Spiral Density Waves in M81

Hsiang-Hsu Wang (speaker) Chien-Chang Feng Wing-Kit Lee Lien-Hsuan Lin Ronald Taam

Institute of Astronomy and Astrophysics, Academia Sinica (ASIAA)

Spiral structure in disk galaxies

!   Winding dilemma

!   Origins: density waves theory, swing amplification, tidally induced spirals, self-perpetuating, etc.

!   Direct comparisons between predictions and observations

Outline!   M81

!   Spiral density waves in M81

!   Summary (I)

!   Hydrodynamic simulations for the gas response to the spiral density waves in M81

!   Summary (II)

M81 (NGC3031)Object  type:  Spiral  galaxy:  SA(s)ab    Distance:  12,000,000  light-‐years  (3.6  Mpc)    Constellation:  Ursa  Major  (the  Big  Bear)    Major  companions:  M82,  NGC3077    Inclination:  58°  (de  Vaucouleurs  et  al.  1991)      

Yun et al. 1994, Nature

HI tidal tailsM82

NGC 3077

One of the nearby galaxies with well observed mass distribution and gaseous kinematics

M81 (II)

Visible light

(Credit: N.A. Sharp (NOAO/AURA/NSF)

Ks band (2.2 μm)

(JARRETT et al. 2003 AJ)

smooth stellar spirals; bulge/old disk stars

HI 21cm

(Braun 1995)

Tidal interaction; rotation curve; large structures

M81 (III)

GALEX FUV-NUV

Gil de Paz et al. 2007hot, young stars

IRAC 3.6μm (SINGS)

old stellar population

IRAC 8μm (SINGS)

dust; tracer of shocks

Galactic shock is important to the formation of GMCs, star formation, substructures

1.  Identifying physical origins of structures appearing in gas and dust

2.  Distinguishing between different mechanisms (theories) by comparing gas responses obtained from simulations to observations

Objectives

Method: performing simulations for a specific target with input parameters well constrained by observations and see what happens

Results: We may tell which mechanism/theory is plausible for a specific galaxy

M81 (IV)

IRAC 3.6 μm IRAC 4.5 μm I band2MASS Ks band

Kendall et al. 2008, MNRAS, 387, 1007Non-axisymmetric residuals

1. A pair of stellar spiral situated well inside the radius of ILR (2.5 kpc)? 2. What is the origin and the pattern speed of inner spirals? 3. Can spiral density wave theory explain the origin of inner spirals? 4. Stellar spirals induced by gaseous spirals? (Kendall et al. 2008)

Questions:

Inner stellar spirals

Ks band (2.2 μm)

(JARRETT et al. 2003 AJ)

We explored the nature of the stellar spirals in M81 within the framework of spiral density wave theory

Feng,…., Wang, …ApJ, 2014, 785, 103

Question:

For a given mass model constrained by observations, can the density wave theory explain the existence of seemly separate inner and outer spiral arms?

modal approach (global theory)

Boundary conditions

regular at the center; outgoing at the outer

Lau & Bertin 1978

Following the governing equations described in Lau & Bertin (1978), we look for discrete unstable modes with the linearized hydrodynamic equations and boundary conditions

Only discrete can fulfill the BC ! = !r + i!i eigenvalue problem

solution: spiral arms

mode n=0

What will happen if the input parameters are constrained by observations?

A three-component model for M81

Two dominate unstable modes are found

mode pattern speed [km/s/kpc] growth rate [km/s/kpc]

Two dominate unstable modes are found

n=0 n=1

⌦p = 34.5⌦p = 25.5

� = �4.8� = �4.5

Toomre’s disk 1963, ApJ; Lau & Bertin 1978, ApJ

disk

spherical halo

Lowe et al. 1994, ApJ. 427, 184

spherical bulge

Athanassoula 1992, MNRAS

regular at the center; outgoing at the outer

boundary conditions

Singularity at r=0 is avoided!

The spiral mode (n=1)Contour: density waves calculated based on our model for the mode n=1

The inner spirals together with the outer spirals can be explained by a single spiral mode, rotating with the same pattern speed.

Summary (I) 1.  Based on observations, a three-component mass model is

built for M81. 2.  Unstable two-armed spiral modes are found for the stellar

disk within the framework of spiral density wave theory. 3.  The spiral shape, the pattern speed as well as the modulation

of arm strength derived from the spiral mode n=1 are in good agreement with observations and serve as the inputs for the study of gas response.

4.  The inner and outer stellar spirals have the same pattern speed

5.  Spiral density wave theory is a plausible theory for explaining the spiral structure in M81

The shape of stellar spirals, the pattern speed and the modulation of arm strength derived from spiral mode (n=1) match well with observations and are

taken as inputs for the study of gas response

We are at the good position of studying gas response to the stellar density waves for M81

mass distribution of spirals

Models for gas disk (I)0th-moment map (Walter et al. 2008) corrected by a factor 1.4 for heavy elements

ellipse: r=4 kpc scalelength of exp. disk: 10 kpc

total gas mass (r

Models for gas disk (II)Velocity dispersion Ianjamasimanana et al. (2012)

single component Gaussian fit: 11.2 km/s (11 km/s) narrow component (cold neutral): 6.7 km/s (7 km/s) broad component (warm neutral): 19.1 km/s (19 km/s)

For M81:

1. super-profile of neutral gas obtained by stacking all pixels in the data cube 2. super-profile is best fitted with two Gaussians associated with CNM and WNM

Toomre’s Q and resonancesToomre’s Q Radii of 4 to 1 resonances

c0: 6.3 kpc c7: 6.1 kpc c11: 5.8 kpc c19: 4.9, 3.8, 3.0 kpc

No inner Lindblad resonance (2:1) is associated with the adopted pattern speed

Q =a

⇡G�0

Q

Parameters and models

sound speed: 7 (CNM), 11 (mixed), 19 (WNM) km/s Forcing : 0.85, 1, 1.15 self-gravitating & non- self-gravitating gases

Constrained within the uncertainties of observations

18 two-dimensional hydrodynamic simulations are performed using the Antares code

1.  The gas responses of different velocity dispersions are assumed to be dynamically decoupled from each other and are treated separately (Dobbs 2008)

2.  The spiral is gradually turned on and reach the full strength at one orbital time

The Antares code

Governing equations@�

@t+r · (�v) = 0

@v

@t+ v ·rv = �rp

��rV

total

Vtotal

= Vhalo

+ Vdisk

+ Vbulge

+ Vgas

+ Vspiral

p = a2�

r2Vgas = 4⇡G��(z)

(continuity equation, σ: surface density, v: velocity vector)

(equation of motion, Vtotal: total potential)

(isothermal equation of state; a : mean turbulent dispersion )

(Poisson’s equation, G: gravitational constant, δDirac delta function)

2D hydrodynamic equations are solved numerically using high-order Godunov code (Yuan & Yen 2005; Yen et al. 2012)

Gas-to-dust conversion function

Results (surface density at 5 orbital times) white ellipses: 4 to 1 resonances

Results (surface density at 10 orbital times) The ring structure

r=5 kpc r=3.8 kpc r=0.9 kpc

1.  The ring structures are well correlated with the locations of innermost 4:1 resonances

2.  The ring structure of models with sound speed 7 km/s fits well with observation.

Results (effects of sound speed, self-gravity & arm strength)

density streaming motion density streaming motion

sound speed

arm strength

self-gravity

Streaming motion: magnitude of velocity departure from the initial axisymmetric velocity field

1.  Gases of different sound speeds react quite differently to the imposed spiral density waves 2.  the overall shock structure is not sensitive to the arm strength and the selfgravity of gas 3.  streaming motions: observed southwest arm (～25 km/s), northeast arm (～50 km/s) (Adler &

Westpfahl 1996)

4.  The inner spiral shocks result from 4 to 1 resonance: models with a=19 km/s is favorable

Results (kinematics)

ellipses: r=4 kpc and corotation

(a)  observed 0th moment (8μm + 21cm)

(b)  0th moment (21cm) + observed iso-velocity contours

(c)  0th moment (21cm) + simulated iso-velocity contours

(d)  observed + simulated iso-velocity contours

contours: -200 to 200 km/s interval: 25 km/s

Results (wiggle instability)

Connection between wiggle instability (Kim^3 2014) and the observations, however, is not straightforward:

1.  Magnetic field is not considered in this work 2.  our simulations and the analysis are two-dimensional 3.  quasi-regularly spaced in simulations vs. irregular spaced in observations

Evolution of total potential vorticity

Summary (II) 1.  The rotation curve, the sound speeds, the surface density of gaseous disk are

initialized based on observations. 2.  The ring structure is identified as a feature of 4:1 resonance associated with the

cold medium (a=7 km/s) 3.  The inner spiral shocks are identified as the 4:1 resonances associated with the

warm medium (a=19 km/s) 4.  The ultrahigh streaming motion observed in the northeast arm is not compatible

with the observed arm strength. Interaction? Stellar feedbacks? 5.  The outward shifted turning points in the southwest arm are well correlated with

the weak HI ridge and might be a result of interactions with companions. 6.  Works need to be done to identify the nature of the wiggles/feathers that appear

in M81

Thank you !