Transcript Document

The Joint Institute for Nuclear Astrophysics
Electron Capture Rates for Neutron Star Crusts.
Ana Becerril-Reyes, Sanjib S. Gupta and Hendrik Schatz.
National Superconducting Cyclotron Laboratory. Michigan State University.
EC in crusts of accreting neutron stars
(models of crust evolution)
10-10
Neutron star EXO
0748-676 (blue sphere)
is part of a binary star
system, and its
neighboring star
(yellow-red sphere)
supplies the fuel for the
thermonuclear bursts.
(Image Credit: NASA)
yr-1
Even at low accretion rates of
Msolar
a neutron star can accrete
enough material from the secondary to replace its entire crust with ashes
of H/He burning not in NSE. Rising electron chemical potential with density
as the ashes are pushed deeper in the crust will switch on energetically
unfavorable EC transitions. This lowers nuclear charge and generates heat.
Threshold effects at low temperature cannot be captured accurately in
tables. Our analytic implementation is fast enough to be used in real-time
inside a reaction network.
Comparison of EC rates to those calculated by
FFN
FULLER, FOWLER & NEWMAN
(FFN)
u,w,q=electron chemical potential, capture threshold, capture q-value in
mec2 units (electron rest mass)
Rising “u” in NS crust allows electrons to overcome unfavorable capture
thresholds.
For pre-threshold captures important in NS crusts:
Log10(Ye) = 10.0
GUPTA & MÖLLER
(G&M)
Spherical Independent Particle
Model.
Z
Nilsson Model.
Allowed (GT) only.
Experimental input (gs->gs or gs->
low-lying forbidden transitions)
Ground state of parent only
included.
(thermal population effects in
Neutron Star Crusts very mild).
Excited states of parent included
R=(ln2*f)/(ft_value for transition from I to J)
Phase space factor:
f(T9 ,u,w,q) = Geff * F
Z
N
This implementation is not susceptible to low-temperature inaccuracies
due to Fermi-Dirac distribution shape (as Gauss-Laguerre quadrature
schemes are in the grid region T9 = 0.01-0.1 when compared to
trapezoidal rule schemes). Inaccuracies are only introduced because we
evaluate distortion of electron wave function at only one “effective”
electron energy. Most approximations ignore the Coulomb Correction
altogether by setting it to unity over the integration range. By retaining an
effective correction we retain the effects of a varying nuclear radius on the
phase space (important for a rate compilation sufficiently global over the
nuclear chart).
Analytic formulation of rate from state “I” in parent to
state “J” in daughter:
Log10(Ye) = 9.0
N
Results of comparisons
(required for Core-Collapse
Supernovae, not for Neutron Star
Crusts)
Comparison between the two compilations of electron capture rates:
No quenching of strength.
Residual interactions using QRPA
We start by comparing the EC rates at (Peter
the lowest
values of temperature and
Möller).
density (T9=0.01 and Log10(Ye) = 1.0). Then we compare rates for higher
values of density, while keeping T9 constant.
Below are shown the absolute values of
 ECR(G & M ) 

 Log10 
T9=0.01 and Log10(Ye) = 1.0, 8.0, 9.0 and R10.0.
 ECR( FFN ) 
0.1
0.2
0.3
0.4
0.5
0.6
0.7
EC Rates for neutron rich nuclei agree fairly well between the two
compilations.
For proton rich nuclei differences may arise due to low lying structure
(experimental data vs. QRPA).
for
The color code for these plots is as follows:
R= 0.001
At Log(rhoYe)=1.0:
0.8
0.9
R1.0
At higher values of Log10(Ye) (e.g. 8.0, 9.0, 10.0) a larger fraction of
strength in daughter nuclei is accessed. Thus, the observed changes in
the calculated rates may be due to:
In FFN deformation for neutron rich nuclei is not taken into account,
but it is in (G & M). Therefore, calculated structure is very different.
Thick black borders denote stable nuclei.
F(u < w,w = 1) = (w4+2qw3+q2w2)(T9 /5.93)f1(z)+(4w3+6qw2+2q2w)
(T9 /5.93)2f2(z) + (12w2+12qw+2q2)(T9 /5.93)3f3(z)+(24w+12q)
(T9 /5.93)4f4(z)+24(T9 /5.93)5f5(z)
For rates in which the initial nucleus is even-even and the final is an
odd-odd, g.s.  g.s. may not be allowed via (GT) transition.
Gupta & Möller calculations do not include experimental input.
For pre-threshold when q < -1 :
F(u < w,w = - q) = 2w2 (T9 /5.93)3f3(z)+12w (T9 /5.93)4f4(z)+
24(T9 /5.93)5f5(z)
Log10(Ye) = 1.0
Where fn(z) is a generalization of the Logarithm function:
f1 (z)=ln(1+z)
fn(z)=[ {(-1)k-1zk}/k n ] (k=1,…N<300 for convergence when n<6)
and z=exp{-(5.93|w-u|)/ T9 } < 1
Where we are now:
Z
EC rates successfully implemented in Neutron Star Crust simulation.
(Gupta, Brown, Schatz, Möller, Kratz. TBP).
N
Where we are headed:
Geff = Coulomb Correction = (p/w)FC (Z,A,w)
evaluated at effective electron energy w=weff extracted from
weff (weff
2
+q)2
Calculating rates with excited states in parent nuclei.
Using these rates in high temperature (T9), high density (Log10(Ye))
conditions in core – collapse supernova simulations.
=5.93*F/(T9 f1(z)).
P = electron momentum, Z = nuclear charge of captor
FC (Z,A,w)= Distortion of electron wave function (for a given electron
energy w) due to nuclear charge and finite size of nucleus.
F= analytic expression above
Log10(Ye) = 8.0
Z
N
This project is funded by the NSF through grant PHY0822648
and the Universities of JINA.