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Stellar evolution tracks of two solar metallicity stars with initial mass of 40M and 80M calculated with the 1D stellar evolution code MESA. The stellar symbols identify the locations corresponding to the three initial conditions of the 3D radiation hydro calculations with Athena listed in Table 1. The Athena calculations are effectively local plane-parallel atmosphere calculations motivated by the MESA models.
Source publication
We perform three dimensional radiation hydrodynamic simulations of the
structure and dynamics of radiation dominated envelopes of massive stars at the
location of the iron opacity peak. One dimensional hydrostatic calculations
predict an unstable density inversion at this location, whereas our simulations
reveal a complex interplay of convective an...
Contexts in source publication
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... have identified specific times in the MESA massive star models with conditions that range from τ 0 /τ c 1 to τ 0 /τ c 1. We label these models as StarDeep, StarMid and StarTop; they have τ 0 /τ c = 15.2, 0.97 and 0.025, re- spectively. Figure 1 shows the positions of these models in the HR diagram. Model StarDeep has an initial mass of 40M . ...
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... initial condition for StarMid has the iron opacity peak and density inversion at 78R . The density inver- sion region is, however, convectively unstable and starts to mix at time 9.4t 0 as shown in the left panel of Figure 10. At time 18.8t 0 , the whole envelope is turbulent (right panel of Fig. 10). ...
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... initial condition for StarMid has the iron opacity peak and density inversion at 78R . The density inver- sion region is, however, convectively unstable and starts to mix at time 9.4t 0 as shown in the left panel of Figure 10. At time 18.8t 0 , the whole envelope is turbulent (right panel of Fig. 10). This temporal evolution is very similar to the run StarDeep, but the properties of the turbulence are different as we now describe. Figure 11 shows the radiation energy density and den- sity weighted vertical velocities (V z,Er , V z,ρ ) as a func- tion of time. After the initial density inversion is broken around 10t 0 , 2.4% of the ...
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... temporal evolution is very similar to the run StarDeep, but the properties of the turbulence are different as we now describe. Figure 11 shows the radiation energy density and den- sity weighted vertical velocities (V z,Er , V z,ρ ) as a func- tion of time. After the initial density inversion is broken around 10t 0 , 2.4% of the mass is lost through the open Figure 10. ...
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... 11 shows the radiation energy density and den- sity weighted vertical velocities (V z,Er , V z,ρ ) as a func- tion of time. After the initial density inversion is broken around 10t 0 , 2.4% of the mass is lost through the open Figure 10. Snapshots of density for the run StarMid at time 9.4t 0 (left) and 18.8t 0 (right). ...
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... 12 (solid line) shows that there is significant turbulent transport of energy below 65R , but the tur- bulent transport falls off rapidly at larger heights. At about the same location 65R , the averaged turbulent velocity V reaches the isothermal sound speed (middle panel of Fig. 12), but is still smaller than the radiation sound speed. Figure 13 shows the time and horizontally averaged vertical profiles of density, temperature, opacity, entropy and accelerations for this run. The iron opacity peak moves inward somewhat in radius, but the density in- version in the initial condition is largely gone, replaced with ...
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... about the same location 65R , the averaged turbulent velocity V reaches the isothermal sound speed (middle panel of Fig. 12), but is still smaller than the radiation sound speed. Figure 13 shows the time and horizontally averaged vertical profiles of density, temperature, opacity, entropy and accelerations for this run. The iron opacity peak moves inward somewhat in radius, but the density in- version in the initial condition is largely gone, replaced with an extended region below 65R over which the den- sity changes very slowly with height. ...
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... above 65R , the density drops quickly with height and the gas temperature starts to deviate from the radiation tem- perature. Here the local optical depth per pressure scale Figure 13. The time and horizontally averaged vertical profiles of density (top panel of a), temperature (bottom panel of a, solid black line for gas temperature and red line for radiation temperature), entropy (panel b), opacity (panel c) as well as accelerations (panel d) for the run StarMid. ...
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... τ becomes smaller than the critical value τ c and the photon diffusion time becomes smaller than the lo- cal dynamic time. This transition to τ τ c is why the advection flux drops significantly in this region (Fig. ...
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... top panel of Figure 12 shows the convective flux calculated based on the time averaged vertical profiles and mixing length theory (eq. 17) with α = 0.45, which is again close to the ratio between the correlation length l ρ and scale height H 0 . ...
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... 60R where τ > τ c , the time averaged advection flux is comparable to the mixing length theory convection flux, which is consistent with Figure 6 for the run StarDeep. However, above 65R the advection flux drops significantly in the simulations, but equation (17) still predicts a very large convection flux because of the decreasing radiation entropy (see panel b of Fig 13). This demonstrates that for τ τ c , convection becomes inefficient and equation (17) significantly over- estimates the amount of advection flux with a constant α. ...
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... vertical profile of τ /τ c , where τ = ρκ t H 0 is the lo- cal optical depth per pressure scale height, shown in the bottom panel of Figure 12 confirms that the transition to inefficient convection happens when τ /τ c < 1. It also happens roughly when the turbulent velocity V becomes larger than the isothermal sound speed (the middle panel of Figure 12), and the superadiabatic parameter˜inparameter˜ parameter˜in- creases significantly to ∼ 0.4 (bottom panel of Figure 12). ...
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... vertical profile of τ /τ c , where τ = ρκ t H 0 is the lo- cal optical depth per pressure scale height, shown in the bottom panel of Figure 12 confirms that the transition to inefficient convection happens when τ /τ c < 1. It also happens roughly when the turbulent velocity V becomes larger than the isothermal sound speed (the middle panel of Figure 12), and the superadiabatic parameter˜inparameter˜ parameter˜in- creases significantly to ∼ 0.4 (bottom panel of Figure 12). Notice that throughout the whole envelope, ˜ is comparable to V /c s as in Figure 6 for the case StarDeep. ...
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... vertical profile of τ /τ c , where τ = ρκ t H 0 is the lo- cal optical depth per pressure scale height, shown in the bottom panel of Figure 12 confirms that the transition to inefficient convection happens when τ /τ c < 1. It also happens roughly when the turbulent velocity V becomes larger than the isothermal sound speed (the middle panel of Figure 12), and the superadiabatic parameter˜inparameter˜ parameter˜in- creases significantly to ∼ 0.4 (bottom panel of Figure 12). Notice that throughout the whole envelope, ˜ is comparable to V /c s as in Figure 6 for the case StarDeep. ...
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... (d) of Figure 13 shows that the volume aver- aged radiation acceleration a r is larger than the gravi- tational acceleration between 50R and 80R , which is also the region where radiation entropy decreases with height. It is thus perhaps surprising that when convec- tion becomes inefficient above 65R and there is little turbulent transport of energy, the envelope does not de- velop a density inversion again. ...
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... is because the den- sity weighted radiation acceleratioñ a r (eq . 14, shown as the dashed black line in panel (d) of Figure 13) is significantly smaller than the volume averaged radiation acceleration a r above 65R . The sumãsum˜sumã r + a g is compa- rable to g at the iron opacity peak around 60R . ...
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... 65R , it drops below g significantly. Figure 14 clarifies the origin of the reduced den- sity weighted radiation acceleration. In particular, it shows that density fluctuations reduce the effective radi- ation acceleration above 65R because there is an anti- correlation between fluctuations of density and radia- tion flux. ...
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... particular, it shows that density fluctuations reduce the effective radi- ation acceleration above 65R because there is an anti- correlation between fluctuations of density and radia- tion flux. The correlation coefficient C ρ,Fr,z in Figure 14 shows this explicitly and is always negative. How- ever, the nature of the anti-correlations changes at dif- ferent heights. ...
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... 65R , however, when τ τ c , the situation changes. Convection becomes in- efficient and F r,z is dominated by the diffusive flux (the advection flux drops as shown in Figure 12). The anti- correlation between ρ and F r,z above 65R is thus not caused by buoyancy. ...
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... it is because the "porosity" of the envelope created by the traveling strong shocks al- lows radiation to propagate through low density regions (Shaviv 1998). This reduces the effective radiation accel- eration significantly (see panel (d) of Figure 13). Note also that in StarMid, the standard deviations of density and temperature (scaled with the horizontally averaged quantities) are significantly larger than the correspond- ing values in the run StarDeep (Figure 9). ...
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... this run, we use a density floor of 10 −10 ρ 0 to avoid numerical difficulties. Figure 15. Time evolution of the density power spectrum kf (ρ) for the run StarTop at height z = 13.7R ...
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... there- fore again explored the linear growth phase for this run by calculating the density power spectrum at the loca- tion of the initial density inversion. The time evolutions of the power kf (ρ) in two modes with horizontal wave- lengths H 0 and 0.26H 0 are shown in Figure 15. As in StarDeep (Fig. 4), the long wavelength mode grows ex- ponentially from close to the beginning, with an e-folding time of 6.25t 0 . ...
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... on the analysis of Blaes & Socrates (2003), we estimate that modes with wave- lengths less than about 2.5H 0 are in the regime where radiative diffusion reduces the growth rate of the convec- tive instability. This is larger than the size of the box, so that all convective modes in the simulation are heavily modified by radiative diffusion (consistent with the fact that τ 0 τ c ). From equation (59) of Blaes & Socrates (2003), we find that the long wavelength mode in Figure 15 should have a growth rate of 0.17/t 0 , assuming a vertical wavelength that is comparable to the horizon- tal wavelength (which is also comparable to the vertical width of the density inversion). This agrees very well with the measured growth rate. ...
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... have not further investigated this possibility, as it is clear that the unsta- ble buoyancy modes dominate the evolution observed in the simulation. Figure 16 shows snapshots of the density structure of the envelope at time 49.1t 0 and 138.9t 0 while the his- tories of the vertical velocities V z,Er , V z,ρ are shown in Figure 17. The whole envelope becomes turbulent af- ter the initial density inversion is destroyed around 50t 0 . ...
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... have not further investigated this possibility, as it is clear that the unsta- ble buoyancy modes dominate the evolution observed in the simulation. Figure 16 shows snapshots of the density structure of the envelope at time 49.1t 0 and 138.9t 0 while the his- tories of the vertical velocities V z,Er , V z,ρ are shown in Figure 17. The whole envelope becomes turbulent af- ter the initial density inversion is destroyed around 50t 0 . ...
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... time 138.9t 0 when V z,Er reaches a minimum, the right panel of Figure 16 shows that there is even a low density hole extending over one pressure scale height H 0 . The mass loss through the open top boundary is negligible for this run. ...
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... an effective acceleratioñ g = −0.06g according to theãthe˜theã r shown in panel (d) of Figure 19 (discussed be- low), the effective dynamic time scale is˜tis˜ is˜t g = 4.6t 0 , which is consistent with the oscillation period of the envelope in Figure 17. Note that the effective scale height is theñtheñ H 0 ≡ c 2 g,0 /|˜g||˜g| = 1.26H 0 , which happens to be similar to H 0 . ...
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... an effective acceleratioñ g = −0.06g according to theãthe˜theã r shown in panel (d) of Figure 19 (discussed be- low), the effective dynamic time scale is˜tis˜ is˜t g = 4.6t 0 , which is consistent with the oscillation period of the envelope in Figure 17. Note that the effective scale height is theñtheñ H 0 ≡ c 2 g,0 /|˜g||˜g| = 1.26H 0 , which happens to be similar to H 0 . ...
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... 18 and 19 show vertical profiles of various time and horizontally averaged quantities in the non- linear state after 55.6t 0 . Unlike the previous two runs StarDeep and StarMid, the averaged advection flux is less than 0.5% of F r,i in the whole envelope as shown in the top panel of Figure 18. This is because τ 0 τ c every- where and gas is not able to trap photons. ...
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... reduces the density weighted radiation acceleratioñ a r (eq. 14), as shown in panel (d) of Figure 19. However, unlike the assumptions made in previous models (Shaviv 1998), the "porosity" of the envelope due to convection cannot re- duce the effective radiation acceleration to a value below g. ...
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... z ≈ 13.3R where the iron opacity peak is located now, ˜ a r is still about 6% larger than g, while a r is about 10% larger than g. This is why the average density profile still shows a mild inversion near the iron opacity peak, as shown in panel (a) of Figure 19. We stress that although the density inversion remains, the resulting structure is nonetheless very different from the hydrostatic density inversion in the initial condition. ...
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... cally, in the regime τ 0 τ c , photon diffusion is so rapid that radiation pressure does not respond to the density and velocity fluctuations. As the turbulent velocity be- comes larger than the isothermal sound speed, shocks are formed in the envelope (Figure 16), which causes the large density fluctuations. This phenomenon is also ob- served in radiation magneto-hydrodynamic simulations of black hole accretion disks ( Turner et al. 2003;Jiang et al. 2013c). ...
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... phenomenon is also ob- served in radiation magneto-hydrodynamic simulations of black hole accretion disks ( Turner et al. 2003;Jiang et al. 2013c). Figure 19 shows that the radiation and gas entropies S r and S g decrease rapidly with height around the iron opacity peak. If we still adopt l ρ /H 0 ≈ 0.4 for the mixing length parameter α, equation (17) over-predicts the flux relative to the simulations by a factor of more than ∼ 3, and the location of the peak in the predicted flux also off- sets from the peak of time averaged advection flux given by the simulations, highlighting that existing models of inefficient convection in the radiation pressure dominated regime are not accurate compared to our simulation re- sults. ...
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... failure of convection to carry a significant energy flux is intimately connected with the turbulent velocities becoming supersonic, at least relative to the gas (isothermal) sound speed. This is expected on theo- retical grounds ( §2) and is also consistent with the sim- ulation results, as shown in the middle panel of Figure 18. The superadiabatic parameter˜isparameter˜ parameter˜is also comparable tõ V /c s and similar to the top region in StarMid ( Figure 12). ...
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... is expected on theo- retical grounds ( §2) and is also consistent with the sim- ulation results, as shown in the middle panel of Figure 18. The superadiabatic parameter˜isparameter˜ parameter˜is also comparable tõ V /c s and similar to the top region in StarMid ( Figure 12). Figure 20 quantifies the large density fluctuations and strong anti-correlation between density and radiation flux in simulation StarTop. ...
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... correlation coefficient C ρ,Fr,z is almost −1 in the turbulent region between 12.8R and 13.6R , while C ρ,T only fluctuates around 0. This demonstrates that unlike for StarDeep, the anti- correlation between density and radiation flux is not due to buoyancy in the radiation pressure dominated regime but is instead due to the photons preferentially diffusing through low density channels. The scaled standard de- viations δρ/ρ and δT /T are also much larger than the corresponding values in StarDeep and StarMid, which is consistent with the images in Figure 16. ...
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... re- sulting density inversions are convectively unstable, but the properties of the resulting convection zones have un- til now been very uncertain when τ 0 τ c and convection is expected to be relatively inefficient. Figures 21 and 22 compare the time and horizontally averaged turbulent properties of our three runs, show- ing the gas, radiation, and kinetic energy densities (Fig. 21) and the ratio of the convective and diffusive energy fluxes, respectively. ...
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... are convectively unstable, but the properties of the resulting convection zones have un- til now been very uncertain when τ 0 τ c and convection is expected to be relatively inefficient. Figures 21 and 22 compare the time and horizontally averaged turbulent properties of our three runs, show- ing the gas, radiation, and kinetic energy densities (Fig. 21) and the ratio of the convective and diffusive energy fluxes, ...
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... initial condition, is absent in the turbulent state. This is because a signifi- cant fraction of the luminosity is transported by convec- tion (Fig. 22), which reduces the radiation acceleration to be sub-Eddington. For StarDeep, the turbulent ve- locity is very subsonic with the turbulent kinetic energy less than 1% of the thermal energy (Fig. 21). The dif- ference between the actual thermal gradient and the adiabatic gradient ad is smaller than 8% of ad . All of these properties are consistent with expectations for efficient ...
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... see this transition in the surface layers of run StarMid. As shown in Figure 12, below 60R , the averaged radiation advection flux is consistent with MLT (eq. 17). ...
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... this case the average radiation advection flux is 1% of the diffusive flux throughout the envelope (Figure 22). If we adopt the non-adiabatic MLT model (e.g., Henyey et al. 1965;Magic et al. 2015) with α = 0.4, which is the ratio of the turbulent correlation length to the pressure scale height, we find that it still significantly over-predicts the convection flux ( Figure 18). The differ- ence is probably caused by a combination of the porosity effect and vertical oscillation of the envelope as explained blow. ...
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... turbulent velocity in StarTop is larger than the isothermal sound speed and strong shocks are formed, driving large density fluctuations. The bottom panel of Figure 21 shows, however, that the kinetic energy den- sity only reaches the gas internal energy density, which is still much smaller than the radiation energy density. The large density fluctuations allow radiation to escape somewhat more efficiently (Shaviv 1998) than through a homogenous medium ("porosity"), reducing the effec- tive radiation acceleration. ...
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... Energy is transported in stars primarily through radiative diffusion and convection, including in the radiation-pressure-dominated extended outer regions of massive star envelopes, where both mechanisms are present. Due to opacity peaks in the envelope (from recombination of ions of iron, helium, and hydrogen), the local radiative luminosity may exceed the Eddington limit in layers of the envelope below sub-Eddington regions (Jiang et al. 2015(Jiang et al. , 2018. Therefore, in these envelopes, density and gas pressure inversions may occur which are thought to contribute to outburst-like "eruptive mass loss" (Joss et al. 1973;Humphreys & Davidson 1994;Paxton et al. 2013). ...
... This is the case when using mixing-length-theory (MLT, e.g., Böhm-Vitense 1958;Cox & Giuli 1968) or even time-dependent 1D formulations (e.g., Kuhfuss 1986;Jermyn et al. 2023). Realistic 3D simulations show the limits of the 1D treatment, stressing the importance of the interplay between radiative transport and the complex landscape of turbulent fluctuations in the stellar envelope (Jiang et al. 2015). However these calculations are computationally very expensive, which has prevented a detailed study of the full parameter space relevant to massive stars. ...
... Indeed, 3D radiationhydrodynamics (RHD) models find enhanced convection in these radiation-and turbulent-pressure-dominated envelopes (e.g., Jiang et al. 2015Jiang et al. , 2018Schultz et al. 2023). Jiang et al. (2015) and Jiang et al. (2018) simulated the envelope of massive stars at specific points in their evolution, and determined that non-steady mass loss outbursts potentially consistent with LBVs can be driven by helium and iron opacity peaks. ...
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... Various multi-dimensional simulations have been performed in recent years to study the outer envelope structures of massive stars, or the properties of line-driven winds in the optically thin part based on the CAK formula [25][26][27][28][29][30][31][32][33][34][35][36][37]. It is not trivial to map 3D stellar structures to 1D models, as turbulence in 3D can cause spatial and temporal correlations between different radiation-hydrodynamic quantities. ...
... These sub-surface convection zones are typically very inefficient, which means energy flux carried by convection is much smaller than the radiative flux, as photon diffusion speed is larger than the typical convective speed, as estimated based on Equation (6). Rosseland mean opacity κ t = κ s + κ a at solar metallicity as a function of density and temperature, which is taken from Figure 2 of [27]. Each line shows the opacity variation with temperature for a fixed density value as indicated in the figure. ...
... Properties of convection in these radiation pressure-dominated massive star envelopes were first studied self-consistently by [27], which solves the 3D radiation hydrodynamic equations in Cartesian geometry under plane parallel approximation using a closure scheme based on variable Eddington tensor (VET) [42,43]. Three models are chosen to cover the effective temperature range from 7.13 × 10 3 K to 4.75 × 10 4 K with luminosity varying from 4 × 10 5 L to 1.3 × 10 6 L based on the MESA stellar evolution models of 80M and 40M stars. ...
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... In addition to increased mass-loss rates, objects close to the Eddington limit may be subjected to envelope inflation (Ishii et al. 1999;Petrovic et al. 2006;Gräfener et al. 2012;Sanyal et al. 2015;Jiang et al. 2015). When stellar evolution modellers employ extrapolated standard O-star mass-loss rates (e.g. ...
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... Another interesting effect of radiation pressure occurs in massive donors, which feature locally super-Eddington luminosities due an iron opacity bump close to their surface (e.g. Jiang et al. 2015 ). The local decrease of gravity near L1 could cause an enhanced MT rate in these donors. ...
Calculation of the mass transfer (MT) rate $\dot{M}_\text{d}$ of a Roche lobe overflowing star is a fundamental task in binary star evolution theory. Most of the existing MT prescriptions are based on a common set of assumptions that combine optically-thick and optically-thin regimes with different flow geometries. In this work, we develop a new model of MT based on the assumption that the Roche potential sets up a nozzle converging on the inner Lagrangian point and that the gas flows mostly along the axis connecting both stars. We derive a set of 1D hydrodynamic equations governing the gas flow with $\dot{M}_\text{d}$ determined as the eigenvalue of the system. The inner boundary condition directly relates our model to the structure of the donor obtained from 1D stellar evolution codes. We obtain an algebraic solution for the polytropic equation of state (EOS). This gives $\dot{M}_\text{d}$ within a factor of 0.9 to 1.0 of existing optically-thick prescriptions and reduces to the existing optically-thin prescription for isothermal gas. For a realistic EOS, we find that $\dot{M}_\text{d}$ differs by up to a factor of 4 from existing models. We illustrate the effects of our new MT model on a 30 M⊙ low-metallicity star undergoing intensive thermal time-scale MT and find that it is more likely to become unstable to L2 overflow and common-envelope evolution than expected according to MT prescriptions. Our model provides a framework to include additional physics such as radiation or magnetic fields.
... Hydrodynamic convection could be triggered by the strong bumps in opacity at 10 4 K from H, 10 4.6 −4.8 K from He and 10 5.2 K from iron (a blackbody at 10 4 peaks at 3000 Å). Massive stars have similarly bright UV emission, and these also show strong winds, powered by UV line driving, as well as turbulent convection triggered by the continuum UV opacity (Jiang et al. 2015 ;Ro 2019 ). Alternativ ely, conv ection could be triggered by the radiation pressure instability. ...
We use the SOUX sample of ∼700 AGN to form average optical-UV-X-rays SEDs on a 2D grid of MBH and L2500. We compare these with the predictions of a new AGN SED model, qsosed, which includes prescriptions for both hot and warm Comptonisation regions as well as an outer standard disc. This predicts the overall SED fairly well for 7.5 < log(MBH/M⊙) < 9.0 over a wide range in L/LEdd, but at higher masses the outer disc spectra in the model are far too cool to match the data. We create optical-UV composites from the entire SDSS sample and use these to show that the mismatch is due to there being no significant change in spectral shape of the optical-UV continuum across several decades of MBH at constant luminosity. We show for the first time that this cannot be matched by standard disc models with high black hole spin. These apparently fit, but are not self-consistent as they do not include the General Relativistic effects for the emission to reach the observer. At high spin, increased gravitational redshift compensates for almost all of the higher temperature emission from the smaller inner disc radii. The data do not match the predictions made by any current accretion flow model. Either the disc is completely covered by a warm Comptonisation layer whose properties change systematically with L/LEdd, or the accretion flow structure is fundamentally different to that of the standard disc models.
... In more helium-rich AGN disks, then, it may be more difficult for stars to drive outflows and stave off accretion. However, the electron scattering opacity may also severely underestimate the actual opacity due to features such as the iron opacity peak, or the potentially stronger opacity peaks due to helium recombination (e.g., Jiang et al. 2015Jiang et al. , 2016Jiang et al. , 2018Cantiello & Braithwaite 2019;Jermyn et al. 2022a), so we present results using both opacity formulas and caution that there is still uncertainty in the opacities relevant to mass loss and the accretion stream, even in this already simplified gray opacity treatment. ...
Disks of gas accreting onto supermassive black holes, powering active galactic nuclei (AGN), can capture stars from nuclear star clusters or form stars in situ via gravitational instability. The density and thermal conditions of these disks can result in rapid accretion onto embedded stars, dramatically altering their evolution in comparison to stars in the interstellar medium. Theoretical models predict that, when subjected to sufficiently rapid accretion, fresh gas replenishes hydrogen in the cores of these stars as quickly as it is burned into helium, reaching a quasi-steady state. Such massive, long-lived (“immortal”) stars may be capable of dramatically enriching AGN disks with helium, and would increase the helium abundance in AGN broad-line regions relative to that in the corresponding narrow-line regions and hosts. We investigate how the helium abundance of AGN disks alters the evolution of stars embedded therein. We find, in agreement with analytical arguments, that stars at a given mass are more luminous at higher helium mass fractions, and so undergo more radiation-driven mass loss. We further find that embedded stars tend to be less massive in disks with higher helium mass fractions, and that immortal stars are less common in such disks. Thus, disk composition can alter the rates of electromagnetic and gravitational wave transients as well as further chemical enrichment by embedded stars.
... Those are rather exotic conditions where the mixing-length theory (MLT, Cox & Giuli 1968), so far used in all evolutionary calculations of SMS, has seldom been tested. The only exception we are aware of is the iron opacity peak convection zone of massive main-sequence stars, where is also of order 0.1 and 3D hydrodynamics simulations have been carried out (Jiang et al. 2015(Jiang et al. , 2017Schultz et al. 2022). ...
Supermassive stars are Population III stars with masses exceeding $10^4\,M_{\odot}$ that could be the progenitors of the first supermassive black holes. Their interiors are in a regime where radiation pressure dominates the equation of state. In this work, we use the explicit gas dynamics code PPMstar to simulate the hydrogen-burning core of a $10^4\,M_{\odot}$ supermassive main-sequence star. These are the first 3D hydrodynamics simulations of core convection in supermassive stars. We perform a series of ten simulations at different heating rates and on Cartesian grids with resolutions of $768^3$, $1152^3$ and $1728^3$. We examine different properties of the convective flow, including its large-scale morphology, its velocity spectrum and its mixing properties. We conclude that the radiation pressure-dominated nature of the interior does not noticeably affect the behaviour of convection compared to the case of core convection in a massive main-sequence star where gas pressure dominates. Our simulations also offer support for the use of mixing-length theory in 1D models of supermassive stars.
