Mellinger

Lesson 10SNR & sequential star

formation

Toshihiro HandaDept. of Phys. & Astron., Kagoshima University

Kagoshima Univ./ Ehime Univ.Galactic radio astronomy

MellingerSupernova & its remnantPart 1

Mellinger

Supernova explosion

▶ Massive main sequence star = OB star■ Gravitation collapse type supernova explosion

Type Ib, Ic, II ← classify with spectra and light curve

■ grav. coll. of Fe core by photo dissoc. or e- capture■ Mass range in main seq. stage is ambiguous.

due to inaccurate mass-loss process

▶ Binary of a white dwarf and a giant■ Binary type supernova explosion

Type Ia

■ Explosion over the mass limit of white dwarf

Mellinger

Supernova remnant

▶ Supernova explosion→expand from a point

▶ Propagate the shock wave in surrounding ISM

▶ Double layer structure■ Expanding material directly from the exploded star■ Gas beyond the shock = post shocked gas■ Shock front

Mellinger

Structure of a SNR

Nuetral ISMIonized ISM

Matter from the star

Mellinger

Supernova remnant (Cas A)

▶ Images in radio, optical, and X-ray■ Shell-like

Mellinger

Supernova remnant (Crab nebula)

▶ Images in radio, optical, and X-ray■ filamentary, filled

Mellinger

Classification of SNRs

▶ Shell-like■ shell structure in radio (apparently ring-like)

▶ Plerion-type or Crab like■ Filled structure in radio■ A pulsar in it?

▶ Mixed-type■ Feature between these two types

Mellinger

Radio spectra of SNRs

▶ Energy distribution of electrons■ Power law (experimental, approximation)

N(E)dE = CE-p dE, p: power index

▶ Spectrum from them shows power law.

▶ When P,all electrons∝ -, = (p-1)/2

Mellinger

Compression of mag. field

▶ Gas compression = B compression■ Frozen-in

▶ Rich in high-energy electrons■ High-energy reaction at SN explosion

▶ Strong B + high energy electrons■ →synchrotron radiation

Mellinger

Shock front

▶ Supersonic expansion in ISM■ Expansion of an HII region■ Expansion of a SNR

▶ Gas compression due to shock wave

▶ Suppose a gas flow■ To simplify we consider the “1-D steady flow”■ Before stating the consideration…

MellingerFluid mechanics & shock wave

Part 2

Mellinger

Fluid mech. : Euler’s view

■ Euler’s viewPhysical quantity as a function of space and timevel. field v(x,t), dens. field (x,t), press. field p(x,t) 、…

■ In the case of 1D steady flow

▶ Eq. of motion of volume elementLagrange’s view

► Moving with a focused object

dv/dt=-∂p/∂xConversion from Lagrange’s to Euler’s

dv/dt =∂v/∂t+v ∂v/∂x=v ∂v/∂x ←steady ∂/∂t=0

Mellinger

Basic fluid mechanics : Euler’s eq.

▶ Eq. of motion on Euler’s view = Euler eq.v ∂v/∂x =-(1/) ∂p/∂x

■ This is for steady 1D flow■ In this case, change along the flow is

v dv =-dp/

Mellinger

Adiabatic gas flow

▶ Adiabatic i.e. isentropic dS=0

▶ In this case, enthalpy change isdw=T dS+Vdp=dp/

■ It gives

∂w/ ∂x=(1/) ∂p/ ∂x■ Euler’s equation is

v ∂v/∂x=-∂w/∂x■ We get (∂/∂x) (w+v2/2)=0, that is

w+v2/2=const. 　← Bernoulli’s equation

Mellinger

Supersonic flow & max vel. of gas

▶ Bernoulli’s equationw+v2/2=const.

■ atT=0K, Press & enthalpy are min p=0, w=0■ Therefore, v<vmax=(2w0)1/2

Max gas velocity blowing out to vacuum

■ Sound velocity, c=(∂p/∂)s1/2 , gives dp=c2 d

∵ Euler’s eq. vdv =-dp/ gives d/dv=-(v)/c2

dj/dv=d(v)/dv=1+d/dv=(1-v2/c2)■ Supersonic flow(v>c), the faster v gives the less flux j.

√2w0c

j=v

v0

Mellinger

Basic equations of fluid

▶ Mass conservation law (continuity equation)■ v=const

▶ Energy conservation law■ ( v2)/2+=const

With dp=dw-Tds, it gives the follwing;(∂/∂t)( v2/2+)=-(∂/∂x)(v(w+v2/2))

■ v(w+v2/2)=const ←Bernoulli’s + continuity’s

▶ Momentum conservation law←eq. of motion■ p+v2=const （← Euler’s eq. vdv =-dp/ ）　

Mellinger

1D steady gas flow (1)

▶ 1D steady flow

▶ Basic eq. for unit mass (w: enthalpy)1v1=2v2=j eq. continuity

p1+1v12=p2+2v2

2 momentum cons.

1v1(w1+v12/2)=2v2 (w2+v2

2/2) energy cons.

▶ Third and first equations givew1+v1

2/2=w2+v22/2 Bernoulli’s principal

v1

w1, 1 w2, 2

v2

p1 p2

Mellinger

1D steady gas flow (2)

▶ For unit volume, V=1/■ Therefore,

j2=(p2-p1)/(V1-V2)p always changes different direction of V.

■ This with Bernoulli’s principal and =w+pV gives

1-2+(p1+p2)(V2-V1)/2=0Quantities 2 are controlled by quantities 1

■ “Rankine-Hugoniot’s adiabatic curve” or “adiabatic curve of the shock wave”

Mellinger

Compression by a shock

▶ For ideal gas, =pV/(-1)■ Input it to Rankine-Hugoniot’s adiabatic curve

V2/V1=[(+1)p1+(-1)p2]/ [(-1)p1+(+1)p2]Rankine-Hugoniot equation

■ Only pressure ratio gives density ratio!■ at the limit of p2≫ p1,

V2/V1=1/2=(-1)/(+1)For monoatomic gas with =5/3, V2/V1=1/4, 2/1=4

► For any gas 1<≦5/3 2/1≧4

Compression by any strong shock has a limit.► By a factor, although depending on a gas

Mellinger

Shock heating

▶ For ideal gas T∝ pV■ Therefore, we got

T2/T1=(p2V2)/(p1V1)

=(p2/p1) [(+1)p1+(-1)p2] / [(-1)p1+(+1)p2]Rankine-Hugoniot equation

■ Only pressure ratio gives temperature ratio!■ at the limit of p2≫ p1,

T2/T1=[(-1) p2]/[(+1) p1]Strong shock can heat up the gas by any factor.

Mellinger

Isothermal shock

▶ When quick cool down just after heating…■ In the case of cool down to T2=T1

■ Pressure ratio is given by the boundary condition.

▶ For ideal gas, T∝ pV=p/▶ Therefore, very strong shock gives

■ Temp. just after shock can infinitely heat up.■ Density after cooling can be infinitely high.

▶ Shock can make post-shock gas much denser!

Mellinger

Shock front velocity

▶ Media 1 is rest = wave front moves at v1.

▶ Mach number M=v/c■ Sound velocity of ideal gas c=(/p)1/2

▶ V2/V1 is shown by M. : shock expressed with M.

V2/V1=[(-1)M12+2]/[( +1)M1

2]

T2/T1=[2M12-(-1)] [(-1)M1

2+2 ]/[( +1)M12]

p2/p1=(2M12-+1)/( +1)

-v1

w1, 1 w2, 2

v2-v1

p1 p2

MellingerSequential SF & spiral arm

Part 3

Mellinger

Triggered starformation

▶ Expansion of an HII region or an SNR■ ISM compressed by a shock

Beyond “critical density”Break a dynamical equlibrium

▶ Trigger the star formation■ Many stars are formed in a star forming region.

Mellinger

Sequential star formation

▶ A formed star is as early type as to the former.■ A single star makes next generation stars.■ → Stars can be made sequentially.

▶ Is it true?■ Only few clear example are observed.

Mellinger

Galactic spiral arm

▶ Many stars

▶ Rich ISM■ Line of dark clouds

▶ Rich star forming regions■ Line of HII regions

▶ How to make such a structure?

Mellinger

Winding problem

▶ With flat rotation…

▶ Spiral arm must be wounded very tightly!■ Inconsistent to the observations

3x107 yr later 1.5x108 yr later

Mellinger

Density wave theory

▶ A pattern of star density■ Pattern velocity ≠ matter velocity

▶ self consistent solution?■ Distribution of stars■ Local grav. field■ Velocity field of stars

Jam=arm

Mellinger

Galactic shock model (1)

▶ Spiral arm = potential (local) minimum■ rapid acceleration + rapid deceleration■ velocity change is supersonic→shock in ISM■ The shock activates star formation.

▶ Compress of ISM and active SF in spiral arm■ Consistent structure of a spiral arm■ Early type stars & HII regions are rich.■ Interstellar matter (ISM) is rich.

Mellinger

Galactic shock model (2)

▶ Expected internal structure of the spiral arm■ Outline structure is consistent.■ Detail structure is inconsistent.

The order of star ageNot-continuous arm

Shock front

Less massive stars

massive stars & HII regions

Dense gas clouds

Spiral arm

Less massive stars

Flow of stars and gas

Mellinger

SSPSF(1)

▶ Another model

▶ Stochastic selfpropagating SF model■ Spiral arm=pattern of SF activity.

Mellinger

SSPSF(2)

▶ Stochastic selfpropagating star formation■ SF region activate SF in the adjacent region.■ Suppress the activity just after form. of many

stars .

▶ asymmetric prop. of SF← differential rot.■ ： adjacent cell is the same = slow propagation■ r ： adjacent cell changes = fast propagation

SF regions elongated along r make trailing arm due to differential rotation.