- Email: [email protected]
The effect of binaries on the space velocity distribution of single pulsars
New Astronomy 4 (1999) 167–172 www.elsevier.nl / locate / newast
The effect of binaries on the space velocity distribution of single pulsars E. De Donder 1 , D. Vanbeveren 2 Astrophysical Institute, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium Received 21 November 1998; accepted 23 February 1999 Communicated by Edward P.J. van den Heuvel
Abstract In this paper we determine the theoretically expected space velocity distribution of single pulsars resulting from real single stars and from disrupted binaries. Hereto we use a population number synthesis (PNS) code that contains a detailed model for single and binary evolution. The binary period evolution and the effect of an asymmetric supernova on the binary parameters are followed in detail. If the progenitor of the pulsar was in a binary, disrupted by an asymmetric supernova explosion, the influence of the orbital velocity of the progenitor and of the binary potential is incorporated. We conclude that: (i) the shape of the pulsar space velocity distribution is mainly determined by the input kick distribution; (ii) the importance of binary evolution depends on the relative fraction of small and large kick velocities. 1999 Elsevier Science B.V. All rights reserved. PACS: 90; 97.60.–s; 97.60.Gb Keywords: Binaries: close; Supernovae; Stars: kinematics; Stars: neutron; Pulsars: general
1. Introduction In order to explain observed characteristics of single and binary neutron stars (NSs) (Portegies Zwart & Verbunt, 1996; De Donder et al., 1997; De Donder & Vanbeveren, 1998; Van den Heuvel & Van Paradijs, 1997) one is tempted to conclude that it is highly probable that NSs are accelerated at birth. The most plausible acceleration mechanism is an asymmetric supernova (SN) explosion. Small ( | 1%) asymmetries in the neutrino flux are sufficient to impart to the NS kicks of the order of 400 km / s (Shklovskii, 1969). 1 2
E-mail: [email protected] E-mail: [email protected]
Using new measurements of proper motions and distance determinations of radio pulsars, new pulsar space velocity distributions are derived with averages varying from | 300 km / s (Hansen & Phinney, 1996; Hartman, 1997) to | 500 km / s (Lorrimer et al., 1997). To determine theoretically the space velocity distribution one has to account for the possibility that a single pulsar may have had a binary past. In this case the pulsar velocity is a combination of the kick velocity at birth and of the orbital velocity of its progenitor before the SN explosion, corrected for the gravitational attraction of its companion immediately after the explosion. Since there is no preferential kick direction, the NS can be as well decelerated as accelerated by the kick in a binary. When a pulsar is
1384-1076 / 99 / $ – see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S1384-1076( 99 )00012-3
E. De Donder, D. Vanbeveren / New Astronomy 4 (1999) 167 – 172
168
born as a single one the observed space velocity is directly related to its kick velocity acquired at birth. In this study we investigate how strongly the predicted space velocity distribution is connected to its initial input kick velocity distribution. In Section 2 we give a short overview of all the assumptions made in our study. In Section 3 we present the model calculations and compare them to the observations.
2. The PNS model To derive theoretically the space velocity distribution of single pulsars we make use of a PNS code that we apply to a population of single stars and close binaries, formed in regions of continuous star formation. The population of single pulsars is simulated by starting from a primordial population (zero age main sequence) and by following the subsequent complete evolution in detail. The same PNS code was already used to derive the predicted output population of OB and WR star runaways, the formation rate of double compact binary stars and to predict the relative rates of SNe. A detailed description of the code and of the models used are given in Vanbeveren et al. (1998a); Vanbeveren et al. (1998b); Vanbeveren et al. (1998c). Here we only sum up the assumptions made: • a power law initial mass function C (M)~M 2g for both single star and primary star masses, • an initial mass ratio distribution f (q) that is flat and the one proposed by Hogeveen (1991), • a period distribution P (P) that is flat in log P (Popova et al., 1982; Abt, 1983) with P ranging from 1 day to 10 years, • an input kick velocity distribution f(vk ). We will consider the following three different types of input kick distributions: • a x 2 like distribution with an average kick velocity kvk l of 500 km / s, f(vk ) 5 1.96 3 10 26 v 3k / 2 e 2vk / 514 ,
(1)
• a x 2 like distribution with an average kick velocity kvk l of 150 km / s,
f(vk ) 5 2.70 3 10 25 v 3k / 2 e 2vk / 60 ,
(2)
• a double peaked kick distribution proposed by Fryer et al. (1998) with | 30% of the pulsars receiving a kick smaller than 50 km / s and | 70% receiving a kick between 500 and 700 km / s. We remark that a Gaussian velocity distribution is also often used. It gives the same results as when using a x 2 like distribution, though the x 2 like distribution describes better the high velocity tail of the space velocity distribution. • a massive binary formation rate f that defines the binary fraction at birth in a whole population of single and binary stars; let us remark here that in order to meet the observed frequency of binaries with a mass ratio q $ 0.2 and period P # 100 days, the total binary formation rate has to be larger than 0.75, • the most recent mass loss rate formulae for mass loss by stellar wind during the WR, RSG and LBV phase, • systems with an initial mass ratio q0 , 0.2 are assumed to merge, • case A / Br systems perform Roche Lobe Overflow (RLOF) for which we adopt the following b law, with b the fraction of mass lost by the primary during RLOF and that is accreted by the secondary:
H
b 5 bmax (5q 2 1) (0.2 # q , 0.4) b5 bmax (q $ 0.4)
with bmax 5 0.5 or 1, • late period systems, case Bc / C, evolve through common envelope evolution (CE). Here we use the spiral-in prescription of Webbink (1984) with 0 , a ce # 1, the efficiency parameter; remark that since we explicitly account for mass loss by stellar wind during evolution, the value of a ce is always smaller than or equal to 1, • systems with primary masses larger than 40 M( follow the Luminous Blue Variable scenario (LBV) (Vanbeveren, 1991), • single stars with an initial mass between 8 M( and 25 M( end their lives as a NS, • components of interacting binaries are considered
E. De Donder, D. Vanbeveren / New Astronomy 4 (1999) 167 – 172
to produce NSs in an initial mass range from 10 M( to 40 M( , • when a black hole (BH) is formed, no SN explosion is assumed to occur, • if a OB1CC (compact companion) performs spiral-in we also apply the formalism of Webbink with 0 , asp # 1, the efficiency parameter. Notice that the value of asp here may be different from ace in the case of a Bc / C binary during CE.
3. The theoretically predicted space velocity distribution
3.1. The first generation single pulsars Analytical formulae for the runaway velocity of the NS and the secondary after binary disruption have been derived by Tauris & Takens (1998). We consider successively all possible channels through which single pulsars can be formed out of binaries. We first perform our computations with the following combination of parameters: f 5 8, g 5 2.7, f (q) 5 flat, ace 5 0.5, asp 5 0.5, bmax 5 1 and a x 2
169
distribution with kvk l 5 500 km / s. For convenience we call this combination the standard parameter set. Starting from a population of single and binary stars we determine the velocity distribution of pulsars originating from binaries that were disrupted after the first SN explosion, from merged binaries and from real single stars. We will call these the first generation single pulsars. We assume that the kick distribution at birth is the same for single stars and binary components. The direction of the kick is supposed to be isotropically distributed. Fig. 1 gives the theoretically predicted velocity distribution of the first generation single pulsars that we expect to observe at birth. If we compare with the input kick distribution (dashed line) we may conclude that: • a slightly larger number of small space velocity pulsars are expected than given by the input kick distribution, however the overall binary effect is small and the shape of the final space velocity distribution of single pulsars is mainly determined by the shape of the input kick velocity distribution. When during disruption the kick is opposite
Fig. 1. Theoretically predicted space velocity distribution of single pulsars (full line) for the standard set of model parameters compared with the input kick distribution (dashed line).
170
E. De Donder, D. Vanbeveren / New Astronomy 4 (1999) 167 – 172
aligned to the pre-SN orbital velocity the resulting space velocity of the NS may be small. In this manner high kick velocities can produce low velocity pulsars. However their number is small. Further we see that the overall space velocity distribution is shifted to lower velocities revealing the effect of the gravitational deceleration of the NS by the OB companion. Although differences due to binary evolution show up, they are too small to observe and it is clear that the pulsar space velocity distribution is dominated by the input kick distribution for average kick velocities of the order of 500 km / s. To investigate the influence of the binary evolutionary parameters on the space velocity distribution, we made a number of calculations for different sets of PNS parameters f, g, f (q), ace , asp , bmax and kvk l (Section 2). These calculations allow us to conclude that: • the differences are small ( , 1%) and so the pulsar velocity distribution is practically independent of the parameters. For an input kick distribution with a lower average kick of 150 km / s, less systems are disrupted through the first SN explosion. Especially large period sys-
tems become disrupted in which the pre-SN orbital velocity of the NS is small and the gravitational influence of the OB companion on the NS is also small. A comparison between the input kick distribution and the predicted pulsar space velocity distribution is given in Fig. 2. Finally Fig. 3 gives the predicted space velocity distribution when using a double peaked input kick distribution as described in Section 2. A small fraction of low velocity pulsars is predicted and most of them come from single stars since kicks smaller than 50 km / s rarely disrupt binaries. We conclude that binary evolution may be important if the input kick velocity distribution has a significant fraction of small kick velocities.
3.2. The second generation of pulsars and the Thorne–Zytkow objects If the binary was not disrupted after the first SN explosion then a second asymmetric SN explosion may disrupt the binary producing two NSs. The old NS may be visible as a recycled pulsar and the other as a young pulsar. For an average kick of 500 km / s the fraction of systems that stays bound after the first SN explosion is of the order of 20%. Only a small fraction ( | 1%–3%, depending on the efficiency
Fig. 2. The same as Fig. 1 but for an average kick velocity of 150 km / s.
E. De Donder, D. Vanbeveren / New Astronomy 4 (1999) 167 – 172
171
Fig. 3. Theoretically predicted space velocity distribution of single pulsars (full line) for the standard set of model parameters compared with the double peaked input kick distribution (bars).
parameter asp ) of these systems survives the spiral-in phase. We have not explicitly calculated their velocity distribution but following the above reasoning we can say that their contribution is small and will
not considerably affect the final space velocity distribution of all single pulsars. A TZO is formed either by spiral-in or by a direct kick (immediately after the SN explosion) of the NS
Fig. 4. Theoretically predicted space velocity distribution of TZOs for the standard set of model parameters.
172
E. De Donder, D. Vanbeveren / New Astronomy 4 (1999) 167 – 172
into the OB star companion after the first SN explosion. The velocity of the TZO is the system velocity acquired during the asymmetric SN explosion. Our calculations predict the distribution given in Fig. 4. If the NS reappears as a pulsar, TZOs significantly contribute to low space velocity pulsars, however their percentage of the total pulsar population is only | 5%–15% (depending on the adopted model parameters). This percentage is small enough to conclude that their contribution to the overall population in the galactic disk is small but may be significant to the population in globular clusters. Observations reveal that a fraction of | 1%–10% of the neutron star population has to stay in the cluster after birth (Bhattacharya & van den Heuvel, 1991): TZOs may be possible progenitors. It is obvious that when the NS collapses to a BH through accretion, TZOs do not contribute to the pulsar population.
3.3. The velocity distribution of the OB star companion and its remnant NS After binary disruption the OB companion travels through space as a single star with a velocity ranging from 0 to 100 km / s. Since the average space velocity of the OB stars is small and kicks are random oriented, the space velocity distribution of the remnant NSs after the SN explosion of the single OB star is slightly broadened compared to the input kick velocity distribution and has the same average velocity.
4. Conclusion In this paper we have studied the space velocity of single pulsars resulting from single stars and from
disrupted binaries. It can be concluded that the effect of close binary evolution on the pulsar space velocity distribution is small when using a x 2 like or Gaussian distribution with mean velocities of 150 and 500 km / s. In this case the space velocity distribution reflects the input kick velocity distribution. Though when dealing with a kick velocity distribution which predicts a large number of small kick velocities, binaries may become important and the single pulsar velocity distribution may be broadened to values of | 100 km / s.
References Abt, H.A., 1983, ARA&A, 21, 343. Bhattacharya, D. & van den Heuvel, E.P.J., 1991, PhR, 203, 1. De Donder, E., Vanbeveren, D., & Van Bever, J., 1997, A&A, 318, 812. De Donder, E. & Vanbeveren, D., 1998, A&A, 333, 557. Fryer, C.L., Burrows, A., & Benz, W., 1998, ApJ, 496, 333. Hansen, B.M.S. & Phinney, E.S., 1996, AAS, 189, 7402. Hartman, J.W., 1997, A&A, 322, 127. Hogeveen, S.J., 1991, Ph.D. Thesis, University of Illinois, Urbana. Lorrimer, D.R., Bailes, M., & Harrison, P.A., 1997, MNRAS, 289, 592. Popova, E.I., Tutukov, A.V., & Yungelson, L.R., 1982, Ap&SS, 88, 55. Portegies Zwart, S.F. & Verbunt, F., 1996, A&A, 309, 179. Shklovskii, I.S., 1969, SvA, 13, 562. Tauris, T.M. & Takens, R.J., 1998, A&A, 330, 1047. Vanbeveren, D., 1991, A&A, 252, 159. Vanbeveren, D., De Donder, E., Van Bever, J., Van Rensbergen, W., & De Loore, C., 1998a, NewA, 3, 443. Vanbeveren, D., Van Rensbergen, W., & De Loore, C., 1998b, in: The Brightest Binaries, Kluwer, Dordrecht. Vanbeveren, D., Van Rensbergen, W., & De Loore, C., 1998c, A&ARv, 9, 63. Van den Heuvel, E.P.J. & Van Paradijs, J., 1997, ApJ, 483, 399. Webbink, R.F., 1984, ApJ, 277, 355.
The effect of binaries on the space velocity distribution of single pulsars E. De Donder 1 , D. Vanbeveren 2 Astrophysical Institute, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium Received 21 November 1998; accepted 23 February 1999 Communicated by Edward P.J. van den Heuvel
Abstract In this paper we determine the theoretically expected space velocity distribution of single pulsars resulting from real single stars and from disrupted binaries. Hereto we use a population number synthesis (PNS) code that contains a detailed model for single and binary evolution. The binary period evolution and the effect of an asymmetric supernova on the binary parameters are followed in detail. If the progenitor of the pulsar was in a binary, disrupted by an asymmetric supernova explosion, the influence of the orbital velocity of the progenitor and of the binary potential is incorporated. We conclude that: (i) the shape of the pulsar space velocity distribution is mainly determined by the input kick distribution; (ii) the importance of binary evolution depends on the relative fraction of small and large kick velocities. 1999 Elsevier Science B.V. All rights reserved. PACS: 90; 97.60.–s; 97.60.Gb Keywords: Binaries: close; Supernovae; Stars: kinematics; Stars: neutron; Pulsars: general
1. Introduction In order to explain observed characteristics of single and binary neutron stars (NSs) (Portegies Zwart & Verbunt, 1996; De Donder et al., 1997; De Donder & Vanbeveren, 1998; Van den Heuvel & Van Paradijs, 1997) one is tempted to conclude that it is highly probable that NSs are accelerated at birth. The most plausible acceleration mechanism is an asymmetric supernova (SN) explosion. Small ( | 1%) asymmetries in the neutrino flux are sufficient to impart to the NS kicks of the order of 400 km / s (Shklovskii, 1969). 1 2
E-mail: [email protected] E-mail: [email protected]
Using new measurements of proper motions and distance determinations of radio pulsars, new pulsar space velocity distributions are derived with averages varying from | 300 km / s (Hansen & Phinney, 1996; Hartman, 1997) to | 500 km / s (Lorrimer et al., 1997). To determine theoretically the space velocity distribution one has to account for the possibility that a single pulsar may have had a binary past. In this case the pulsar velocity is a combination of the kick velocity at birth and of the orbital velocity of its progenitor before the SN explosion, corrected for the gravitational attraction of its companion immediately after the explosion. Since there is no preferential kick direction, the NS can be as well decelerated as accelerated by the kick in a binary. When a pulsar is
1384-1076 / 99 / $ – see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S1384-1076( 99 )00012-3
E. De Donder, D. Vanbeveren / New Astronomy 4 (1999) 167 – 172
168
born as a single one the observed space velocity is directly related to its kick velocity acquired at birth. In this study we investigate how strongly the predicted space velocity distribution is connected to its initial input kick velocity distribution. In Section 2 we give a short overview of all the assumptions made in our study. In Section 3 we present the model calculations and compare them to the observations.
2. The PNS model To derive theoretically the space velocity distribution of single pulsars we make use of a PNS code that we apply to a population of single stars and close binaries, formed in regions of continuous star formation. The population of single pulsars is simulated by starting from a primordial population (zero age main sequence) and by following the subsequent complete evolution in detail. The same PNS code was already used to derive the predicted output population of OB and WR star runaways, the formation rate of double compact binary stars and to predict the relative rates of SNe. A detailed description of the code and of the models used are given in Vanbeveren et al. (1998a); Vanbeveren et al. (1998b); Vanbeveren et al. (1998c). Here we only sum up the assumptions made: • a power law initial mass function C (M)~M 2g for both single star and primary star masses, • an initial mass ratio distribution f (q) that is flat and the one proposed by Hogeveen (1991), • a period distribution P (P) that is flat in log P (Popova et al., 1982; Abt, 1983) with P ranging from 1 day to 10 years, • an input kick velocity distribution f(vk ). We will consider the following three different types of input kick distributions: • a x 2 like distribution with an average kick velocity kvk l of 500 km / s, f(vk ) 5 1.96 3 10 26 v 3k / 2 e 2vk / 514 ,
(1)
• a x 2 like distribution with an average kick velocity kvk l of 150 km / s,
f(vk ) 5 2.70 3 10 25 v 3k / 2 e 2vk / 60 ,
(2)
• a double peaked kick distribution proposed by Fryer et al. (1998) with | 30% of the pulsars receiving a kick smaller than 50 km / s and | 70% receiving a kick between 500 and 700 km / s. We remark that a Gaussian velocity distribution is also often used. It gives the same results as when using a x 2 like distribution, though the x 2 like distribution describes better the high velocity tail of the space velocity distribution. • a massive binary formation rate f that defines the binary fraction at birth in a whole population of single and binary stars; let us remark here that in order to meet the observed frequency of binaries with a mass ratio q $ 0.2 and period P # 100 days, the total binary formation rate has to be larger than 0.75, • the most recent mass loss rate formulae for mass loss by stellar wind during the WR, RSG and LBV phase, • systems with an initial mass ratio q0 , 0.2 are assumed to merge, • case A / Br systems perform Roche Lobe Overflow (RLOF) for which we adopt the following b law, with b the fraction of mass lost by the primary during RLOF and that is accreted by the secondary:
H
b 5 bmax (5q 2 1) (0.2 # q , 0.4) b5 bmax (q $ 0.4)
with bmax 5 0.5 or 1, • late period systems, case Bc / C, evolve through common envelope evolution (CE). Here we use the spiral-in prescription of Webbink (1984) with 0 , a ce # 1, the efficiency parameter; remark that since we explicitly account for mass loss by stellar wind during evolution, the value of a ce is always smaller than or equal to 1, • systems with primary masses larger than 40 M( follow the Luminous Blue Variable scenario (LBV) (Vanbeveren, 1991), • single stars with an initial mass between 8 M( and 25 M( end their lives as a NS, • components of interacting binaries are considered
E. De Donder, D. Vanbeveren / New Astronomy 4 (1999) 167 – 172
to produce NSs in an initial mass range from 10 M( to 40 M( , • when a black hole (BH) is formed, no SN explosion is assumed to occur, • if a OB1CC (compact companion) performs spiral-in we also apply the formalism of Webbink with 0 , asp # 1, the efficiency parameter. Notice that the value of asp here may be different from ace in the case of a Bc / C binary during CE.
3. The theoretically predicted space velocity distribution
3.1. The first generation single pulsars Analytical formulae for the runaway velocity of the NS and the secondary after binary disruption have been derived by Tauris & Takens (1998). We consider successively all possible channels through which single pulsars can be formed out of binaries. We first perform our computations with the following combination of parameters: f 5 8, g 5 2.7, f (q) 5 flat, ace 5 0.5, asp 5 0.5, bmax 5 1 and a x 2
169
distribution with kvk l 5 500 km / s. For convenience we call this combination the standard parameter set. Starting from a population of single and binary stars we determine the velocity distribution of pulsars originating from binaries that were disrupted after the first SN explosion, from merged binaries and from real single stars. We will call these the first generation single pulsars. We assume that the kick distribution at birth is the same for single stars and binary components. The direction of the kick is supposed to be isotropically distributed. Fig. 1 gives the theoretically predicted velocity distribution of the first generation single pulsars that we expect to observe at birth. If we compare with the input kick distribution (dashed line) we may conclude that: • a slightly larger number of small space velocity pulsars are expected than given by the input kick distribution, however the overall binary effect is small and the shape of the final space velocity distribution of single pulsars is mainly determined by the shape of the input kick velocity distribution. When during disruption the kick is opposite
Fig. 1. Theoretically predicted space velocity distribution of single pulsars (full line) for the standard set of model parameters compared with the input kick distribution (dashed line).
170
E. De Donder, D. Vanbeveren / New Astronomy 4 (1999) 167 – 172
aligned to the pre-SN orbital velocity the resulting space velocity of the NS may be small. In this manner high kick velocities can produce low velocity pulsars. However their number is small. Further we see that the overall space velocity distribution is shifted to lower velocities revealing the effect of the gravitational deceleration of the NS by the OB companion. Although differences due to binary evolution show up, they are too small to observe and it is clear that the pulsar space velocity distribution is dominated by the input kick distribution for average kick velocities of the order of 500 km / s. To investigate the influence of the binary evolutionary parameters on the space velocity distribution, we made a number of calculations for different sets of PNS parameters f, g, f (q), ace , asp , bmax and kvk l (Section 2). These calculations allow us to conclude that: • the differences are small ( , 1%) and so the pulsar velocity distribution is practically independent of the parameters. For an input kick distribution with a lower average kick of 150 km / s, less systems are disrupted through the first SN explosion. Especially large period sys-
tems become disrupted in which the pre-SN orbital velocity of the NS is small and the gravitational influence of the OB companion on the NS is also small. A comparison between the input kick distribution and the predicted pulsar space velocity distribution is given in Fig. 2. Finally Fig. 3 gives the predicted space velocity distribution when using a double peaked input kick distribution as described in Section 2. A small fraction of low velocity pulsars is predicted and most of them come from single stars since kicks smaller than 50 km / s rarely disrupt binaries. We conclude that binary evolution may be important if the input kick velocity distribution has a significant fraction of small kick velocities.
3.2. The second generation of pulsars and the Thorne–Zytkow objects If the binary was not disrupted after the first SN explosion then a second asymmetric SN explosion may disrupt the binary producing two NSs. The old NS may be visible as a recycled pulsar and the other as a young pulsar. For an average kick of 500 km / s the fraction of systems that stays bound after the first SN explosion is of the order of 20%. Only a small fraction ( | 1%–3%, depending on the efficiency
Fig. 2. The same as Fig. 1 but for an average kick velocity of 150 km / s.
E. De Donder, D. Vanbeveren / New Astronomy 4 (1999) 167 – 172
171
Fig. 3. Theoretically predicted space velocity distribution of single pulsars (full line) for the standard set of model parameters compared with the double peaked input kick distribution (bars).
parameter asp ) of these systems survives the spiral-in phase. We have not explicitly calculated their velocity distribution but following the above reasoning we can say that their contribution is small and will
not considerably affect the final space velocity distribution of all single pulsars. A TZO is formed either by spiral-in or by a direct kick (immediately after the SN explosion) of the NS
Fig. 4. Theoretically predicted space velocity distribution of TZOs for the standard set of model parameters.
172
E. De Donder, D. Vanbeveren / New Astronomy 4 (1999) 167 – 172
into the OB star companion after the first SN explosion. The velocity of the TZO is the system velocity acquired during the asymmetric SN explosion. Our calculations predict the distribution given in Fig. 4. If the NS reappears as a pulsar, TZOs significantly contribute to low space velocity pulsars, however their percentage of the total pulsar population is only | 5%–15% (depending on the adopted model parameters). This percentage is small enough to conclude that their contribution to the overall population in the galactic disk is small but may be significant to the population in globular clusters. Observations reveal that a fraction of | 1%–10% of the neutron star population has to stay in the cluster after birth (Bhattacharya & van den Heuvel, 1991): TZOs may be possible progenitors. It is obvious that when the NS collapses to a BH through accretion, TZOs do not contribute to the pulsar population.
3.3. The velocity distribution of the OB star companion and its remnant NS After binary disruption the OB companion travels through space as a single star with a velocity ranging from 0 to 100 km / s. Since the average space velocity of the OB stars is small and kicks are random oriented, the space velocity distribution of the remnant NSs after the SN explosion of the single OB star is slightly broadened compared to the input kick velocity distribution and has the same average velocity.
4. Conclusion In this paper we have studied the space velocity of single pulsars resulting from single stars and from
disrupted binaries. It can be concluded that the effect of close binary evolution on the pulsar space velocity distribution is small when using a x 2 like or Gaussian distribution with mean velocities of 150 and 500 km / s. In this case the space velocity distribution reflects the input kick velocity distribution. Though when dealing with a kick velocity distribution which predicts a large number of small kick velocities, binaries may become important and the single pulsar velocity distribution may be broadened to values of | 100 km / s.
References Abt, H.A., 1983, ARA&A, 21, 343. Bhattacharya, D. & van den Heuvel, E.P.J., 1991, PhR, 203, 1. De Donder, E., Vanbeveren, D., & Van Bever, J., 1997, A&A, 318, 812. De Donder, E. & Vanbeveren, D., 1998, A&A, 333, 557. Fryer, C.L., Burrows, A., & Benz, W., 1998, ApJ, 496, 333. Hansen, B.M.S. & Phinney, E.S., 1996, AAS, 189, 7402. Hartman, J.W., 1997, A&A, 322, 127. Hogeveen, S.J., 1991, Ph.D. Thesis, University of Illinois, Urbana. Lorrimer, D.R., Bailes, M., & Harrison, P.A., 1997, MNRAS, 289, 592. Popova, E.I., Tutukov, A.V., & Yungelson, L.R., 1982, Ap&SS, 88, 55. Portegies Zwart, S.F. & Verbunt, F., 1996, A&A, 309, 179. Shklovskii, I.S., 1969, SvA, 13, 562. Tauris, T.M. & Takens, R.J., 1998, A&A, 330, 1047. Vanbeveren, D., 1991, A&A, 252, 159. Vanbeveren, D., De Donder, E., Van Bever, J., Van Rensbergen, W., & De Loore, C., 1998a, NewA, 3, 443. Vanbeveren, D., Van Rensbergen, W., & De Loore, C., 1998b, in: The Brightest Binaries, Kluwer, Dordrecht. Vanbeveren, D., Van Rensbergen, W., & De Loore, C., 1998c, A&ARv, 9, 63. Van den Heuvel, E.P.J. & Van Paradijs, J., 1997, ApJ, 483, 399. Webbink, R.F., 1984, ApJ, 277, 355.