Deformation of Galactic Centre Stellar Cusp due to growing Gas Disc

Karamveer Kaur & Prof. S.SridharRaman Research Institute KK & SS - arXiv:1709.04263

Nuclear Star Clusters(NSCs)

* Densest of known stellar systems shrouding massive black holes (MBHs) at the centres of most of galaxies

* Massive ~ 105 - 107 Msun and compact ~ 5 pc in size * Multiple populations of stars – varied ages

* Various structural components – Cuspy old spheroidal component; Discy, ring – like features composed of young stars

* MW NSC – Resolved due to proximity

Moving to MW - NSC ...

Milky Way NSC - within 1 pc

Massive BH ~ 4 X 106 Msun

Radius of influence ~ 2 pc

Cusp of old stars

Gallego-Cano et al,Schodel et al 2017

Cusp of old stars

Gallego-Cano et al,Schodel et al 2017

* Mass enclosed within 1 pc ~ 106 Msun

* Single power law density profile within ~ 3 pc with index ~ 1.23

Young stars

Young stars

* ~ 200 young WR & O type stars within 0.13 - 0.5 pc

* Compact discy profile + randomly oriented planes

* Reminiscent of stellar disc (undergone dynamical evolution)

Yelda et al 2014

Subr et al 2009

Massive accretion disc

Levin & Beloborodov 2003

Massive accretion disc

* Thin disc with steep radial surface density profile (Power law index ~ 1.5)

* Disc mass Md within 1 pc ~ 105 Msun.

Christopher et al 2005Etxaluze et al 2011

Levin & Beloborodov 2003

How does the gravity of massive accretion disc

effects the Cusp morphology ?

Flattenned Cusp

Schodel et al 2014 - larger scales ... Feldmeier et al 2017

Stellar Cusp Model ρc (r )∝r

−γρc(r)∝r

−γ

φ c(r)∝r2−γ

F0∝(−E)2 γ+n−3

2 Ln

* Spherical power law density: Mass enclosed within 1 pc

* The potential

* Distribution Function : Anisotropic Parameter β = -n/2 – Tangentially Biased system

γ=1.25

n=0.5

Gallego-Cano et al,Schodel et al 2017

Feldmeier-Krause et al 2017

M c=106 M sun

Gas Disc Model

ρd (r ,θ)∝r−2.5[δ(θ−π

2)+ 9

16(1−|cosθ|)2]

* Density profile: 73 % mass Planer component 27% mass in Extended component Mass within 1 pc slowly growing

* The potential:

M d

Secular Dynamics Region of Influence:

T kep∼2×104 yr

Sridhar & Touma 2016

a∼0.5 pc

Secular Dynamics Region of Influence

T sec=M

M BHT kep∼2×10

5 yr

Coordinates

Coordinates

(I=√G M BH a ,w)

(L=I √1−e2 , g)(Lz=Lcos i , h)

Orbit averaged Potentials* Spherically Symmetric Distributions (Cusp Here) Retrograde planer precession of apses Eccentricity of rings remain same

φ c(r )→Φc(I , L)

Orbit averaged Potentials* Mass Distribution in a disc Retrograde precession of nodes Eccentricity “e” of rings evolves as it precesses

φ d (r ,θ)→Φd (I , L , Lz , g)

Nodal Regression

Linear Evolution

F (I , L , Lz , g , τ)=F0(I , L)+F1(I , L , Lz , g , τ)

H (I , L , Lz , g , τ)=Φc (I , L)+Φd (I , L , Lz , g , τ)Self- gravity of F1 neglected

Adiabatic growth of disc

∂F1∂ τ +Ωc

∂F1∂ g

=∂F0∂ L

∂Φd∂ g

Linearised Collisionless Boltzmann Equation: Linearised wrt deformation & disc potential

F1=1Ωc

∂F 0∂ L

Φd(g)

Linear Deformation F1

F1∝a−1 Greater contribution from

Small Size Orbits

Linear Deformation F1

F1∝a−1

(1−e2)n−2

2 (...e2+...e4+...e6)

High e - Orbits

Linear Deformation F1

F1∝a−1

(1−e2)n−2

2 (...e2+...e4+...e6)

(... sin i+... sin2 i)

High inclination Orbits

Linear Deformation F1

F1∝a−1

(1−e2)n−2

2 (...e2+...e4+...e6)

(... sin i+... sin2 i)

cos(2 g)

Linear Deformation F1

F1∝a−1

(1−e2)n−2

2 (...e2+...e4+...e6)

(... sin i+... sin2 i)

cos(2 g)

Sign Determining Term

Apse Close to disc plane(g = 0O) ---> Overdensity

Apse farther from disc plane(g = 90O)---> Underdensity

Orbital Dynamics again..Shaping up Deformation

Slower Apse Precession near g = 0O,180O implies Overdensity

Lz/I = 0.1 Lz/I = 0.5

a = 0.5 pc

Density Deformation

ρ1ρ1(10

−2 M c/rc3) ρ=ρc+ρ1(M c /rc

3)

Flattened Density Profile1/2 - Opening angle for Deformation ~ 33o

Projected Density

LOS 45o LOS 90o

Radially decreasing Flattenning

Flattenning : Axis Ratio

Discussion1. The quantitative degree of flatness – non-linear theory of adiabatic capture into reesonance (Sridhar & Touma 1996)– the inclusion of effect of librating orbits.

2. It’s of interest to see the evolution of deformed cusp under self-gravity. N-body simulations will help.

3. Considering perturbations by warped accretion disc will lead to triaxial deformation of cusp.

4. Will be interesting to see whether NSC is flattened in inner parsecs in future observations.

5. Generic to the NSCs of other galaxies - discy component of young stars.

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