

2 steps flagged · score 6.0 of 10

The claimed four-source agreement can reduce to fitting alpha, and the AGN 'radius' is obtained by inverting the measured delay.

  1. fitted input called prediction [Section 6, Eq. (6.1) and the following source list]
    "By using this formula it is possible to obtain an excellent agreement between the experimental and theoretical delays found in: [list of four sources] ... In this general formula the α-viscosity parameter plays an important role, and usually it is hard to be determined. However, if the other parameters are known, because experimentally determined, the formula (6.1) can be used for determining α, taking into account the experimental delay measured in a certain source."

    The claimed validation of Eq. (6.1) is the agreement between τ_th and τ_exp for A0535+26, SS Cygni, Aql X-1, and GRO J1655-40. But the paper immediately states that Eq. (6.1) can be inverted to determine α from the measured delay, and it gives no independent values of α, m, dot-m, or T0 for these sources. Thus the listed τ_th values are not shown to be independent predictions: if α is inferred from τ_exp, the equality τ_th ≃ τ_exp is forced by construction rather than being a test of the formula.

  2. self definitional [Section 7, Eq. (6.3) and Table 2]
    "Taking τff = τobs, BKG17 obtained a radius of the optical flash ropt as: ropt = 1.65 × 10^12 τobs m^{1/3} cm (6.3) ... However, with the formula (6.3) BKG17 justify the experimental time delay between optical and X-ray flashes observed in AGNs."

    Equation (6.3) does not predict the AGN delay; it is obtained by setting τff equal to the observed τobs and solving for ropt. The table then labels this inverted radius as 'ropt = rt', identifying it with the tidal radius. Consequently, the 'agreement' in Table 2 is a consistency check on the assumed stellar and black-hole parameters, not an independent derivation of τobs from first principles. The observed delay is an input to Eq. (6.3), so using Eq. (6.3) to 'justify' the delay is circular by construction.

full rationale

The paper's two central quantitative relations are imported from the authors' earlier BKG17 paper and are not rederived here. For the galactic sources, Eq. (6.1) is presented as if it reproduces four measured delays, but the text states that the free α parameter can be determined from the experimental delay itself. With no per-source parameter values given, the reported τ_th ≃ τ_exp values are consistent with inversion rather than with independent prediction. For the AGN case, Eq. (6.3) is literally the inverse of the observed delay under an assumed free-fall model: setting τff = τobs and solving for ropt, then calling that radius rt, makes the 'predicted' radius an algebraic rearrangement of the input delay. The paper also leans heavily on self-citations (GBK13, BKG17), but that alone would not be circular; the circularity is the inversion of the measured quantity into the claimed output. Because the central four-source 'agreement' and the AGN radius both reduce at least partially to construction or fitting, a score of 6 is appropriate: some independent content may exist in BKG17, but the present paper does not exhibit an independent prediction.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central equations are not derived in this text. Eq. 6.1 depends on a viscous-disk model with parameters m, Mdot, T0, and alpha, of which alpha is explicitly treated as inferable from the delay it is supposed to predict. Eq. 6.3 defines ropt in terms of tau_obs by free-fall kinematics, making the AGN comparison a self-consistency check. No new entities are proposed; the model components are inherited from cited prior work.

free parameters (1)
  • alpha (Shakura-Sunyaev viscosity parameter)
    Eq. 6.1 contains alpha^{4/5}. Section 6 explicitly says that if other parameters are known, the formula can be used to determine alpha from the observed delay, so the listed tau_th values may select alpha rather than test the formula.
assumptions (4)
  • domain assumption Turbulent viscosity in a Shakura-Sunyaev thin disk transports an enhanced mass flux inward and produces the optical-to-X-ray delay.
    Invoked in Sections 5 and 6 as the mechanism behind Eq. 6.1; it is a physical modeling assumption inherited from disk theory, not demonstrated in this paper.
  • domain assumption For AGN tidal disruption, debris with low angular momentum falls quasi-spherically at nearly free-fall speed.
    Section 7 states this flow geometry as the basis for Eq. 6.3. The paper offers no independent evidence for low angular momentum in the disrupted debris.
  • domain assumption The observed optical-X-ray delay in AGNs is the free-fall time from the tidal radius to the inner hot region.
    This identification is what turns Eq. 6.3 into an explanation. Without it, the inferred ropt has no dynamical meaning.
  • domain assumption The disrupted star is a moderate-mass giant with radius of tens to hundreds of solar radii.
    Table 2 compares the inferred ropt with stellar radii and concludes they are characteristic of giants. This depends on assuming a roughly one-solar-mass disrupted star.

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Pith. "Pith review of Time lag in transient galactic and extragalactic accreting sources." pith.science (2026). https://pith.science/paper/GYGDIWJW

@misc{pith2026190809667,
  author       = {Pith},
  title        = {Pith review of: Time lag in transient galactic and extragalactic accreting sources},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GYGDIWJW}},
  note         = {Machine review of arXiv:1908.09667}
}
abstract

X-ray binaries are cauldrons of fundamental physical processes which appear along practically the whole electromagnetic spectrum. The sub-class of X-ray transient sources show multifrequency behaviour which deserve particular attention in order to understand the causing physics. These binary systems consist of a compact star and an optical star, therefore there is a mutual influence between these two stars that drive the low energy (LE) (i.e. radio, IR, optical) and high energy (HE) (i.e. UV, X-ray, $\gamma$-ray) processes. The LE processes are produced mostly on the optical star and the HE processes mostly on the compact star, typically a neutron star. Thus it appears evident that through the study of LE processes it is possible to understand also the HE processes and vice versa. In this paper we will discuss this problem starting from the experimental evidence of a delay between LE and HE processes detected for the first time in the X-ray/Be system A0535+26/HDE245770 (e.g. Giovannelli \& Sabau-Graziati, 2011; Giovannelli, Bisnovatyi-Kogan \& Klepnev, 2013 (here after GBK13); Giovannelli et al., 2015b). This delay is common in cataclysmic variables (CVs) and other binary systems with either a neutron star or a black hole. Since a delay between LE processes and HE processes has been experimentally observed in several active galactic nuclei (AGNs), we will discuss also the tidal disruption of stars by massive BHs, following the original idea of Rees (1998): stars in galactic nuclei can be captured or tidally disrupted by a central black hole. Some debris would be ejected at high speed, the remainder would be swallowed by the hole, causing a bright flare lasting at most a few years.

Figures

Figures reproduced from arXiv: 1908.09667 by the authors.

Figure 1
Figure 1. clearly explain all the mysteries of our Universe (Giovannelli, 2000). People who are able to read this sentence can understand that "The truth is written in the book of the Nature. We must learn to read this book" [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Classification of X-ray binaries (adapted from Giovannelli, 2015). 6 [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Left panel: accretion in X-ray binary systems disk-fed and wind-fed (adopted from Giovannelli & Sabau-Graziati, 2001, adapted from Blumenthal & Tucker, 1974). Right panel: mixed transfer (adopted from Giovannelli & Sabau-Graziati, 2001, after Nagase, 1989). 3.2 X-ray/Be systems The X-ray/Be binaries are the most abundant group of massive X-ray binaries in the galaxy, with a total inferred number of between 103 and 1… view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: Classification of HMXBs (adopted from Giovannelli, 2015). 8 [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: Spin period vs orbital period for X-ray pulsars. Disk–fed systems are clearly separated by systems having as optical counterparts either OB stars or Be stars (adopted from Giovannelli & Sabau-Graziati, 2001, after Corbet, 1984, 1986). Most of the systems having a Be pr…
Figure 6
Figure 6. Figure 6: X-ray flux versus time of A 0535+26. X-ray measurements are reported with red lines and asterisk, upper limits with green arrows, and predicted fluxes with light blue stars. Periods of real detected X-ray outburst and optical measurements are also marked (adopted from …
Figure 7
Figure 7. Figure 7: Sketch of the viscous accretion disk model for explaining the time-delay between X-ray and optical flashes (adopted from GBK13). By using the ephemerides given by GBK13, namely: JDopt−outb = JD0(2,444,944) ± n(111.0 ± 0.4) days that fixed the reference point at the dat…
Figure 8
Figure 8. Figure 8: Intensity of the X-ray flare of A 0535+26 versus the variation of V magnitude of HDE 245770 around the periastron passage (adapted from Giovannelli et al., 2015b). We have also found a relationship between the equivalent width (EW) of Hα and Ix. The values of Hα-EW hav…
Figure 9
Figure 9. Figure 9: Intensity of the X-ray flare of A 0535+26 versus the equivalent width of Hα of HDE 245770 around the periastron passage (data taken from Camero-Arranz et al., 2012; Yan, Li & Liu, 2012; Giovannelli et al., 2015b) (figure adopted from Fasano, 2015). by Giovannelli, Gual…
Figure 10
Figure 10. Figure 10: The predicted March–April 2010 X-ray outburst of A 0535+26 (Giovannelli, Gualandi & Sabau￾Graziati, 2010) after the 93th passage at the periastron after 811205-E (Caballero et al., 2010a,b,c,d; Ca￾ballero et al., 2011). The astonishing fact that definitively demonstra…
Figure 11
Figure 11. Figure 11: The Periastron passage at the 22nd cycle before 811205-E (JD 2502) (red line) precedes of ∼ 14 days the X-ray outburst of A 0535+26 which starts approximatively on JD 2516 (after Rosenberg et al., 1975). The vertical blue line indicates the day April 7, 1975 (JD 2,442…
Figure 12
Figure 12. Figure 12: Minimum X-ray luminosity (0.5-10 keV) versus orbital period for BH LMXBs and NS LMXBs. The diagonal hatched areas delineate the regions occupied by the two classes of sources and indicate the dependence of luminosity on orbital period (adapted from McClintock, Narayan…
Figure 13
Figure 13. Figure 13: Softness ratio versus hardness ratio for galactic compact systems. Light yellow ellipse marks the zone where BHs in high state lie, light turquoise ellipse marks the zone of the BHs in low state and NSs, and light fuchsia ellipse marks the zone of the X-ray pulsars (G…

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