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Page 1: velocity& Δ - JILAjila.colorado.edu/~pja/astr2030/lecture10.pdf · Chandrasekhar limit Author: Phil Armitage Created Date: 2/14/2013 6:23:21 PM ...

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posi+on  

velocity  Δx

Δv

Pressure  (gradient)  that    supports  a  white  dwarf    is  a  quantum  mechanical  effect  

Pressure  increases  with  the  density:  electrons  are  forced  into  states    of  higher  energy  (larger  v)  

0.6  Msun  

1  Msun  

More  massive  white  dwarf  has  stronger  gravity:  •   need  larger  pressure  gradient  •   requires  higher  density  •   so  much  so  that  radius  goes  down!  

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0.6  Msun  

1  Msun  

1.4  Msun  

Fastest  electrons  “slow”  

Faster   Electrons  almost  have  v  =  c  

Higher  density                  faster  electrons                    higher  P  

But  when  v  ~  c,  speeds  can’t  get  any  higher!  Higher  density  fails  to  increase  pressure…  

1.4  Msun  

Subrahmanyan  Chandrasekhar  

There  is  a  maximum  mass  of    white  dwarf  that  can  be  held  up  by  electron  degeneracy    pressure  

1.4  Solar  masses,  called  the  Chandrasekhar  limit  

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1.4  Msun  

No  white  dwarfs  with  masses    exceeding  the  limit  are  known,    most  are  ~0.6  Msun  

In  mass  transfer    binaries,  gas  can  be  accreted  by  a  white  dwarf  from  a  mass  losing  ordinary  star  

What  happens  when  mass  reaches  the  limit?  

“Type  1a”  supernova  in  the  Pinwheel    galaxy  (2011)  

All  have  very  similar  luminosity  

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Nothing  is  le[  behind…  

Higher  T                

Faster  fusion  (higher  kine+c  energy  of  colliding  nuclei)  

Higher  pressure  

Stellar  core  expand  

Cools  off  

Stable  feedback  

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Higher  T                

Faster  fusion  (higher  kine+c  energy  of  colliding  nuclei)  

Same  quantum  mechanical  degeneracy  pressure  

Unstable  feedback  

hea+ng  

Iron  core:  

•   most  stable      nucleus  

•   no  energy  from    further  fusion    possible  

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This  +me  no  thermonuclear  explosion:  can’t    get  any  more  energy  out  of  iron  from  nuclear    reac+ons  

Core  collapses  

At  very  high  densi+es  protons  and  electrons  combine  to  form  neutrons  

If  neutron  degeneracy  pressure  is  enough  to    halt  collapse,  core  bounces  and  we  get  an    explosion  again  

How  could  we  tell  observa+onally  if  a  supernova  is  a  white  dwarf  supernova  or  a  core  collapse  supernova?  

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How  could  we  tell  observa+onally  if  a  supernova  is  a  white  dwarf  supernova  or  a  core  collapse  supernova?  

See  spectrum  of    hydrogen  in  the  core  collapse  case:  outer  layers  of  the  star  didn’t  undergo  fusion  

Core  collapse  supernova  leave  something  behind:  a  neutron  star  (or  some+mes  a  black  hole)