Mass loss

Although the tidal radius for a solar-mass star at r=0.04 pc is 40 AU, the tidal radius at the cloud's pericentre distance of r p =270 AU=10−3 pc is only d t =1 AU (m * /M ⊙ )1/3. At the most recently observed epoch1, the cloud was approximately 6 r p from the black hole, with a tidal radius of 6 AU (m * /M ⊙ )1/3. Hence, the circumstellar disc is already experiencing substantial tidal disruption. At the same time, the Galactic centre hosts an extreme flux of ionizing and far ultraviolet (FUV) photons. Proto-planetary discs in the ionizing environment near O stars in the Trapezium cluster are known to experience photoevaporation10. The stars experience mass loss due to heating both by FUV and by Lyman limit photons11. The former heat the disc to ∼103 K, generating outflows at the sound speed of ∼3 km s−1, corresponding to the escape velocity at a distance ∼100 AU (m * /M ⊙ ) from the star. Well within this distance, the FUV-driven outflow is diminished, though not entirely quenched12. At the ∼10 AU and smaller distances of interest here and given the extreme ionizing environment, Lyman continuum (ionizing) photons dominate the outflow, generating a ∼104 K ionized outflow moving at the sound speed of ∼10 km s−1. This speed matches the escape velocity at a distance of d esc ∼10 AU (m * /M ⊙ ) from the star. Loss from smaller distances occurs at a reduced rate, but still generates a ∼10 km s−1 outflow by the time the gas reaches d esc .

Which process—tidal stripping or photoevaporation—dominates mass loss from the disc? Currently, tidal stripping dominates the unbinding of mass from the star, and at large distances from the star, tidal stripping determines the ultimate fate of the gas. However, the outflow properties of the observed cloud are nevertheless currently determined by photoevaporation. This can be understood as follows. Gas at a distance d>d t from its host star is accelerated by the tidal potential to a relative speed of Δv, as it moves of order its own distance away from its host star: , so that , with . For d=d t , . At the cloud's current separation from SgrA*, at the tidal radius, comparable to the wind outflow rate. Hence, the motion of tidally decoupled gas is dominated by the tidal field. At earlier times in the star's plunge, Δv was smaller, meaning that wind gas flowed out of the tidal radius faster than tidally disrupted gas. Currently, near the disc edge, the dynamics of previously ejected gas are set by properties of the wind, while on the ∼100 AU scale of the cloud, tidal evolution overwhelms wind motions.

Although the current mass disruption rate of the proto-planetary disc, , is larger than the wind outflow rate, , wind gas emitted at earlier times dominates the currently observed cloud. In the short time that the infalling star has spent in an enhanced tidal field with d t <d out , the disc has only had the opportunity to expand by a fraction of its ∼10 AU size. At d=8 AU, the time since d t =d along the infalling star's orbit is Δt=3 yr for m * =0.3 M ⊙ . Decoupled material has travelled only ∼ΔvΔt∼4 AU further from the host star in that time. Figure 2 illustrates this point. We ask how far a test particle, released at a given disc radius, d, from the star when d t =d and moving only under the gravity of the black hole, will be from its current orbit. Exterior to the decoupled material, gas originally launched in a wind dominates.

Figure 2: Expansion of the infalling gas. As the star plunges towards the Galactic centre, its disc and the surrounding photoevaporative wind are tidally disrupted. For a fiducial stellar mass of , we plot the distance, d, of gas from the host star at the current epoch (solid line) and at the time of pericentre passage (dashed line) as a function of separation from the host star at the time of tidal decoupling. The dotted line represents no change. We assume that the material is instantaneously decoupled from the star when its separation equals the tidal radius and that it subsequently moves as a test particle in the gravitational field of the supermassive black hole. At the time of its decoupling, the test particle is started with the orbital parameters that the cloud had at time d/v * before decoupling, and the full separation between the test particle and the star is thereafter calculated as a function of time. Red portions of the curve represent gas initially in the disc, whereas blue portions represent gas initially in the photoevaporative cloud. For gas currently observed in the cloud, the tidal evolution depicted here dominates the wind structure at large scales, while the wind outflow at ∼10 km s−1 dominates the structure of recently ejected gas near the disc rim. At pericentre, tidal evolution determines the structure of the entire wind. Full size image

The tidal decoupling rate in the disc is , where Σ(d) is the original surface density of the disc and at the current position in the cloud's orbit. For illustration, we choose a profile similar to the minimum-mass solar nebula: Σ=Σ 0 (d/d 0 )−1 with Σ 0 =2×103 g cm−2 and d 0 =1 AU (ref. 5). This choice yields a current , where we set d equal to the current tidal radius. Photoevaporation, on the other hand, gives mass loss rates13,14 of yr−1 for discs with sizes d out >d esc , where Φ i,49 is the ionizing luminosity, Φ i , in units of 1049 s−1 of a source at distance D from the disc, with D pc =D/(1 pc).

The photoevaporation mass loss can be derived as follows. At d=d esc , the escape velocity is comparable to the wind's sound speed c s =10 km s−1. For d ≳ d esc , , where m p is the mass of a proton and we have neglected an order unity correction arising from the non-sphericity of the flow. We refer to the surface layer of the disc within which photoionization heats disc gas to ∼104 K as the 'base of the wind.' At the base of the wind, a balance between photoionization and radiative recombination yields a number density of , where α rec =2.6×10−13 cm3 s−1 is the Case B radiative recombination coefficient for hydrogen at a temperature of 104 K, and we have used the fact that the optical depth to ionizing photons is unity. Hence, . Though this expression is only good to order of magnitude, its coefficient is in fortuitously good agreement with more detailed wind models13,14. Observations yield 1050.8 s−1 Lyman continuum photons in the central parsec1,15, corresponding to Φ i,49 =63. Using D=1 pc, . The central concentration of S-stars within 0.01 pc, which we estimate to contribute Φ i,49 =0.2 from each of ten approximately 10 M ⊙ stars comparable to the second-most luminous Trapezium star13, yields a small total of Φ i,49 =2 but in a more concentrated region. At the current position of the cloud, these stars contribute for D=6×10−3 pc. At D=0.04 pc, this number is 35. For d=10 AU and smaller, mass loss from these ionizing fluxes dominates over FUV-driven mass loss. Using an intermediate value of . On the cloud's original orbit, , allowing our nominal disc, which contains ∼10−2 M ⊙ between 1 and 8 AU, to survive for ∼106 yr. Disc masses several times larger are plausible, and hence a proto-planetary disc could have survived until the current time on the star's birth orbit in the ring.

Dynamics of stripped gas

Currently, gas farther than ∼12 AU from the star (for m * =0.3 M ⊙ ; see Fig. 2) was originally ejected in the photoevaporative wind. This ejected material (which starts in a ring-like configuration) itself undergoes tidal stripping. Along the star's original orbit, the extent of the wind moving at ∼10 km s−1 is set by the original 24 AU tidal radius. As gas requires only 10 years to travel 24 AU at ∼10 km s−1, this wind scale applies even if the wind region was disrupted by close stellar encounters or more distant encounters with the black hole at some point in the past.

As the star plunges towards the Galactic centre, its disc and wind are pulled off in shells as the tidal radius shrinks (Fig. 3). The time for a parcel of wind to travel at 10 km s−1 from 10 to 100 AU is comparable to the 70-yr time to plunge to pericentre on the cloud's current orbit. This wind-generated cloud in turn experiences tidal disruption. By its current location, the original wind cloud will have reached an extent of a few hundred AU. Figure 2 illustrates this extent for . We note that although previous close encounters with the black hole may have stripped the disc to smaller than its original size, the disc wind is regenerated over each orbit. As long as the disc size exceeds d esc and most of the disc mass remains intact, our wind calculation remains valid. If the disc is stripped to smaller sizes, a wind will still be blown, but with reduced .

Figure 3: Disc and wind structure. Schematic diagram of the disc and wind structure on the star's original orbit in the young stellar ring (a) and at the current epoch (b). On its original orbit, the star (black circle) hosts a protoplanetary disc (grey), which is limited in extent (vertical black line) to approximately one-third of the star's tidal radius, d t (dashed circle). Photoionization efficiently launches a wind beyond d esc , where gas is heated enough that its thermal velocity is comparable to the stellar escape velocity (vertical red line). From the wind-launching region (blue), gas flows outward (red arrows) until it passes the tidal radius and is stripped from the star. At the current epoch, d t has shrunk, causing both the disc and the wind to tidally expand. Full size image

Ram pressure of the ambient gas exceeds the ram pressure of the photoevaporative wind when , where n amb is the ambient number density of gas and v * is the star's velocity along its orbit. The characteristic density of ambient gas within the central 1.5 pc is n amb ∼ 103 cm−3 (ref. 16). Models place the density at ∼3×102–6×103 cm−3 at the cloud's current location and ∼(1–5)×102 cm−3 on its original orbit17. Along the star's original orbit, , and the ram pressure force from the disc wind roughly balances ram pressure with the ambient medium at the star's tidal radius. Currently, , so ram pressure with the surrounding medium has increased by 1–2 orders of magnitude at comparable separations from the star, and the tidally disrupted photoevaporative wind is undergoing ram pressure stripping. Nevertheless, at the current tidal radius, the two pressures remain in rough balance and our estimates of the mass loss rate are therefore valid. As the cloud continues its plunge towards the super-massive black hole, its outer (tidally detached) extent will be shaped by ram pressure stripping.

Figure 4a displays the inferred ionized density of the cloud as a function of radial scale. From the total Brγ line luminosity, the discovery paper1 calculates an electron density of , in excellent agreement with our prediction. In Fig. 4a, we also plot the contribution to the total line luminosity as a function of radial scale. As the luminosity is proportional to n2d3, this contribution peaks at the outer edge of the disc, but the contribution from the extended cloud falls off slowly, as 1/d, so that about 1/5 of the line luminosity comes from 100 AU scales. We note that though the majority of Brγ emission comes from the 10–20 AU scale of the tidally expanded disc, the majority of the mass in the cloud is at large scales, as the cloud mass is proportional to nd3 ∝ d. At these large scales, full hydrodynamic simulations including ram pressure stripping and tidal gravity in 3D are required to match in detail the surface brightness, shape and velocity width of the observed emission. One might naively expect the surface of the cloud to be Kelvin–Helmholtz unstable1. However, observations of cold fronts in X-ray clusters indicate that gas clouds moving at a Mach number of order unity through a hot (∼keV) ambient medium maintain a smooth surface, probably owing to 'magnetic draping'18.