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REVIEW 3 major objections 8 minor 53 references

Be star disks form from localised, mildly super-Keplerian mass ejections

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2026-07-07 20:22 UTC pith:HR3RHSTU

load-bearing objection First 3D SPH simulations of localized Be star mass ejection, compared with simultaneous TESS photometry and spectroscopy. The qualitative picture holds; the quantitative match has a real gap in the Hα spectroscopic timescale. the 3 major comments →

arxiv 2607.05270 v1 pith:HR3RHSTU submitted 2026-07-06 astro-ph.SR

The birth of Be star disks III. SPH models of localised mass ejections

A. C. Rubio , A. C. Carciofi , D. Baade , J. Labadie-Bartz , T. H. de Amorim , I. A. Gabitova , M. W. Suffak This is my paper
classification astro-ph.SR
keywords diskejectionmasshighlocalisedmodelsdecretiondisks
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper uses 3D smoothed particle hydrodynamics (SPH) simulations to test whether localised, short-duration mass ejections from a rotating equatorial patch of a Be star can build a Keplerian decretion disk and reproduce the photometric, spectroscopic, and polarimetric signatures of observed 'flickers' — brief outbursts seen in Be stars. The authors systematically vary the geometry, rotation speed, viscosity, and injection radius of the ejected material, then post-process the hydrodynamic output with a radiative transfer code to generate synthetic observables that they compare to a well-documented flicker in the Be star f Car. The central claim is that a specific combination of conditions — material ejected at 1.05 times the Keplerian orbital speed (mildly super-Keplerian), high viscosity (alpha = 1.0), mass-loss rate of order 10^-6 solar masses per year per steradian, and injection from a narrow azimuthal sector (about 0.2 radians wide) very close to the stellar equator — produces synthetic light curves, H-alpha line profiles, line-asymmetry oscillations, and polarimetric signals that qualitatively match the observed flicker. Sub-Keplerian ejection fails to lift enough material into orbit; strongly super-Keplerian ejection produces disk behaviour inconsistent with observations; too-wide ejection angles erase the characteristic cyclic line asymmetries; and injection from above the stellar surface (a magnetic lever-arm scenario) produces oscillation frequencies too low to match the observed near-1:1 correlation with the orbital frequency at the equator. The paper also demonstrates that during active mass ejection the forming disk is strongly asymmetric, vertically perturbed, and dynamically far from the steady-state assumptions of standard viscous decretion disk theory, with circularisation occurring only days after ejection ceases.

Core claim

The key result is that the qualitative shape and timescale of Be star flicker observables — the rapid photometric rise and slower decay, the cyclic violet-to-red asymmetry oscillations in H-alpha, and the peak separation behaviour — are reproduced when and only when the mass ejection is localised to a narrow equatorial sector, mildly super-Keplerian (gamma = 1.05), and highly viscous (alpha = 1.0). The cyclic asymmetry oscillations arise because the ejected material forms an azimuthally concentrated clump that orbits the star, partially eclipsing it at high inclinations and creating periodic V/R variations in the emission line profile. These oscillations dampen as the material circularises,即

What carries the argument

The SPH injection volume: a 3D region defined by radial extent, vertical height, and azimuthal opening angle, rotating at gamma times the Keplerian orbital frequency, from which particles are ejected with an added isotropic ballistic velocity. The gamma parameter controls how much angular momentum the ejected material carries; alpha (the Shakura-Sunyaev viscosity parameter) controls how fast the material spreads into a circular disk; the opening angle controls how azimuthally concentrated the ejecta remain. Together these determine whether a disk forms, how large it grows, and whether the resulting observables match real Be star flickers.

Load-bearing premise

The density of each simulation is scaled after the fact to match the observed photometric and H-alpha amplitudes of f Car, meaning the mass-loss rate of ~10^-6 solar masses per year per steradian is not independently predicted but is a fitting parameter. The qualitative agreement in the shapes of the observable curves does not depend on this scaling, but the specific mass-loss rate does.

What would settle it

If future observations of Be star flickers with simultaneous photometry, spectroscopy, and polarimetry show V/R oscillation frequencies that deviate systematically from the orbital frequency at the stellar equator, or if they show no photometric oscillations at high inclinations, the model's core predictions about the geometry and dynamics of the ejection would be falsified.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If the model is correct, the near-1:1 correlation between V/R oscillation frequencies and the stellar orbital frequency at the equator can be used as a diagnostic of the stellar radius and mass, providing an independent constraint on Be star fundamental parameters.
  • The finding that only mildly super-Keplerian injection works quantifies the angular momentum excess that any physical mechanism (pulsation, magnetic activity, or otherwise) must supply — roughly an additional 50 km/s beyond what a sub-critically rotating star provides at its equator.
  • The prediction of partial eclipses by the orbiting density enhancement at high inclinations offers a testable signature: edge-on Be stars should show photometric oscillations at the Štefl frequency during outbursts, while pole-on stars should not.
  • The model provides benchmark constraints on mass-loss rate (~10^-6 Msun/yr/str) and injection geometry that any future physical model of the Be phenomenon — whether pulsation-driven or magnetically driven — must satisfy.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The density-scaling procedure means the mass-loss rate is effectively a fitted parameter rather than a prediction; an independent determination of Be star flicker mass-loss rates (e.g., from polarimetric monitoring) would provide a critical test of whether the preferred model's 10^-6 Msun/yr/str is physically correct or merely a convenient rescaling.
  • The mismatch between simulated and observed H-alpha dissipation timescales — the model's emission decays too slowly — suggests that physics missing from the SPH treatment (radiative ablation, radially variable viscosity, or non-isothermal effects) may be dynamically important during the circularisation phase, and that the isothermal alpha-disk approximation may break down in the inner disk during
  • The abrupt phase shift in V/R oscillations at the end of mass injection in the models, which has no clear observational counterpart, may indicate that real Be star mass ejections ramp down gradually rather than terminating instantaneously — a prediction about the temporal profile of the ejection mechanism itself.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 8 minor

Summary. This paper presents 3D SPH simulations of localized, short-duration mass ejections from Be star equatorial regions, post-processed with the HDUST radiative transfer code to produce synthetic photometric, spectroscopic, and polarimetric observables. The authors systematically vary injection geometry (azimuthal extent, vertical height, injection radius), angular velocity (gamma), and viscosity (alpha), comparing synthetic observables to a well-documented flicker event in the Be star f Car from Paper I. The preferred model (gamma=1.05, alpha=1.0, R_inj=1.01 R_eq, Delta_phi=0.2 rad) qualitatively reproduces the photometric flicker morphology, H-alpha line profile shapes, EW_V/EWR oscillation frequencies, and polarimetric amplitudes. The authors find that mildly super-Keplerian injection, high viscosity, and mass-loss rates of order 10^-6 Msun/yr/str are required, and that the disk circularizes within a few days. The paper also demonstrates that sub-Keplerian injection is ineffective at forming disks, that large azimuthal opening angles suppress the observed V/R asymmetries, and that injection near the stellar equator is favored over a magnetic lever-arm scenario.

Significance. This is the first study to confront 3D SPH simulations of localized Be star mass ejections with simultaneous photometric and spectroscopic observations of flicker events, representing a genuine advance in connecting surface dynamics to disk build-up. The systematic parameter exploration over gamma, alpha, Delta_phi, Delta_z, and R_inj provides falsifiable constraints on the mass ejection geometry. The identification of the partial eclipse mechanism for photometric oscillations at high inclination and the test of the lever-arm injection scenario against the observed 1:1 frequency correlation are specific, testable contributions. The use of HDUST for full NLTE radiative transfer on 3D SPH outputs is computationally demanding and adds credibility to the synthetic observables. The qualitative agreement with f Car is encouraging and lays a foundation for future quantitative model-fitting.

major comments (3)
  1. Sect. 4.1.3 and Table 2: The central claim (abstract and Sect. 5) states that the preferred model 'reproduces the behaviour of the reference flicker' and 'can account for the short-timescale photometric, spectroscopic, and polarimetric variability.' However, the PS_W dissipation slope at 200h is 72 km/s/h for the model vs. 25 km/s/h for f Car — a factor of ~3 discrepancy — and the H-alpha EW also decays too slowly (Sect. 4.1.3: 'the decay of H-alpha EW is much slower than in the data'). These occur at alpha=1.0, the maximum value in the Shakura-Sunyaev prescription. The authors acknowledge this in Sect. 5.2 and suggest radially variable viscosity or radiative ablation as remedies, but neither is included. Since the abstract claims the model accounts for spectroscopic variability, the mismatch in a key spectroscopic diagnostic (PS_W timescale) should be reflected more carefully in the phr
  2. Sect. 4.2: The density of each model is scaled post-hoc to match observed photometric and H-alpha amplitudes of f Car (Sect. 4.2: 'the density of each model was adjusted up or down to approximately match the observed amplitudes'). The preferred model's density was lowered by 40%, and Table 3 shows scaling factors ranging from 0.2 to 4.0 across models. This means the quoted mass-loss rate of ~10^-6 Msun/yr/str is not independently predicted but is a fitting parameter. The qualitative agreement in curve shapes is independent of this scaling, but the mass-loss rate claim in the abstract should be qualified as derived from fitting rather than predicted.
  3. Sect. 4.6 and Table 1: The lever-arm model uses gamma=1.01 (not 1.05 as in the preferred model), yet the comparison is presented as a test of injection radius. Since gamma directly affects decretion efficiency (69% at gamma=1.05 vs. ~100% at gamma=1.01 with higher R_inj), the separate effects of R_inj and gamma are confounded in this comparison. The text should clarify whether the conclusion about the lever-arm scenario being disfavored holds when gamma is held fixed.
minor comments (8)
  1. Table 1 lists Delta_z values as '0.2*, 1.0 R_eq' but Sect. 4.5 refers to '0.1 (in our preferred model) and 0.5 R_eq.' Please reconcile these values.
  2. Sect. 4.1.3, paragraph on H-alpha: 'the dip in EW is not as clear as f Car's' — the phrasing is ambiguous about whether the model underproduces or overproduces the EW dip depth.
  3. Fig. 2 caption: 'This sketch is not to scale' — consider adding approximate scale information or labeling R_eq for context.
  4. Sect. 3: The isothermal assumption (T_d = 0.6 T_eff = 12 kK) is noted, but Appendix C shows the disk is far from isothermal. A brief comment in Sect. 3 on the expected impact of this approximation on the dynamics would strengthen the discussion.
  5. Table 3: The AM decretion rate for gamma=1.0 (3.8e39 g cm^2 s^-2 str^-1) appears inconsistent with the text in Sect. 4.2, which references ~1.25e38 g cm^2 s^-2 str^-1 from Rimulo et al. (2018). Please clarify the comparison.
  6. Sect. 5.2: 'there is a remarkable agreement' — given the PS_W and EW timescale mismatches, consider softening this to 'qualitative agreement.'
  7. Abstract: 'Material, and the injection radius' appears to be a truncated sentence fragment.
  8. Sect. 4.3: The constraint on Delta_phi is stated as 'less than ~60% of the stellar equator' in the abstract but '~64%' in Sect. 4.3. Please use a consistent value.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for a careful and constructive report. The referee correctly identifies three areas where the manuscript's claims or presentation can be sharpened. We address each major comment below and propose concrete revisions in all three cases.

read point-by-point responses

  1. Referee: Sect. 4.1.3 and Table 2: The central claim (abstract and Sect. 5) states that the preferred model 'reproduces the behaviour of the reference flicker' and 'can account for the short-timescale photometric, spectroscopic, and polarimetric variability.' However, the PS_W dissipation slope at 200h is 72 km/s/h for the model vs. 25 km/s/h for f Car — a factor of ~3 discrepancy — and the H-alpha EW also decays too slowly (Sect. 4.1.3: 'the decay of H-alpha EW is much slower than in the data'). These occur at alpha=1.0, the maximum value in the Shakura-Sunyaev prescription. The authors acknowledge this in Sect. 5.2 and suggest radially variable viscosity or radiative ablation as remedies, but neither is included. Since the abstract claims the model accounts for spectroscopic variability, the mismatch in a key spectroscopic diagnostic (PS_W timescale) should be reflected more carefully in the phr

    Authors: The referee is correct that the factor of ~3 discrepancy in the PS_W dissipation slope and the too-slow H-alpha EW decay are significant, and that the abstract and Sect. 5 overstate the level of agreement for these spectroscopic diagnostics. We will revise the manuscript as follows. (1) The abstract will be modified to state that the model 'qualitatively reproduces the photometric and polarimetric behaviour and the H-alpha line profile shapes, though the spectroscopic dissipation timescale is slower than observed by a factor of ~3.' (2) In Sect. 5, we will add an explicit caveat that the PS_W and EW decay rates are not reproduced at the quantitative level, even at alpha=1.0, and that this points to missing physics (radially variable viscosity, radiative ablation, or non-isothermal effects). (3) We will soften the language in Sect. 4.1.3 to make clear that the agreement is qualitative in shape and amplitude but not in dissipation timescale for the spectroscopic diagnostics. We agree that the current phrasing is stronger than the evidence supports for these specific diagnostics. revision: yes

  2. Referee: Sect. 4.2: The density of each model is scaled post-hoc to match observed photometric and H-alpha amplitudes of f Car (Sect. 4.2: 'the density of each model was adjusted up or down to approximately match the observed amplitudes'). The preferred model's density was lowered by 40%, and Table 3 shows scaling factors ranging from 0.2 to 4.0 across models. This means the quoted mass-loss rate of ~10^-6 Msun/yr/str is not independently predicted but is a fitting parameter. The qualitative agreement in curve shapes is independent of this scaling, but the mass-loss rate claim in the abstract should be qualified as derived from fitting rather than predicted.

    Authors: The referee is correct. The mass-loss rate is not independently predicted; it is derived by scaling the SPH density to match the observed photometric and H-alpha amplitudes. The qualitative agreement in curve shapes, frequencies, and relative amplitudes is independent of this scaling, but the absolute mass-loss rate is indeed a fitting parameter. We will revise the abstract to state that the mass-loss rate is 'inferred by scaling the model density to match the observed amplitudes' rather than presenting it as a prediction. We will also add a sentence in Sect. 4.2 making this distinction explicit: the curve shapes and frequencies are predictions of the SPH dynamics, while the absolute mass-loss rate is constrained by the amplitude matching. Table 3 already lists the scaling factors transparently, so no change is needed there. revision: yes

  3. Referee: Sect. 4.6 and Table 1: The lever-arm model uses gamma=1.01 (not 1.05 as in the preferred model), yet the comparison is presented as a test of injection radius. Since gamma directly affects decretion efficiency (69% at gamma=1.05 vs. ~100% at gamma=1.01 with higher R_inj), the separate effects of R_inj and gamma are confounded in this comparison. The text should clarify whether the conclusion about the lever-arm scenario being disfavored holds when gamma is held fixed.

    Authors: The referee raises a valid point about the confounding of gamma and R_inj in the lever-arm comparison. We acknowledge that the two parameters are not independently varied in this test. However, the primary diagnostic that disfavors the lever-arm scenario is not the decretion efficiency (which is indeed affected by both parameters) but the EW_V/EWR oscillation frequency, which is set by the orbital frequency at the injection radius and is therefore a direct constraint on R_inj alone. At R_inj=1.25 R_eq, the orbital frequency is lower regardless of gamma, and the model cannot reproduce the observed 1:1 correlation between the EW_V/EWR frequency and the orbital frequency at the stellar equator. This conclusion holds independently of gamma. We will add a clarifying sentence in Sect. 4.6 stating this explicitly: that while gamma and R_inj are both changed in this comparison, the key discriminant is the EW_V/EWR frequency, which depends on R_inj but not on gamma. We also note that the manuscript already acknowledges (end of Sect. 4.6) that the lever-arm scenario cannot be wholly excluded given the uncertainty in R_eq. revision: partial

Circularity Check

1 steps flagged

Mass-loss rate is a fitted parameter, not a prediction; qualitative claims are independently grounded.

specific steps
  1. fitted input called prediction [Sect. 4.2, Table 3, and Abstract]
    "the density of each model was adjusted up or down to approximately match the observed amplitudes in brightness and Hα EW seen in the data of f Car. In practice, this means that each HDUST simulation has its own 'effective' mass ejection rate. For our preferred model, the observables shown in Figs. 5 and 7 use a scaled mass ejection rate of Ṁ_scaled_ejec = 1.0×10^-6 M⊙ yr^-1 str^-1 (that is, the density is lowered by 40% from the original SPH results)"

    The abstract states 'a mass-loss rate of the order 10^-6 M⊙ yr^-1 str^-1 are required' as a result. However, this value is not independently predicted: it is obtained by scaling the SPH density up or down until the synthetic photometric and Hα amplitudes match the observed f Car data. The scaling factor (0.4 for the preferred model, ranging from 0.2 to 4.0 across models) directly determines the reported mass-loss rate. By construction, the 'required' mass-loss rate equals the value that reproduces the observed amplitudes. The paper is transparent about this procedure, and the qualitative findings (which γ values work, curve shapes, V/R frequencies, circularisation timescales) are independent of the density scaling. But the specific quantitative claim about Ṁ ~ 10^-6 is a fit renamed as a '

full rationale

The paper's central qualitative claims — that mildly super-Keplerian injection (γ=1.05) with high viscosity (α=1.0) and confined azimuthal extent can reproduce the observed flicker morphology — are independently grounded in the SPH dynamics and do not depend on the density scaling. The self-citations (Bjorkman & Carciofi 2005 for the diffusion timescale, Carciofi et al. 2025 for the PS_W definition, Paper I for observational data) are methodological or data references, not load-bearing theoretical premises that would make the derivation circular. The one circular element is that the mass-loss rate (~10^-6 M⊙/yr/str) is presented as a 'required' result when it is actually determined by fitting model density to observed amplitudes. The paper is transparent about this scaling, and the qualitative conclusions stand without it. This is a minor circularity affecting one quantitative output, not the central derivation.

Axiom & Free-Parameter Ledger

8 free parameters · 5 axioms · 1 invented entities

The paper has 8 free parameters, of which 7 are varied in the exploration grid and 1 (t_outburst) is fixed. The mass-loss rate is effectively a fitted parameter via post-hoc density scaling. The isothermal disk assumption and torque-free inner boundary are ad-hoc modeling choices acknowledged as caveats. No new physical entities are invented; the injection volume is a numerical construct with parameters constrained by observational comparison.

free parameters (8)
  • alpha (viscosity parameter) = 1.0 (preferred), 0.1 (comparison)
    Shakura-Sunyaev viscosity parameter, chosen by comparing dissipation timescales to observations. Not fitted quantitatively but selected by visual comparison.
  • gamma (rotational velocity factor) = 1.05 (preferred), also 0.9, 1.0, 1.2
    Multiplicative factor on Keplerian orbital speed at injection radius. Selected by visual comparison with f Car data.
  • Delta_phi (azimuthal opening angle) = 0.2 rad (preferred), also 2.0, 4.0, 6.0
    Azimuthal extent of injection volume. Constrained to <4 rad by requiring V/R oscillations consistent with observations.
  • Delta_z (vertical height) = 0.2 R_eq (preferred), also 1.0 R_eq
    Vertical extent of injection volume. Selected to avoid double-hump pattern in H-alpha EW not seen in data.
  • R_inj (injection radius) = 1.01 R_eq (preferred), also 1.25 R_eq
    Center of injection volume. Selected to match observed 1:1 correlation between V/R frequency and orbital frequency.
  • v_i (isotropic ballistic speed) = 20 km/s (preferred), also 50 km/s
    Isotropic velocity component of injected particles. Set to approximately the sound speed in the disk.
  • Mdot_ejec (mass ejection rate, scaled) = ~1.0e-6 Msun/yr/str (preferred, after scaling)
    Density of each model scaled post-hoc to match observed photometric and H-alpha amplitudes of f Car. Scaling factors range from 0.2 to 4.0 across models.
  • t_outburst (ejection duration) = 42.4 h
    Fixed duration of mass ejection in all simulations, corresponding to three stellar orbits. Not varied.
axioms (5)
  • domain assumption Viscous decretion disk (VDD) model: Be disks grow through viscosity-driven angular momentum transport.
    Invoked throughout Sect. 1 and 3 as the framework. The SPH code uses the alpha-disk viscosity formulation (Shakura & Sunyaev 1973).
  • ad hoc to paper The disk is isothermal at T_d = 0.6 T_eff = 12 kK throughout the SPH simulation.
    Stated in Sect. 3. Appendix C.1 shows the actual temperature structure is far from isothermal, acknowledged as a caveat.
  • ad hoc to paper The inner boundary condition is torque-free.
    Sect. 5.2 acknowledges this is 'clearly an oversimplification' given the velocity gradient between the sub-Keplerian stellar surface and the Keplerian inner disk edge.
  • domain assumption No binary companion is present.
    Sect. 3 states no binary companion is included, unlike previous works using the same code. Justified for f Car which has no known companion.
  • domain assumption Stellar parameters for f Car: M=7.6 Msun, R_eq=5.8 Rsun, T_eff=20 kK.
    From Zorec et al. (2016), used as fixed inputs. R_eq has uncertainty of 1.3 Rsun, which affects the orbital frequency comparison.
invented entities (1)
  • Injection volume independent evidence
    purpose: Construct to insert SPH particles with specified geometry and kinematics, representing the mass ejection site without assuming a physical mechanism.
    The injection volume is a numerical construct, not a claimed physical entity. Its parameters are constrained by comparison with observations (V/R frequencies, photometric amplitudes). The paper explicitly states 'our injection volume is simply a construct to insert particles in the simulation, as we make no assumptions on how the star is flinging the material into orbit' (Sect. 3).

pith-pipeline@v1.1.0-glm · 33180 in / 3752 out tokens · 224328 ms · 2026-07-07T20:22:04.122728+00:00 · methodology

0 comments
read the original abstract

Classical Be stars exhibit mass ejection events that feed their viscous decretion disks. Recent TESS space photometry and simultaneous spectroscopy revealed that these flickers are localised, short-lived, and associated with near-Keplerian rotating material close to the stellar surface. We aim to constrain the geometrical and dynamical conditions required for a localised surface ejection to generate a Keplerian decretion disk and to predict the corresponding photometric, spectroscopic, and polarimetric observables. Material, and the injection radius. The SPH outputs were post-processed with the radiative transfer code HDUST to obtain synthetic observables. We scaled the density of the models to match the reference flicker for the Be star f\,Car. A mildly super-Keplerian rotation of the injection volume, a high viscosity, and a mass-loss rate of the order $10^{-6}\,\rm M_\odot \, yr^{-1} \, str^{-1}$ are required for the ejected material to remain in orbit and form a small disk. The synthetic observables reproduce the behaviour of the reference flicker. The simulations confirm that during mass ejection the disk is asymmetric and dynamically evolving, and circularises within a few days after the end of the flicker. Models with too wide mass ejection angle or too high angular velocity fail to reproduce the observed light curve and line profile behaviour. The models are consistent with mass ejection happening very close to the stellar equator. Localised, short-duration, mildly super-Keplerian ejections combined with high viscosity and high mass-loss rates can account for the short-timescale variability of the circumstellar environment of Be stars. Be disks can be formed from such outbursts and realistic 3D injection geometries are essential to connect surface dynamics to disk build-up within the framework of the viscous decretion disk model.

Figures

Figures reproduced from arXiv: 2607.05270 by A. C. Carciofi, A. C. Rubio, D. Baade, I. A. Gabitova, J. Labadie-Bartz, M. W. Suffak, T. H. de Amorim.

Figure 1
Figure 1. Figure 1: Observational data for the Be star f Car, from Paper I. The top-left panel: TESS light curve, bottom-left panels show EW, EWV/EWR and PSW for the H𝛼 profiles obtained with NRES. In the top panel, the grey line is the light curve with high-frequency variability (> 0.5 d −1 ) removed. In the third panel, the grey line is the fit of the EWV/EWR to a sinusoidal function. The right panel: H𝛼 profiles at four ep… view at source ↗
Figure 2
Figure 2. Figure 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Evolution of the simulation with 𝛾 = 1.05, 𝛼 = 1.0, 𝑅inj = 1.01, Δ𝑟 = 0.01 𝑅eq, Δ𝑧 = 0.2 𝑅eq, and Δ𝜙 = 0.2 rad. The first four rows show the 2D radial velocity map (polar plots), and line plots for the radial velocity and surface density (Σ) for four distinct snapshots (top to bottom, 15, 43, 70 and 160 h). Six wedges (each 60°wide) are defined in the polar plots by the colours on their borders (these colo… view at source ↗
Figure 4
Figure 4. Figure 4: Average values of eccentricity of the particles orbits (top panel) and disk scale height (bottom panel) inside radial bins, evolving with time, as denoted by different colours. The first column shows the model described in Sec. 4.1, and the second shows the model with larger Δ𝑧, discussed in Sec. 4.5. The eccentricity drops with time while the scale height goes from a higher inner disk to a flaring disk af… view at source ↗
Figure 5
Figure 5. Figure 5: Photometry and H𝛼 line measurements for our preferred model with 𝛾 = 1.05, 𝛼 = 1.0, 𝑅inj = 1.01, Δ𝑟 = 0.01 𝑅eq, Δ𝑧 = 0.2 𝑅eq, and Δ𝜙 = 0.2 rad. Colours indicate different inclination angles. Panels on the right show the H𝛼 profile for the four snapshots highlighted in [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Emitted, transmitted, scattered and full flux as calculated by HDUST for our preferred model, seen at 85°. The photometric oscilla￾tions present in the transmitted flux (i.e. flux that comes directly from the star, unimpeded) dictate the oscillations in the full flux. We note the jump in scale on the y-axis, as the full and transmitted fluxes are one order of magnitude larger than the emitted and scattered… view at source ↗
Figure 7
Figure 7. Figure 7: Comparison between models with sub-Keplerian (𝛾 < 1.0), Ke￾plerian (𝛾 = 1), and super-Keplerian (𝛾 > 1.0) mass injection. The top panel compares the number of particles injected and accreted. The sec￾ond panel shows the efficiency of mass decretion: a value of 1 indicates that all ejected particles remain in orbit; conversely, a value of zero means complete reaccretion. The three bottom panels compare HDUS… view at source ↗
Figure 8
Figure 8. Figure 8: Comparison between models with 𝛾 = 1.05, but varying the azimuthal extent of the injection volume (Δ𝜙) in the first column, the viscosity parameter 𝛼 in the second column, the vertical height Δ𝑧 in the third column, and the injection radius 𝑅inj in the fourth column. The model in dark blue in all panels is our preferred model, described in detail in Sect. 4.1. The top panel shows the efficiency of mass dec… view at source ↗
Figure 9
Figure 9. Figure 9: EWV/EWR variations for the model with 𝛾 = 1.05, 𝛼 = 1.0 and 𝑅inj = 1.01 (top panel), and a model with the same parameters, but with 𝑅inj = 1.25 (bottom panel), for 50° inclination. In both panels, the coloured lines represent comparisons with a sinusoidal function (Eq.2 of Paper I) with a frequency of 1.71 c d−1 , the orbital frequency of f Car. The red lines show the best solutions we found when analysing… view at source ↗

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