Neutron star natal kick and jets in core collapse supernovae
DDraft version December 18, 2017
Preprint typeset using L A TEX style emulateapj v. 12/16/11
NEUTRON STAR NATAL KICK AND JETS IN CORE COLLAPSE SUPERNOVAE
Ealeal Bear and Noam Soker Draft version December 18, 2017
ABSTRACTWe measure the angle between the neutron star (NS) natal kick direction and the inferred directionof jets according to the morphology of 12 core collapse supernova remnants (SNR), and find that thedistribution is almost random, but missing small angles. The 12 SNRs are those for which we couldboth identify morphological features that we can attribute to jets and for which the direction of theNS natal kick is given in the literature. Unlike some claims for spin-kick alignment, here we rule outjet-kick alignment. We discuss the cumulative distribution function of the jet-kick angles under theassumption that dense clumps that are ejected by the explosion accelerate the NS by the gravitationalattraction, and suggest that the jet feedback explosion mechanism might in principle account for thedistribution of jet-kick angles. INTROCUTIONMany core collapse supernovae (CCSNe) leave behind aneutron star (NS) remnant that is born with a significantnon-zero velocity, called natal kick velocity, with typicalvalues of 200 −
500 km s − and up to about 1000 km s − (e.g., Cordes et al. 1993; Lyne & Lorimer 1994; Chat-terjee et al. 2005). These values are larger than whatcan be accounted for by the disruption of a close binarysystem. Therefore, it is likely that an asymmetrical ex-plosion mechanism is the cause of the natal kick velocity(e.g., Lai et al. 2006; Wongwathanarat et al. 2013; forrecent summary of many studies on the natal kick seeJanka 2017). In a recent through study, Katsuda et al.(2018) find from X-ray measurements of six supernovaremnants (SNRs) that elements between silicon and cal-cium are generally ejected opposite to the direction ofNS motion. This, they argue, supports the connection ofNS natal kick to asymmetrical explosion.Other mechanisms that have been proposed in thepast, cannot work. Asymmetric neutrino emission by it-self cannot account for the observed kick velocities (e.g.,Lai 2003; Wongwathanarat et al. 2010; Nordhaus et al.2010, 2012; Katsuda et al. 2018 and references therein).Scenarios that are based on momentum imparted byasymmetrical two opposite jets cannot explain the highnatal kick velocities as they require massive jets, andhence, as argued by, e.g., Nordhaus et al. (2012), theyrequire rapid pre-collapse core rotation, and therefore,this scenario might be at best viable for a small por-tion of natal kick cases. Possible combinations of thesescenarios have also been raised. For example, the com-bination of magnetic fields and rapid rotation which cancause jets that might induce a kick (e.g., see discussionby Wang et al. 2006). As the source of the momentumof the NS is the two asymmetrical opposite jets, accord-ing to this mechanism the jets’ axis (defined as the linealong the directions of the two opposite jets) and kickdirection tend to be aligned. This is in contradictionwith the results we present in the present study. In whatfollow we will not consider these and other mechanisms Department of Physics, Technion – Israel Instituteof Technology, Haifa 32000, Israel; [email protected];[email protected] (e.g., Charbonneau & Zhitnitsky 2010), and we will referonly to asymmetrical explosion mechanisms that impartmomentum to the newly born NS.Many observational and theoretical papers study anddiscuss the relation between the spin and kick directions(e.g., Spruit & Phinney 1998; Fryer & Kusenko 2006; Ng& Romani 2007; Wang et al. 2007). In the Crab nebula(Kaplan et al. 2008) and the Vela nebula (Lai et al. 2001)observations imply an almost alignment between the NSkick direction and the spin direction. While some papersfind a strong correlation between the kick and the spindirections (e.g., Dodson et al. 2003; Johnston et al. 2005,2006), other papers, such as Bray & Eldridge (2016), findno statistical preference for the kick orientation. Ng &Romani (2006) find that spin-kick angle in the pulsar ofthe Crab nebula is 26 ◦ rather than the previously deter-mined angle of 8 ◦ (also Wang et al. 2007).In a recent study Holland-Ashford et al. (2017) com-pare both the directions and magnitudes of the NSkick velocities with the asymmetrical geometry of SNRs.They look at the dipole, quadrupole, and octupole power-ratios of the SNR morphologies, and find no correlationof SNR asymmetry with the magnitude of the kick ve-locity. They do find that the NS kick directions are pref-erentially opposite to the bulk of the X-ray emission.In the present study we compare kick directions withanother geometrical property of the SNRs. We exam-ine the relation between the kick direction and the lineconnecting the two opposite ears of SNR, or other mor-phological features that hint at jets. We follow Grichener& Soker (2017) and generally define ears as two oppositeprotrusions from the main SNR shell. We further takethe view that the ears were shaped by jets launched fromthe newly born NS during the explosion of the SN (Grich-ener & Soker 2017; Bear et al. 2017). The ears’ axis isdefined as the line connecting the tips of the two ears.Hence, from here on we will refer to ears’ axis and jets’axis as meaning the same, but keep in mind that whatwe observe in the SNRs are the ears.It is not clear if the jets we study here can leave a markduring the SN phase itself. Piran et al. (2018) attributethe excess of high velocity material in hydrogen-strippedCCSNe to relativistic choked jets that accelerated mate-rial to high velocities. The jets we discuss here might be a r X i v : . [ a s t r o - ph . H E ] D ec weaker and the SN main shell more massive. From thetypical ears we observe during the SNR phase, we canestimate that the velocity of the ears is only ≈ − erg (Papish & Soker 2011) and up tosuper-energetic (or superluminous) CCSNe, even when amagnetar is formed (e.g., Soker 2016a; Chen et al. 2017;Soker & Gilkis 2017).We construct our paper as follows. In section 2 wediscuss each of the 12 SNRs for which we could bothidentify ears (or another morphological feature that hintat jets) in available images and find the kick directionin the literature. The important new result in that sec-tion is the collection of the 12 projected angles betweenthe kick direction and the direction of the ears’ (jets’)axis in the 12 SNRs. These angles are summarized insection 2.1. We discuss each SNR in more detail in sec-tion 2.2. Readers who are interested only in the resultsand their analysis can skip section 2.2. In section 3 weanalyze the distribution of these angles and compare itwith two distributions, a random distribution and a dis-tribution which assumes that the kick and jets’ axis areperpendicular to each other. We discuss the results inthe frame of the jets feedback explosion mechanism. We TABLE 1Angles between the jets’ axis and the NS kick direction
SNR PSR α Jets φ SpinCassiopeia A 88 GPuppis A PSR J08214300 40 GRCW 103 1E 1613485055 80 BPKS 1209-51 1E 1207.4-5209 54 HereCTB 109 1E 2259+586 42 HereS147 PSR J0538+2817 40 G 12 NRG292.0+1.8 PSR J11245916 70 B 22, 70 W,PVela B0833-45 30 G 10 NRG327.1-1.1 45 Here3C58 PSR J0205+6449 60 G 21 NRCrab PSR B0531+21 18 G 26 NRW44 PSR B1853+01 15 G
The first and second columns list the name of the SNR andthe NS, respectively. The angle α (in degrees) is our mea-sured angle between what we take as the jets’ axis and theNS kick direction. The fourth column lists the source forthe jets’ axis: G: Grichener & Soker (2017); B: Bear et al.(2017); Here: this study. The angle φ (in degrees) is the an-gle between the NS kick direction and the NS spin for whichthe references are given in the last column: NR: Ng & Ro-mani (2007); W: Wang et al. (2006); P: Park et al. (2007). present our short summary in section 4. THE ANGLES BETWEEN KICK DIRECTIONAND JETS AXIS2.1.
Sample and measured angles
In this section we review 12 SNRs for which we foundin the literature both morphological features that we canidentify with jets and the direction of the motion of theircentral NS. We list the SNRs and the name of their NSsin the first and second columns of Table 1, respectively.We measured the angle α between the direction of theNS natal kick and the line along the directions of thetwo opposite jets, which we term the jets’ axis. We listthe values of α in the third column, and the source forthe assumed jets’ axis in the fourth column of Table 1.Because in some cases the two ears are not exactly onopposite sides of the center and/or in some cases one ortwo of the ears do not possess exact symmetry aroundan axis, we cannot always determine accurate jets’ axisdirection. We estimate that these departures from pureaxi-symmetry lead to general uncertainties in the valuesof α for the different SNRs that are about several degrees,e.g., about ± ◦ . When available, we also list the angle φ between the NS spin and the kick direction (fifth col-umn), and the references for that value (sixth column).Morphological features that we identify with jets aremainly two opposite ears (defined in section 1) and twoopposite bright arcs. The identification of jets withears follows our earlier papers, and it is based on themorphologies of planetary nebulae with ears and similarstructures that are attributed to jets (Bear et al. 2017;Bear & Soker 2017; Grichener & Soker 2017). As well,Tsebrenko & Soker (2013) demonstrated that jets canform ears in SNRs of Type Ia SNe. The flow that leadsto ears in remnants of CCSNe is somewhat different thanthat in Type Ia SNe. The last jets to be launched by theexploding massive star carry a small, but non-negligibleenergy of the main supernova shell. Each jet pushes itsway from inside and leaves a mark on the outskirts of theSNR (Tsebrenko & Soker 2013). If the jets are stronger,they can penetrate throughout the shell and form a mor-phology like in RCW 103 (Bear et al. 2017). The jets’axis is taken to be along the line connecting the two op-posite ears or along the arcs. For 9 SNRs we take thedirection of the jets from previous papers, as listed in thefourth column of Table 1. For 3 other SNRs we assumehere the axis of the two opposite jets.In the present study we are concerned only with themorphologies of the ears and other features that indicatejets. The relative brightness of the ears and the mainSNR shell might depend on local conditions that includethe intensity and morphology of the magnetic field lines,the population of high energy electrons, and clumps thatresult from the CSM or ISM. The magnetic fields andhigh energy electrons determine the X-ray and radio syn-chrotron emission. Thermal X-ray emission and the pop-ulation of high energy electrons depend on shocks, thatin turn depend also on dense clumps. But neither ofthese factors that determine the emission will change inany significant manner the morphology of the ears. Onlya massive CSM or ISM medium can do that.In section 2.2 we describe each SNR in more detail.Readers who are interested only in the results and theiranalysis can skip section 2.2 and go directly to the anal-ysis in section 3.2.2. Detailed description of SNRs
In the figures to follow we draw both the jets’ axis andthe NS natal kick direction in the upper panel for eachof the 12 SNRs. From there we calculated the angle be-tween the kick direction and jets’ axis, as listed in thethird column of Table 1. Other panels in the figures tofollow are intended to show the NS natal kick directionand the jets’ direction as taken from the literature. Weturn to describe in short each SNR and its basic proper-ties that might be relevant to the analysis.
Cassiopeia A (Cas A, 3C 461, G111.7-2.1).
Cas A isat a distance of 3 . M (cid:12) (e.g., Willingale et al. 2003), and its ageis assumed to be 330 yr (e.g., Yakovlev et al. 2011). Itresulted from an asymmetric type IIb explosion (e.g.,Krause et al. 2008). Jets have previously been modeledfor Cas A (e.g., Schure et al. 2008). One of the outcomesfrom their model is that jets can accompany the explosioneven if the SNR appears spherically symmetric. DeLaney& Satterfield (2013) estimate the proper motion of theNS star as V NS = 390 ±
400 km s − . The upper panelin Fig. 1 is an X-ray image taken from Hwang et al.(2004), where the white arrow points in the direction ofNS motion taken from Holland-Ashford et al. (2017) aspresented in the middle panel. The red double-headedarrow in the upper panel is along the direction of thetwo opposite jets taken from Grichener & Soker (2017)as presented in the lower panel. Puppis A (G260.4-03.4).
Its age is estimated as rang-ing from 3700 − Cassiopeia A
Fig. 1.—
The upper panel is an X-ray image of SNR CassiopeiaA (Hwang et al. 2004). The image shown is a three-color imageof Cas A with red = Si He α (1.782.0 keV), blue = Fe K (6.526.95keV), and green= 4 . . . − . NS (called RX J08224300) transverse motion is measuredat 1570 ±
240 km s − towards the west-southwest, assum-ing a distance of 2 kpc (Winkler & Petre 2007). We drawthe jets’ axis and the kick direction in the upper panel ofFig. 2. The NS motion is taken from Holland-Ashfordet al. (2017) as shown in the middle panel, and the jets’axis is taken from Grichener & Soker (2017) as shown inthe lower panel. RCW 103 (G332.4-00.4).
On the upper panel in Fig.3 (taken from Bear et al. 2017 and based upon Rea etal. 2016), we mark the proposed jets’ axis in yellow ar-rows. The NS motion is marked in a white arrow takenfrom (Holland-Ashford et al. 2017) as noted in the lowerpanel. Although there are no ears in this SNR, in aprevious paper (Bear et al. 2017; see figure 3 there) wehave compared the morphology of this SNR to severalplanetary nebulae and from that deduced the direction
Fig. 2.—
The upper panel is a 1.4 GHz radio image of SNRPuppis A taken from Reynoso & Walsh (2015), to which we addedthe jets’ axis and kick direction. The flux density scale is shownat the right. The NS kick direction is marked in a white arrow(upper panel), based on the middle panel (Holland-Ashford et al.2017. Details for this panel are the same as in Fig. 1.) The lowerpanel is taken from Grichener & Soker (2017) and gives a full viewof Puppis A in X-ray, where red, green, and blue correspond to the0.3-0.7, 0.7-1.0, and 1 . − . of the jets that have shaped this SNR. RCW 103 esti-mated age is ≈ ≈ . ≈ − − (for more details see Torii et al.1998). PKS 1209-51/52 (G296.510.0).
This SNR is at a dis-tance of ≈ . ≈ Fig. 3.—
The upper panel is an X-ray image of RCW 103 in threeenergy bands (low=red, medium=green, highest=blue) combinedwith an optical image from the Digitized Sky Survey. The originalimage is from the Chandra website and it is based on Rea et al.(2016), while the yellow arrows that depict the direction of the jetswere added by Bear et al. (2017). A white arrow is the NS kickdirection, copied from the lower panel that is taken from Holland-Ashford et al. (2017). Arrows in the lower panel are as in Fig.1. yellow arrows connected by a cyan-dotted line in Fig. 4.
CTB 109 (G109.1-01.0).
CTB 109 is a radio and X-raybright shell-type SNR at a distance of ≈ . S 147 (G180.01.7).
Its distance is estimated as1 .
47 kpc, its age is taken to be 20 −
100 kyr, and thespin-kick angle is 12 ◦ (e.g., Ng et al. 2007; Romani 2005).The kick velocity of the NS (PSR J0538+2817) of S147is estimated as ≈
800 km s − (e.g., Romani & Ng 2003).The upper panel in Fig. 6 is taken from Gvaramadze(2006) based on Drew et al. (2005). We added the whitearrow to mark the NS motion as reported by Gvaramadze(2006). It is consistent with the direction from the ge-ometric center of S 147 to the present position of thepulsar as marked by a white plus sign. We mark the Fig. 4.—
An image of SNR PKS1209-51 with the NS direction ofmotion marked by a white arrow (taken from Holland-Ashford etal. 2017). Green arrow is as in Fig. 1. The yellow arrows presentour proposed direction of the two jets that shaped this SNR duringthe explosion.
Fig. 5.—
Images of the SNR CTB 109. The upper panel is a0 . − . jets’ direction according to the lower panel taken fromGrichener & Soker (2017). Fig. 6.—
The upper panel is an H α image of the supernovaremnant S 147 taken from Gvaramadze (2006) based on Drew etal. (2005). We added a white arrow to indicate the NS (pulsarPSR J0538+2817) motion according to (Gvaramadze 2006), fromthe center of the SNR towards the NS (white plus sign). The whiteline drawn in the east-west direction shows the bilateral symmetryaxis of the SNR (for more details see Gvaramadze 2006). The jets’axis that we mark by the double-headed red arrow on the upperpanel is based on the lower panel taken from Grichener & Soker(2017). G292.0+1.8.
G292.0+1.8 is a Galactic oxygen-richCCSNR (e.g., Bhalerao et al. 2015). Its pulsar J11245916is apparently off the geometric center of the SNR andwith an estimated velocity of 770 km s − , a distance of4 . ◦ or less. Others also point to a misalignment butderive much smaller angles, e.g., 22 ◦ (Wang et al. 2006).On the upper panel of fig. 7 we mark the NS motion(white arrow) copied from the middle panel taken fromHolland-Ashford et al. (2017), and the jets’ axis (double-headed red arrow) based on the lower panel taken fromGrichener & Soker (2017). Vela (G263.9-03.0).
Vela is at a distance of ≈ −
500 pc (e.g., Miceli et al. 2008; Aschenbach et al. 1995respectively) and at an age of ≈ yr (e.g., Miceli etal. 2008). The progenitor mass is estimated as ≈ M (cid:12) (e.g., Chen & Gehrels 1999). The angle between theNS spin and kick direction is considered to be alignedat 10 ◦ (e.g. Pavlov et al. 2001; Ng & Romani 2007).Garc´ıa et al. (2017) analyze two opposite Si-rich knots Fig. 7.—
The upper panel is a composite image of G292.0+1.8taken from the Chandra gallery and based on Park et al. (2007).Red, orange, green and blue colors represent different X-ray lines,while white represents the optical band. The middle panel is takenfrom Holland-Ashford et al. (2017). We copied the white arrowthat represents the NS motion to the upper panel. Green arrow isas in Fig. 1. The lower panel is taken form
Bear et al. (2017) to indicate the jets’ axis between the protrusions. We copied thejets’ axis to the upper panel (red double-headed arrow). in Vela, and argue that they were ejected by jets. Thedirection of the axis of their suggested two opposite jetsis almost perpendicular to the NS kick velocity, and isdifferent than what we take here to be the jets’ axis.Such a case might be the outcome of the jittering jetsexplosion mechanism (see section 1). The two double-jets were launched at two different times out of severaljets’-launching episodes (Papish & Soker 2011). The twoupper panels in Fig. 8 focus on the NS (pulsar B083345)and its direction of motion. The two lower panels in- dicate possible jet directions, taken from Grichener &Soker (2017) and Garc´ıa et al. (2017), respectively. Weassume that the jets’ axis is as in the third panel (Grich-ener & Soker 2017). Taken the jets’ axis from the fourthpanel as suggested by Garc´ıa et al. (2017) would give alarger value of α . G327.1-1.1.
Its estimated age is ≈ − It is at a distance of ≈ ≈
830 yr (e.g., Kothes 2013).Slane et al. (2004) discuss the jet morphology of thisSNR, but they focus on the curved features of the jet.Ng & Romani (2007) measured the angle between thespin and the kick direction of the NS (PSR J0205+6449)to be 21 ◦ . The NS motion as we marked it on the upperpanel of Fig. 10 is according to Bietenholz et al. (2013).The lower panel shows the jets’ axis as was marked byGrichener & Soker (2017). The Crab (G184.6-05.8).
It was formed by either aType II or a Type Ib SN (e.g., Polcaro & Martocchia2006) that exploded in 1054. The upper panel of Fig.11 is taken from Caraveo & Mignani (1999) where theymarked the direction of the NS (PSR B0531+21) by ablack arrow. The lower panel shows the jets’ axis as wasmarked by Grichener & Soker (2017), that we copiedas a red double-headed arrow to the upper panel. Asdiscussed by Wang et al. (2007), the spin-kick angle ofthe crab pulsar B0531+21 has previously been consideredto be aligned (8 ◦ ) but now the angle is estimated to be26 ◦ (e.g., Ng & Romani 2006). W44 (G034.6-00.5).
The age and distance of W44 areestimated to be ≈ ,
000 yr and ≈ . ANALYSISIn Fig. 13 we present the cumulative distribution func-tion of the projected angle α between the NS kick direc-tion and the jets’ axis. We recall that we assume thatthe ears are formed by jets, and take the direction of Fig. 8.—
The upper panel is a 2 . each ear as the direction of a jet that inflated the ear Fig. 9.—
The upper panel is a composite image of G327.1-1.1(from Chandra website based on Temim et al. 2009; blue: X-ray;red: radio-MOST; yellow: radio-ATCA; RGB: infrared). The yel-low arrow (upper panel) represents the NS kick direction (from theChandra website). The lower panels are from Temim et al. (2015).We mark with a double-headed yellow arrow what we identify asthe plane of the torus, and in the upper panel we mark with a cyandotted double-headed arrow our assumed jets’ axis. (see section 1). In some SNRs that have no ears we takethe jets’ axis to be along the two opposite bright arcs.The straight orange line on Fig. 13 depicts the expecteddistribution for a random angle (no correlation) betweenthe SN kick and jets directions, while the convex blueline represents the expected distribution when for all ob-jects the NS kick is perpendicular to the jets’ symmetryaxis.The equation for the convex blue line is derived byprojecting the two perpendicular lines (those of the jets’direction and of the kick direction) onto the plain of thesky, giving each possible orientation in space the appro-priate weight. Let 0 ≤ θ ≤ π be the angle between thekick direction and the line of sight. The direction of thejets’ axis is in the plane perpendicular to the kick direc-tion. Let 0 ≤ φ < π be the angle of the jets’ axis inthat plane, where β = 0 corresponds to the case whenthe jets’ direction is just behind the kick direction. Therelative weight of this position is 2 sin θ dθ dφ . The pro-jected angle on the sky between the kick and jets’ axisis given by tan α = tan φ/ cos θ . Numerically integrating Fig. 10.—
The upper panel is a 1 . Fig. 11.—
The upper panel is an HST image of the inner CrabNebula together with an arrow in the direction of motion of theCrab pulsar as marked by Caraveo & Mignani (1999). The num-bers 1 to 4 are common reference stars. In the upper panel weadded the proposed jets’ axis with a red double-headed arrow ac-cording to the lower panel taken from Grichener & Soker (2017).The background image in the lower panel is a composite image fromChandra‘s gallery assembled from X-ray (blue; Seward et al. 2006),optical (red-yellow; Hester 2008) and IR (purple; NASA/JPL-Caltech/Univ). over all possible values of θ and φ with the appropriate Fig. 12.—
The upper panel is a 1 . . weight, gives the distribution for the perpendicular case.We performed a Kolmogorov-Smirnov test for the com-patibility of the sample of 12 objects with the two dis-tributions. We find the maximum distance on the graphbetween the observed and expected random distributionsto be D = 0 .
2. From this we calculate P = 0 .
67, namely,there is a chance of 67% that the 12 objects are compati-ble with the random distribution (straight line). For thecompatibility with the perpendicular distribution (lowerblue line) we find D = 0 .
33 from which we calculate P = 0 .
12. Namely, we can reject the perpendicular dis-tribution with 88% confident. We raise below a thirdpossibility.Before we raise this third possibility, we must empha-size in the strongest possible way that we obtain this dis-tribution from only 12 objects. Therefore, there are verylarge uncertainties in how the real distribution shouldlook like. With many more objects it might turn out tobe a random distribution, or else, less likely, it might turnout to be more like the perpendicular distribution. Be-low, we simply assume, with all the caution we can apply,that the cumulative distribution function we find here is (degrees) w Fig. 13.—
The cumulative distribution function W α of pro-jected jets-kick angles for the 12 observed objects (black line). Thestraight orange line is the expected random cumulative distribu-tion function, while the convex blue line is the expected cumulativedistribution function when in all cases the NS kick velocity is per-pendicular to the jets’ axis. close to the real one. The basic feature in the cumu-lative distribution function is that relative to a randomdistribution systems are missing for angles of α (cid:46) ◦ .This is the place to reemphasize that while most previ-ous studies of the kick direction in CCSNe have assumedthat the explosion is driven by neutrinos, basically thedelayed neutrino mechanism (e.g. M¨uller 2016, for a re-cent review), we adopt the jet feedback explosion mech-anism (for a review see Soker 2016b).The cumulative distribution function of the angle α has a very interesting pattern. Below about 40 degreesit follows a perpendicular distribution. This is mainlybecause objects with α (cid:46) ◦ are missing. From about 40degrees to 90 degrees it follows the random distribution.In any case, the possibility that the NS kick velocity isparallel to the axis of the jets direction is ruled out.We can think of two basic types of relations betweenthe kick and the jets directions that can explain the miss-ing objects with low values of α (cid:46) ◦ . In the first possi-bility the jets determine the allowed kick direction, whilein the second possibility the mechanism that leads to aNS natal kick forces jets in specific directions.To demonstrate these, we assume that the kick isformed by dense clumps that are formed by instabili-ties in the ejecta near the NS (e.g., Scheck et al. 2006;Wongwathanarat et al. 2010). We note that four of theSNRs in our sample (Cassiopeia A, Puppis A, RCW103, G292.0+1.8) were studied by Katsuda et al. (2018)who find that the kick is due to asymmetrical explo-sion. The instabilities are likely to result from the stand-ing accretion-shock instability (SASI; see, e.g., Abdika-malov et al. 2015; Fern´andez 2015; Moreno M´endez &Cantiello 2016; Blondin et al. 2017; Kazeroni et al. 2017),or convective overturn that is formed by neutrino heat-ing (Wongwathanarat et al. 2013). One or more dense clumps that are expelled by the explosion, gravitation-ally attract the NS and accelerate it, in what is termedthe gravitational tug-boat mechanism (Janka 2017). Thegravitational tug-boat mechanism is a relatively long-duration process lasting several seconds after accretionhas ended, and when the dense regions are acceleratedfrom about 100 km to several thousands km from theorigin (Wongwathanarat et al. 2013; Janka 2017).Wongwathanarat et al. (2010) find (their fig. 2) fortheir 4 models that the angles between the NS spin andthe NS kick are in the range of ≈ ◦ − ◦ . Namely,they are more likely to be perpendicular than aligned.Wongwathanarat et al. (2013) find in their simulationsthat according to the gravitational tug-boat mechanismin the frame of the delayed neutrino explosion mecha-nism, there is no correlation between the spin and kickdirections. M¨uller et al. (2017) obtain similar results. Intheir simulation the NS spin and NS kick start out as al-most perpendicular. After further mass accretion on tothe newly born NS the angular momentum axis changes,and the relative angle decreases to 42 ◦ . What they findas the spin of the NS is analog to the general directionof the jets’ axis in the jet feedback explosion mechanism.It is not necessarily the exact jets’ axis because the jetsmight jitter (see section 1).Wongwathanarat et al. (2010) and Wongwathanaratet al. (2013) also find that in the gravitational tug-boatmechanism in the frame of the delayed neutrino mech-anism the NS final velocity is opposite to the directionof the maximum explosion strength. Janka (2017) dis-cusses how the ejection of mass along the polar directions(spin-axis) is delayed, and more mass resides there. Asa consequence the kick direction tends to align with theangular momentum axis, but only when a strong spiralSASI mode are present. In the jet feedback explosionmechanism more mass is concentrated at late times inthe equatorial regions, and there is no spin-kick align-ment.Let us then return to the two possibilities within theframe of the jet feedback explosion mechanism, wherethe angular momentum axis of the accreted gas tends toavoid small angles with respect to the direction of con-centration of mass in the instabilities. In the first possi-bility the pre-collapse core has a non negligible angularmomentum. When it collapses not much material is ac-creted on to the neutron star from the polar directions(Papish et al. 2015). Jets are launched in the generaldirection of the angular momentum axis. Instabilitiescan lead to stochastic component of the accreted angu-lar momentum, and the jets might jitter in the vicinityof the angular momentum direction. In any case, thejets further prevent accretion in the vicinity of the polardirections. Dense clumps will not form close to the po-lar directions, but rather will tend to form closer to theequatorial plane. Hence, the NS kick will not occur closeto the polar directions. The direction of the jets and thedirection of the NS natal kick will avoid each other.In the second possibility the initial angular momen-tum does not play a significant role. We start withdense clumps and follow the numerical results of Papish& Soker (2014). When dense clumps are accreted toform an accretion disk, the jets tend to be perpendicularto the accretion direction of dense clumps, and the jetsin turn further force accretion perpendicular to their di-0rection of propagation. This behavior leads to a planarjittering-jets pattern (Papish & Soker 2014), where thejets’ symmetry axes of different jet-launching episodestend to share the same plane. Dense clumps tend toform along directions perpendicular to this plane. If thenatal kick is caused by dense clumps, this again causesthe NS natal kick direction and the direction of jets’ axisto avoid each other.The real situation might be even more complicated.The ‘jump’ from the perpendicular distribution to therandom one comes with concentration of objects, basi-cally two extra objects, around α = 45 ◦ . Due to thesmall number statistics we cannot tell whether this effectis real. It might be, however, a real effect if the missingobjects at low values of α are not distributed equally athigher values of α , but rather are concentrated on theboundary between the ‘forbidden’ and ‘allowed’ regionsof α .Over all, the jet feedback explosion mechanism mightaccount for the tentative cumulative distribution func-tion for the angle α that we find in the present study. SUMMARYWe searched the literature for SNRs of CCSNe wherewe could both identify morphological features, such asears, that we can attribute to jets and for which thedirection of the NS natal kick was determined. We found12 such SNRs, as we present in Figs. 1-12, and measuredthe projected (on the plane of the sky) angle between theline connecting the two assumed opposite jets, i.e., thejets’ axis, and the NS kick. We summarized the results inTable 1, and plotted the cumulative distribution function(black line) of the angles in Fig. 13. We also plotted therethe cumulative distribution functions that are expectedfrom a random distribution (straight orange line) andthe distribution expected for a case where the NS kick isalways perpendicular to the jets’ axis (convex blue line).In section 3 we compared the cumulative distributionfunction to the distribution expected from a random dis-tribution and to the distribution expected for a casewhere the NS kick is always perpendicular to the jets’ axis. The cumulative distribution function we find forthe 12 SNRs has a 67% chance to be compatible withthe random distribution (straight orange line on Fig. 13),and 12% to be compatible with the perpendicular distri-bution (lower convex blue line). The basic feature of thecumulative distribution function is that it fits the ran-dom distribution at large angles but is missing systemswith small angles relative to the random distribution.We discussed two possibilities to explain this property,if it is real. Both possibilities assume that dense clumpsthat are ejected by the explosion accelerate the NS bythe gravitational tug-boat mechanism (Wongwathanaratet al. 2013; Janka 2017), and that jets explode the CC-SNe (Papish & Soker 2011; Soker 2016b). Basically, thejets prevent the formation of dense clumps along theirpropagation direction, or the dense zones supply most ofthe gas to the accretion disk that launches jets more orless perpendicular to the directions of the dense zones.The motivation behind this study is the jet feedbackexplosion mechanism of massive stars. According to thejet feedback explosion mechanism jets that are launchedby the newly born NS or black hole drive the explosion ofCCSNe. The negative feedback mechanism implies thatas long as the jets did not explode the entire core the NS(or black hole if formed) continues to accrete mass fromthe core. The jets shut themselves off only when they re-move the entire core. The last episodes of mass accretionoccurs while jets have already expelled the core. There-fore, the last jets that the NS (or black hole) launches ex-pand more freely and can leave an imprint on the ejecta.One of the imprints might be two opposite ears in theSNR (Grichener & Soker 2017; Bear et al. 2017).The main finding of our study is that the jet feedbackexplosion mechanism, which we consider to be the mostpromising mechanism to explode all CCSNe, can in prin-ciple account for the distribution of angles between thejets’ axis and the NS kick velocity.This research was supported by the Asher Fund forSpace Research at the Technion and the Israel ScienceFoundation.
REFERENCESAbdikamalov, E., Ott, C. D., Radice, D., et al. 2015, ApJ, 808, 70Aschenbach, B., Egger, R., & Tr¨umper, J. 1995, Nature, 373, 587Bear, E., Grichener, A., & Soker, N. 2017, MNRAS, 472, 1770Bear, E., & Soker, N. 2017, MNRAS, 468, 140Becker, W., Prinz, T., Winkler, P. F., & Petre, R. 2012, ApJ, 755,141Bhalerao, J., Park, S., Dewey, D., Hughes, J. P., Mori, K. andLee, J.-J. 2015, ApJ, 800, 65Bietenholz, M. F., Kondratiev, V., Ransom, S., Slane, P., Bartel,N. and Buchner, S. 2013, MNRAS, 431, 2590Blondin, J. M., & Mezzacappa, A. 2007, Nature, 445, 58Blondin, J. M., Gipson, E., Harris, S., & Mezzacappa, A. 2017,ApJ, 835, 170Bolte, J., Sasaki, M., & Breitschwerdt, D. 2015, A&A, 582, A47Bray, J. C., & Eldridge, J. J. 2016, MNRAS, 461, 3747Carter, L. M., Dickel, J. R., & Bomans, D. J. 1997, PASP, 109,990Caraveo, P. A., & Mignani, R. P. 1999, A&A, 344, 367Cardillo, M., Tavani, M., Giuliani, A., Yoshiike, S., Sano, H.,Fukuda, T., Fukui, Y., Castelletti, G. and Dubner, G. 2014,A&A, 565, A74Castelletti, G., Dubner, G., Golap, K., & Goss, W. M. 2006,A&A, 459, 535Charbonneau, J., & Zhitnitsky, A. 2010, Cosmology Astropart.Phys., 8, 010Chatterjee, S., Vlemmings, W. H. T., Brisken, W. F., et al. 2005,ApJ, 630, L61 Chen, W., & Gehrels, N. 1999, ApJ, 514, L103Chen, K.-J., Moriya, T. J., Woosley, S., Sukhbold, T., Whalen,D. J., Suwa, Y., & Bromm, V. 2017, ApJ, 839, 85Cordes, J. M., Romani, R. W., & Lundgren, S. C. 1993, Nature,362, 133DeLaney, T., & Satterfield, J. 2013, arXiv:1307.3539Dodson, R., Legge, D., Reynolds, J. E., & McCulloch, P. M. 2003,ApJ, 596, 1137Drew, J. E., Greimel, R., Irwin, M. J., et al. 2005, MNRAS, 362,753Dubner, G., Loiseau, N., Rodr´ıguez-Pascual, P., et al. 2013, A&A,555, A9Duncan, A. R., Stewart, R. T., Haynes, R. F., & Jones, K. L.1996, MNRAS, 280, 252Fern´andez, R. 2015, MNRAS, 452, 2071Frail, D. A., Giacani, E. B., Goss, W. M., & Dubner, G. 1996,ApJ, 464, L165Fryer, C. L., & Kusenko, A. 2006, ApJS, 163, 335Gaensler, B. M., & Slane, P. O. 2006, ARA&A, 44, 17Garc´ıa, F., Su´arez, A. E., Miceli, M., Bocchino, F., Combi, J. A.,Orlando, S., & Sasaki, M. 2017, A&A, 604, L5Giacani, E. B., Dubner, G. M., Kassim, N. E., Frail, D. A., Goss,W. M., Winkler, P. F. and Williams, B. F. 1997, AJ, 113, 1379Giacani, E. B., Dubner, G. M., Green, A. J., Goss, W. M., &Gaensler, B. M. 2000, AJ, 119, 281Gilkis, A., & Soker, N. 2014, MNRAS, 439, 4011Gilkis, A., & Soker, N. 2016, ApJ, 827, 401