a r X i v :a s t r o -p h /0111505v 1 27 N o v 2001
Astronomy &Astrophysics manuscript no.(will be inserted by hand later)
On the duration of the subsonic propeller state of neutron stars
in wind-fed mass-exchange close binary systems
Nazar R.Ikhsanov 1,2
1
Max-Planck-Institut f¨u r Radioastronomie,Auf dem H¨u gel 69,D-53121Bonn,Germany e-mail:ikhsanov@mpifr-bonn.mpg.de
2
Central Astronomical Observatory of the Russian Academy of Sciences at Pulkovo,Pulkovo 65–1,196140Saint-Petersburg,Russia
Received ;accepted
by2怎么不火了Abstract.The condition for the subsonic propeller →accretor state transition of neutron stars in wind-fed mass-exchange binary systems is discussed.I show that the value of the break period,at which the neutron star change its state to accretor ,presented by Davies &Pringle (1981)is underestimated by a factor of 7.5.The correct value
is P br ≃450µ16/2130˙M −5/7
15(M/M ⊙)−4/21s.This result forced us to reconsider some basic conclusions on the efficiency of the propeller spindown mechanism.
Key words.accretion –propeller spindown –Stars:close binaries –Stars:neutron star
1.Introduction
The sequence of states which a magnetized neutron star in a wind-fed mass-exchange binary system follows as it spins down from the initially very short periods can be expressed in the form of the following chain:ejector →propeller →accretor .This classification,first suggested by Shvartsman (1970),reflects three different evolutionary stages and three different mechanisms of energy release responsible for the neutron star emission.
The spindown of a neutron star in the state of ejector is governed by the canonical spin-powered pulsar mech-anism.The spindown power dominates the star energy budget and is spent predominantly to the generation of magneto-dipole waves and particle acceleration.The pulsar-like spindown ceases when the pressure of the ma-terial being ejected by the neutron star can no longer bal-ance the pressure of the surrounding gas.The stellar wind plasma penetrates into the neutron star light cylinder and interacts with the star magnetosphere.This corresponds to the neutron star state transition:ejector →propeller .Neutron star in the state of propeller is spinning down due to the interaction between its fast rotating magneto-sphere and the surrounding material.Davies et al.(1979)and Davies &Pringle (1981)have shown that during this state the star magnetosphere is surrounded by a spherical quasi-static envelope in which the plasma temperature is of the order of the free-fall temperature,T (R )≃T ff(R )=
GM ns m p刘亦菲干爹陈金飞
V s (R m )
,
where R m is the magnetospheric radius,ω=2π/P s is the neutron star angular velocity and V s (R m )
is the sound speed at the magnetospheric radius,which according to Eq.(1)is of the order of the free-fall velocity,V ff:V s (R m )≃V ff(R m )=
R m
.
我只是个传说mv(2)
On this basis Davies et al.(1979)distinguished three sub-states of the propeller state 1:(b)very rapid rotator (κ≫1);(c)supersonic propeller (κ>∼1)and (d)subsonic propeller (κ<1).
In cases ‘b’and ‘c’the magnetospheric radius of the neutron star exceeds its corotational radius,R cor =
GM ns
1
According to their classification case ‘a’corresponds to the pulsar-like he ejector state.
阎维文母亲伴奏2Nazar R.Ikhsanov:On the duration of the subsonic propeller state This means that the neutron star in these cases is in the
centrifugal inhibition regime and hence,the effective ac-
cretion onto its surface is impossible.
In the case‘d’the magnetospheric radius is smaller
than the corotational radius.In this situation the plasma
being penetrated from the base of the envelope into the
star magneticfield is able toflow along the magneticfield
lines and to accrete onto the star surface.However the
effective plasma penetration into the magnetosphere does
not occur,if the magnetospheric boundary is interchange
stable.According to Arons&Lea(1976)and Elsner&
Lamb(1976)the onset condition for the interchange in-
stability of the magnetospheric boundary reads
T<T cr≃0.3Tff.
This means that the neutron star can change its state from
the subsonic propeller to accretor only when the cooling of
the envelope plasma(due to the radiation and convective
motions)dominates the energy input to the envelope due
to the propeller action by the neutron star.
Investigating this particular situation Davies&Pringle
(1981,hereafter DP81)have shown that the energy input
to the envelope dominates the energy losses until the spin
period of the star reaches the break period,P br.Assuming
the following values of the neutron star parameters:the
magnetic momentµ=1030µ30G cm3and the mass m=
1(M ns/M⊙),and putting the strength of the stellar wind
(in terms of the maximum possible accretion rate)˙M0=
莫小凤1015M15g s−1they estimated the value of the break period
as60s.
However,putting the same values of parameters and
value of P br to be of the order by a factor
of7.5larger than that previously estimated in DP81.In
this letter I present the calculations and show that this
result forced us to change some basic conclusions about
the origin of the long periods X-ray pulsars.
2.Break period
According to the picture presented by Davies&Pringle
the magnetosphere of the neutron star in the state of sub-
sonic propeller is surrounded by the adiabatic(p∝R−5/2)
spherically symmetrical plasma envelope.Until the energy
input to the envelope dominates the energy losses the tem-
perature of the envelope plasma is of the order of the free-
fall temperature,T≃Tffand,correspondingly,the sound
speed is of the order of the free-fall velocity,V s≃Vff.
Under this condition the height of the homogeneous atmo-
sphere through out the envelope is comparable to R and
thus,the envelope is extended from the magnetospheric
radius,
R m≃r m≡ µ2
2GM ns
2/7=(3)
=1.2×109cmµ4/7
30˙M−2/7
15
m−1/7,
up to the accretion radius of the neutron star,
Rα≡2GM ns
Energy radiated in the lifetime of a blob
.
Under the conditions of interest this parameter can be
expressed as(for discussion see DP81,page221)
Γ=M2Mach V t t br V2s R,(5)
where t br is the bremsstralung cooling time:
t br=6.3×104 T1011cm−3 −1s.(6)
Here,n is the number density of the envelope plasma
which at the base of the envelope can be evaluated as
n(R m)=
µ2
Nazar R.Ikhsanov:On the duration of the subsonic propeller state 3
As it has been shown in DP81the cooling of the envelope during the subsonic propeller state occurs first at its in-ner radius.Thus,the energy input to the envelope due to the neutron star propeller action dominates the radiative losses if Γ(R m )>∼1.
Combining Eqs.(1–7)I find the condition Γ(R m )>∼1to be satisfied if the spin period of the neutron star is P s <∼P br ,where the break period is P br ≃450µ16/21
30
˙M −5/715
m −4/21s .(8)
This value of the break period exceeds the value of
P br presented in DP81by a factor of 7.5(see Eq.4.8in DP81).Hence the natural question about the reason of this inconsistency arises.One of the most possible reasons is that Davies &Pringle have mistakenly used the value of
the magnetospheric radius:4.4×108µ4/730˙M −2/715
m −1/7
cm (see Eq. 3.2.3of their paper)instead of the correct value which is expressed in their paper by Eq.(2.5),
<109µ4/730˙M −2/715m −1/7
cm.Taking into account that P br (R m )∝R 5/2
m one finds that the correct value of P br should be larger than that derived in DP81by a factor of 7.very close to the value of the break period obtained in this letter.
3.Discussion
One of the main astrophysical reasons for the investiga-tion of the spindown of neutron stars is the existence of X-ray sources which display pulses with long periods (in excess of 100s).On the basis of their calculations Davies &Pringle suggested that the periods of neutron stars spin-ning down due to propeller mechanism can be as long as 100s only if the stars are situated in the weak stellar wind,
<˙M
0<4×1014g s −1.They also pointed out that in this case however it is difficult to account for a substantial pop-ulation of long period pulsators.
In the light of the recalculated value of the break pe-riod obtained in this paper (Eq.8)I find that the propeller mechanism can be responsible for the long spin period of a neutron star even if it is situated in the essentially stronger stellar wind:
˙M 0<∼8×1015µ16/1530
m −4/15P −7/5100g s −1,(9)
where P 100is the observed spin period of the neutron star
expressed in units of 100s.The corresponding spindown time-scale of the neutron star in the state of subsonic pro-peller is
τd ≃105µ−2
30m I 45P 100yr ,
(10)
4.Conclusion
The value of the break period at which the spinning down
neutron star changes its state from the subsonic propeller to accretor obtained by Davies &Pringle (1981)is un-derestimated by a factor of 7.5.The incorporation of the re-estimated value of the break period into the spindown scenario suggested by Davies &Pringle shows that the propeller mechanism can be responsible for the origin of the long period X-ray pulsators even if the strength of
the stellar wind,in which a neutron star is situated,is in excess of 1015g s −1.The analysis of the spin evolution of a neutron star situated in the strong stellar wind will be presented in a forthcoming paper.
Acknowledgements.I acknowledge the support of the Follow-up program of the Alexander von Humboldt Foundation.The work was partly supported by the Federal program “INTEGRATION”under the grant KO 232.
References
Arons J.,Lea S.M.,1976,ApJ 207,914
Davies R.E.,Fabian A.C.,Pringle J.E.,1979,MNRAS 186,779Davies R.E.,Pringle J.E.,1981,MNRAS 196,209(DP81)Elsner R.F.,Lamb F.K.,1976,Nature 262,356
Cox J.P.,Guili R.T.,1968,“Principles of Stellar Structure”,
Gordon &Breach,New York
Shvartsman V.F.,1970,Radiofizika 13,1852
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