Draft version February 18, 2015 A Preprint typeset using LTEX style emulateapj v. 05/12/14 TOWARD AN EMPIRICAL THEORY OF PULSAR EMISSION XI. UNDERSTANDING THE ORIENTATIONS OF PULSAR RADIATION AND SUPERNOVA “KICKS” Joanna M. Rankin Physics Department, University of Vermont, Burlington, VT 05405 USA: [email protected] Draft version February 18, 2015 ABSTRACT Two entwined problems have remained unresolved since pulsars were discovered nearly 50 years ago: the orientation of their polarized emission relative to the emitting magnetic field and the direction of putative supernova “kicks’ relative to their rotation axes. The rotational orientation of most pulsars can be inferred only from the (“fiducial’) polarization angle of their radiation, when their beam points directly at the Earth and the emitting polar fluxtube field is k to the rotation axis. Earlier studies have been unrevealing owing to the admixture of different types of radiation (core and conal, two polarization modes), producing both k or ⊥ alignments. In this paper we analyze the some 50 pulsars having three characteristics: core radiation beams, reliable absolute polarimetry, and accurate proper motions. The “fiducial’ polarization angle of the core emission, we then find, is usually oriented ⊥ to the proper-motion direction on the sky. As the primary core emission is polarized ⊥ to the projected magnetic field in Vela and other pulsars where X-ray imaging reveals the orientation, this shows that the proper motions usually lie k to the rotation axes on the sky. Two key physical consequences then follow: first, to the extent that supernova “kicks’ are responsible for pulsar proper motions, they are mostly k to the rotation axis; and second that most pulsar radiation is heavily processed by the magnetospheric plasma such that the lowest altitude “parent’ core emission is polarized ⊥ to the emitting field, propagating as the extraordinary (X) mode. Keywords: pulsars: general — techniques: polarimetric; emission mechanisms: non-thermal 1. INTRODUCTION tion modes [Backer & Rankin (1980); Manchester et al. Radio pulsars now contribute importantly to many (1975)] many assumed in the absence of any direct proof fields of physical science, but paradoxically, two funda- that the “primary” polarization mode must be k. mental coupled issues have remained unresolved since This easy presumption was dashed in the new millen- they were discovered 47 years ago: the orientation of nium by X-ray imaging of the Vela pulsar [Helfand et al. their linearly polarized emission relative to the mag- (2001); Radhakrishnan & Deshpande (2001)] where arcs netic field in their polar fluxtube emitting regions and indicated the orientation of the star’s rotation axis Ω rel- the origin/orientation of their often large space veloci- ative to its polarization and proper-motion (PM) direc- ties (and thus proper motions) relative to their rotation tions. Shockingly, the radiation was polarized ⊥ to the axes. Most pulsars are known only by their lighthouse- projected magnetic field B plane, a circumstance then like radio signals, and thus we have no direct means of beautifully confirmed for the radio emission (Johnston determining the orientation of a pulsar’s rotation axis et al. 2005, hereafter Johnston I)—and this pulsar’s ra- on the sky, which is crucial both to interpreting the po- dio emission is almost completely linearly polarized, so larization direction of the radiation and the orientation there was no OPM ambiguity. of the proper motion relative to the spin axis. Pulsars In an earlier paper (Rankin 2007, hereafter Paper I) radiate because highly energetic outward-going charges we investigated the PPA vs. PM alignments of a num- are accelerated by the curved dipolar field within their ber of pulsars, drawing strongly on Johnston I as well as other sources. Here, a “fiducial” polarization position polar regions, so it is crucial to understand how this ra- P A diation is polarized relative to the (projected) B field angle (PPA) 0, at a (“fiducial”) rotational phase rep- orientation on the sky. Figure 1 shows how this field resenting the magnetic axis longitude, is measured and appears splayed when a pulsar’s beam points directly at referred to infinite frequency as a proxy for the (unseen) the Earth—the “fiducial” instant—and that the emission orientation of the rotation axis Ω. These were com- reaching us is associated with that bundle in the plane pared with well determined proper-motion (PM) direc- tions P AV , and the differences Ψ showed strong peaks of the rotation axis Ω. Clearly, we have no knowledge ◦ ◦ of the radial component of a pulsar’s space velocity and at both 0 and 90 . Given, however, that most of the only weak estimates of the radial component of Ω. pulsars showed strong OPM activity in their profiles, it At one time it seemed obvious that pulsar radiation was not possible to draw general conclusions about the must be polarized k to the projected magnetic field di- polarization orientation with respect to the projected B rection. How could it be otherwise given that both the direction. curving B field and the resulting curvature acceleration The second coupled key question is how a pulsar’s rota- lie in the same plane? Even after the discovery that pul- tion vector Ω is oriented with respect to its space velocity sars emit in two orthogonal (hereafter OPM) polariza- (of which we can usually measure only their projections on the plane of the sky)? The possibility of a corre- 2 Joanna M. Rankin Figure 1. Diagram showing the splayed curving field lines—here shown in projection—associated with pulsar emission at the “fidu- cial” instant when the beam faces the Earth directly. Both the magnetic axis M and pulsar rotation axis Ω are indicated in re- lation to the “fiducial” field lines (magneta) associated with the Figure 2. Polarization profile of B1706–16 from Johnston I show- radiation we receive at that instant. The projected fiducial field is ing its highly depolarized single core-component profile at 1369 MHz. The roughly linear, negative-going PPA (black curve) plot- k to the rotation axis Ω and thus used as a proxy for Ω which is ◦ otherwise usually not observable. Also indicated is the emission- ted in the upper panel connects smoothly with the PPA – 90 beam structure consisting of two concentric conal beams (outer: (blue) curve on the trailing edge of the profile, coinciding with the blue and inner: green) and the central core beam (yellow) in rela- minimum in the linear polarization (red curve) in the lower panel tion to a typical sightline traverse (black dashed). Any of the three where the total power (black) and circular polarization (green) are also plotted. The PPAs are referred to infinite frequency, and the beams can be present in a given pulsar and different sightline paths PA result in different profile types. Profiles with a core beam are of pri- V value is shown as a horizontal (cyan) line. See text. mary interest here—that is, the core-single (St) where it appears on its own; triple (T) profiles where one of the cones is present; and five-component (M) profiles where both cones appear. ⊥ to the projected B direction. This double ambigu- ity of proper-motion direction and OPM orientation has plagued efforts to settle how supernovae contribute to lation was raised early [Shklovskii (1969); Gott et al. pulsar velocities. (1970); Tademaru & Harrison (1975)] as their large pe- Although much of our earlier work had focused on clas- culiar velocities were realized, initially through scintilla- sifying the properties of different pulsar profile popula- tion studies. Though no binary pulsar was then known, tions according primarily to their emission geometry and their presumptive birth in the disruption of such systems frequency evolution [Rankin 1983, 1990, 1993a, 1993b; appeared to be a significant factor in their PMs. How- Rankin et al. (1989); Mitra & Rankin (2011); hereafter ever, binary disruption ultimately seemed inadequate to ET I, IV, VIa,b, — & IX], our analysis in Paper I failed account for the very large velocities of some pulsars. The- to use this information, despite the fact that most of the orists then began to explore other mechanisms for their stars there under consideration had long been classified acceleration—in particular the question of whether natal through detailed study. Most of the pulsars in the John- supernovae imparted “kicks” to their progeny. ston I study exhibited core, core-cone, or core-double This “kick” question has a complex history which cone profiles of the core-single (St), triple (T) or five- is nicely summarized in (Noutsos et al. 2012). Suf- component (M) types (see Fig. 1), and most of the 90◦ fice it to say that theorists suggested ingenious “kick” alignments pertained to pulsars of these types, but this mechanisms—both k and ⊥ to the orientation of a pul- circumstance was not then observed or interpreted. sar’s rotation Ω (as well possibly in combination?). In large part this failure stemmed from the complex- Mechanisms such as Galactic acceleration are known ity of the PPA traverses in some pulsars with bright which would tend to alter such “birth” alignments (e.g., core components. A number exhibit PPA traverses Noutsos et al. 2013), however the analyses quoted above that are readily fitted by the expected rotating-vector indicate that a surprisingly large proportion of pulsars ◦ ◦ (RVM) model (Radhakrishnan & Cooke 1969), while oth- show Ψ orientation close to either 0 or 90 . Again, ers have depolarized, OPM-active components with dis- however, the orientation of Ω cannot usually be deter- torted PPA traverses that have proven difficult to explain mined directly, but only though the fiducial PPA proxy P A and interpret. Recently, several detailed analyses of par- 0 that is complicated by OPM radiation either k or ticular bright pulsars with prominent core emission have Orientations of Pulsar Radiation and Supernova “Kicks” 3 counter-clockwise from North on the sky—and second, they must be referred to infinite frequency by accurately unwrapping the Faraday rotation of the PPAs.