Mellinger Lesson 10 SNR & sequential star formation Toshihiro Handa Dept. of Phys. & Astron., Kagoshima University Kagoshima Univ./ Ehime Univ. Galactic radio astronomy

Mellinger Supernova & its remnant Part 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 ISM Ionized 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…

Mellinger Fluid mechanics & shock wave Part 2

Mellinger Fluid mech. : Euler’s view ■ Euler’s view Physical quantity as a function of space and time vel. 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 element Lagrange’s view ►Moving with a focused object  d v /dt=-∂p/∂x Conversion from Lagrange’s to Euler’s d v /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 d v =-dp/ 

Mellinger Adiabatic gas flow ▶ Adiabatic i.e. isentropic dS=0 ▶ In this case, enthalpy change is dw=T dS+Vdp=dp/  ■ It gives ∂w/ ∂x=(1/  ) ∂p/ ∂x ■ Euler’s equation is v ∂ v /∂x=-∂w/∂x ■ We get (∂/∂x) (w+ v 2 /2)=0, that is w+ v 2 /2=const. ←Bernoulli’s equation

Mellinger Supersonic flow & max vel. of gas ▶ Bernoulli’s equation w+ v 2 /2=const. ■ atT=0K, Press & enthalpy are min p=0, w=0 ■ Therefore, v < v max =(2w 0 ) 1/2 Max gas velocity blowing out to vacuum ■ Sound velocity, c=(∂p/∂  ) s 1/2, gives dp=c 2 d  ∵ Euler’s eq. v d v =-dp/  gives d  /d v =-(  v )/c 2 dj/d v =d(  v )/d v =1+d  /d v =  (1- v 2 /c 2 ) ■ Supersonic flow( v >c), the faster v gives the less flux j. √2w0√2w0 c j=vj=v v 0

Mellinger Basic equations of fluid ▶ Mass conservation law (continuity equation) ■  v =const ▶ Energy conservation law ■ (  v 2 )/2+  =const With dp=  dw-  Tds, it gives the follwing; (∂/∂t)(  v 2 /2+  )=-(∂/∂x)(  v (w+ v 2 /2)) ■  v (w+ v 2 /2)=const ←Bernoulli’s + continuity’s ▶ Momentum conservation law←eq. of motion ■ p+  v 2 =const （ ←Euler’s eq. v d v =-dp/  ）

Mellinger 1D steady gas flow (1) ▶ 1D steady flow ▶ Basic eq. for unit mass (w: enthalpy)  1 v 1 =  2 v 2 =j eq. continuity p 1 +  1 v 1 2 =  p 2 +  2 v 2 2 momentum cons.  1 v 1 (w 1 + v 1 2 /2)=  2 v 2 (w 2 + v 2 2 /2) energy cons. ▶ Third and first equations give w 1 + v 1 2 /2=w 2 + v 2 2 /2 Bernoulli’s principal v1v1 w 1,  1 w 2,  2 v2v2 p 1 p 2

Mellinger 1D steady gas flow (2) ▶ For unit volume, V=1/  ■ Therefore, j 2 =(p 2 -p 1 )/(V 1 -V 2 ) p always changes different direction of V. ■ This with Bernoulli’s principal and  =w+pV gives  1 -  2 +(p 1 +p 2 )(V 2 -V 1 )/2=0 Quantities 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 V 2 /V 1 =[(  +1)p 1 +(  -1)p 2 ]/ [(  -1)p 1 +(  +1)p 2 ] Rankine-Hugoniot equation ■ Only pressure ratio gives density ratio! ■ at the limit of p 2 ≫ p 1, V 2 /V 1 =  1 /  2 =(  -1)/(  +1) For monoatomic gas with  =5/3, V 2 /V 1 =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 T 2 /T 1 =(p 2 V 2 )/(p 1 V 1 ) =(p 2 /p 1 ) [(  +1)p 1 +(  -1)p 2 ] / [(  -1)p 1 +(  +1)p 2 ] Rankine-Hugoniot equation ■ Only pressure ratio gives temperature ratio! ■ at the limit of p 2 ≫ p 1, T 2 /T 1 =[(  -1) p 2 ]/[(  +1) p 1 ] 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 T 2 =T 1 ■ 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 v 1. ▶ Mach number M= v /c ■ Sound velocity of ideal gas c=(  /p) 1/2 ▶ V 2 /V 1 is shown by M. : shock expressed with M. V 2 /V 1 =[(  -1)M ]/[(  +1)M 1 2 ] T 2 /T 1 =[2  M 1 2 -(  -1)] [(  -1)M ]/[(  +1)M 1 2 ] p 2 /p 1 =(2  M  +1)/(  +1) -v1-v1 w 1,  1 w 2,  2 v2-v1v2-v1 p 1 p 2

Mellinger Sequential 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 3x10 7 yr later 1.5x10 8 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 age Not-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.