1. Introduction

What are the aspects studied of the central celestial object of the Milky Way?

What is the description of a layered disc?

What are the characteristic emissions?

Are there flares in the Milky Way disc?

In the work of Pringle et al. ^[1], the system of a compact object and its accretion object onto it is considered, where the accretion object is gaseous, spinning, and endowed with angular momentum. The X-ray emission from the gaseous material falling into the blackhole is calculated. The framework is ibidem described as with ’rapid irregular variability’.

The analysis of the emission of the accretion object of the milky way allows one to exclude the presence of a celestial object different from a blackhole, i.e. after the destination of the emitted radiation.

In the work of Shakura et al. ^[2], a layered structure is assumed of the disc. The inner layers are ’hotter’, while the layers from the outer region are ’cold’; the bulk of the radiation is hypothesized to be emitted from the ’upper’ layers of the disc, which is ’hotter’, as ultraviolet radiation and as soft X-rays radiation.

The efficiency of the angular momentum transfer is assumed to be constant along the disc, while the local radiations spectrum is described from the ’upper’ layers as depending functionally on R the cylindrical radial variable, and on the z distance, such that an integral of the spectrum Jv as a function of the frequencies can be written as

The accretion rates of the disc coinciding with the matter flux determines the Eddington critical luminosity as implied after the equating the radiation pressure force of the matter which is completely ionized with the gravitational attraction from the Relativistic star; the efficiency of the gravitational release mechanisms therefore determines the luminosity; higher luminosities are obtained if the hard radiation from the ’hotter’ layers is then absorbed in the outer layers, where the X rays initial emission and the ultraviolet one are saturated after broad recombination and accompanied of ’resonance’ emission lines.

As a result, the friction between the neighbouring layers of the disc is responsible of the loss of angular momentum inducing matter to fall into the blackhole, ad it induces the release of gravitational energy. The efficiency of the angular momentum transfer is obtained after applying the energy equipartition theorem when the radiation energy is taken into account, where turbulent velocity is present, and the transonic behaviour is obtained after the introduction of the speed of sound b as a parameter in the parameter of efficiency of momentum transfer, which after which the discs are qualified, where the most of the energy is emitted in the regions of maximal temperatures.

In the work of Shakura et al. ^[2], the subcritical regimes are studied, where Newtonian mechanics is utilised; it is my aim to stress that there gravitational pressure should not be neglected in the study of saturation, i.e. the GR analysis is still needed also at different accretion rates.

In the work of Marin et al. ^[3], one of the mechanisms of the flares are described, according to the experimental data available of the molecular clouds reflecting the emitted radiation, after which the characteristic lines are obtained.

1.1. A More Detailed Characterization of the Disc

What are the major causes of the instabilities?

Form the work of Balbus et al. ^[4], the presence of shear instabilities is studied for axisymmetric perturbations of the disc due to the presence of a weak magnetic field, where the instability regimes are characterized as independent of the magnetic field strength, while the role of the poloidal component of the field and that of the toroidal component of the field ar outlined as responsible of the ’unsuccessfullness’ of the classical Raighleight criterion to be applied, i.e., ibidem, the disc is assumed as consisting of gaseous material where the dynam-ics of the gas is analyzed within the framework of the fluid theory; it is now my aim to stress that the role of the gravitational pressure is not negligible in the examination of the experimental data available for recombination in the regime of saturation when the shear instability is present.

It is nevertheless now possible to examine the models according to which the two-temperature layered disc models have been applied for the interpretation of the phenomenological evidence.

2. The Accretions Disc

How is the accretion object onto a blackhole discriminated?

How are the disc shapes determined?

The accretion disc onto a blackhole is described in ^[1] according to the mass flux value: in the case the mass flux is large enough, the radiation is due to the disc alone; if the mass flux is so small to allow radiation pressure prevent the gravitational energy from efficient emission, the flarings are expected.

Form the work of Shapiro et al. ^[5], the description o the emergent continuous radiation spectrum from the complete disc is provided with. In this case, numerical calculations techniques proposed are:

I) the disc is divided into ’concentric rings’;

II) the the-know average surface gravity is calculated within each ring, from which a ’model atmosphere’ paradigm is attributed;

IV) X-ray polarization of each ring is calculated for each ring, i.e., the flux is also written.

From the Kompane’et equation, the emission spectrum is written after Eq. 15 from ibidem as

being ∝ the viscosity, n the isotropic photon occupation number, E the photon energy, T_el the electron temperature, photon source, the means rate of photon escape from the disc; the complete spectrum is obtained afterthe sum of the contributions of each ring as from the work of Lightman et al. ^[6].

The principal emission mechanism is assumed as thermal bremsstrahlung; furthermore, electron scattering, comptonization, and optical thickness are also considered.

Each ring is taken such that is can be considered homogeneous and isothermal such that the ’Rosseland mean photon’ is allowed to be emitted.

Radiative transfer theory can also be applied from SCRIVI.

3. The Analysis of Sgr A^∗

What are the characteristics of the Galactic disc?

In the work of Marin et al. ^[3], possible flares from the central blackhole of the Milky Way are described.

Ibidem, the shape of the X-ray continuum and the fluorescent iron lines are depicted as due from the giant molecular clouds from the blackhole SGR A^∗.

Ibidem, observations from the polarized X-ray emission towards the molecular clouds from the galactic centre are reported.

The luminosity of Sgr A is also studied.

3.1. The Two-Temperature Disc

A layered structures of rings can be assumed of discs, where the inner region is characterized as ’hotter’, and the outer region is qualified as ’colder’, for the polarizations of the emissions to be studied. The parameter of efficiency of momentum transfer can be assumed as constant along the radial extension of the disc, as from the -disc model of Shakura and Sunyaev ^[2].

In the work of Shapiro et al. ^[5], a two-temperature accretion disc onto a black-hole is described: both the instances of the nonrotating blackhole spacetime an

that of a rotating blackhole spacetimes are considered.

A novel analysis is ibidem proposed for an accretion disc onto a blackhole, which is hotter and gas-pressure dominated, geometrically thicker in the inner region than in the outer one; here, a 8 − keV spectrum is predicted in the case of Cygnus X-1 after inverse Compton scattering of the soft X-ray photons; the Kompane’et equation ^[7][8] is proposed. The need for the new setting is ibidem explained as dictated after the impossibility of according the hard X-ray part of the spectrum as summarized in ^[3] from the previously-postulated ’cold’ models from ^[1] and from ^[7].

The two temperatures of this disc are selected after the two conditions: a) the maximum value of the temperature Tmaxis one found after the complete’internalization’ of the gravitational energy of an ’optically-thin gas’; b) the minimum temperature Tmin is that found after the local thermal equilibrium (LTE) as an ’optically thick gas’.

In the case of nonrotating blackholes, after the work of Pringle et al. ^[1], the flux F(r) at the radius r is written as

being a the radiation constant, M the mass, ˙M the accretion rate, and F 

where the flux F(r) has to be calculated at th point of maximal emission.

The temperature T_max is calculated after the gravitational binding energy of a ion located at the inner edge of the disc at the radius R_inner as

with m_P the mass of the proton.

Rotating blackholes are approached as form the work of Thorne et al. ^[6], after which the case of rapidly-rotating blackholes is issued; after numerical analysis, a two-component spectrum is described: a low-energy component ^[7] attributed to the thermal emission from the outer. optically-thick region of the disc, while the high-energy component is hypothesized to be originated from the comptonization of X-ray photons which undergo inverse Compton scattering from high-energy thermal electrons: in the hotter region, the viscous heating is balanced after the radiative cooling.

The disc structure can be studied after the solution of the hydrostatic equilibrium equation, the angular-momentum conservation equation and the equations

of state

In the work of Shapiro et al. ^[5], the Newtonian disc picture is proposed.

The general requirement must be imposed, that the electron heating rates and the electron cooling ones should equal in the steady state.

3.2. Structure of the Two-Temperature Disc

The two-temperature disc is built after the following assumptions:

1) the gas pressure is dominating the dynamics, as P >> Pel;

2) the gas must be optically his for absorption  << 1 being  the absorption optical depth;

3) ions and electrons should be related after collisional energy exchange; plasma instabilities should be negligible;

4) the model of pure hydrogen is here taken;

5) a non-rotating blackhole spacetime is examined;

6) great abundance of soft photons is hypothesized, i-e-, the cooling should be ruled after the unsaturated comptonized process. I here remark that plasma instabilities from 3) should be negligible when the vorticity regime is absent for the comparison with a gaseous flow to be possible, i.e. when thermal instabilities and secular instabilities are absent.

The comptonization is the governing mechanism of the cooling phenomena of the inner region of the disc, the ’inverse unsaturated Compton cooling equation’expressing the ion energy balance (i.e., the electron-ion energy exchange) as

with V_t being the electron-ion coupling rate. The shock heating is ibidem prescribed to become relevant only at high viscosity.

The inner region of the disc is ruled after inverse unsaturated Compton cooling equation, on which the electron-energy balance

is imposed, being Ur the radiation energy density.

From the paradigm of Zel’dovich et al. ^[9], from kes the scattering capacity, one has that

with the prescription

From eq. 14 from ibidem, Att is the ratio of inverse Compton scattering with respect to the free-emission in the two-temperature structure.

In the work of Lightman et al. ^[10], the steady disc model of Shakura and Sunyaev ^[7] is further studied after constant, being the instabilities negligible.

The ’net polarization’ is taken as achieved after the last scattering in the disc.

The photons are described as flying in the direction normal to the surface.

The polarization of a constant- ring is written as

with p(v) the probability that a photon frequency is emitted in an unpolarized manner at the unit absorption optical depth and undergoes electron scattering

before its escape flight from the disc is performed; is the polarization of the emerging photon from pure electron scattering- the unit absorption optical depth is ruled after  

3.3. Application of the Numerical Techniques to the Observed Emission of Sgr A^∗

An application of the techniques proposed in ^[5] is made in ^[3]; ibidem, a circular region is selected as containing reflected photons from several ’hot’ spot of

reflected emission, i.e., from the scattering clouds.

The spectral model is constructed ibidem as consisting of: thermal emission; reflected emission; fluorescent lines; scattering continuum.

4. Instabilities of the Milky Way Blackhole

How are the instabilities of the milky Way Blackhole studied?

In the recent summary of Blaes et al. ^[11], the state-of-the current understandings of the instabilities of non-stationary discs is discussed as following from the classical viscosity theory; the methodologies followed ibidem are the studies of the physical uncertainties of the measured quantities, after which the time

evolution of the disc is tailored out.

Ibidem, the Magneto-Hydro-Dynamics (MHD) models are numerically implemented after the surface density is assumed as that obtained after an arbitrary

radial profile of angular velocity.

Ibidem, the angular momentum transfer is paradigm is that assigned after the Rafikov radiated flux ^[12], with which the angular momentum transfer is specified as the derivative of the viscous torque with respect to the Keplerian angular momentum, where the kinetic viscosity is expressed as a product of power-law functions of the surface density (i.e., the density which is obtained after the integration of the density over the thickness of the disc) and of the radial variable.

Ibidem, the long-standing interrogation about how to discriminate among the different forces resulting in blackholes, in neutron stars and in objects form binary systems is proposed again; it is my purpose to stress that a GR implementation of MHD should be wished, where GR-MDH analysis is needed, when the differential-rotation variables should be included for a nowadays understanding of the accretion flows approached in ^[13].

In the work of Ciurlo et al. ^[14], the specifications of the blackhole SGR A* are looked for as those of a low-luminosity one with variable emissions; the complexity of the dynamics in accretion flows is ibidem delineated also after the consequences of the features of the star motions of the stars orbiting it. As an example, the presence of a dark mass is interpreted when the velocity dispersion elation, calculated as functions of the classical radial distance, were taken into account: it is my study to outline that the radial distances calculated should be those originated from the position 4-vector xμ, when the GR normalization of the velocity 4-vector vμ is taken for the observer solidal with the photon.

Ibidem, some of the results from the Event Horizon Telescope (EHT) device allowing for the image of a bright ring surrounding the shadow of the black-hole object are commented, whose angular resolution is one obtained afterthe Very-Long-Baseline-Interferometry (VLBI) techniques for the event horizon to

be observed (as from Fig. 3 from ibidem).

Ibidem, the variability possibilities are recalled a the short-term variability, after which the time correlation between the X-ray flares and the infrared ones is written, and the long-term variability, after which the history of energy activity is obtained as an indirect indication of thee phenomena resulting from its Central Molecular Zone: for these purposes, after the modellizations from ^[15], it is my understanding that the fundamental Braginsky equations should be also applied for loss mechanisms in plasmas ^[16], which have not been taken into account yet after the limitations imposed after the analysis of implementation of the comparison between the fluid dynamics as after the discrimination of avoiding the presence of secular instabilities and that of thermal instabilities.

5. Instabilities in the Milky Way Blackhole

What is the vertical structure of the disc?

In the work of Balbus et a. ^[4] the theory of instabilities of accretion discs with respect to axisymmetric perturbations is revised according to the paradigms of dynamical shear local instabilities when due to a weak magnetic field. The mode is ibidem proposed as apt to be applied to gaseous systems in differential rota-tion regimes; the effects of the instability are pointed out as to be individuated in the variation of the growth rate, which is described as proportional to the angular rotation velocity and in ’independent’ of the magnetic field strength: the poloidal component of the field and the toroidal one are discerned: the mo-

tions within the gas are described within the fluid theory. Moreover, ibidem, the wavenumbers if the instabilities are characterized after the Alfv´en velocity; also, this phenomenon is analyzed as independent of the strength of the magnetic field.

In the work of Hawley et al. ^[17], the Keplerian shear flow onto a central compact object is studied; the initial configuration of a cylindrical Keplerian Couette flow of a gas of equation of state governed as r= 5/3is taken, where a layer form the vertical thickness is chosen: only the radial gravitational force and the centrifugal force are considered in radial balance as initial condition, i.e., the effective vertical pressure and density gradients are neglected, where these quantities are considered as constant. The pertinent numerical simulation is explained to be implemented ibidem. It is my aim to stress that the hypothesis of a Keplerian angular velocity is taken as acceptable only if secular instabilities and/or if thermal instabilities are present: thermal instabilities is gaseous discs are theoretized in ^[18], while secular instabilities are investigated within the same problem in ^[19]. More precisely, in ^[20], the mode of secular instabilities of the disc is applied to supermassive blackholes perfect-fluid accretion discs, from which the possibility of the presence of transient X-ray sources is calculated within this approximation.

In the work ^[21], magnetic shear instabilities of a ionized, ’compressible’ gas or plasma of the accretion disc onto a central compact object are considered for

numerical simulation of MHD: the radial boundary conditions are implemented after the tool replacing the cylindrical coordinates with the corotating reference frame for which the radial divergence is vanishing such that the angular velocity is different from the Keplerian one, and can be written as a function of the gravitational forces which are taken as depending on the cylindrical radial coordinate. The buoyancy and the resistivity are neglected from this model; the dissipation scale i discussed: as a result, the significant fluid motion is individuated within the analysis. The role of reconnection is investigated accordingly, from which the study of the time evolution of the poloidal magnetic field energy density demonstrated to be dependent of the resolution of the numerical simulation within this regime in Fig. 13 from ibidem. It is also important to point out that the ’vertical stratification’ is not studied within these items of investigation. For these purposes, the forces resulting from laminar motion and those from viscous hydrodynamics are treated from ^[22]: within the description of the prefect fluid, the modalities of the gas capture are recapitulated in ^[23] after the Radiatively inefficient accretion flow (RIAF) mechanisms introduced after ^[24] where, within the framework of the absence of the convection (i.e., in the absence of vertical shear) the consequences are individuated in the analytical expression of the radial profile of the density.

6. Recently-Raised Interrogations

What are the timely open research guidelines about the Milky Way blackhole spacetime?

Which are the aspects about which it is necessary to shed light?

In the work of Liu et al. ^[25], the attempt is presented to approach a unifying treatment of the Shakura-Sunyaev disc, of the Shapiro-Lightman-Eardley model, of the slim disc and of the advection.dominated flow accretion object, where the thick dic is height-averaged. Ibidem, the accretion object is described as gaseous, in which the gravitational pressure is neglected, and where the velocities are obtained after a pseudo-Newtonian potential. The consequent analytical description in that where the Keplerian velocity is modified after the scheme of Artemova et al. ^[26] from the free-fall acceleration; as a result, the examples are listed, among which the Newtonian potential and the potential from the free-fall acceleration at rest are considered: indeed, it is my aim to stress that a useful treatment would be that where the velocities are taken as those from the reference frame of the observer solidal with the photon in the gravitational potential of the gravitating object in the blackhole spacetime, where the gravitational pressure term is calculated accordingly, i.e. the role of the _tt of the metric tensor should be recast.

The Velikhov-Chandrasekhar MRI after turbulence is introduced in ^[27] after ^[17] from a numerical point of view for the sake of the explanation of the failure of the application of the Rayghleight criterion as caused after the transition from MHD to GRMHD; the role of the MRI in the transport of angular momentum is recalled in ^[28] after viscosity and after the magnetic diffusivity when the accretion object exhibits different differential rotation ar different radii, where the regimes studied in ^[29] have to be scrutinized and applied to the recent research of ^[30].

In ^[31], the MRI in perfect fluid is analysed; the study is here stressed not to apply to gaseous accretion objects as global turbulence heating would be requested after ^[31] when the role of the thermal equilibrium curves pointed out in ^[32] and in ^[33] is present.

It is my care to outline that the study from [4] should be further upgraded to a swirling accretion object, in which the ionization phenomenon is only partial as from ^[34].