High Neutron Star Birth Velocities and Gravitational Radiation During Supernova Explosions

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arXiv:astro-ph/9701073v2 15 Jan 1997 h olpe(ogl,tebnigeeg faneutron a of energy rem- during binding a released the as is star (roughly, energy holes collapse of black amount the possibly, enormous or, An nant. stars neutron hind 0 mshsrcnl enotie rmosrain of least observations at from of obtained velocity been kick recently a has for km/s evidence 100 direct explo- velocities a addi- supernova Next, high the without sion. during obtained Such velocity”) be (“kick 1994). recoil hardly al. tional could et pulsars (Frail young velocities km/s of pulsar 900 higher to su- even up young revealed Lorimer with remnants & associated (Lyne pernova pulsars km/s of of 400-500 led Observations factor about 1994). scale a of values by distance to velocities pulsar up pulsar two the observed the of increasing sup- revision to observational the serious First, receive port. to anisotropy collapse (1970). Shklovskii and rse ovnetyi em ftefato fteenergy the of the (ex- fraction anisotropy the in released, of collapse escape terms This in conveniently can symmetrical. pressed collapse it purely the of not that provided is part radiation a gravitational of neutrinos, form by away ried rt oe fmsie( degen- are massive evolved Ib of of and cores collapse II gravitational erate type the Supernovae by nature. triggered in known events Gravitational S.N.Nazin Explosions and Supernova Velocities during Birth Radiation Star Neutron High 1 2 eto aefo ihnadsac f3 p.A the At Mpc. 30 of interferometers distance laser de- a advanced their of within and rms-level from explosions emitted supernova rate waves Ib tection and gravitational II we of type cores, during amplitude stellar the of collapse compute asymmetric during originate Abstract. 1996 ..., accepted 1996, ... Received uenve general Supernovae: words: Key year. rqece 300 frequencies 1(20.;0.41 08.19.4) 08.14.1; (02.07.2; 01 are: codes thesaurus later) Your hand by inserted be (will no. manuscript A&A trbr srnmclIsiue ocwUiest,119 University, Moscow Institute, Astronomical Sternberg aut fPyis ocwUiest,173 ocw Russ Moscow, 117234 University, Moscow Physics, of Faculty trqie oeta 0yasfrteie fthe of idea the for years 20 than more required It uenv xlsosaeaogtems violent most the among are explosions Supernova ∼ 0 . 15 ǫM M 1 suigteosre usrvlcte to velocities pulsar observed the Assuming ⊙ n ..Postnov K.A. and ⊙ c 2 rvttoa ae tr:nurn— neutron Stars: — waves Gravitational − c a rtitoue yOeny(1965) Ozernoy by introduced first was ) 2 00H h xetdrt saot1per 1 about is rate expected the Hz 1000 .Atog oto hseeg scar- is energy this of most Although ). > 0M 10 ⊙ 1 , tr n ev be- leave and stars ) 2 h ≈ 10 − 22 at 9 ocw Russia Moscow, 899 ia f distributed velocity kick (3-D) as repro- space the best the assuming are that duced velocities found transverse they pulsar evolution Machine”), Lyne-Lorimer star “Scenario binary so-called of (the calculations Monte-Carlo Using high direct 1996a,b). at Prokhorov form & asymptotic Postnov power-law (Lipunov, neu- a velocities a has to birth imparted at velocity star kick tron the that recognition a was 1992; Imshennik also (see observed ability 1993). as Bisnovatyi-Kogan the km/s, velocities shown kick 400-500 may produce has of to birth (1996) emission calcula- anisotropic Hayes at recent neutrino & star of example, Burrows For neutron of reasons. a different tions of to velocity due result- kick be asymmetry the collapse the in The in 1996). J0045-7319 ing al. PSR et in (Kaspi orbit SMC pulsar binary precessing where lwrta h awlintail maxwellian the than slower bu aigti itiuini hta ihvelocities high at that is distribution ( this having about te eto tr cur tbrhsget a oesti- to way a suggests birth at acquire stars neutron ities con- realistic being uncertainties from and involved. difficulties far numerical enormous still all sidering are Unfortunately, review). calculations a these for Müller 1996 (see output ( cluster dis- Virgo the of from detectable tance be To (GW). waves (e.g. gravitational distribution velocity 1996). kick Spreeuw the & Zwart for Portegies assumed is times nnmrclcluain hseeg a enfudto found 10 been typically has tiny, energy very this be calculations numerical in nryeitddrn Nepoinsol eabout be should GW explosion the SN a detectors, ∆ during bar emitted and energy interferometric laser based > v ( E x n ftecneune fLn n oie’ result Lorimer’s and Lyne of consequences the of One eetees h eonto fhg diinlveloc- additional high of recognition the Nevertheless, of source a be may collapse stellar anisotropic The ) 10 = ∝ 0 ms tge rcial as practically goes it km/s) 500 x 1+ (1 − = 3 M x v/v x 0 6 ⊙ . . 19 72 c 0 2 , ) 1 Ton 95 cuz19) However, 1996). Schutz 1995; (Thorne v / 0 2 0 ms nipratthing important An km/s. 400 = ∼ − 9 8Mc yftr ground- future by Mpc) 18 − 10 ∝ − exp( 7 v ftettlenergy total the of ASTROPHYSICS − − ASTRONOMY 3 v . 17 2 19.5.2018 ,wihsome- which ), hti much is that , AND (1) 2 S.N.Nazin et al.: High Neutron Star Birth Velocities and Gravitational Radiation during Supernova Explosions mate ǫ from observations, regardless of the unknown collapse anisotropy mechanism(s). Indeed, the kinetic energy 2 of the neutron star motion, ∆E = MNSv /2, where MNS is the neutron star mass, may be considered as a lower limit to the energy emitted in GW. Assuming MNS =1.4 2 M⊙, we obtain ǫ =0.7 (v/c) . With the distribution law (1) the fraction of high× velocity pulsars is ∞ P (> x)= f(ξ)dξ 0.38 x−2.17 (2) Zx ≃ (the power-law asymptotics is valid for x > 2). For example, the fraction of pulsars with v > 1000 km/s is 0.05. Of course, there should exist a maximum cut- off≈ velocity; it must be higher than the maximum pulsar velocities observed, 2000 km/s (x > 5), but its exact value only slightly changes∼ the normalization coefficient. For ǫ = 10−4 (v 3200 km/s) we obtain P (> 8) 0.004, i.e. every 250-th≈ neutron star may be born with the≈ high velocity required. The neutron star galactic birth-rate is determined by that of massive (> 10 M⊙) stars, which is 1/25 years ≈ −2 35 assuming Salpeter mass function f(M)dM M . dM Fig. 1. The log N(> hc) − log hc curve of the number of ∝ GW-bursts caused by core collapse supernovae as seen by a and the mean galactic star formation rate of 1 M⊙ per h year. Using the relations ǫ =0.7(v/c)2, x = v/(400km/s) GW-detector with an rms-sensitivity c at the unitary signal-to-noise ratio in 1-year integration time. The supernova and Eq. (2) we may write galactic birth rate of high- rate are calculated for the baryonic matter distribution within velocity pulsars as the region of 30 Mpc from Sun according to Tully’s Nearby −2.17 −1 −5 −1.085 −1 Galaxies Catalog (Tully 1988) with account for the SN-rate R =0.38/25 x yr 1.3 10 ǫ−3 yr (3) ≈ × dependence on the morphological type of the galaxies. The (here and below subscripts indicate the quantities mea- distribution of SN-generated GW-amplitudes is taken assum- sured in units of the corresponding power of ten, e.g. ing Lyne-Lorimer kick velocity distribution (see the text). The −3 hatched region encompasses the assumed GW frequencies from ǫ−3 ǫ/10 ) The≡ characteristic amplitude of the GW burst from a 1 kHz (lower boundary) to 300 Hz (upper boundary). The bro- ken curve represents the SN rate assuming constant GW energy SN located at a distance r is (Thorne 1987; Schutz 1996) −4 fraction ǫ = 10 (from Lipunov et al. 1995) with contributions 1/2 of local group of galaxies indicated. −22 1/2 1kHz 18Mpc hc =5 10 ǫ−3 (4) × fc r where fc is the characteristic frequency of the burst. This the realistic baryon matter distribution within 30 Mpc level should be detectable by the advanced LIGO inter- ≈ ferometer. The event rate from the volume V of the Uni- according to Tully’s Nearby Galaxies Catalog (Tully 1988) verse is (e.g. Phinney 1991; see also Lipunov, Postnov & (see Lipunov et al. 1995 for more detail). The result is pre- 3 Prokhorov 1996b) 0.01 (galactic rate) (V/Mpc ). sented in Fig. 1. The hatched region corresponds to GW- Using Eqs. (3) andR≈ (4) we find× × frequencies of the signal from 300 Hz (upper boundary) to 1 kHz (lower boundary). For comparison, we reproduce the 4 −1 0.42 −3/2 −3 log N log h calculated for constant ǫ = 10− (Lipunov et (0.08yr ) ǫ−4 f1 h−22 R≈ kHz (5) al. 1995).− Clearly, the more realistic ǫ-distribution yields −1 0.42 −3/2 −3 (1yr ) ǫ−3 f h−22 . an order of magnitude smaller event rate because the rate ≈ 300Hz of SN explosions with higher ǫ strongly decreases. The This means that we have chance to observe 1 GW-burst shape of the curve is smoothed by the f(v) distribution. per year caused by SN II and Ib explosions at a level of −22 The mean ǫ for Lyne-Lorimer velocity distribution (1) is h = 10 provided that the energy is carried out at 2 6 rms ǫ v f(v)dv 4.4 10− . the frequency 300 Hz. h i∝ ≈ × R Since hc √ǫ v, the distribution of the GW-bursts It is seen from the figure that a few events per year are caused by the∝ SN∼ explosions from a given distance r will expected at the noise level of the advanced-LIGO rms- have the form (1). This enable us to compute the cumula- sensitivity 10−22. At the initial laser interferometers ∼ −21 tive distribution of the number of events with the ampli- sensitivity level hrms 10 the expected SN rate is tude higher than a given one (log N(>h ) log h ) using very low, 0.01 per year.≈ c − c ∼ S.N.Nazin et al.: High Neutron Star Birth Velocities and Gravitational Radiation during Supernova Explosions 3

In our analysis, we have not used any particular mech- Phinney, E.S. 1991, ApJ 380, L17 anism for the collapse anisotropy and tried to rely on Portegies Zwart, S.F., Spreeuw, H.N. 1996, A&A 312, 670 the observational properties of pulsars which are reliable Shklovskii, I.S. 1970, AZh 46, 715 products of supernova explosions. The only assumption Schutz, B.F. 1996, in Les Houches Astrophysical School on we used is that the pulsar kick velocities are entirely due Gravitational Waves, edited by J.-A. Mark and J.-P. La- to the supernova explosion asymmetry. Of course, not ev- sota (Cambridge Univ. Press, Cambridge, England, 1996, in press) (preprint AEI-003 February 1996) ery core collapse supernova may give rise to a pulsar. For Thorne, K.S. 1987, in 300 Years of Gravitation, edited by S.W. example, some pulsar studies suggest the galactic pulsar Hawking and W. Israel (Cambridge University Press, Cam- birth-rate 1/125 1/250 yr−1 (Lorimer et al. 1993), much − bridge, England) smaller than the galactic SN II rate. Additionally, some Thorne, K.S. 1995, in Particle and Nuclear Astrophysics and other mechanisms of the collapse anisotropy may oper- Cosmology in the Next Millenium, edited by E.W. Kolb and ate. This means that our results can be considered as a R.D. Peccei (World Scientiﬁc Publ., Singapore) lower limit and the actual detection rate may be higher. Tully, R.B. 1988, Nearby Galaxies Catalog (Cambridge Univer- We conclude that insofar as the observed pulsar velocities sity Press, Cambridge, England) is a measure of the core collapse anisotropy, gravitational radiation bursts from supernova explosions should be detectable by the advanced laser interferometers and bar detectors in 1-year integration. The authors thank Prof. Vladimir Lipunov for helpful discussions. The work is supported by the INTAS grant No 93-3364, grant of Russian Fund for Basic Research No 95-02-6053 and by the Center for Cosmoparticle Physics “COSMION” (Moscow, Russia). The work of S.Nazin was also supported by the grant of ISSEP No a96-1523.

Note added in proof In a recent paper, Hartman (1996) argued that the observed transverse pulsar velocity distribution is repro- duced equally well assuming the Paczy´nski (1990) distribution for initial pulsar velocity p(x)dx (1 + x2)−2 with x = v/(600km/s). The same analysis∝ as for our distribution (1) shows that the resulting log N(> hc) log hc curve does not change appreciably giving appoximately− the same ǫ 4 10−6. h i≈ ×

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