Some characteristics of plasma in a white dwarf

Vanea COVLEA*, Alexandru JIPA, Marius CĂLIN*, Oana RISTEA, Cătălin RISTEA, Tiberiu EȘANU, Călin BEȘLIU, Ionel LAZANU

Atomic and Nuclear Chair, Department of Stucture of Matter, Atmospheric and Earth Physics, Astrophysics, Faculty of Physics, University of Bucharest, Romania

* vanea.covlea@yahoo.com, *mariuscalin@brahms.fizica.unibuc.ro

Some conclusion

Results

Data analysis

Bibliography 1. T. Padmanabhan – Theoretical Astrophysics, Volume II: Stars and Stellar Systems, Cambridge University Press, 2000 2. Arnab Rai Choudhuri – Astrophysics for Physicist, Cambridge University Press, 2010 3. Malcolm S. Longair – High Energy Astrophysics, 3rd Edition, Cambridge University Press, 2011 4. S. Chandrasekhar – An Introduction to the Study of Stellar Structure, The University of Chicago Press, 1938 Acknowledgment: This work was supported by a grant: PN-II-ID-PCE 34/05.10.2011 of the Romanian National Authority for Scientific Research, CNCS – UEFISCDI

For a white dwarf can be calculated the plasma parameters, taken into account the specific properties of such dense matter. From these preliminary calculations, the degenerate electron plasma of a white dwarf is a cold, extreme dense and strong coupled plasma.

The mass - radius relation for white dwarfs may be estimated using the usual algebraic approximation to the differential equations of stellar structure and an analytical approximation to the equation of state for degenerate electron gas.

with the Chandrasekhar’s mass

Debye length

Debye number

Langmuir frequency

Electron mean free path

Coulomb effective cross section

The end point in the evolution of main-sequence stars with an initial mass of consists of a degenerate core after the ejection of significant amount of matter in the form of a planetary nebula. The core will predominantly be made of helium or carbon. In such a remnant, the pressure support in the core is provided by an ideal (non-interacting) gas of degenerate electrons, whereas most of the mass density is contributed by a non-degenerate gas of carbon or helium ions. The Fermi energy of the electrons in such a system is higher than the kinetic temperature of the system and hence the electrons can be taken to be a zero-temperature Fermi gas. We have in such a white dwarf a degenerate electrons plasma. We try to calculate some specific parameters of plasma such as: Debye length, Langmuir frequency, Debye number, etc. Our calculation is based on white dwarfs with a mass between (0,8 - 1,4) a temperature from 10,000K to 30,000K and a core made of carbon (µe = 2).

M

M)8 - 1(

Debye length vs. mass ratio Debye number vs. mass ratio Langmuir frequency vs. mass ratio The electron mean free path at different temperatures

R(x106 m) ρ (x109 kg/m3) ne (x1036 m-3) ωp (x1018s-1)

0.8 6.94 1.42 0.4244 3.6855

0.9 6.181 2.01 0.6008 4.3852

1 5.421 2.979 0.8905 5.3374

1.1 4.641 4.747 1.419 6.739

1.2 3.802 8.639 2.5824 9.0901

1.3 2.824 21.081 6.3012 14.2005

1.4 1.413 168.05 50.2212 40.0915

Radius, density of white dwarf, number density of electrons and Langmuir frequency

Debye length and Debye number at different temperatures of a white dwarf for different mass ratio

Te (K) rC (x10-10

m) σ (x10-18

m2)

10,000 11,139 3,898

15,000 74,263 17,325

20,000 55,697 0,9745

25,000 44,558 0,6237

30,000 37,131 0,4331

The values of the Coulomb effective cross section for electron in white dwarf plasma

Introduction

Te=10,000K Te=15,000K Te=20,000K Te=25,000K Te=30,000K

M/Mo lmfp(x10-19 m) lmfp(x10-19 m) lmfp(x10-19 m) lmfp(x10-19 m) lmfp(x10-19 m)

0.8 60,448 13,600 241,792 377,754 544,047

0.9 42,700 96,072 170,800 266,866 384,310

1 28,824 64,853 115,299 180,149 259,430

1.1 18,079 40,676 72,316 112,990 162,715

1.2 0,9935 22,354 39,743 62,096 89,424

1.3 0,4071 0,9160 16,285 25,445 36,643

1.4 0,0510 0,1149 0,2043 0,3192 0,4597

The electron mean free path for white dwarf plasma at different temperatures

n

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01 l

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2

e

pm

ne

nmfp l

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Cr

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Ch MM

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Che M

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M

MRR

MM

M/MO

λD (x10-14 m) ND (x10-6)

M/MO

λD (x10-14 m) ND (x10-6)

M/MO

λD (x10-14 m) ND (x10-6)

M/MO

λD (x10-14 m) ND (x10-6)

M/MO

λD (x10-14 m) ND (x10-6)

0.8 1.0593 2.1132 0.8 1.297 3.878 0.8 1.4981 5.977 0.8 1.6749 8.3527 0.8 1.8348 10.9807

0.9 0.8903 1.7759 0.9 1.0904 3.262 0.9 1.2591 5.0234 0.9 1.4077 7.0201 0.9 1.542 9.2272

1 0.7313 1.4588 1 0.895 2.642 1 1.0342 4.126 1 1.1562 5.7652 1 1.2666 7.5795

1.1 0.5793 1.1556 1.1 0.709 2.1184 1.1 0.8192 3.2676 1.1 0.9159 4.5668 1.1 1.0034 6.0047

1.2 0.4294 0.8566 1.2 0.5259 1.573 1.2 0.6073 2.4228 1.2 0.679 3.3862 1.2 0.7438 4.4512

1.3 0.2749 0.5483 1.3 0.3367 1.0074 1.3 0.3887 1.5543 1.3 0.4346 2.1666 1.3 0.4761 2.8484

1.4 0.0973 0.1942 1.4 0.1192 0.3562 1.4 0.1377 0.5492 1.4 0.1539 0.7668 1.4 0.1686 1.0082

Te = 10,000K Te = 15,000K Te = 20,000K Te = 25,000K Te = 30,000K