ULXs as magnetized sub-Eddington advective accretion flows around stellar mass black holes
aa r X i v : . [ a s t r o - ph . H E ] A ug August 28, 2019 0:28 WSPC Proceedings - 9.75in x 6.5in main page 1 ULXs as magnetized sub-Eddington advective accretion flows aroundstellar mass black holes
Banibrata Mukhopadhyay
Ultra-luminous X-ray sources (ULXs) have been puzzling us with a debate whether theyconsist of an intermediate mass black hole or super-Eddington accretion by a stellar massblack hole. Here we suggest that in the presence of large scale strong magnetic fieldsand non-negligible vertical motion, the luminosity of ULXs, particularly in their hardstates, can be explained with sub-Eddington accretion by stellar mass black holes. Inthis framework of 2.5D magnetized advective accretion flows, magnetic tension plays therole of transporting matter (equivalent to viscous shear via turbulent viscosity) and weneither require to invoke an intermediate mass black hole nor super-Eddington accretion.Our model explains the sources, like, NGC 1365 X1/X2, M82 X42.3+59, M99 X1 etc.which are in their hard power-law dominated states.
Keywords : accretion disks; ULXs; magnetic fields; black holes.
1. Introduction
While the existence of stellar mass black holes of mass M . M ⊙ and supermas-sive black holes of mass M & M ⊙ are confirmed, there is no direct evidence forblack holes of mass in between. Scientists believing in the continuous mass distri-bution argue for the existence of such black holes, called intermediate mass blackhole. However, many others argue that there is no such obvious expectation as theorigins of stellar mass and intermediate mass black holes are completely different.Nevertheless, there are ultra-luminous X-ray sources (ULXs) observed in galaxiesaround, which apparently cannot be explained by the conventional idea of stellarmass black holes accreting at a sub-Eddington limit. Hence, the proposal is that thesources harbor an intermediate mass black hole, particularly when they reveal lowertemperature in the underlying multicolor black hole spectra . However, there is an-other idea behind ULXs that they are stellar mass black holes only but accretingat a super-Eddington rate: candidates for slim accretion disk .Nevertheless, none of the above ideas is a conventional one. There are significantevidences that X-ray binaries are sub-Eddington accretors and there is no directevidence yet of galactic black hole mass M & M ⊙ (though the detection ofgravitational wave argues for the black hole mass larger than that determined inX-ray astronomy). Here our story lines start. We show that ULXs in hard statescan be explained by a stellar mass black hole accreting at a sub-Eddington ratewith advection in the presence of large scale strong magnetic field. Hence, bythe interplay between magnetic field and advection, X-ray binaries could be quiteluminous in the hard state. For that we neither require an intermediate mass blackhole nor super-Eddington accretion. Hence, while still the existence of intermediate ugust 28, 2019 0:28 WSPC Proceedings - 9.75in x 6.5in main page 2 black hole, even appeared as ULX, is not ruled out, some ULXs in hard states,e.g. NGC 1365 X1/X2, M82 X42.3+59, M99 X1 etc., are suggested to be highlymagnetized stellar mass black hole sources only.We model a combined disk-outflow coupled system with the inclusion of verticalvelocity and large scale magnetic stress explicitly. This is essentially a 2.5D mag-netized advective accretion disk model. We show that energetics and luminositiesof such a flow are in accordance with ULXs.
2. Magnetized disk-outflow coupled system
We consider a magnetized, viscous, advective disk-outflow/jet symbiotic systemwith cooling around black holes. We consider the large scale magnetic and tur-bulent viscous stresses both and depending on the field strength one of them maydominate over other. Here we assume a steady and axisymmetric flow and all theflow parameters: radial velocity ( v r ), specific angular momentum ( λ ), outflow orvertical velocity ( v z ), fluid pressure ( p ), mass density ( ρ ), radial ( B r ), azimuthal( B φ ), and vertical ( B z ) components of magnetic field, are functions of both ra-dial and vertical coordinates. Throughout we express length variables in units of GM BH /c , where G is the Newton’s gravitational constant, M BH the mass of BH,and c the speed of light. Accordingly, we also express other variables. Hence, thecontinuity and momentum balance equations are respectively ∇ . ( rρ v ) = 0 , and ( v . ∇ ) v = F − ρ ∇ (cid:18) p + B π (cid:19) + ( B . ∇ ) B πρ + 1 ρ ∇ . W , (1)where v and B are velocity and magnetic field vectors respectively, | F | is the mag-nitude of the gravitational force for a BH in the pseudo-Newtonian framework .The importance of generalized viscous shearing stress tensor ( W = W ij ) is takingcare explicitly in this formalism. Various components of W ij are written in termsof α -prescription with appropriate modifications . We also have to supplementthe above equations with the equations for no magnetic monopole and induction,as respectively ∇ . B = 0 and ∇ × ( v × B ) + ν m ∇ B = 0 , (2)where ν m is the magnetic diffusivity. We consider equation (2) in the very largemagnetic Reynolds number ( ∝ /ν m ) limit, which is the case for an accretion disk.We further have to supply the energy balance equations for ions and electrons bytaking into account the detailed balance of heating, cooling and advection. Themagnetized energy equations for ions and electrons read asΓ ′ (cid:20) v r (cid:26) ∂p∂r − Γ pρ ∂ρ∂r (cid:27) + v z (cid:26) ∂p∂z − Γ pρ ∂ρ∂z (cid:27)(cid:21) = Q + − Q ie , (3)where Γ = 32 − β − β + β (4 − β )3 β M − β , and Γ ′ = 24 − β − β ) , ugust 28, 2019 0:28 WSPC Proceedings - 9.75in x 6.5in main page 3 Γ ′ (cid:20) v r (cid:26) ∂p e ∂r − Γ p e ρ ∂ρ∂r (cid:27) + v z (cid:26) ∂p e ∂z − Γ p e ρ ∂ρ∂z (cid:27)(cid:21) = Q ie − Q − , (4)where Q + represents the viscous and magnetic (Ohmic) heats generated in the flow, Q ie the Coulomb coupling estimating the amount of heat transferred from ions toelectrons, and finally Q − the radiative cooling rate through electrons via differentcooling processes including bremsstrahlung, synchrotron and inverse Comptoniza-tion of soft photons supplied from the Keplerian disk. Various cooling formalismsare adopted from past works . In order to solve the equations semi-analytically,we make a reasonable hypothesis in the disk-outflow symbiotic region that the ver-tical variation of any dynamical variable (say, A ) is much less than that with radialvariation, that allows us to introduce ∂A/∂z ≈ sA/z , where s is just the degree ofscaling and is a small number.
3. Disk hydromagnetics and energetics
Figure 1 shows disk-outflow hydromagnetics revealing that large scale strong mag-netic fields are able to transport angular momentum adequately rendering furthersignificant v r and v z with decreasing r . The angular momentum profile turns outto be similar to that obtained based purely on α − viscosity and hence W ij when thefield is weak. However, the benefit with large scale magnetic stress is that it renderssignificant vertical outflow along with radial inflow. It is confirmed from Figs. 1d,ethat close to the black hole magnetic field could be even ∼ G with an efficientmagnetic shear compared to α − viscosity induced viscous shear.Now energetics can be estimated based on above hydromagnetism. The energyequation in conservative form under steady state condition is given by ∇ . F = 0 with F i = ρv i (cid:18) v Γ − pρ + B π + Φ (cid:19) + v j M ij − v j W ij , (5)where i, j correspond to r or φ or z , indicating radial or azimuthal or vertical com-ponent of the respective variables with v = v r + λ /r + v z , Φ is the gravitationalpotential, and M ij is the magnetic stress tensor with standard definition, given by M ij = B π δ ij − B i B j π . (6)The outflow power extracted from the disk is computed at the disk-outflow surfaceregion. It defines as P j ( r ) = Z πr " ρv z ( v Γ − pρ + Φ − λr W φz + v r W rz !) + v z π B r + B φ − v r v z B r B z − λrv z B φ B z ! h dr. (7)This accretion induced outflow power contains contributions from mechanical andenthalphy powers, and those of viscous and Poynting parts. Our model is restricted ugust 28, 2019 0:28 WSPC Proceedings - 9.75in x 6.5in main page 4 M BH = 20 M ⊙ , ˙ m = 0 . ugust 28, 2019 0:28 WSPC Proceedings - 9.75in x 6.5in main page 5 vertically up to the disk-outflow coupled region, above which outflow may decoupleand accelerate. Hence this computed power is basically the initial power of anyastrophysical jets at the launching region. Also the disk luminosity can be computedfrom the cooling mechanisms and can be defined as L = Z Z h Q − πr dz ! dr. (8)The variation of disk luminosity, whose magnitude is the most important observablein the present context, is shown in Fig. 1f. At an arbitrary r , the luminosity isobtained by integrating from the outer disk radius r out to that corresponding r .For the case of a stellar-mass black hole of mass M BH = 20 M ⊙ with total massaccretion rate ˙ m = 0 .
05 Eddington rate, the maximum attainable luminosity, basedon the integration over whole disk, is L ∼ × erg s − . This value is quiteadequate to explain observed luminosities of ULXs in hard states. Table 1 enlistssome ULXs with their respective power-law indices, indicating their harder nature.It is very interesting that the luminosity of the sources L ∼ erg s − , which canbe explained by a stellar mass black hole accreting at a sub-Eddington rate in thepresence of strong magnetic fields, as described in Fig. 1f.Table 1: Some ULX sources in a hard power-law dominated state.Source Γ L . −
10 keV (10 erg s − )M99 X1 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − .
4. Summary
ULXs and the question of plausible existence of intermediate mass black hole inthe universe are both puzzling us for quite sometime. Some authors argue ULXsto be the sources of an intermediate mass black hole. Some others argue ULXs tobe super-Eddington acrretors by a stellar mass black hole. The later group furtherargues that there is no need to expect a continuous mass distribution of black holesfrom stellar mass to supermassive scales. We suggest quite differently and uniquely.We show that at least some of ULXs are nothing but the highly magnetized accretingsources of stellar mass black holes accreting at a sub-Eddington rate only. Therequired field magnitude is of the order of 10 G to explain ULXs in hard states,which is well below the underlying Eddington value. Therefore, at least some of ugust 28, 2019 0:28 WSPC Proceedings - 9.75in x 6.5in main page 6 ULXs could just be stellar mass black holes. While this suggestion leaves thequestion for the existence of intermediate mass black hole wide open, it argues forthe power of magnetically dominated/arrested accretion flows to explain enigmaticastrophysical sources.
Acknowledgment
The author thanks Tushar Mondal of IISc for discussion and drawing the figure.
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