Nuclear Structures and Gas Accretion toSupermassive Black Holes in Disk Galaxies
Nov. 16, 2017 @ Ishigaki Island, Japan

Woong-Tae KimSeoul National University
Woo-Young Seo (SNU), Sang-Hyuk Moon (SNU)
Juntai Shen (SHAO), Zhi Li (SHAO), Bruce Elmegreen (IBM)Outline
I. Formation of Nuclear Rings
II. Star Formation in Nuclear Rings
III. 3D Self‐consistent models for the formation of a bar
and nuclear ring
IV. Nuclear Spirals and Gas Accretion in Weakly BarredGalaxies

NGC 1097

nuclear ring

dust lanes
nuclear spirals

central BH

ring + circumnuclear disk

Red: HCN
Yellow: HCO+Onish+14• The observed rotation curve of the central region of NGC 1097 is consistent
with MBH=1.4 × 108 M⊙.
Hsieh+11

Mnuc=1.6×108M⊙
Mring=1.4×109M⊙

CO(J=2‐1) overlaid on Paα

Total SFR ~ 5M⊙ yr−1
(Hummel+87)

• Some galaxies have relatively straight dust lanes, whileothers have curved ones.

NGC 6951: Δα=9oComeron+09

NGC 4321: Δα=73o• Some galaxies have a relatively large nuclear ring, whileothers have smaller one.

NGC 1343: 1.2kpc × 0.9kpc
NGC 1300: 0.3kpc × 0.2kpc
Mazzuca+09

• Some galaxies have tightly wound nuclear spirals, whileothers have loosely wound ones.

Peeples & Martini 2006

I. Formation of Nuclear Rings• Regarding nuclear rings, it has been widely accepted that rings
form via resonant interactions of the gas with the bar potential.
– This notion was driven by the fact that observed nuclear
rings are located near the inner Lindblad resonances (e.g.,Combes & Gerin 85; Knapen+95; Comeron+10).

Lindblad Resonance
Circularslightly orbit
circular orbit = circular orbit + epicycle orbit
Lindblad resonance occurs
at the radius where

Rings due to ILR?
• Yet, there is no convincing theoretical argument for the ringformation due to the ILR.
– Bar torque is very week near the ILRs.
– Resonance is a secular process, occurring over a very long timescale.
– Resonance tends to disperse the material, rather than gathering
it (e.g., gaps in planetary rings and the asteroid belt).

Bar Torque• The bar torque appears to be a primary parameter that controls theproperties of bar substructures.
• Ferrers barr(Qb)• Bar strength parameter Qb

where FT = tangential force due to a bar
FR = radial force due to mass distribution (galaxy rotation)(e.g., Combes & Sanders 1981; Laurikainen & Salo 2002; Block et al. 2004)

Bar Strength of Model Galaxies vs. Observations• The trend of Qb becoming
larger for a more elongatedbar in the observational
estimates is consistent withthe results of our galaxymodels.
– fbar = 0.3–0.5 for n = 1– fbar = 0.25–0.35 for n = 0• In terms of where themaximum bar toque occurs,
the observed bars are best
represented byfbar = 0.25–0.35 and n=0.
Data from Comeron+10

Model with Qb=0.23 (fbar=0.3, a/b=2.5)
Kim+12

Ring Formation•••

The inflowing speed is so large that the bar torque cannot stop gas motions
across the inner Lindblad resonance.
The inflowing gas keeps moving in and eventually forms a nuclear ring at thelocation where the centrifugal force balances the external gravitational force.
Ring formation is due to centrifugal barrier, rather than resonance!

Sizes of Nuclear Ringslarger Qb

Ring Size

• A stronger bar induce stronger shocks and thus removes a larger
amount of angular momentum from the gas, resulting in a smaller
nuclear ring in size.
• The ring position is in general well inside the inner Lindblad
resonance of the bar potential.
– Ring formation is not by the resonances but by the centrifugalbarrier.

Comparison With Observed Ring Sizes
Comeron et al. (2010)
Mazzuca et al. (2011)• Both observational and numerical results show that stronger bars canpossess smaller rings.
• For Qb < 0.2, the agreement between observational and numerical results
is quite good.
• For Qb > 0.2, the ring size in our models corresponds roughly to theupper envelope of the observational results.

Effects of Ωb and ρbul
Li, Shen, & Kim (2016)• The ring size decreases with increasing Ωb almost linearly, whileincreasing with increasing ρbul.
– Only the gas inside the corotation resonance loses angularmomentum to move in, and RCO is a decreasing function of Ωb.
– Models with larger ρbul rotate faster and can thus provide therequired centrifugal barrier for the inflowing gas at larger radii.

II. Star Formation in Nuclear Rings

Star Formation Rate in Rings• Nuclear rings in barred galaxies are sites of intense star formation.
• Some important observational results that may provide clues as tohow star formation occurs in nuclear rings.
• The present star formation rate (SFR) vs Qb– In the range ~0.1–10 M⊙ yr−1, depending on the bar strength(Mazzuca+08).

Mazzuca+08
Comeron+10

Longevity of Ring SFR• Short‐lived star formation: a single burst• Long‐lived star formation– Multiple episodic bursts– Continuous star formation• Population synthesis modeling favors long‐lived starformation (~ a few Gyrs) either with multiple episodic bursts(Allard+06, Sarzi+07) or continuous rates (van der Laan+13)
rather than short‐lived SF.

Azimuthal Age Gradient• Some galaxies (e.g., NGC 1343, IC 4933, NGC 7552) show an
age gradient of star clusters along the azimuthal direction in
nuclear rings (Mazzuca+08, Ryder+10, Brandel+12), while othergalaxies do not show apparent age gradients.

dust lane

NGC 1343

contact point

dust lane

Hα Equivalent width(Mazzuca+08)

Two Modes of Ring SF (Böker+08)• Popcorn model: SF occurs in dense clumps randomly distributed
along a nuclear ring  no age gradient• Pearls‐on‐a‐string model: SF takes place preferentially at thecontact points between a ring and the dust lanes.  age gradient.

• It appears that rings with age gradients have, on average, asmaller SFR than those without noticeable age gradients.

Numerical Methods• SF Prescription– Critical density corresponding to the Jeans condition.
– Star formation efficiency ε ~ 1% (Krumholz & Tan, 2007)• SF probability P= εΔt/tff– 90% of gas turns into a particle that represents a starcluster• Typical mass of each star cluster ~ 105M⊙• Delayed SF feedback via SN events– In the form of momentum injection– Delay time = 10 Myr.

Star Formation In Nuclear Rings
Model with SF feedback included(Seo & Kim 2014)

Star Formation Rate
• SFR is well correlated with themass inflow rate to the rings.
• SFR shows a strong primary
burst lasting for about 100 Myrand then decays to small values
below ~ 1 M⊙ yr−1.
– The primary burst is causedby the rapid gas infall due tothe bar growth (occurringover tbar=0.2 Gyr).
– The secondary bursts are due
to re‐entry of the ejected gas
from the primary burst.

Ring SFR

Mass inflow rate to the ringalong the dust lanes.

Azimuthal Age Gradient• The presence or absence of azimuthal age gradients of youngstar clusters in nuclear rings depends on the SFR.
– No azimuthal age gradient if SFR > 1 M⊙ yr−1.
• The maximum SFR that can be afforded to two contact points– εff : SF efficiency (~1%)– ΣCP : gas surface density at the contact points corresponding
to the Jeans mass
– rNR, Δr, Δφ: radius, width, angular extent of a nuclear ring– tff: free‐fall time

Ring SF with Spiral Arms•armswith bymoderate
GasSpiral
inflows
driventhe arms
drive
Gasstrength
inflowscan
drivenbyradial
the bar−1
mass inflows of ~1 M⊙ yr ,provided the corotation
resonance of the arms is atlarge R (Seo & Kim 2014).
• Spiral arms can continuouslytransport fresh gas fromouter regions to the bar
region, capable of enhancing
SFR at late time in the ring.

without spirals
with spirals

III. Three-Dimensional Models
Seo & Kim (in preparation)• So far, our simulations were limited to 2D, isothermal models that
employ fixed gravitational potentials for stellar bars.
• However, stellar bars in real galaxies form, evolve, and decay, during
which they gravitationally interact with the gaseous component.
• We run fully 3D self‐consistent models using GIZMO (Hopkins 2015,2016).
– A second‐order accurate Lagrangian, mesh‐free, Godunov‐typecode– Include radiative cooling/heating– SF feedback by mass and momentum injection via SNe and winds.
– Gas + Stars + DM : 11x106 particles– Vary the gas fraction (fgas = 0, 5, 10%) andthe Toomre stability parameter (Q = 1.0 and 1.2).

Overall Evolution
Stellar Disk

Gaseous Disk

Models with Q=1.2
Stellar disk
strengthpattern speed

semi-major axis

Models with Q=1.2
Stellar disk

Gaseous disk

• Gas redistribution due to a non‐axisymmetric bar potential.
• The gas in the bar region istransferred to the central nuclear
ring, increasing the central massconcentration (CMC).
• Bar weakening is due to the CMC(Shen & Sellwood 2004; Berentzen etal. 2007).

Models with Q=1.2• In the stable models, the gas
disk does not actively
participate in large‐scale
gravitational instability.
• The presence of gas tends tomake a bar weaker.
• The model with fgas = 10%
does not form a strong stellar
bar since gravitational
instability of the pure stellar
disk is not strong enough.

Models with Q=1.0• The presence of gas tends toform a bar earlier and stronger,
although it decays faster due to
CMC compared to the Q=1.2
counterpart.
• Since the disk is initiallyunstable, the gas rapidly turns
into stars.
• Newly‐formed stars haverelatively low velocity
dispersions and thus effectively
cool down the stellar disk.
• The bar formation occurs earlier
as the gas fraction increases.

Evolution of Gas Structures
Stable models

Unstable models

Rring (kpc)

Evolution of the Ring Size

• Early stage (before t=2 Gyr) : Rring fluctuates.
– The rapid increase in the bar strength tend to make the ring smaller.
– The increased CMC makes the ring grow in size.

• Late stage (after t=2 Gyr) : Rring grows with time
– After the bar strength reaches a peak value, the changes in the CMC
and bar pattern speed make the ring larger.
• Consistent with the results under a fixed bar potential.

Mass Accretion to BH
fgas=5%• The nuclear activity of agalaxy can be measured interms of the Eddington
ratio:

λ < 0.1 for classical Seyferts 1 (Meyer-Hofmeister & Meyer 2011)
λ ~ 10-2 for Seyferts 2 (Bian & Gu 2007)
λ ~ 10-3 for low-luminosity Seyferts 2 (Ho 2008)

NGC 7479

NGC 986

NGC 1300

NGC 1512

IV. Nuclear Spirals in Weakly Barred Galaxies(Kim & Elmegreen 2017)(Elmegreen et al. 2002)

NGC 4736

(Elmegreen et al. 1998)

NGC 2207 and IC 2163

Numerical Models• Consider two galaxy models that differ in the amount of shear
in the rotation curve– MIL model with high shear mimics the center of the Milky Way– GAL model corresponds to disk galaxies with low shear, likeNGC 3041

• SMBH with M=3x106M at the center
MIL= high shear

GAL= low shear

Oval Potentials• To represent a weak bar or oval distortion at galaxy centers, weintroduce a simple, rigidly‐rotating gravitational potential

with m=2 and Φa/cs2=0.1.

MIL= high shear

GAL = low shear• Due to the geometric effect, nuclear spirals turn to shocks at small radii
even if the potential perturbations are very weak.
• The background shear affects the morphologies of the nuclear spirals andshocks significantly.
– Spirals are tightly wound and the shocks are inclined when shear ishigh, leading to a formation of a circumnulcear disk.

Gas Accretion to a SMBHMILGAL• Time‐average mass accretion rates

Eddington Ratio• The nuclear activity of a galaxy can be measured in terms of theEddington ratio– λ < 0.1 for classical Seyferts 1 (Meyer‐Hofmeister & Meyer 2011)– λ ~ 10‐2 for Seyferts 2 (Bian & Gu 2007)– λ ~ 10‐3 for low‐luminosity Seyferts 2 (Ho 2008)• Gas inflows driven by shock fronts in nonlinear nuclear spirals canaccount for observed levels of AGN activity in Seyfert galaxies,depending on the amount of gas in the disk and the amplitude of theexternal potential.

Summary• Formation of nuclear rings– Not by resonances but by the centrifugal barrier that the inflowing gas
cannot overcome.
– Galaxies with stronger bars host smaller nuclear rings• Star formation in nuclear rings– An azimuthal age gradient of star clusters is expected when SFR is low(less than 1 M⊙ yr−1 in our models) in which case SF occurs mostly at thecontact points.
• Bar formation in 3D models– Models with Q=1.0 form a bar more rapidly and strongly as the gas

fraction increases, while the presence of gas make the bar strength
weaker in the Q=1.2 models.
– The ring grows in size in the late phase due to increase in CMC anddecrease in the bar pattern speed.

• Nuclear spirals in weakly‐barred galaxies.

– Due to the geometric effect, nuclear spirals readily shock at small
radii even if the potential perturbations are very weak, leading to theformation of CNDs when shear is high.
– Can feed SMBHs at the centers of gas‐rich disk galaxies.

Job Announcement• A postdoctoral research position is available, now and until if
is filled, in the Computational Astrophysics Group at theSeoul National University (SNU) to work in the areas ofdynamics of protoplantary disks or star formation andfeedback, etc.
• Applicants must hold a PhD in astronomy or a related field by
the start date of the appointment.
• Appointment is initially for two years, with extension to athird year possible.
• CV, a statement of current and future research interests, twoletters of recommendation• Inquiries about the position by email to wkim@astro.snu.ac.kr.