A Galactic Dynamo in Spiral Galaxies:
Effects of Steady Spiral Arms and their Pattern Speeds
Sho NAKAMURA, Makoto HATTORI (Tohoku Univ.)

2015 June 03-05, Galaxy Evolution workshop @ Nagoya Univ.

IntroductionGrand-design Spiral Galaxies

flowRoberts, 1969
Fletcher+, 2011
(M51, λ=6cm)

Spiral galaxies have magnetic fields along the spiral arms
@ galactic plane.

Introduction
Previous WorkPrevious Work

Gomez & Cox, 2002

isothermal, initial B ~ a few µG

Motivation

Motivation
渦状腕があると
1. 磁場の進化
2. 最終的に出来る磁場の幾何構造にどのような影響を与えるか、実際にシミュレーションした。

Model&Methodsupdate:Oct. 21, 2012, presented by Shuations
HD equations

Model: Basic Equations

update:Oct. 21, 2012, presented

asic MHD equations∂ρ+ ∇ · (ρu) = 0
∂t
"#$
∂ρ !
+ ∇ · (ρu) = 0∂
1 2
1(ρu) + ∇∂t· ρuu + pgas +B I−
BB = −ρ∇Φ + ρΩ2sp R − 2ρΩsp × u
8π

∂t

4π!
"#$
%!∂ (ρu)" + ∇ · ρuu +#$p + 1 B 2 I − &1 BB = −ρ∇Φ + ρΩ2 R − 2ρΩ × ugassp∂e1 218π2 sp
2∂t4π
+∇·
e + pgas +Bu−
(B · u)B = u · (−ρ∇Φ + ρΩ R) − ρ Λ(Tgas )∂t8π"4π#$%!
∂e1 2+∇·e + pgas +B∂t8π∂B− ∇ · (uB − Bu) = 0∂t&sp

1u−(B · u)B = u · (−ρ∇Φ + ρΩ2sp R) − ρ2 Λ(T4π∂B− ∇ · (uB − Bu) = 0∂tp = (γ − 1)e, γ = 5/3pgas
1 21 2egas =, γgas = 5/3, e = ρu + egas +B , u = v − Ωsp Reϕγgas − 128π∂ecr+ ∇(ecr v) = ∇(K̂∇ecr ) − pcr (∇ · v) + QSN∂t∂ecr∂t+ ∇(ecr v) = ∇(K̂∇ecr ) − pcr (∇ · v) + QSN

⎨ 10−31 T (42 × 10 <4 Tupdate:Oct.
4 2012,
10 T<7.9×1021,
presented by Sh(4×10<T<7.9×10) )
gas
gas
gas
gas
Bi Bj
Λ(Tgas ) =
Λ(T)
=
gas
−21.2−21.24104 < Tgas < 2.5 × 105 ) 5
Kij = K⊥ δ⎪(KK⊥10) 2 (7.9 ×(7.9×ij +10∥ −⎪⎪10 < Tgas < 2.5 × 10 )⎪⎪B⎪⎪⎪−10.4 −255⎪⎪HD equations10T(2.5×10<T<5.6×10)5update:Oct.
21, 2012, p⎪
gas
⎪
gas
−10.4−25⎪⎪⎧⎪10T(2.5×10<T<5.6×10)⎪gas⎩
gas5⎪4 )0(5.6×<102 ×<10Tgas
⎪
⎪
0(T)
gas
⎪
⎩ 0⎪
5⎪
(5.6 × 10 < T )equations

Basic
SpiralEquations
Potential⎪
basic MHD equations⎪⎪⎪ 104(2 × 104 < Tgas
gas < 4 × 10 )⎪⎨ 10−31
2+ Φ4 ϕ, z; t)Φ(R, ϕ, z; t) = Φz)gasz) 4+<ΦT
(R,z)
+
Φ
(R,(4(R,× 10<7.9×10)
bulge (R, Tdischalo
spgas∂ρΛ(Tgas ) =−21.2
45⎪+ ∇ · (ρu) = 010(7.9×10<T<2.5×10)⎪gas⎪
Φ(R,ϕ,z;t)
=
Φ
(R,z)
+
Φ(R,z)+
Φ(R,z)+Φ(R,ϕ,z;t)
∂t
⎪
bulge
dischalosp%!
"⎪−10.4 2−2
55 potential #$&non-axisymmetric⎪10(R/RaT) gas (2.5 z×a 10 < Tgas < 5.6 × 10 )R⎪∂ρ⎪Φsp (R, ϕ, z; t) = !
Φdisc (R, z)ϵ"∇#2 3/2 + 2 $25 cos m ϕ − Ωsp t + cot isp lnsp ⎪+·(ρu)=0⎩Rphase{1 +0 (R/Rz0 < Tgas )∂1 2a ) } (5.61z ×+10∂t2−21.85∂t(ρu) + ∇ · ρuu + pgas +8π!

BI−

BB 2= −ρ∇Φ + ρΩsp R − 2ρΩsp × u
4π(R/R)z"#aa$Φsp (R,%!
ϕ,Φ(R,z; t)ϕ,=Φ(R,z)ϵ∂ t)1+ Φ2halo (R,+1 + Φsp (R, ϕ, z; t)discspz;=Φ(R,z)+Φ(R,z)z)2bulge
disc2
3/2" (ρu) + ∇ ·#$ρuu {1&22+ +pgas+BI−BB=−ρ∇Φ+ρΩ(R/R)}
sp R − 2z+zaa 2∂t8π4π∂e1 21% · u)B! =2u · (−ρ∇Φ + ρΩsp"R) − ρ2 Λ(T#$&+∇·e + pgas +Bu−(Bgas )∂t
8π %!
(R/Rza &R" 4π#$ a )+cot isp ln
Φsp (R,z)ϵ∂eϕ, z; t) = Φdisc (R,13/2
sp 1m 2 ϕ − Ω×cost+sp22 + z 2= u · (−ρ∇Φ + ρΩ2 R+ (R/R) } (B ·zu)B+∇·e + pgas + {1 Bua−sp
Rphasea∂t
8π4π%!
"#$&∂BR− ∇ · (uB − Bu) = 0× cos m ϕ − Ωsp t + cot
isp ln2004, Wada+ 2011
Wada+∂tRphase∂B− ∇ · (uB − Bu) = 0
∂t
pϵsp
==
(γ0.025,− 1)e,Raγ ==7kpc,5/3 za = 0.3kpc, m = 2, Ωsp = 15kms−1 kpc−1 , isp = 15◦ , Rphase = 0.1kpc
pgas
1 21 2egas =, γgas ="5/3, e =# ρu +" egas +# B
γgas − 12 28πzR∂ecr
ρdisc = ρdisc,0 exp −sech+ ∇(ecr v) = ∇(K̂∇e)−p(∇·v)+QcrcrSNRdisczdisc∂t∂ecr+ ∇(ecr v) = ∇(K̂∇ecr ) − pcr (∇ · v) + QSN#"∂tupdate:Oct. 21, 2012, presented by Shuations
HD equations

Model: Basic Equations

update:Oct. 21, 2012, presented

asic MHD equations∂ρ+ ∇ · (ρu) = 0∂t"#$∂ρ !
+ ∇ · (ρu) = 0∂1 2
1(ρu) + ∇∂t· ρuu + pgas +B I−
BB = −ρ∇Φ + ρΩ2sp R − 2ρΩsp × u
8π

∂t4π!
"#$%!∂ (ρu)" + ∇ · ρuu +#$p + 1 B 2 I − &1 BB = −ρ∇Φ + ρΩ2 R − 2ρΩ × ugassp∂e1 218π2 sp
2
∂t4π
+∇·
e + pgas +Bu−(B · u)B = u · (−ρ∇Φ + ρΩ R) − ρ Λ(Tgas )

∂t8π
"4π
#$%!
∂e1 2
+∇·
e + pgas +B∂t8π∂B− ∇ · (uB − Bu) = 0∂t&sp

1u−(B · u)B = u · (−ρ∇Φ + ρΩ2sp R) − ρ2 Λ(T4π∂B− ∇ · (uB − Bu) = 0∂tp = (γ − 1)e, γ = 5/3pgas
1 21 2egas =, γgas = 5/3, e = ρu + egas +B , u = v − Ωsp Reϕγgas − 128π

∂ecr+ ∇(ecr v) = ∇(K̂∇ecr ) − pcr (∇ · v) + QSN∂t∂ecr∂t+ ∇(ecr v) = ∇(K̂∇ecr ) − pcr (∇ · v) + QSNModel: Initial Conditionhydrostatic halo, T ~106K-23-26-29Log(density)

thin disc, T ~104K
Bφ(µG)

0.01-0.01

weak Bφ, β ~104

Results

Results(t=0Myr)
Log(density)-23-24-25-26Log(temperature)6543

Results(t=220Myr)
Log(density)-23-24-25-26Log(temperature)6543

Results(t=750Myr)
Log(density)-23-24-25-26Log(temperature)6543Results
t=0MyrBφ(µG)
t=276Myr

t=340Myr

t=600Myr

t=750Myr

t=900Myr

100-10100-1015Time Evolution of Bφ(R=5kpc)

0−5−10−15Bφ, [µG]510~300-400Myr

0500

1000Time, [Myr]1500

Bφ(µG), t=600Myr
100-10Bφ(µG), t=750Myr

100-10100-10Bφ(µG), t=900MyrResults

B-field Reversals Induced by Spiral Arms
spiral potential

Bφ>0

Nishikori+ 2006
Machida+ 2013

B-field Reversals Induced by Spiral Arms
spiral potential
Bφ<0Bφ>0

Nishikori+, 2006
Machida+, 2013

Time Evolution of Magnetic Energy
1e−13
1e−15

R=5kpc, R=10kpc
R=15kpc, R=20kpc

1e−17

Magnetic Energy Density

1e−11e-folding time ~ 30Myr, 130Myr,
175Myr, 240Myr

0500

1000
Time, [Myr]

1500

150
10050

Ω

=psmk
15cpk/s/RCR~15kpc

0v..[km/s]vφ, [km/s]

200250Effects of Spiral Pattern Speed

0510R, [kpc]1520R, [kpc]内側ほど磁場が増幅==>内側ほど渦状腕を頻繁に通過==>磁場増幅のタイムスケールはΩspに依存？

ConcludingRemarks

Concluding Remarks
渦巻き銀河を意識した3次元MHD simulationの結果・・・
1. 磁気流体的銀河衝撃波が形成==>劇的な磁場増幅 tevolution << tdyn
2. 磁気流体銀河衝撃波＋磁気浮力不安定性==>磁場の頻繁な反転, ハロー部の磁化
3. 磁場の増幅率==>Ωspに依存する可能性あり(今後シミュレーション予定)

Thank youfor your attention