Depletion of bright red giants in the Galactic center during its active phases
Michal Zajaček, Anabella Araudo, Vladimír Karas, Bożena Czerny, Andreas Eckart
DDraft version October 1, 2020
Typeset using L A TEX twocolumn style in AASTeX63
Depletion of bright red giants in the Galactic center during its active phases
Michal Zajaˇcek , Anabella Araudo ,
2, 3
Vladim´ır Karas , Bo˙zena Czerny , and Andreas Eckart
5, 6 Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotnikow 32/46, 02-668 Warsaw, Poland ELI Beamlines, Institute of Physics, Czech Academy of Sciences, CZ-25241 Doln´ı Bˇreˇzany, Czech Republic Astronomical Institute of the Czech Academy of Sciences, Boˇcn´ı II 1401, CZ-14100 Prague, Czech Republic Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotnikow 32/46, 02-668 Warsaw, Poland I. Physikalisches Institut der Universit¨at zu K¨oln, Z¨ulpicher Strasse 77, D-50937 K¨oln, Germany Max-Planck-Institut f¨ur Radioastronomie (MPIfR), Auf dem H¨ugel 69, D-53121 Bonn, Germany (Received June 1, 2019; Revised January 10, 2019; Accepted October 1, 2020)
Submitted to ApJABSTRACTObservations in the near-infrared domain showed the presence of the flat core of bright late-typestars inside ∼ . γ -ray Fermi bubbles and bipolar radio bubbles. Ex-tended, loose envelopes of red giant stars can be ablated by the jet with kinetic luminosity in the rangeof L j ≈ –10 erg s − within the inner ∼ .
04 pc of Sgr A* (S cluster region), which would leadto their infrared luminosity decrease after several thousand jet-star interactions. The ablation of theatmospheres of red giants is complemented by the process of tidal stripping that operates at distancesof (cid:46) (cid:38) .
04 pc, whichcan explain the flat density profile of bright late-type stars inside the inner half parsec from Sgr A*.
Keywords:
Galaxy: center — stars: supergiants — galaxies: jets — stars: kinematics and dynamics INTRODUCTIONThe Galactic center supermassive black hole (here-after SMBH) with the mass of 4 . × M (cid:12) is locatedat the distance of 8 . Corresponding author: Michal Zajaˇ[email protected] ded in the Milky Way NSC, which is one of the denseststellar systems in the Galaxy (Sch¨odel et al. 2014), andin addition, it is surrounded by an ionized, neutral, andmolecular gas and dust (see e.g. Moser et al. 2017, andreferences therein).The NSC consists of both late-type (red giants, super-giants and asymptotic giant branch stars) and early-typestars of O and B spectral classes (Krabbe et al. 1991;Do et al. 2009; Buchholz et al. 2009; Gallego-Cano et al.2018), which implies star-formation during the wholeGalactic history, albeit most likely episodic (Pfuhl et al.2011) with the star-formation peak at 10 Gyr, the min-imum at 1-2 Gyr and a recent increase in the last fewhundred million years.In the innermost parsec of the Galactic center, thereis a surprising abundance of young massive OB/Wolf-Rayet stars formed in-situ in the last 10 million years(Ghez et al. 2003). These young stars form an unrelaxed a r X i v : . [ a s t r o - ph . H E ] S e p Zajacek et al. cusp-like distribution. On the other hand, former stud-ies of the distribution of late-type stars showed that theyexhibit a core-like distribution inside the inner ∼ . K ≈
18 exhibit a cusp-likedistribution within the sphere of influence of Sgr A*with a 3D power-law exponent of γ (cid:39) .
43. In com-parison, there is an apparent lack of bright red giantswith K = 12 . −
16 at the projected radii of (cid:46) . K <
17 within0 . − . K < .
5, although the number of miss-ing giants appears to be lower than 100 according totheir analysis. Although the surface brightness distri-bution of late-type stars brighter than 15.5 magnitudesappears to be rather flat, already in Fig. 11 of Buchholzet al. (2009) the inner point at 0 . (cid:48)(cid:48) (where 1 (cid:48)(cid:48) ∼ .
04 pcat the Galactic center) of the distribution of the late-type stars as well as of the distribution of all the starsindicates the presence of a cusp.In summary, there appears to be an internal mecha-nism within the NSC that preferentially depleted bright,large red giants on one hand, which has led to their ap-parent core-like distribution, and at the same time hasbeen less efficient for early-type as well as fainter late-type stars on the other hand. Such a mechanism has al-tered either the spatial, luminosity, or the temperaturedistribution of the bright red-giant stars so that theyeffectively fall beyond the detection limit or they rathermimic younger, “bluer” stars. So far, mainly the follow-ing four mechanisms have been discussed to explain theapparent lack of bright red giants, • complete or partial tidal disruption of red giantsby the SMBH (Hills 1975; Bogdanovi´c et al. 2014;King 2020) (envelope removal), • envelope stripping by the collisions of red giantswith the dense clumps within a self-gravitating ac-cretion disc (Armitage et al. 1996; Amaro-Seoane& Chen 2014; Kieffer & Bogdanovi´c 2016; Amaro-Seoane et al. 2020) (envelope removal), • collisions of red giants with field stars and com-pact remnants (Phinney 1989; Morris 1993; Genzelet al. 1996; Bailey & Davies 1999; Alexander 2005;Davies & King 2005; Dale et al. 2009) (enveloperemoval), • mass segregation effects: the dynamical effectof a secondary massive black hole (Baumgardtet al. 2006; Merritt & Szell 2006; Portegies Zwartet al. 2006; Matsubayashi et al. 2007; L¨ockmann& Baumgardt 2008; Gualandris & Merritt 2012)or of an infalling massive cluster (Kim & Morris2003; Ernst et al. 2009; Antonini et al. 2012) or ofstellar black holes (Morris 1993) (altered spatialdistribution),where in the parentheses we include the mechanism re-sponsible for altering the population of late-type stars.The importance of star–star and star–disc interactionswas also analyzed generally for active galactic nuclei interms of the effects on the accretion disk and Broad Lineregion structure as well as the NSC orbital distribution(Zurek et al. 1994; Armitage et al. 1996; Karas & ˇSubr2001; Vilkoviskij & Czerny 2002; MacLeod & Lin 2019;Kieffer & Bogdanovi´c 2016).We propose here another mechanism based on the jet-star interactions (Barkov et al. 2012a; Araudo et al.2013; Araudo & Karas 2017), which most likely coex-isted with the mechanisms proposed above. In par-ticular, the star–accretion disc collisions are expectedto be accompanied by star–jet crossings during previ-ous active phases of Sgr A*. Since red-giant stars havetypically large, loosely bound tenuous envelopes, densecompact cores, and slow winds with the terminal veloc-ity (cid:46)
100 km s − , they are in particular susceptible tomass removal in encounters with higher-pressure mate-rial (MacLeod et al. 2012; Amaro-Seoane & Chen 2014;Kieffer & Bogdanovi´c 2016). Therefore during the redgiant–jet interactions, the jet ram pressure will removethe outer layers of the stellar envelope during the pas-sage. We illustrate this idea in Fig. 1.After several star–jet crossings, the atmosphere isremoved similarly as for repetitive star–disc crossings(Amaro-Seoane et al. 2020) and the giant is modifiedin a way that it follows an evolutionary track in theHertzsprung-Russell (HR) diagram approximately alongthe constant absolute magnitude towards higher effec-tive temperatures. We show that this mechanism quitelikely operated in the vicinity of Sgr A* during its active The estimate of the terminal wind velocity is given by the escapevelocity v esc = 62 (cid:16) M (cid:63) M (cid:12) (cid:17) / (cid:16) R (cid:63) R (cid:12) (cid:17) − / km s − . epletion of bright red giants jet Sgr A*black hole red giantL ,R ,T modi fi ed giantL ,R ,T accretion disc Bow shockdetachedshockedenvelope R stag atmosphere core after several encounters Figure 1.
Illustration of the jet-red giant interaction in thevicinity of Sgr A* during its active phase. The large, looselybound envelope of the red giant (coloured as red and orange),which has an initial luminosity, radius, and temperature( L , R , T ), is ablated by the jet ram pressure during sev-eral encounters since the lifetime of the jet t jet ∼ . ∼ . P orb ∼ a/ . / yr. After a few hundred encoun-ters, star has modified parameters ( L , R , T ), which changethe overall outlook of the giant in the near-infrared domain.Inspired by Barkov et al. (2012a) and Bosch-Ramon et al.(2012). Seyfert-like phase in the past few million years (Bland-Hawthorn et al. 2019) when the jet kinetic luminositycould have reached ∼ erg s − . In principle, even inthe quiescent state, a tidal disruption event every ∼ years, which can be estimated for the Galactic center(Syer & Ulmer 1999; Alexander 2005), can temporar-ily reactivate the jet of Sgr A* and some of the brightred giants could be depleted during its existence. Thismakes the red giant–jet interaction in the Galactic cen-ter relevant and highly plausible in its recent historyand the dynamical consequences can be inferred basedon the so-far detected traces of the past active phase ofSgr A* as well as the currently observed stellar densitydistribution.Previous jet-star interaction studies were focused onthe emergent non-thermal radiation, in particular in thegamma-ray domain, and mass-loading and chemical en-richment of jets by stellar winds (see e.g. Komissarov1994; Barkov et al. 2012a; Bosch-Ramon et al. 2012;Araudo et al. 2013; Bednarek & Banasi´nski 2015; de la Cita et al. 2016). Here we focus on the effect of the jeton the stellar population. In most of the jetted activegalactic nuclei, this is perhaps a secondary problem sincestellar populations in the host bulge cannot be resolvedout, i.e. one can only analyze the integrated starlight.In contrast, within the Galactic center NSC, one cannot only disentangle late- and early-type stars, but itis also possible to study their distribution as well askinematics of individual stars. Although in the currentlow-luminosity state there is not firm evidence for thepresence of a relativistic jet, there are nowadays severalmultiwavelength signatures of the past active Seyfert-like state of Sgr A* that occurred a few million yearsago (Bland-Hawthorn et al. 2019; Heywood et al. 2019;Ponti et al. 2019). However, even in the current qui-escent state of Sgr A*, studies by Yusef-Zadeh et al.(2012) and Li et al. (2013) indicate the existence ofa low-surface-brightness pc-scale jet. In addition, thepresence of the cometary-shaped infrared-excess bow-shock sources X3, X7 (Muˇzi´c et al. 2010) and recentlyX8 (Peißker et al. 2019) indicates that the star–outflowinteraction is ongoing even in a very low state of theSgr A* activity. The morphology of these sources canbe explained by the interaction with a strong accretionwind originating from Sgr A* or with the collective windof the cluster of young stars.This paper proposes a new mechanism that could haveaffected the current population of bright late-type stars,namely their appearance as well as number counts inspecific magnitude bins, in the Galactic center. We ap-ply analytical and semi-analytical calculations to assesswhether the potential past jet–star interactions couldhave had an effect on the stellar population in the sphereof influence of Sgr A*. Although the analytical calcu-lations introduce several simplifications, we show thatthe mechanism could have operated and the estimatednumber of affected red giants is in accordance with theup-to-date most sensitive studies (Gallego-Cano et al.2018; Habibi et al. 2019). A more detailed computa-tional treatment including magnetohydrodynamic nu-merical simulations as well as a stellar evolution willbe presented in our future studies.The paper is structured as follows. In Section 2, wederive the stagnation radius, basic timescales, and theremoved envelope mass for red-giant stars interactingwith the jet of Sgr A* during its past active phase. InSection 3, we discuss the observational signatures in thenear-infrared domain. Subsequently, in Section 4, weestimate the number of red giants that could be affectedby the jet interaction and visually depleted from theimmediate vicinity of Sgr A*. In Section 6, we discussadditional processes related to the red giant–jet interac- Zajacek et al. tion in the Galactic center. Finally, we summarize themain results and conclude with Section 7. DERIVATION OF JET-STAR STAGNATIONRADIUS AND THE JET-INDUCED STELLARMASS-LOSSThe evidence for the active phase of Sgr A* thatis estimated to have occurred 4 ± γ -ray bubbles with total energy contentof 10 − erg (Bland-Hawthorn et al. 2019). Thefirst evidence for the nuclear outburst was the kpc-scale1.5 keV ROSAT X-ray emission that originated in theGalactic center (Bland-Hawthorn & Cohen 2003). TheX-ray structure coincides well with the more recentlydiscovered Fermi γ -ray bubbles extending 50 ◦ north andsouth of the Galactic plane at 1-100 GeV (Su et al.2010). The X-ray/ γ -ray bubbles are energetically con-sistent with the nuclear AGN-like activity associatedwith the jet and/or disc-wind outflows with jet power L j = 2 . +5 . − . × erg s − and age 4 . +0 . − . Myr (Miller& Bregman 2016). In comparison, the starburst originof the Fermi bubbles is inconsistent with the bubble en-ergetics by a factor of ∼
100 (Bland-Hawthorn & Cohen2003). On intermediate scales of hundreds of parsecs,the base of the Fermi bubbles coincides with the bipolarradio bubbles (Heywood et al. 2019) as well as with theX-ray chimneys (Ponti et al. 2019).Using hydrodynamic simulations, Guo & Mathews(2012) reproduce the basic radiative characteristics ofthe Fermi bubbles with the AGN jet duration of ∼ . − . L j ≈ − erg / (0 . − . . × − . × erg s − . The jet is dominated by the kinetic lumi-nosity L j = η j L acc , where η j is the conversion efficiencyfrom the accretion luminosity L acc to the jet kineticluminosity. The accretion luminosity is L acc (cid:46) L Edd ,where the Eddington luminosity is L Edd = 5 . × (cid:18) M • × M (cid:12) (cid:19) erg s − (1)and η j < . L j ≈ . × erg s − . We will consider L j ≈ − erg s − , where the lower limit is givenby the putative jet present in the current quiescent state(Yusef-Zadeh et al. 2012), with the inferred kinetic lumi-nosity of L min ∼ . × erg s − , and the upper limitis given by the Eddington luminosity.We assume a conical jet with a half-opening angle θ and width R j = z tan θ , where z is the distance toSgr A*. The jet footpoint for Sgr A* can be estimatedto be located at z ∼ × − ( M • / × M (cid:12) ) pc = 52 R Schw (Junor et al. 1999), where R Schw = 2 GM • /c =3 . × − ( M • / × M (cid:12) ) pc is the Schwarzschild ra-dius. Any red giant or supergiant with radius R (cid:63) andmass m (cid:63) is not expected to plunge below z since thetidal disruption radius r t = R (cid:63) (2 M • /m (cid:63) ) / (Hills 1975;Rees 1988) is at least a factor of two larger, r t R Schw = 1 20 (cid:18) R (cid:63) R (cid:12) (cid:19) (cid:18) M • × M (cid:12) (cid:19) (cid:18) m (cid:63) M (cid:12) (cid:19) − . (2) R (cid:63) = 10 R (cid:12) and m (cid:63) = 1 M (cid:12) are typical intermediatevalues for the evolved late-type giants with extendedenvelopes (Merritt 2013). For numerical estimates, weconsider the range of radii for red giants and supergiants, R (cid:63) ∼ − R (cid:12) , as indicated by the Hertzsprung-Russell diagram. These late-type stars have the largerange of bolometric luminosities, L (cid:63) ∼ − L (cid:12) ,and the temperature range of T (cid:63) ∼ − K ∼ . R (cid:63) = 4 R (cid:12) , T (cid:63) = 5000 K and K ∼ . R (cid:63) = 1000 R (cid:63) , T (cid:63) = 3000 K. More specifically, we fo-cus on the late-type stars of K = 16 mag and brighter,which appear to form a core-like density distribution inthe central 0 . R (cid:63) ∼ R (cid:12) and larger for an age of 5 Gyr. The late-typestars that are completely absent in the S-cluster (inner ∼ .
04 pc) were inferred to have R (cid:63) = 30 R (cid:12) and larger(Habibi et al. 2019). Therefore, numerical estimates aretypically scaled to R (cid:63) = 30 R (cid:12) unless otherwise indi-cated.We will further focus on the region between the tidalradius of red giants and the outer edge of the S cluster,which approximately corresponds to the Bondi radiusof the hot bremsstrahlung plasma (Baganoff et al. 2003;Wang et al. 2013), R B = GM • c = 0 . (cid:18) M • × M (cid:12) (cid:19) (cid:18) T p K (cid:19) − pc , (3)which is two-three orders of magnitude larger thanthe tidal radius of red giants, R B ∼ . × R Schw .More generally speaking, the population of predomi-nantly B-type stars lies within the innermost arcsecond( ∼ .
04 pc, S cluster), while the population of youngmassive OB/Wolf-Rayet stars stretches from ∼ .
04 pcup to ∼ . The stellar radius is the sum of the core radius and the enveloperadius, R (cid:63) = R c + R env . epletion of bright red giants r from thecenter of the star can be estimated as P sw ∼ ρ w v =˙ m w v w / (4 πr ), where ˙ m w is the mass-loss rate and v w isthe terminal wind velocity. Using typical values for redgiants with ˙ m w ≈ − M (cid:12) yr − and v w ≈
10 km s − (e.g. Reimers 1987; de la Cita et al. 2016) P sw = 0 . (cid:18) ˙ m w − M (cid:12) yr − (cid:19) (cid:16) v w
10 km s − (cid:17) ×× (cid:18) r R (cid:12) (cid:19) − erg cm − . (4)The ram pressure of a relativistic jet with bulk motionLorentz factor Γ is P j = Γ ρ j v , where the jet density is ρ j = L j / [(Γ − c σ j v j ] and σ j = πR is the jet cross-sectional area. By assuming v j ∼ c and Γ ∼
10 the jetkinetic pressure for Sgr A* can be written as P j ≈ L j σ j c = L j πcz tan θ = 0 . (cid:18) L j erg s − (cid:19) (cid:18) z .
04 pc (cid:19) − erg cm − , (5)where we have assumed θ (cid:39) . ◦ that corresponds tothe jet sheath half-opening angle estimated for the cur-rent candidate jet of Sgr A* (Li et al. 2013). Note thatthe innermost arcsecond ( z ∼ .
04 pc) is also the outerradius of fast-moving stars in the S cluster (Genzel et al.2010; Eckart et al. 2017). For red giants, ˙ m w ≈ − − − M (cid:12) yr − according to Reimers(1987). Figure 2.
Stagnation radius R stag /R (cid:12) . The two horizon-tal white-solid lines indicate the radial extent of the S clusterbetween the S2 pericenter distance and the outer radius at ∼ .
04 pc. The two white-dashed lines stand for the atmo-sphere radius limits of late-type stars in the S cluster, 4 R (cid:12) and 30 R (cid:12) (Habibi et al. 2019). The dot-dashed green linesindicate the jet luminosity limits that would yield the stellaratmosphere ablation at 30 and 4 R (cid:12) at z = 0 .
02 pc.
By equating P sw = P j , we obtain the stagnation dis-tance R stag R (cid:12) = 27 (cid:18) z .
04 pc (cid:19) (cid:18) ˙ m w − M (cid:12) yr − (cid:19) ×× (cid:16) v w
10 km s − (cid:17) (cid:18) L j erg s − (cid:19) − (6)which characterizes by how much the red-giant envelopecan be ablated by the jet in one encounter. Note that R stag < R (cid:63) for late-type giants and supergiants with R (cid:63) ∼ − R (cid:12) (see Figure 2). The very tenuouswind of red giants cannot balance the jet ram pressureand therefore the jet plasma impacts on the stellar sur-face. As a consequence, a fraction of the stellar envelopeis removed as estimated by Eq. (6).Interestingly, giant stars with R (cid:63) (cid:38) R (cid:12) appearto be missing in the S cluster. Only late-type starswith R (cid:63) between 4 and 30 R (cid:12) (with absolute bolomet-ric magnitudes between − .
05 and 3 .
32, respectively, forthe effective temperature of 4000 K) were detected byHabibi et al. (2019) (see their figure 2). Stars with4 ≤ R (cid:63) /R (cid:12) ≤
30 within 0 .
02 pc have R stag /R (cid:63) ∼ × ≤ L j / erg s − ≤ . × , as it is indicatedin Fig. 2. This is in agreement with the estimated jetpower L j ∼ . × erg s − from X- and γ -ray bubbles(Miller & Bregman 2016). Therefore, an apparent lackof late-type giant stars with envelopes R (cid:63) (cid:38) R (cid:12) inthe inner ∼ .
04 pc of Galactic center could result fromthe jet-induced ablation of the stellar envelope duringthe last active phase of Sgr A*, a few million years ago.
Zajacek et al.
Figure 3.
Mass removed from the red-giant envelope fora single jet–star interaction, ∆ M in Eq. (14), for the casewith L j = 10 erg s − , m (cid:63) = 1 M (cid:12) , and θ = 12 . ◦ . The twohorizontal lines indicate the radial extent of the S clusterbetween the S2 pericenter distance and the outer radius at z ∼ .
04 pc. Dashed lines indicate ∆
M/M (cid:12) = 10 − , 10 − ,and 10 − . The dot-dashed green line corresponds to ∆ M =3 × − M (cid:12) , which is equivalent to ∆ M = 6 × g inequation 6 of Barkov et al. (2012a). Basic timescales of the jet-star interaction
The red giant, will enter the jet and not mix withits sheath layers on the surface if v orb (cid:38) v sc , where v orb ∼ ( GM • /z ) / is the Keplerian orbital velocity ofthe star around Sgr A* and v sc ∼ c (Γ ρ j /ρ (cid:63) ) is the soundspeed inside the shocked obstacle. This condition canbe written as ρ (cid:63) ρ j (cid:38) . × (cid:18) z .
01 pc (cid:19) (cid:18)
Γ10 (cid:19) (cid:18) M • × M (cid:12) (cid:19) − , (7)which means that stellar atmosphere layers of the com-parable density or greater than indicated by Eq. (7) willenter the jet and the less dense upper layers will mixwith the jet surface layers.Once inside, the bow shock is formed inside thejet on the very short timescale of t bs ∼ R (cid:63) /c ∼ R (cid:63) / R (cid:12) ) s. A shock also propagates throughthe red giant atmosphere on the shock-crossing or dy-namical timescale, t d ∼ R (cid:63) /v sc , whose lower limit isimposed by the condition of penetration, v orb (cid:38) v sc ,which leads to t d (cid:38) R (cid:63) /v orb = R (cid:63) (cid:112) z/ ( GM • ) ∼ R (cid:63) / R (cid:12) )( z/ .
01 pc) / ( M • / × M (cid:12) ) − / s.The dynamical, shock-crossing time is at least ∼ t d /t bs (cid:38) z/ .
01 pc) / ( M • / × ) − / . The star-crossing time through the jet can be esti-mated as t (cid:63) ∼ R j /v orb . Using R j = z tan θ and thecondition v sc (cid:46) v orb , we obtain t (cid:63) t d (cid:46) z tan θR (cid:63) ∼ , (8)which implies that the shock propagates throughout thedetached envelope, which is dragged by the jet andmixed with its material. Eventually, after several t d ,the envelope material will reach the velocity of v j ∼ c .Note that t (cid:63) /t d ∼ z ∼ − pc, hence the re-moved envelope material should be dragged by the jetthroughout the whole NSC.The ablated red giant after the first cross-ing through the jet would first expand adiabati-cally to the original size on the thermal expansiontimescale t exp ∼ R (cid:63) /c s = R (cid:63) (cid:112) µm H / ( k B T atm ) =0 . R (cid:63) / R (cid:12) )( T atm / K) − / yr because of the pres-sure of the warmer underlying layers as the star adjustsits size to reach a hydrodynamic equilibrium. This ex-pansion timescale is shorter than the orbital timescale P orb = 2 π (cid:18) z GM • (cid:19) / == 47 (cid:18) z .
01 pc (cid:19) / (cid:18) M • × M (cid:12) (cid:19) − / yr . (9)Kieffer & Bogdanovi´c (2016) infer a similar timescale forthe envelope expansion using the hydrodynamic simula-tions of red giant–accretion clump collisions. Accordingto their Fig. 7, the envelope expands to a larger sizethan the original stellar radius in t exp ∼ . t dyn afterthe star emerges from the accretion clump, where t dyn is a dynamical timescale of the star, t dyn ∼ . (cid:18) R (cid:63) R (cid:12) (cid:19) / (cid:18) m (cid:63) M (cid:12) (cid:19) − / yr , (10)which leads to t exp ∼ . × .
32 yr ≈ . t KH ≈ Gm (cid:63) R (cid:63) L (cid:63) = 210 (cid:18) m (cid:63) M (cid:12) (cid:19) (cid:18) R (cid:63) R (cid:12) (cid:19) − (cid:18) L (cid:63) L (cid:12) (cid:19) − yr , (11)where we estimated the stellar luminosity using L (cid:63) =4 πR (cid:63) σT (cid:63) for T (cid:63) = 3500 − R (cid:63) ∼ − R (cid:12) and stellar luminosities L (cid:63) ∼ − . × L (cid:12) , t KH epletion of bright red giants ∼ yrs for the smallestgiants to ∼ .
43 yr for the largest ones.Based on the comparison between the time betweenjet-star collisions t c = P orb / t c (cid:38) t KH , i.e. thestar had enough time to radiate away the accumulatedcollisional heat and it cools down and shrinks before thenext collision. For the case when t c < t KH , there is notenough time to radiate away the excess collisional heatand the star is warmer and larger at the time of thesubsequent collision - these are so-called warm collid-ers. In the nuclear star cluster when the jet was active,there were both types of colliders with the approximatedivision given by t c ≈ t KH , which leads to z c ≈ Gm / (cid:63) M / • R / (cid:63) L / (cid:63) π / = 0 . (cid:18) m (cid:63) M (cid:12) (cid:19) / (cid:18) M • × M (cid:12) (cid:19) / ×× (cid:18) R (cid:63) R (cid:12) (cid:19) − / (cid:18) L (cid:63) L (cid:12) (cid:19) − / pc . (12)The length-scale z c implies that red giants locatedinside the inner S cluster were collisionally heated upand bloated, which increased their mass removal dur-ing repetitive encounters with the jet. Stars orbitingat larger distances managed to cool down and shrinkin size before the next collision, which has subsequentlydiminished their overall mass loss. However, note thatEq. (12) is a function of stellar parameters m (cid:63) , R (cid:63) , and L (cid:63) , hence z c differs depending on the red-giant stageand its mass. For the smallest late-type stars with R (cid:63) ∼ R (cid:12) and L (cid:12) ∼ . L (cid:12) , z c ∼ . R (cid:63) ∼ R (cid:12) and L (cid:12) ∼ . × L (cid:12) have z c ∼ . Jet-induced envelope removal
The stellar evolution after a jet-star encounter is gen-erally complicated given that the envelopes of red giantsbecome bloated after the first passage through the jet.This is because of the pressure of lower, hotter layersand their subsequent nearly adiabatic expansion, whichcan make the red giant even larger and brighter (Kieffer& Bogdanovi´c 2016). Note that the number of encoun-ters n cross = 2 t jet /P orb , where t jet ∼ . (cid:29)
1. In particular, n cross ∼ × (cid:18) t jet . (cid:19) (cid:18) M • × M (cid:12) (cid:19) (cid:18) z .
01 pc (cid:19) − . (13) The number of encounters is also at least two orders ofmagnitude larger than the one expected from the star–accretion clump interaction investigated by Kieffer &Bogdanovi´c (2016) and Amaro-Seoane et al. (2020). Af-ter the first passage, the bloated red giant has an evenlarger cross-section than before the encounter, which in-creases the mass removed during subsequent encounters(Armitage et al. 1996; Kieffer & Bogdanovi´c 2016). Thejet–star interaction phase proceeds during the red-giantlifetime, which is t rg ∼ yr (MacLeod et al. 2012).During the red giant phase, there are n orb = t rg /P orb ∼ . × ( z/ .
01 pc) − / orbits around Sgr A*, out ofwhich n cross /n orb = 2 t jet /t rg ∼
1% involve the interac-tion with the jet, assuming there was only one period ofincreased activity of Sgr A* in the last 100 million years.This ensures that the repetitive jet-red giant interactionleads to a substantial mass-loss and the upper layer ofthe envelope is eventually removed.The mass removal in a single passage due to the at-mosphere ablation ∆ M can be estimated through thebalance of the jet ram force and the gravitational forceacting on the envelope, i.e. P j πR (cid:63) (cid:39) G ∆ M m (cid:63) /R (cid:63) ,giving (Barkov et al. 2012a)∆ M max1 M (cid:12) ≈ × − (cid:18) L j erg s − (cid:19) (cid:18) R (cid:63) R (cid:12) (cid:19) ×× (cid:18) z .
04 pc (cid:19) − (cid:18) θ . (cid:19) − (cid:18) m (cid:63) M (cid:12) (cid:19) − . (14)In Fig. 3 we plot ∆ M . Note that ∆ M (cid:28) m (cid:63) and,therefore, the orbital dynamics is not significantly af-fected by the single passage through the jet. However,given that ∆ M ∝ R (cid:63) z − , the mass-loss can be aboutone thousandth to one hundredth of the mass of a starfor the largest giants on the asymptotic giant branchwith R (cid:63) ∼ R (cid:12) and distances an order of magni-tude smaller than z (cid:39) .
04 pc (see the yellowish regionin Fig. 3). In fact, the value of ∆ M = 6 × g =3 × − M (cid:12) discussed by Barkov et al. (2012a) for pow-erful blazars in connection to their very high-energy γ -ray emission can be reached in the Galactic center forred giants with radii R (cid:63) > R (cid:12) at z < .
01 pc. Sucha large mass-loss with a certain momentum with respectto the star can already have an effect on the orbital dy-namics, taking into account repetitive encounters of thered giant with the jet. In other words, the mass re-moval takes place at the expanse of the kinetic energyof the star, which has implications for the dynamics ofthe nuclear star cluster, see also Kieffer & Bogdanovi´c(2016) for discussion. In addition, already for jets witha lower power corresponding to the active phase of theGalactic center, jet-red giant interactions can affect theshort-term TeV emission in these sources. These effects
Zajacek et al. are beyond the scope of the current paper and will beinvestigated in our future studies.The mass removal during a single jet encounter givenby Eq. (14) can be considered as an upper limit sincewe assume that the cross-section of the star is given byits radius during the whole passage of the star throughthe jet, hence ∆ M max1 ≈ P j πR (cid:63) / ( Gm (cid:63) ). However, thisis only an approximation as realistically, during a fewshock-crossing or dynamical timescales t d the ram pres-sure of the jet will shape the red giant and its detachedenvelope into a comet-like structure, see Fig. 1, for whichthe interaction cross-section is given by R stag ratherthan by R (cid:63) , which gives us a lower limit on the massremoval, ∆ M min1 ≈ P j πR / ( Gm (cid:63) ) ≤ ∆ M max1 . UsingEq. (6), ∆ M min1 can be expressed in terms of the basicparameters of the star and the jet and it can numericallybe expressed by the same units as in Eqs. (14) and (6),∆ M min1 M (cid:12) ≈ c ( ˙ m w v w z tan θ ) Gm (cid:63) L j == 2 . × − (cid:18) L j erg s − (cid:19) − (cid:18) m (cid:63) M (cid:12) (cid:19) − ×× (cid:18) ˙ m w − M (cid:12) yr − (cid:19) (cid:16) v w
10 km s − (cid:17) (cid:18) z .
04 pc (cid:19) , (15)where we adopted θ ∼ . ◦ as before. In compari-son with ∆ M max1 in Eq. (14), which is proportional to z − , ∆ M min1 in Eq. (15) increases as z . This impliesthat ∆ M min1 ≤ ∆ M max1 holds for z ≤ z stag , where at z stag , R (cid:63) = R stag . In other words, only at z < z stag the mass removal due to the jet activity from the redgiant atmosphere is possible, while at distances largerthan z stag , the jet ablation is limited to the stellar-windmaterial, as is the case for the observed comet-shapedsources X3, X7, and X8 (Muˇzi´c et al. 2010; Peißker et al.2019). From Eq. (6), the relation for z stag follows as, z stag ≈ . (cid:18) R (cid:63) R (cid:12) (cid:19) (cid:18) θ . (cid:19) − (cid:18) L j erg s − (cid:19) ×× (cid:18) ˙ m w − M (cid:12) yr − (cid:19) − (cid:16) v w
10 km s − (cid:17) − pc . (16)The dependence of z stag on the stellar radius and themass-loss rate is shown in Fig. 4 (left panel). It is ap-parent that the volume around the reactivated Sgr A*,where the jet-ablation can occur for a particular redgiant, depends considerably on ˙ m w , which spans overthree orders of magnitude depending on the evolutionarystage, ˙ m w ≈ − − − M (cid:12) yr − (Reimers 1987). Inparticular, for red giants with R (cid:63) = 10 R (cid:12) , z stag shrinksfrom 0 .
047 pc to 0 . m w = 10 − M (cid:12) yr − to 10 − M (cid:12) yr − . In Fig. 4 (right panel), we show an exemplary casefor the mass removal range from the red giant atmo-sphere (red giant with the parameters of R (cid:63) = 100 R (cid:12) ,˙ m w = 10 − M (cid:12) yr − , and v w = 10 km s − ) due to thesingle crossing through the jet with the luminosity of L j = 10 erg s − and the opening angle of 25 ◦ . To-wards z stag , the mass removal due to a single encounterapproaches the mean value of ∆ M = ∆ M max1 ( z = z stag ) = ∆ M min1 ( z = z stag ),∆ M M (cid:12) = ˙ m w v w R (cid:63) Gm (cid:63) == 2 . × − (cid:18) ˙ m w − M (cid:12) yr − (cid:19) (cid:16) v w
10 km s − (cid:17) ×× (cid:18) R (cid:63) R (cid:12) (cid:19) (cid:18) m (cid:63) M (cid:12) (cid:19) − . (17)Because of the estimated several thousands of redgiant–jet encounters according to Eq. (13), the cumu-lative mass loss from the red giant can be derived as∆ M ∼ n cross ∆ M , giving∆ MM (cid:12) ≈ − (cid:18) L j erg s − (cid:19) (cid:18) R (cid:63) R (cid:12) (cid:19) (cid:18) z .
01 pc (cid:19) − × (cid:18) θ . (cid:19) − (cid:18) m (cid:63) M (cid:12) (cid:19) − (cid:18) t jet . (cid:19) (cid:18) M • × M (cid:12) (cid:19) . (18)In Fig. 5, we plot ∆ M for L j = 10 and 10 erg s − ,and R (cid:63) = 50 and 100 R (cid:12) . Additionally, we plot ∆ M for the longer jet lifetime of t jet = 1 Myr and L j =10 erg s − and R (cid:63) = 100 R (cid:12) , which can be consid-ered as an upper limit of ∆ M for a red giant orbitingSgr A*. We find that ∆ M within the S cluster is compa-rable to the mass removal inferred from red giant–clumpcollision simulations by Kieffer & Bogdanovi´c (2016).In Fig. 5, we plot the upper and the lower limits of∆ M obtained by Kieffer & Bogdanovi´c (2016). Beyond z = 0 .
03 pc, ∆ M for the star–jet interaction is progres-sively smaller than 3 . × − M (cid:12) , which implies thatthe jet impact on the stellar evolution is the most pro-found for S cluster red giants. In this region, there alsolies the division between the warm and the cool col-liders as discussed in Subsection 2.1, with warm collid-ers present inside z c ∼ .
04 pc, which is also markedin Fig. 5 with a vertical dot-dashed line. Since warmcolliders are warmer and bigger, this further enhancesthe mass removal inside the S cluster. In addition, themass removal due to the jet interaction is of a com-parable order of magnitude as the mass loss expectedfrom cool winds during the time interval of the ac-tive jet ∆ M w ≈ ˙ m w t jet ∼ . − × − M (cid:12) when epletion of bright red giants − − − − z [ pc ] − − − − − − − ∆ M [ M (cid:12) ] maximum mass removal, ∆ M max1 , R = R ? minimum mass removal, ∆ M min1 , R = R stag mean mass removal, ∆ M Figure 4.
Mass removal during a single encounter of the red giant with the jet.
Left panel:
The colour-coded distancein parsecs from Sgr A* where R (cid:63) = R stag as a function of ˙ m w and R (cid:63) . The dashed white lines mark z stag equal to 0 .
004 pc,0 .
04 pc, and 0 . Right panel:
An exemplary mass removal range ∆ M min1 –∆ M max1 (green-shaded region) for R (cid:63) = 100 R (cid:12) , ˙ m w = 10 − M (cid:12) yr − , v w = 10 km s − , L j = 10 erg s − , and θ = 12 . ◦ . The dot-dashedvertical orange line marks z stag , see Eq. (16), where R (cid:63) = R stag . The red dashed line marks the mean mass removal ∆ M , seeEq. (17), ∆ M = ∆ M max1 ( z = z stag ) = ∆ M min1 ( z = z stag ). Figure 5.
Cumulative mass removal ∆ M due to the repeti-tive red giant–jet encounters as a function of the distancefrom Sgr A*. We fixed L j = 10 and 10 erg s − and R (cid:63) = 50 and 100 R (cid:12) . In addition, we plot ∆ M for L j =10 erg s − , R (cid:63) = 100 R (cid:12) , and a longer duration of thejet activity, t jet = 1 Myr. For comparison, we also showthe mass removal limits as inferred by Kieffer & Bogdanovi´c(2016) for the red giant–clump collisions and the mass rangeas expected from the cumulative red giant (RG) mass lossdue to stellar winds analyzed by Reimers (1987). The reddot-dashed line marks the division between warm and coolcolliders according to Eq. (12). ˙ m w ≈ − − − M (cid:12) yr − (Reimers 1987), as it is in-dicated by the shaded rectangle in Fig. 5. This impliesthat the jet–star interaction perturbs the stellar evolu-tion of passing red giants, in particular in the innermostparts of the nuclear stellar cluster. Note that, on one hand, ∆ M is supposed to be a lowerlimit since after the first passage through the jet, the gi-ant is expected to expand to an even larger radius beforethe next encounter, which increases the mass removalefficiency (Kieffer & Bogdanovi´c 2016). On the otherhand, resonant relaxation of stellar orbits as well as ajet precession may change the frequency of the jet-starinteractions (see Sections 4 and 6.1) and therefore n cross should be considered as an upper limit of the numberof encounters. Overall, ∆ M in Eq. (18) can be ap-plied as an approximation for the total mass removaldue to the giant-jet interactions. Hence, the truncationof stellar envelopes of late-type stars by the jet dur-ing active phases of Sgr A* appears to be efficient andcomplementary to other previously proposed processes,mainly tidal disruptions of giants and stellar collisionswith other stars and/or the accretion disc. MISSING RED GIANTS IN THENEAR-INFRARED DOMAINRed giants are post-main-sequence evolutionarystages of stars with initial mass 0 . M (cid:12) (cid:46) m (cid:63) (cid:46) M (cid:12) .These stars exhausted hydrogen supplies in their coresand the hydrogen fusion into helium continues in theshell. As a result, the mass of the helium core graduallyincreases and this is linked to the increase in the atmo-sphere radius as well as the luminosity. Stellar evolu-tionary models of red giants show that their atmosphereradius and the bolometric luminosity depend primarilyon the mass of the helium core m c as (Refsdal & Weigert0 Zajacek et al. L (cid:63) L (cid:12) ≈ . µ . µ + 10 . µ ,R (cid:63) R (cid:12) ≈ . × µ µ + 1 . µ , (19)where µ c ≡ m c /M (cid:12) . This also holds for red supergiantswith carbon-oxygen cores and burning hydrogen and he-lium in their shells (Paczy´nski 1970). In the red giantstage, the dominant energy source is the p-p processand hence the luminosity is mainly determined by thegrowth rate of the helium core ˙ m c L (cid:63) L (cid:12) (cid:39) . (cid:18) ˙ m c − M (cid:12) yr − (cid:19) . (20)Eqs. (19) and (20) imply that the bolometric lumi-nosity is not significantly affected by the jet-red giantinteraction, since only the tenuous shell is ablated bythe jet and the dense core is left untouched. Then theeffective temperature T of the ablated giant is T T = (cid:18) R R (cid:19) , (21)where T is the original effective temperature and R and R are the atmosphere radii before and after thetruncation, respectively. Here we implicitly assume thatthe red giant underwent n coll interactions with the jetduring the active phase given by Eq. (13), which even-tually leads to the decreased radius of R ≈ R stag ac-cording to Eq. (6). The luminosity in the infrared do-main between frequencies ν and ν can be expressedusing the Rayleigh-Jeans approximation as L IR (cid:46) / π/c ) R (cid:63) k B T (cid:63) ( ν − ν ) ∝ R (cid:63) T (cid:63) (see Alexander 2005,for a similar analysis), which using Eq. (21) leads to L L ∼ (cid:18) R R (cid:19) . (22)For instance, the ablation of a red giant atmospherefrom 120 to 30 R (cid:12) would result in the increase of ef-fective temperature by a factor of 2 and a decrease bya factor of 8 in the IR luminosity or ∼ .
26 mag. Theablation of the envelope from 120 to 4 R (cid:12) would resultin the decrease by as much as ∼ . Strictly speaking, for T (cid:63) = 5000 K, the condition k B T (cid:63) > hν applies for wavelengths longer than 2 . µ m. As an exemplary case, we set up a simplified tempo-ral evolution of a red giant using Eqs. (19) and (20).We perform this calculation to estimate the potentialdifference in near-infrared magnitudes and the colourchange for late-type stars before and after the active jetphase – it does not represent realistic stellar evolutiontracks, but can provide insight into the basic trends inthe near-infrared magnitude evolution and the effectivetemperature. We evolve the stellar luminosity and theradius for an increasing core mass µ c = µ c0 + ˙ µ c d t , where µ c0 = 0 .
104 and the time-step is d t = 10 yr. The over-all evolution from µ c0 to µ c = 0 .
55 takes ∼ . × yr,when neither the effect of stellar winds nor that of rota-tion is taken into account. The initial and the final coremasses were chosen according to the limiting values forlighter stars, m (cid:63) < M (cid:12) , in which case µ minc ∼ . µ maxc ∼ .
5. These are stars with degenerate heliumcores and hydrogen burning shells (Refsdal & Weigert1971). The lower core-mass value of 0.1 also approx-imately corresponds to the Sch¨onberg-Chandrasekharlimit. The total duration is comparable to the time thatstars of 1 M (cid:12) spend on the giant and the asymptoticgiant branches, which is of the order of 10 yr accordingto MacLeod et al. (2012).To assess the observational effects of the star–jetcollision in the near-infrared domain, we calculatethe effective temperature at each step using T (cid:63) = T (cid:12) ( L (cid:63) /L (cid:12) ) / ( R (cid:63) /R (cid:12) ) − / . Subsequently, we calcu-late the monochromatic flux density in K-band (2.2 µ m)and L’-band (3.8 µ m) using F ν = ( R (cid:63) /d GC ) πB ν ( T (cid:63) ),where B ν ( T (cid:63) ) is the spectral brightness given by thePlanck function at the given effective temperature. Thecorresponding magnitudes are calculated using m K = − . F K /
653 Jy) and m L (cid:48) = − . F K /
253 Jy),from which the color index follows as CI= m K − m L (cid:48) .For the analysis in this section as well as in Section 5,we calculate intrinsic stellar magnitudes m K and m L (cid:48) .The calculated magnitudes and colours can then be com-pared to extinction-corrected magnitudes and the de-rived surface-brightness profiles of the nuclear star clus-ter, i.e. those corrected for the foreground extinction.To compare our results to observed magnitudes and de-rived surface profiles that are just corrected for the dif-ferential extinction but not for the foreground extinction(Buchholz et al. 2009; Habibi et al. 2019; Sch¨odel et al.2020), it is necessary to increase the magnitudes usingthe corresponding mean extinction coefficients (see e.g.,Sch¨odel et al. 2010), in particular A K = 2 . ± .
12 magand A L (cid:48) = 1 . ± .
18 mag.The imprint of the ablation of the stellar atmosphereby a jet, whose kinetic luminosity is fixed to L j =2 . × erg s − , is modelled by assuming that the ra- epletion of bright red giants Table 1.
Parameters at the time of the jet-ablation and those of the final state of a red giant, which is evolved from the coremass of µ c = 0 .
104 to 0 .
55. The upper three lines contain parameters of the ablated red giants orbiting at distances 0.001, 0.01,and 0.1 pc (first column). The second column lists the time, at which the ablation occurred with respect to the initial state of µ c = 0 . R (cid:63) = R stag . The fourth column lists the effective temperatureat the time of truncation. The fifth column lists the final effective temperature at the final stage of their evolution (when µ c = 0 . CI = m K − m L , at the final state. The bottom line corresponds to thefinal state of a normal, unaffected evolution.Ablation distance [pc] Ablation time [yr] R abl (cid:63) [ R (cid:12) ] T abl (cid:63) [K] T fin (cid:63) [K] m abl K [mag] m fin K [mag] CI fin . × .
45 6205 68 759 19 . . − . . × .
45 4662 21 744 15 . . − . . × .
51 3526 6 876 10 . . − . .
21 (final radius) - 2 871 - 7 .
47 0 . Figure 6.
Near-infrared magnitude (K-band, 2 . µ m, dered-dened) and temperature (or color index that is color-coded)of a red giant after crossing the jet n coll times. We com-pare three temperature– K s -band magnitude curves affectedby the series of collisions with the jet at z = 0 . .
01, and0 . µ c = 0 .
104 to0 . M (cid:12) with the time-step of 10 years. At each time-stepwe calculate R (cid:63) and L (cid:63) using Eqs. (19). The overall evolu-tion takes ∼ × years. For comparison, we also showthe evolutionary tracks for the normal evolution (black solidline) and the evolution affected by the star–clump collisions(lines according to the legend for different clump surface den-sities listed in parentheses) as calculated by Amaro-Seoaneet al. (2020) (abbreviated as AS+20) using the CESAM code(Morel & Lebreton 2008). dius of an interacting red giant keeps evolving accord-ing to Eq. (19) when R (cid:63) < R stag at a given distance z from Sgr A*. After the stellar radius reaches the scaleof the stagnation radius at a given distance z , we set R (cid:63) = R stag for the rest of the evolution which can by jus-tified by the fact that the red giant propagates throughthe jet n coll -times and the envelope is removed afterrepetitive encounters. The expected number of encoun- ters is 6 × , 2 × , and 632 for z = 0 .
001 pc, 0 .
01 pc,and 0 . . .
01, and0 . R (cid:63) = R stag at the corresponding distance as well as the parametersfor the final state of ablated giants in Table 1. Thisis compared to an unaffected final state with the coremass of 0 . M (cid:12) ; see the bottom row of Table 1. Thebasic signature of the jet-star interaction is that the stargets progressively warmer (with a bluer, more negativecolor index) and fainter in the near-infrared K s -band incomparison with the normal evolution without any at-mosphere ablation. This trend is more apparent for redgiants that are closer to Sgr A* because of the smallerjet-star stagnation radius and hence a larger fraction ofthe stellar atmosphere that is removed.Although we do not calculate stellar evolutionarytracks, only basic trends in terms of near-infrared mag-nitude and effective temperature, our results are consis-tent with those of Amaro-Seoane et al. (2020) who calcu-lated evolutionary tracks specifically for late-type starsablated due to the red giant–accretion clump collisions.They show in their Fig. 2 that the collision affects thestellar evolution of a red giant in a way that after repet-itive encounters it follows a track along a nearly con-stant absolute bolometric magnitude towards higher ef-fective temperatures. The constant absolute bolometricmagnitude or bolometric luminosity in combination withan increasing effective temperature results in the dropin the near-infrared luminosity, since L IR /L bol ∝ T − (cid:63) .We used their evolutionary tracks calculated using the2 Zajacek et al.
CESAM code (Morel & Lebreton 2008) for estimating K s -band near-infrared magnitudes. These tracks are de-picted in Fig. 6 for the case of a normal evolution of astar with M (cid:63) = 1 . M (cid:12) and R (cid:63) = 60 R (cid:12) (black solidline) and different collision cases for clumps with sur-face densities in the range Σ = 2 × − g cm − (seethe legend). Qualitatively, the perturbed stellar evo-lutionary tracks follow the temperature trends that wecan also observe for giant–jet collisions: ablated giantsmove towards higher effective temperature. Also, theybecome fainter in the near-infrared domain in compari-son with an unperturbed evolution. The main differencein comparison with the analysis of Amaro-Seoane et al.(2020) is their trend towards larger magnitudes (starsbecome fainter), while we see a small gradual increasein brightness. This difference is due to our simplyingassumption of a constant radius after the series of col-lisions with the jet, while in reality the radius shouldevolve, especially after the jet ceases to be active. Since L IR ∝ R (cid:63) T (cid:63) , the near-infrared luminosity grows linearlywith increasing temperature for the fixed stellar radius.This motivates further exploration of the effect of star–jet collisions using a modified stellar evolutionary code.For asymptotic giant branch stars, an extreme transi-tion from a red, cool luminous giant to a hot and faintwhite dwarf is possible when it is completely strippedoff of its envelope. This was studied by King (2020)for tidal stripping close to the SMBH, but cannot beexcluded also for asymptotic giant-branch stars and jetcollisions for a case when the giant star is at millipar-sec separation from Sgr A* and less, in which case thestagnation radius is typically a fraction of the Solarradius. In fact, an active jet can enlarge the volumearound the SMBH where asymptotic giant-branch starsare turned into white dwarfs. Considering Eq. (6), wecan derive that in order for R stag to be of the order ofa white-dwarf radius R wd ∼ . R (cid:12) , the giant needs toorbit the SMBH at z ≈ .
15 mpc so that the jet with L j = 10 erg s − can truncate it down to the white-dwarf size. The stellar interior that is not affected bytidal forces is characterized by the Hill radius r Hill ≈ z (cid:18) m (cid:63) M • (cid:19) = 29 (cid:18) z .
15 mpc (cid:19) ×× (cid:18) m (cid:63) M (cid:12) (cid:19) (cid:18) M • × M (cid:12) (cid:19) − R (cid:12) , (23)from which we see that tidal forces alone will not trun-cate the giant down to its white-dwarf core since r Hill >R stag at z .In summary, the jet-star interaction could have af-fected the appearance of late-type giants in the central Figure 7.
Number of red giants crossing the jet per orbitalperiod (black solid line, see Eq. (26)). The average numberof red giant/jet interactions at z ≤ .
04 pc and 0.3 pc areplotted in green dot-dashed and blue-dashed lines, respec-tively. arcsecond by making them warmer or bluer in terms ofa colour and hence fainter in the near-infrared domain. FRACTION OF RED GIANTS INTERACTINGWITH THE JETWe estimate the number of late-type stars, i.e. starsthat form a cusp, that could have passed and interactedwith the jet during its estimated life-time of ∼ . − . . n RG ≈ n ( z/z ) − γ ,with n (cid:39)
52 pc − , z (cid:39) . γ (cid:39) .
43 (Gallego-Cano et al. 2018). The expected number of late-typestars within a certain distance z out is N (cid:63) ( < z out ) = (cid:90) z out n RG ( z )4 πz (cid:48) d z (cid:48) = 4 πn z γ z − γ out − γ (24)giving N (cid:63) ≈
610 and 25.8 inside 0.3 and 0.04 pc, respec-tively. The number of stars inside the jet at any timeis given by the jet covering factor f j in a spherical vol-ume V (cid:63) = (4 / πz . By considering a conical jet and acounter-jet with the total volume V j = 2 / πR z out , thecovering factor is f j = V j /V (cid:63) ∼ ( R j /z out ) and the num-ber of red giants inside the jet is N j ( < z out ) = f j N (cid:63) ( 2. Then the average num-ber of red giants that are simultaneously inside the jetis N j ≈ . . 62 inside 0.3 pc and 0.04 pc, respec-tively.To estimate the number of stars crossing the jet peran orbital timescale, we first calculate the jet-crossingrate per a unit of time. Since we focus on the region z (cid:46) . epletion of bright red giants r h ∼ σ (cid:63) ∼ v orb = (cid:112) GM • /z ; see e.g. ˇSubr & Haas (2014).With the jet cross-section S jet ≈ zR j ∼ z tan θ , thenumber of late-type stars entering both the jet and thecounter-jet per a unit of time is˙ N RG ≈ n RG σ (cid:63) S jet (cid:39) n z γ (cid:112) GM • tan θz − γ . (25)The number of red giants crossing the jet per orbitaltimescale is N RG = ˙ N RG P orb = 4 πn z γ tan θz − γ , (26)where the orbital period in the sphere of influence ofthe SMBH follows from the third Keplerian law, P orb =2 πz / / √ GM • . In Fig. 7 we plot N RG . The averagenumber of crossing giants per orbital period in the regionwith an outer radius z out is N RG = 4 π − γ n z γ tan θz − γ out . (27)In particular, N RG (cid:39) . N RG (cid:39) 82 when z out =0 . 04 pc (S cluster) and z out = 0 . N RG represents all late-type stars thatcross the jet sheath per orbital period on average. Thefraction of giants whose envelopes could have beenstripped off by the jet can be estimated by comparingthe radii of stars with the corresponding stagnation ra-dius at a certain distance from Sgr A*. The basic con-dition for the ablation is that R (cid:63) (cid:38) R stag at a given z from Sgr A*. In particular, for z = 0 . 04 pc and thejet luminosity of L j = 10 erg s − , the minimum stel-lar parameters for ablation are R (cid:63) = 27 R (cid:12) , µ c = 0 . L (cid:63) = 129 L (cid:12) , T (cid:63) = 3743 K, m abl = 11 . m abl denotes the upper magnitude limit, below whichstars are expected to be affected by the jet. Using theK-band luminosity function approximated by the powerlaw, d log N/ d m K = β with β (cid:39) . η = N abl /N tot × 100 = 10 β ( m abl − m max )+2 %, where m max is the limiting magnitude, which we set to 18 magaccording to Pfuhl et al. (2011). Then for z = 0 . 04 pcand L j = 10 erg s − we get η = 1 . z = 0 . L j = 10 erg s − , we obtainthe minimum parameters of ablated stars as follows, R (cid:63) = 338 R (cid:12) , µ c = 0 . L (cid:63) = 6081 L (cid:12) , T (cid:63) = 2775 K, m abl = 6 . 95 mag with η = 0 . L j to 10 erg s − , weget R (cid:63) = 2 . R (cid:12) , µ c = 0 . L (cid:63) = 3 . L (cid:12) , T (cid:63) = 4960 K, Figure 8. The coherence timescale T coh for different numberof stars in the S cluster according to the legend. The shadedarea stands for the expected lifetime of the jet during theprevious Seyfert-like activity of Sgr A*. m abl = 16 . η = 26 . 5% for z = 0 . 04 pc and R (cid:63) = 33 . R (cid:12) , µ c = 0 . L (cid:63) = 181 L (cid:12) , T (cid:63) = 3645 K, m abl = 11 . η = 0 . 95% for z = 0 . ∼ . 3% of thetotal observed sample and stars brighter than 12 magconstitute only 1 . z out = 0 . 04 pc (Habibi et al. 2019) as well as to the ∼ 100 missing late-type giants in the larger region with z out = 0 . t , for which P orb (cid:28) ∆ t (cid:28) T coh and thecoherence timescale T coh = P orb π √ N (cid:63) M • m (cid:63) = (cid:115) − γ πGn z γ M • m (cid:63) z γ (28)4 Zajacek et al. Table 2. Limiting minimal stellar radii, maximum apparent K-band magnitudes (dereddened), and the fraction of ablatedgiants for two distances from Sgr A* (0.04 pc and 0.5 pc) and two luminosities of its jet (10 erg s − and 10 erg s − ).Distance L j = 10 erg s − L j = 10 erg s − . 04 pc R (cid:63) = 27 R (cid:12) , m abl = 11 . η = 1 . R (cid:63) = 2 . R (cid:12) , m abl = 16 . η = 26 . . R (cid:63) = 338 R (cid:12) , m abl = 6 . η = 0 . R (cid:63) = 33 . R (cid:12) , m abl = 11 . η = 0 . is inversely proportional to the square root of the num-ber of enclosed stars, the angular momentum of a teststar changes linearly with time.The inclination of stellar orbits would change by ∼ π only when T coh ( z ) (cid:46) t j ∼ . − . z out ∼ . 04 pc) is 26 < N (cid:63) < 10 000,where the lower limit considers only late-type stars ac-cording to the analysis by Habibi et al. (2019) and theupper limit stands for all the stars including compactremnants. The upper limit is supposed to be closer tothe actual number of stellar objects since the number ofold neutron stars and stellar black holes in the centralarcsecond could be of that order of magnitude (Morris1993; Deegan & Nayakshin 2007; Zhu et al. 2018). Thetotal number of massive objects naturally affects the co-herence timescale by more than an order of magnitude.In Fig. 8 we plot T coh . We see that when N (cid:63) ∼ T coh is comparable to the lifetime of the jet in theinner parts of the S cluster. In summary, the coherentresonant relaxation makes the number of affected giantsbigger and the estimates per orbital timescale N RG canbe considered as a lower limit. Another more hypothet-ical effect that can enlarge the number of affected giantsis the jet precession (see Section 6.1).The vector resonant relaxation can affect the numberof encounters, n cross , see Eq. (13). In case T coh > t jet ,i.e. for a smaller number of enclosed objects ( N (cid:63) (cid:46) n cross is still mainly determined by t jet , see Eq. (13).However, then the mean number of interacting giants N RG is also not significantly enlarged. On the otherhand, if T coh (cid:46) t jet , then n cross is reduced approximatelyby a factor of 2 θ/π , which assumes that the angularmomentum vector shifts linearly with time during T coh .In that sense, the interaction timescale with the jet is t int ∼ T coh (2 θ/π ). Considering T coh ∼ t jet , the numberof crossings is n RRcross ∼ (cid:18) T coh . (cid:19) (cid:18) M • × M (cid:12) (cid:19) (cid:18) z . 01 pc (cid:19) − , (29)which is smaller by an order of magnitude in comparisonwith n cross . EFFECT OF JET-ABLATION ON SURFACEBRIGHTNESS PROFILE OF NSC To assess the observational signatures of the jet-ablation of late-type stars, we generate a mock sphericalcluster of stars. Their initial spatial distribution follows n RG = n ( z/z ) − γ with n = 52 pc − , z = 4 . γ ∼ . 43 (Gallego-Cano et al. 2018). This spatial profilesuggests that there are in total ∼ . M (cid:12) to 100 M (cid:12) following the Initial Mass Function(IMF) according to Kroupa (2001), i.e. ζ ( m (cid:63) ) = m − α(cid:63) , where α = 0 . , m (cid:63) < . M (cid:12) ,α = 1 . , . M (cid:12) < m (cid:63) < . M (cid:12) ,α = 2 . , m (cid:63) > . M (cid:12) . (30)The Chabrier/Kroupa IMF is a good approximation forthe observed mass distribution of the late-type NSCpopulation (Pfuhl et al. 2011).In the next step, we assigned the core mass to each starof the mock cluster. Here we fix the ratio between thecore mass and the stellar mass to µ c /m (cid:63) = 0 . 4, whichis in between the value inferred from the Sch¨onberg-Chandrasekhar limit and the final phases of the stellarevolution, where the white-dwarf core constitutes mostof the mass for the Solar-type stars. For more precisesimulations, core masses from the stellar evolution of theNSC should be adopted, however, here we are interestedin the first-order effects of the jet activity on the surfacebrightness distributions.To construct the surface brightness profiles of the late-type population after the active jet phase in differentmagnitude bins, we followed these steps:1. We calculated L (cid:63) ( µ c ) and R (cid:63) ( µ c ) using Eq. 19.2. If the jet was set active with a certain luminosity L j , we compared R (cid:63) and R stag for a given dis-tance z of the star. If R (cid:63) ≥ R stag , then we set R (cid:63) = R stag . In this case we also implicitly as- The Sch¨onberg-Chandrasekhar limit expresses the ratio betweenthe isothermal core mass and the stellar mass, m ic /m (cid:63) (cid:39) . µ env /µ ic ) ∼ . 1, where µ env and µ ic are mean molecularweights for the envelope and the isothermal core, respectively. epletion of bright red giants RA [arcsec] D E C [ a r c s e c ] stellar radius [ R ] m K [ m a g ] Figure 9. Initial properties of the Monte-Carlo generated mock NSC. Left panel: The projected surface density distributionof 4000 stars with the illustrated active jet with the half-opening angle of θ = 12 . ◦ . The gray streamers illustrate the Minispiralarms according to the Keplerian model of Zhao et al. (2009). Right panel: The K-band magnitude (dereddened)–stellar radiusrelation for our generated NSC. sumed that at a given distance, all of the stars, forwhich R (cid:63) ≥ R stag , are eventually ablated by thejet, hence the resonant relaxation was assumed tobe efficient and hence T coh < t jet .3. We estimated the effective temperature of a starusing T (cid:63) = T (cid:12) ( L (cid:63) /L (cid:12) ) / ( R (cid:63) /R (cid:12) ) − / .4. From the Planck function B ν ( T (cid:63) ) we calculatedthe monochromatic flux in the K s -band (2 . µ m) F ν ( R (cid:63) , T (cid:63) ) = ( R (cid:63) /d GC ) πB ν ( T (cid:63) ) and the corre-sponding apparent magnitude m K (dereddened).The initial relation between the K s -band magnitudeand the stellar radius is shown in Fig. 9 in the rightpanel. We calculate the projected stellar density us-ing the concentric annuli with the mean radius R andthe width of ∆ R , σ (cid:63) = N (cid:63) / (2 πR ∆ R ), where N (cid:63) is anumber of stars in an annulus. We estimate the uncer-tainty of the stellar number counts as σ N ≈ √ N (cid:63) . Subse-quently, we construct the surface stellar profiles in two-magnitude bins starting at m K = 18 mag up to m K = 10mag, i.e. in total four bins; see Fig. 10. In the top leftpanel of Fig. 10, we plot the nominal projected distribu-tion without considering the effect of jet. The brightnessprofile for all four magnitude bins can be approximatedby simple power-law functions, N ( R ) = N ( R/R ) − Γ ,whose slopes are listed in Table 3. Hence, the initial clus-ter distribution is cusp-like. In the top right panel, weshow the case with an active jet with the luminosity of L j = 10 erg s − . We see that the profile for the bright-est stars in the 10-12 mag bin becomes flat in the innerarcsecond and can be described as a broken power-lawfunction, N ( R ) = N ( R/R br ) − Γ [1+( R/R br ) ∆ ] (Γ − Γ ) / ∆ ,where R br is a break radius, Γ is a slope of the inner part,Γ marks the slope of an outer part, and ∆ denotes thesharpness of transition. The larger surface brightnessvalues for this magnitude bin may be interpreted by anextra input of ablated giants with the initial magnitudes m K < 10 mag that after the ablation fall into bins witha larger magnitude. Finally, we increase the jet lumi-nosity to L j = 10 erg s − , which makes the flatteningof the brightest giants even more profound. The starsin the 12-14 mag bin also exhibit a flatter profile insidethe inner arcsecond for this case, which shows the sig-nificance of the jet luminosity in affecting the observedsurface profile of the NSC. We list the power-law slopesfor both a simple and a broken power-law function andthe break radii, where available, for all the magnitudebins and the three jet-activity cases in Table 3.Fig. 10 demonstrates a potential signature of the jetactivity on the surface profile of the NSC. It is impor-tant to study differential profiles, i.e. the distribution indifferent magnitude bins, since the lower-luminosity jetstarts affecting the profile of bright stars (smaller mag-nitudes), while with an increasing jet luminosity, thefainter stars become affected as well, starting at smallerprojected radii ( < (cid:48)(cid:48) ). Our Monte-Carlo simulationsuggests that the active jet phase with L j (cid:46) erg s − Zajacek et al. Projected radius [arcsec] N / a r c s e c No jet Projected radius [arcsec] N / a r c s e c Jet with L j = 10 erg s Projected radius [arcsec] N / a r c s e c Jet with L j = 10 erg s Figure 10. Potential effect of the jet activity on the surface distribution of the initially cuspy late-type NSC. The calculationsassume that the coherent resonant relaxation timescale is comparable or shorter than the jet lifetime ( ∼ . Top left panel: The projected profile of an initial cuspof late-type stars with the surface slope of Γ ∼ . − . Top right panel: Amodified projected profile for the jet luminosity of 10 erg s − . The 10-12 mag surface profile flattens inside the inner arcsecond,while the fainter stars (12-18 mag) keep a cusp-like profile. Bottom panel: A modified surface profile for the jet luminosityof L j = 10 erg s − . The profile of the brightest stars (10-12 mag) flattens even more and decreases inside the inner arcsecond.The stars with 12-14 mag exhibit a flat profile as well in the inner arcsecond. The stars in the 14-16 mag and 16-18 mag binskeep the cuspy profile. For all three panels, the solid lines represent the single and the broken power-law function fits to thesurface stellar distribution in four magnitude bins. The slopes and the break radii are listed in Table 3. likely affected the late-type stars with m K ≤ 14 magthat exhibit the flat profile inside the inner arcsecond.The fainter stars of m K > 14 mag can still keep a cusp-like profile after the jet ceased its enhanced activity.For better quantitative comparisons with observa-tions, it is necessary to include the stars of differentages and hence different core masses. This is rathercomplex as there were recurrent star-formation episodesin the NSC, with 80% of the stellar mass being formed5 Gyr ago, the minimum in the star-formation rateclose to 1 Gyr, and the renewed star-formation in thelast 100-200 million years, although with the ten-timeslower star-formation rate than at earlier episodes (Pfuhl et al. 2011). These findings were confirmed by Sch¨odelet al. (2020), who estimate that 80% of stars formed 10Gyr ago or earlier, then about 15% formed 3 Gyr ago,and the remaining fraction in the last 100 Myr. Fur-thermore, the dynamical effects such as the mass seg-regation and the relaxation processes could also haveplayed a role in shaping the final observed profile of theNSC, and in addition we might expect other bright-giant depletion processes (Alexander 2005). Despitethese difficulties in comparing theoretical and observedprofiles, the basic trend shown in Fig. 10, in particularfor L j = 10 erg s − (bottom panel), is consistent withthe observational findings of Sch¨odel et al. (2020), who epletion of bright red giants m K = 14 . − 14 mag bin (including foreground field ex-tinction), which shows a flat/decreasing profile in theiranalysis. In our panels in Fig. 10, this corresponds tothe dereddened bins 10-12 and 12-14 mag, whose profilesbecome affected for L j = 10 erg s − starting from theprojected radii below one arcsecond. However, Sch¨odelet al. (2020) also note that precise surface profiles forlate-type stars are difficult to construct due to the con-tamination at all magnitude bins by an unrelaxed pop-ulation of young stars. Habibi et al. (2019) report acusp-like profile for late-type stars of m K < 17 mag(including foreground extinction), which approximatelycorresponds to our bin of 14-16 mag (yellow points) thatmaintains the cusp-like profile even for the largest jetluminosity (bottom panel). In conclusion, the expectedtrend of preferential depletion of bright late-type starsby the jet is confirmed. DISCUSSIONWe investigated the effects of a jet during an activephase of Sgr A* in the last million years on the appear-ance of late-type giant stars with atmosphere radii morethan 30 R (cid:12) . We found that especially in the innermostarcsecond of the Galactic center (the S-cluster), the up-per layers of the stellar envelope could be removed bythe jet ram pressure. Hence, the jet-red giant interac-tions during the active phase of Sgr A* could have con-tributed to the depletion of bright late-type stars. Inother words, the atmosphere ablation by the jet wouldalter the red giant appearance in a way that would makethem look bluer and fainter in the near-infrared bands(mainly K’ and L bands), in which stars in the Galacticcenter region are generally monitored. In the following,we outline several additional effects that could be asso-ciated with the jet/RG interaction.6.1. Enlarging the number of affected stars by the jetprecession Jet precession is a phenomenon that accompanies thelaunching of jets during the evolution of galaxies andstellar binaries. It is caused by perturbations due tothe misalignment of the accretion flow and the blackhole spin, so-called Lense-Thirring precession, or by asecondary black hole. The jet precession was proposedto explain a long-term flux variability in radio galaxies,e.g. OJ 287 (Britzen et al. 2018), 3C84 (Britzen et al.2019a), 3C279 (Abraham & Carrara 1998), the neutrinoemission from TXS 0506+056 (Britzen et al. 2019b), aswell as in X-ray binaries (Monceau-Baroux et al. 2015;Miller-Jones et al. 2019).For the Galactic center, the Lense-Thirring precessionof the hot thick accretion flow was analyzed by Dex- ter & Fragile (2013) in relation to the near-infrared andmm variability of Sgr A*. This effect would also trans-late to the precession of the jet under the assumptionit is coupled to the disc via the launching mechanism(Blandford–Payne mechanism; see Blandford & Payne1982). The jet precession is also suggested by wide UVionization cones with the opening angle of 60 ◦ (Bland-Hawthorn et al. 2019), which is larger by a factor of afew expected for the jet opening angle of ∼ ◦ (Li et al.2013).We estimate the factor by which the volume of theaffected red giants is enlarged. We adopt the jet preces-sion half-opening angle of Ω p ≈ ◦ based on the scale ofUV ionization cones (Bland-Hawthorn et al. 2019). Dur-ing the precession motion, the jet circumscribes a conewith the radius R p = z sin Ω p . The factor by which thevolume at given distance z enlarges is given by f prec = 2 πR p R j = π sin Ω p tan θ ∼ . , (31)when θ = 12 . ◦ and Ω p = 30 ◦ . The number of affectedlate-type stars would then increase by the same factorto N j ≈ 105 and 4 . . . 04 pc, respectively,which is comparable to the number of missing brightred giants at these scales – 100 at z < . z < . 04 pc (Habibi et al.2019). The factor derived in Eq. (31) should be treatedas an upper limit on the volume enlargement since itassumes that the precession period is comparable to orless than the jet lifetime, but it could also be longer.On the other hand, larger volume means that the starsare affected correspondingly less (over a shorter periodof time) by the jet action, which is spread in differentdirections with the precession duty cycle.6.2. High-energy particle acceleration and jetmass-loading due to jet/star interactions The detection of the Fermi bubbles in the GeV domainindicates the presence of relativistic particles emittinggamma-rays. Guo & Mathews (2012) considered thatparticles can be accelerated in the jet launching regionor in the jet termination shocks. Note however thatthe coexistence of the jet with the dense NSC in theGalactic center makes jet/star interactions very likely.The NSC is composed of both early- and late-type stars.In the former case, the powerful wind of OB and Wolf-Rayet stars makes the stagnation distance R stag >> R (cid:63) and therefore a double bow-shock structure is formed(Araudo et al. 2013). In the latter case, the slow windsof low-mass stars cannot create a big bow shock aroundthe stars, but a shock in the jet will be formed anyway.In both cases, particles can be accelerated through the8 Zajacek et al. Table 3. Summary of the power-law slopes (for both single and broken if relevant) for the four magnitude bins (two-magnitudeintervals starting at 18 mag up 10 mag in the near-infrared K s -band; magnitudes are dereddened) and three jet-activity cases(no jet, L j = 10 erg s − , L j = 10 erg s − ).Magnitude bin No jet Jet L j = 10 erg s − Jet L j = 10 erg s − . . . . . . . . . 2, Γ = 0 . R br = 1 (cid:48)(cid:48) . − . 08, Γ = 1 . R br = 0 . (cid:48)(cid:48) broken: Γ = 0 . 04, Γ = 2 . R br = 6 . (cid:48)(cid:48) Fermi I acceleration mechanism in the bow shocks (Bell1978). Even when the interaction with massive stars isa better scenario to accelerate particles up to highestenergies (given that the size of the acceleration region is ∼ R stag ), acceleration of particles up to GeV-energies isnot difficult to achieve.Barkov et al. (2010, 2012b) consider the interaction ofAGN jets with red giant stars to explain the TeV emis-sion in radiogalaxies and blazars. The mass strippedfrom the red giant forms clouds moving in the jet direc-tion, see also our Fig. 1. Particles are accelerated in thebow shock around the cloud formed by the pressure ex-erted by the jet from below. Another shock propagatesinto the cloud and as a consequence, it will heat up andexpand. After a certain time, there will be a populationof relativistic particles in the jet as well as a chemicalenrichment by stellar envelopes (Perucho et al. 2017).These effects were previously not taken into account inthe jet models of the Fermi bubbles.6.3. Chemically peculiar stars as remnant cores ofablated red giants The past ablation of red giants by the jet would con-tribute to the apparent lack of late-type stars in thecentral region of the Galactic center. Another potentialimprint of the past jet-red giant interaction would be thepresence of chemically peculiar, high metallicity stars inthe NSC. This can be predicted from the fact that as thejet ram pressure removes upper hydrogen- and helium-rich parts of the stellar atmosphere, the lower metal-richparts as well as the denser core are exposed. In fact, twolate-type stars at ∼ . A collimated jet or a broad-angle disc wind? In the current analysis, we took into account mainlyhighly collimated nuclear outflow – jet – with the small half-opening angle close to ∼ ◦ . The analysis of theUV ionization cones by Bland-Hawthorn et al. (2019) in-dicates a half-opening angle of ∼ ◦ , which could be asignature of the jet precession as we discussed in Sec. 6.1or alternatively disc winds with a larger opening angle.In case the jet would be absent and the disc wind wouldbe present with the larger half opening angle, the ex-pected stagnation radius would be proportionally largersince R stag ∝ tan θ . Assuming the same kinetic luminos-ity L j = 10 erg s − and the outflow velocity close to c (ultrafast outflows), the ratio of the stagnation radii is R windstag /R jetstag = tan θ wind / tan θ jet ≈ . 6, which yields for R windstag ∼ R (cid:12) using Eq. (6). The ablation effect wouldstill take place but only for the largest red giants with R (cid:63) (cid:38) R (cid:12) at the outer radius of the S cluster. Thestagnation radius of 30 R (cid:12) would be reached at the dis-tance of z ∼ . 017 pc for the same stellar parameters aswe assumed in Eq. (6) and a larger outflow half-openingangle of 30 ◦ .6.5. Recurrent Seyfert-like activity and TDEs The X-ray/ γ -ray Fermi bubbles were created duringthe increased Seyfert-like activity about 3 . ± ∼ . − . ∼ 400 years ago, which is in-ferred from the X-ray reflections or propagating bright- epletion of bright red giants ∼ –10 years depending onthe stellar type (Syer & Ulmer 1999; Alexander 2005;Komossa 2015). For completeness, we note that the jetis not always formed during the TDE (Komossa 2015).However, for a few months to years, the TDE can trig-ger a jet activity similar to the Seyfert sources (Hills1975). Due to the short duration of the TDE betweenseveral months to years given by the steep dependencyof the luminosity on time, L ∝ t − / , the average num-ber of interacting stars would be given by the estimatescalculated in Section 4. In general, the number of ab-lated red giants in the S cluster would be of the order ofunity. The jet precession driven by the Lense-Thirringeffect (Lodato & Pringle 2006) could enlarge this num-ber depending on the precession period and Ω p (see Sec-tion 6.1).6.6. Comparison with other mechanisms – the regionof efficiency The jet-induced alternation of the population of late-type stars is not necessarily an alternative to other pro-posed mechanism, listed in the introductory Section 1.In reality, it could have co-existed simultaneously dur-ing the past few million years with other previously pro-posed mechanisms, in particular the tidal disruption ofred-giant envelopes as well as direct star-disc interac-tions. This follows from the fact that these mechanismshave different length-scales of their efficiency, as we fur-ther outline in the paragraphs below.First, the tidal disruption of red-giant envelopes takesplace on the smallest scales – less than one millipar-sec from Sgr A* – as given by the tidal radius, r t ≈ R (cid:63) (2 M • /m (cid:63) ) / , r t (cid:46) (cid:18) R (cid:63) R (cid:12) (cid:19) (cid:18) m (cid:63) M (cid:12) (cid:19) − (cid:18) M • × M (cid:12) (cid:19) R (cid:12) = 0 . 14 mpc = 354 R Schw . (32)The resonant relaxation process (discussed in Section 4),in particular the scalar resonant relaxation, can causean increase in orbital eccentricities and thus effectivelyinduce the tidal disruption of giants as their orbital dis-tance decreases below r t close to the pericenter of theirorbits. This could have contributed to the dearth of brighter red giants in the inner ∼ . r t but stillsmaller than the total extent of 0 . z (cid:46) . 04 pc, according tothe cumulative mass removal distance profile in Fig. 5.Another way to constrain the region of the maximum ef-ficiency is to use the relation in Eq. 6 for the stagnationradius, from which we derive the distance z . It followsthat for the maximum jet luminosity of L j = 10 erg s − and the stagnation radius range of R stag = 4 − R (cid:12) , weobtain the distance range z jet = 0 . − . 44 pc. Hence,within the S cluster, z (cid:46) . 04 pc, R stag would be effec-tively below 4 R (cid:12) , which corresponds to K ∼ 16 magstars for a typical age of 5 Gyr. Therefore, the jet lu-minosities close to the Eddington limit for Sgr A* arerequired to truncate the atmospheres of late-type starsof K (cid:46) 16 mag. For the moderate jet luminosity of L j = 10 erg s − , the distance range decreases by anorder of magnitude to z j = 0 . − . 04 pc, hence onlythe brighter giants with R (cid:63) = 30 R (cid:12) ( K ∼ . K ∼ 16 mag wouldremain largely unaffected by the jet.Finally, the star–clumpy disc collisions are the mostefficient for the disc surface densities Σ > g cm − typical of self-gravitating clumps (Kieffer & Bogdanovi´c2016; Amaro-Seoane et al. 2020), which can form atlarger distance scales where the condition for gravita-tional instability is met as given by the Toomre instabil-ity criterion (Milosavljevi´c & Loeb 2004). In the Galac-tic center, this region likely corresponds to 0 . (cid:46) z (cid:46) . z (cid:46) . ∼ . . Observational signatures and falsifiability The jet-ablation mechanism likely operated in the cen-tral S cluster region ( < . 04 pc) for stars of large atmo-sphere radii of 10 R (cid:12) , and especially for supergiants of ∼ R (cid:12) even at larger distances up to ∼ . Zajacek et al. signatures of the jet-ablation on the pre-existing cuspof late-type stars. Some of them have more possibleinterpretations due to other mechanisms operating si-multaneously in the complex nuclear star cluster aroundSgr A*. The signatures proposed here can serve as aguideline towards confirming the jet activity and in par-ticular the jet-star interaction in the central parsec. Onthe other hand, if other explanations become more likely,these can also serve as suitable falsifiability criteria forthe jet-ablation theory. The signatures can be outlinedas follows:(i) Flattening of the density distribution for brighterlate-type stars. This is a classical signature ofthe preferential bright late-type star depletion,which has more interpretations due to mecha-nisms, which likely operated on different scales;see Subsection 6.6. Therefore, this signatureshould be treated with caution. However, we haveshown in Section 5 that the jet active for a suf-ficiently long time can have an impact on thesurface-brightness profile of the Nuclear Star Clus-ter when it reaches the kinetic luminosity at least10 erg s − ; see also Section 5 and Fig. 10. In par-ticular, brighter giants with m K < 14 mag couldexhibit a flat profile due to the jet activity in-side the inner arcsecond ( z (cid:46) . 04 pc). Such atrend has also been recently reported by the high-sensitivity photometric analysis of Sch¨odel et al.(2020).(ii) Detection of high metallicity stars. The jet-ablation of red giant and supergiant shells couldreveal metal-rich deeper layers. A jet-ablationmechanism can be considered as one of the expla-nations for the occurrence of stars with anomalousmetal concentrations in their atmospheres, as wasfound by Do et al. (2018), see also Subsection 6.3.(iii) Cluster of remnant white dwarfs at millipasecscales. In relation to point (ii), an extreme case ofjet-ablation could lead to the exposure of degener-ate cores for asymptotic giant-branch (AGB) stars.This is analogous to the ablation by tidal stripping(King 2020), however, the jet-ablation has a largerlength-scale for Sgr A*. As we derived in Sec-tion 3, the AGB stars could be jet-ablated downto the white-dwarf cores for z < . − . 15 mpcfor L j = 10 − erg s − . The tidal strippingto the size of 10 − R (cid:12) is only possible essentiallybelow the event horizon. There has not been adirect observation of white dwarfs at such smalldistances from Sgr A*, however, the hard X-ray flux peaking at Sgr A* was hypothesized to origi-nate in the cluster of accreting white dwarfs (Perezet al. 2015).(iv) Cusp of remnant blue OB stars. As we have shownin Section 3, the late-type stars could be turned toblue stars of spectral type OB by the jet-ablationmechanism. In Table 1, we show that the effectivetemperature could be of a few × K, and withthe stagnation radius of R stag = 4 . R (cid:12) , the K-band magnitude was estimated to reach m K ∼ m K ∼ . ∼ . ∼ . epletion of bright red giants γ -ray bubbles (Su et al.2010; Ackermann et al. 2014). Recently, the anal-ysis of the tilted, partially ionized disk in the innerGalaktic latitudes has shown that its optical lineratios are characteristic of low-ionization nuclearemission regions (LINERs; Krishnarao et al. 2020).The bipolar ionization structure is energeticallyin favor of the Seyfer-like jet activity rather thanthe star-formation event (Bland-Hawthorn et al.2019).In summary, the jet-activity signs listed in points (i)–(vii) indicated the past enhanced activity of the jetand its interaction with the surrounding circumnuclearmedium, including the nuclear star cluster. Althougheach of the above-mentioned points can have alternativeexplanations, the absence of all of these signatures wouldsuggest that the jet did not operate in the past and ourhypotheses would then be strongly disfavored. Futuredetailed observations by the Extremely Large Telescope(ELT) in combination with detailed numerical simula-tions of the jet-star interactions close to Sgr A* willhelp to reveal the signatures of the current and the pastjet–star interactions. SUMMARY AND CONCLUSIONSWe presented a novel scenario to explain the lack ofbright red giants in the inner regions of the Galactic cen-ter in the sphere of influence of the currently quiescent,but previously active radio source Sgr A*. Taking thisincreased activity into account, we focused on the effectof the jet on late-type stars at (cid:46) . (cid:63) , we consid-ered the interaction of red giants with a jet of a typical active Seyfert-like nucleus with the expected kinetic lu-minosity L j = 10 − erg s − . Given that red giantshave a very slow wind, the jet can significantly ablatethe stellar envelope down to at least ∼ R (cid:12) withinthe S cluster ( z (cid:46) . 04 pc) after repetitive encounters.Specifically, at z = 0 . 02 pc, the stagnation radius is 4 ≤ R stag /R (cid:12) ≤ 30 for 2 . × ≤ L j / erg s − ≤ . × .Hence, the higher luminosity end that corresponds tothe less frequent events that formed the Fermi bubblescan ablate the stellar atmospheres of late-type giantsby a factor of ∼ . M ≈ × − M (cid:12) ≈ M Earth for red giants with radii R (cid:63) > R (cid:12) at distances smaller than 0 . 01 pc for asingle encounter. After at least thousand of red giant–jet encounters, we expect the cumulative mass loss of atleast ∆ M ≈ − M (cid:12) at the orbital distance of 0 . 01 pc.This is comparable to the values inferred from red giant–accretion clump simulations. The proposed mechanismcan thus help to explain the presence of late-type starswith the maximum atmosphere radius of ∼ R (cid:12) withinthe S cluster as inferred from the near-infrared observa-tions.The reduction in the mass and radius of the red giantatmosphere after repetitive jet-star crossings will pro-duce an estimated decrease in the near-infrared K-bandmagnitude by 1 . 9, 5 . 3, and 8 . . 1, 0 . 01, and 0 . 001 pc fromSgr A*, respectively. Simultaneously, the color indexwould decrease to negative values, i.e., the stars shouldappear bluer with a higher effective temperature. Themean expected number of red giant-jet crossings perorbital period is 3 . . 04 pc, and 82 . . erg s − , ∼ . 5% of currently detectable late-typestars located at z = 0 . 04 pc (S cluster) with radii largerthan 2 . R (cid:12) and K-band magnitudes smaller than ∼ − erg s − show that profiles of mainlybrighter late-type stars with m K < 14 mag (dered-dened, < 16 mag with the foreground extinction in-cluded) are flattened by the jet inside the inner arcsec-2 Zajacek et al. ond ( (cid:46) . 04 pc). Fainter stars keep the initially assumedcusp-like projected profile.In summary, the interaction of red giants with the jetof Sgr A* during its enhanced activity could contributeto the observed lack of bright red giants and hence affecttheir surface-brightness profile in the central parts of thenuclear star cluster. More likely, this mechanism oper-ated in parallel with other previously proposed mecha-nisms, such as the star–disc interactions, star–star col-lisions, and tidal disruption events that have differentspatial scales of efficiency. Detailed numerical computa-tions of red giant–jet interactions in combination with amodified stellar evolution will help to verify our analyt-ical estimates. ACKNOWLEDGMENTSWe thank the referee for constructive comments thathelped us to improve our manuscript. MZ, BC and VKacknowledge the continued support by the National Sci-ence Center, Poland, grant No. 2017/26/A/ST9/00756(Maestro 9), and the Czech-Polish mobility program(MSMT 8J20PL037). AA and VK acknowledge theCzech Science Foundation under the grant GACR 20-19854S titled “Particle Acceleration Studies in As-trophysical Jets”, and the European Space AgencyPRODEX project eXTP in the Czech Republic. Thiswork was carried out partly also within the Collabo-rative Research Center 956, sub-project [A02], fundedby the Deutsche Forschungsgemeinschaft (DFG) projectID184018867. The work on this project was partiallycarried out during the short-term stay of MZ within thePolish-Czech bilateral exchange program supported byNAWA under the agreement PPN/BCZ/2019/1/00069.MZ also acknowledges the NAWA financial support un-der the agreement PPN/WYM/2019/1/00064 to per-form a three-month exchange stay at the AstronomicalInstitute of the Czech Academy of Sciences in Prague.REFERENCES