The modeling of the Vela pulsar pulses - from optical to hard gamma-ray energy
aa r X i v : . [ a s t r o - ph . H E ] A ug The modeling of the Vela pulsar pulses - fromoptical to hard gamma-ray energy
B. Rudak ∗ CAMK, Rabia´nska 8, 87-100 Toru´n, PolandE-mail: [email protected]
J. Dyks
CAMK, Rabia´nska 8, 87-100 Toru´n, PolandE-mail: [email protected]
The pulsed radiation from PSR B0833-45 (Vela) has a phased-averaged spectral energy distribu-tion (SED) of an apparently simple structure across a wide energy range, from optical light to hardgamma-rays. However, the Vela pulses in narrow energy bands reveal astonishing complexity ofthe directional pattern of the radiation. These pulses are, therefore, a unique clue to the underly-ing radiative processes. We present the results of a 3D modeling of the Vela radiation propertieswithin an outer-gap scenario. We show how the inverse Compton scattering of photons by pri-mary and secondary particles in its magnetic and non-magnetic regimes reproduces qualitatively,and in some cases quantitatively, the observed energy-dependent pulses of Vela. ∗ Speaker. c (cid:13) Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). http://pos.sissa.it/ he modeling of the Vela pulsar pulse profiles
B. Rudak
1. Introduction
The Vela pulsar (PSR B0833-45) is one of best studied rotation-powered pulsars in the high-energy radiation domain due to its proximity. No wonder, there have been many theoretical effortsto explain the mechanisms of its activity, applying various models. This paper presents an attemptto model inverse Compton scatterings expected between various sets of relativistic electro-positronpairs operating in the pulsar magnetosphere and two different radiation fields: 1) non-thermal near-IR to optical emission interpreted as due to synchrotron emission originating near the acceleratinggaps; 2) thermal X-rays from the neutron star surface. The consequences of those interactions areshown to be present at the optical domain as well as the very-high energy domain (VHE).
2. The Outer Gap model
The physical model of OG used in this work is unavoidably simplified due to the fact thatsome aspects of physical conditions in OG pose still open questions. We use a standard corotatingmagnetosphere in the low charge density approximation. The magnetic field is taken as a vacuumretarded dipolar solution. The numerical 3D code calculates curvature radiation (CR) from primarycharges in the inertial observer frame (IOF) as described in [8] and [4]. The charges (primarypairs) are subject to an accelerating electric field which is assumed to be constant in the gaps (i.e.no azimutal or radial dependence is considered). The assumed accelerating field E || allowed theprimaries to reach Lorentz factors of a few × . The model doesn’t follow the pair creation dueto interaction of CR photons with a soft-photon field. Instead, we assume that secondary pairs areformed in a layer which is attached to (placed on top of) the outer gap layers. These pairs are thesource of the soft photon field - synchrotron radiation (SR) which extends across the wide energyrange, from hard X-rays to UV and optical up to midIR, and likely to far IR ( ∼ .
001 eV). Todetermine the directional characteristic of the SR radiation which would agree with the observedpulses from the Vela pulsar, with used the geometrical version of OG ([8]). The geometrical modelassumes a uniform distribution of emissivity in the energy range of interest, with photons emittedtangentially to local magnetic filed lines. Therefore, for a given location of the layer in terms of themagnetic-line footprints on the polar cap, the pulses of radiation (CR in the case of the gap, or SRin the case of the secondary-pairs layer) will be a function of two angles: the inclination angle α ofthe magnetic axis with respect to the spin axis, and the viewing angle ζ between the line-of-sightand the spin axis. Taking the thickness of both layers to be the same and equal 0.1 (ie. 10% of thepolar-cap radius) the best set of α and ζ was determined as 70 deg and 79 deg, respectively. Theresulting ’geometrical’ lightcurves of CR (gamma-rays) and SR (optical) along with the data arepresented in Fig.1. The optical lightcurve in the geometrical model consists of two peaks locatedat phases 0.25 and 0.5, similarly as two major peaks (called P1 and P2, respectively) observed inthe lightcurve of Vela ([9]). Also, the shape and thickness of the model peaks are roughly similarto the observed peaks. The similar situation is for the geometrical and observed lightcurves in thegamma-rays, where two peaks are located at phases 0.13 and 0.56 ([1]).Two important ingredients of the physical model are:1) The electron-positron pairs of γ ∼
100 present in the inner part of open magnetic field-lines, ie.concentrated around the magnetic axis (hereafter ’the inner PC pairs’). The justification for this2 he modeling of the Vela pulsar pulse profiles
B. Rudak
Figure 1:
Two pronounced peaks in the lightcurves of the Vela pulsar, in optical ([9] and in gamma-raysabove 100 MeV ([1]) - upper left panel and upper right panel, respectively - are interpreted as due to syn-chrotron emission from secondary pairs and curvature emission due to primary pairs, respectively. Assumingthat the gamma-rays come from the outer gaps of the thickness 0 .
1, and the optical light comes from layersof the same thickness but adjacent to the outer gaps, an auxilary geometrical model was used to determinethe inclination angle α and the viewing angle ζ of Vela by reproducing the shapes and rotational phases ofall four peaks. A satisfactory match was found for α =
70 deg and ζ =
79 deg, and these values were nextused in the physical model. component it twofold: a) the outer gap and its adjacent SR layer occupy about 20% (in terms ofthe polar cap radius) of the magnetic-field lines at the outer rim of the polar cap; there is no reasonto prevent the inner part of polar cap to develope a potential drop across it, high enough to leadeventually to the creation of electron-positron pairs; b) a narrow radio pulse ("a core" emission) ispresent in Vela.2) The field of thermal soft X-ray emission from the Vela surface ([15]).Three different ICS processes were considered in an attempt to either predict or to explain theexistence of specific features in the Vela’s non-thermal radiation:1. primary electrons in the gap interacting with optical-infrared photons originating from theSR layer,2. inner PC pairs interacting with optical-infrared photons originating from the SR layer,3. inner PC pairs interacting with thermal X-ray photons from the neutron star surface.These processes are expected to lead to the formation of, respectively,:1. spectral component in the VHE range,2. core-like pulse (known as P4) detected in optical as well as in UV ([9], [18]) at the phase ofthe radio core pulse,3. core-like pulse detected in hard X-rays ([11]) at the phase of the radio core pulse (see also[12] for the compilation of all lightcurves available).3 he modeling of the Vela pulsar pulse profiles
B. Rudak
3. Results
An important role in shaping the resulting directionality of the ICS emission in this case playsthe bending of trajectories of the SR photons in the corotating frame (CF) with respect to theprimary electrons moving along magnetic field lines in the gaps. For high inclination angles thisleads to lower rates of photon-electron collisions at at the leading side than at the trailing side (seefig.6 in [7]). -0.4 -0.2 0.0 0.2 0.4 φ ζ ob s [ ° ] a) -2 0 2 4 6 8log ε [MeV]-15-10-50 l og ε F ε b) -1.0 -0.5 0.0 0.5 1.0 φ -7 -6 -6 -6 °. c) Figure 2:
Panel a) : The photon map shows the distribution of ∼ α =
70 deg. The horizontal line is for ζ =
79 deg and two periods of rotation are shown for the phase φ for clarity. Panel b) : The phase-averagedenergy spectrum of the ICS component for ζ =
79 is shown. The Y-axis scale is in ’model’ units. Panel c) : The lightcurve of the ICS at ∼ . − . . − . Fig.2 presents the photon map of ICS in the VHE range, as well as the phase averaged spectrumand the lightcurve for the viewing angle chosen in the previous section and Fig.3 shows the phaseaveraged spectra of ICS and CR, with the normalization to match the maximum energy flux ofCR with the value derived from observations. Note, that an overall shape of the modelled CRcomponent has too little power at the low-energy part ( ∼
100 MeV) as well as above ∼
10 GeV.This is a well known fact, and there have been attempts to cure it by introducing a set of gaps withdifferent external currents and with the time variability at least of the crossing time-scale of thelight cylinder ([13], [20]). The observed gamma-ray spectrum would then be a superposition ofCR components from these gaps. Other ways out have also been proposed recently (e.g. [10]). Forthe purpose of this work, the precise shape of the CR component is not essential, however; the keyelement are ultrarelativistic electrons in the gap due to an assumed electric field there (see Section1).Two cases of the input SR spectrum were considered to interact with primary pairs from the gaps4 he modeling of the Vela pulsar pulse profiles
B. Rudak via the ICS, both with identical power-law model dN / dE = K ( E optical ) = E − Γ , with Γ = . ∼ . ∼ − eV in the far-IR (in principle, one cannot exclude that the SRspectrum extends that far, although no observations exist supporting such a statement) . In the firstcase, the scatterings proceeds in the Klein-Nishina regime, and the result is marked with dashedline in Fig.3. In the second case, the scattering proceeds in both, the K-N and Thomson, regimes,and the result is marked in Fig.3 with continuous line. Figure 3:
The phase-averaged SED in HE and VHE range are shown (for ζ =
79 deg) resulting from theOG model of Vela. The HE part (left-hand side of the panel) is due to CR of primary pairs in the outer gaps.[Note: see the text for comments on the shape of the CR component] The VHE component is due to ICSof the SR emission (originating in the SR layer) on primary pairs. The dashed line component correspondsto the SR spectrum extending from optical to near-IR; the continous line component corresponds to anotherpossibility - with the SR spectrum for the SR spectrum assumed from the optical range up to the far-IR. Thered line indicates the most up-to-date differential sensitivity of the CTA South around the TeV range ([14]).
With justification given in Section 1 we assume the presence of inner PC pairs with moderateLorentz factors ( ∼ < .
65 on the polar cap. The pairs are followedup to the distance of 0 . R LC (the light cylinder radius) as they interact via the ICS with photonsfrom the SR layer. The first case of the SR spectrum mentioned in the previous subsection is used(i.e. with the lower limit at ∼ . ∼ . he modeling of the Vela pulsar pulse profiles B. Rudak -1.0 -0.5 0.0 0.5 1.0
Figure 4:
The photon map for α =
70 deg shows the distribution of optical photons ( ∼ ζ =
79 deg (top left panel). The resulting phase-averaged ICS spectrum(note: the Y-axis scale is in ’model’ units) and the ICS lightcurve for ∼ The inner PC electron-positron pairs are also capable of scattering thermal photons from theneutron star surface. After [15] we took a blackbody spectrum with T bb = K and total luminosity L X = × erg/s. The pairs we followed up to 0 . R LC in the altitude. In the range of interest,between ∼ ∼
30 keV, the scatterings proceed in the magnetic resonance regime ([6]),forming thus a strong flux of X-ray photons at phase 0.0 (Fig.5). This may explain the presenceof the narrow peak at phase ∼ . The simplified OG model used in this work is the first attempt to account for the presence ofspecific features in the lightcurves of Vela in optical, UV and hard-Xrays at the phase where theradio core peak is located. If the origin of the optical and hard-Xray "core" peaks presented above iscorrect, it will be an addidtional argument (besides the radio core peak) for an inner gap operatingin the central part above the polar cap. The coexistence of inner and outer gaps which occupydifferent magnetic-field lines would have to be taken into account by new models of dissipativemagnetospheres.Moreover, a spectral component in the VHE gamma-ray domain is found of potential inter-est to the Cherenkov Telescope Array (CTA), provided a rather long integrated time of observa-tions (a least 50 hours) is granted (see [14] for the expected CTA-South sensitivity of point-like6 he modeling of the Vela pulsar pulse profiles
B. Rudak
Figure 5:
The photon map for α =
70 deg shows the distribution of X-ray photons ( ∼
10 keV) formeddue to the ICS between the inner PC pairs and the X-rays from the neutron star surface; the continoushorizontal line is for ζ =
79 deg (top left panel). The resulting phase-averaged ICS spectrum (note: theY-axis scale is in ’model’ units) and the ICS lightcurve for ∼ sources). The energy flux of the VHE component is much smaller than derived in the past with’one-dimensional’ models of the OG ([17], [3]), which also are inconsistent with the HESS upperlimits ([2]). It is, however, much bigger than the flux expected in other models of Vela (e.g. [10],[16]).A detailed account of the method and the results presented in this contribution will be given else-where (Rudak & Dyks 2017, in prep.). Acknowledgments
BR acknowledges discussions with Iwona Mochol and Arache Djannati-Ataï. The authorsacknowledge financial support by the National Science Centre grant DEC- 2011/02/A/ST9/00256.
References [1] A.A. Abdo et al.
The Vela Pulsar: Results from the First Year of Fermi LAT Observations , ApJ (713) 154.[2] F.A. Aharonian et al.
Search for pulsed VHE gamma-ray emission from young pulsars with HESS , A&A (466) 543.[3] F.A. Aharonian and S.V. Bogovalov
Exploring physics of rotation powered pulsars with sub-10 GeVimaging atmospheric Cherenkov telescopes , New Astronomy (8) 85.[4] Bai, A. Spitkovsky,
Modeling of Gamma-ray Pulsar Light Curves Using the Force-free MagneticField , ApJ (715) 1282. he modeling of the Vela pulsar pulse profiles B. Rudak[5] A.A. Danilenko, D.A. Zyuzin, Yu.A. Shibanov, S.V. Zharikov,
The Vela and Geminga pulsars in themid-infrared , MNRAS (415) 867.[6] C.D. Dermer,
Compton scattering in strong magnetic fields and the continuum spectra of gamma-raybursts - Basic theory , ApJ (360) 197.[7] J. Dyks and B. Rudak,
Shaping the gamma-ray pulsar profiles: caustic effects versus intrinsicemissivity , [8] J. Dyks, A.K. Harding, B. Rudak, Relativistic Effects and Polarization in Three High-Energy PulsarModels ApJ (606) 1125.[9] C. Gouiffes,
Optical Observation of the VELA Pulsar , Neutron Stars and Pulsars : Thirty Years afterthe Discovery : Proceedings of the International Conference on Neutron Stars and Pulsars held onNovember 17-20, 1997, at Tachikawa Hall, Rikkyo University, Tokyo, Japan. Edited by N. Shibazaki[et al.]. Tokyo, Japan : Universal Academy Press, c1998. (Frontiers science series) (24) 363.[10] A.K. Harding and C. Kalapotharakos,
Synchrotron Self-Compton Emission from the Crab and OtherPulsars , ApJ (811) 63.[11] A.K. Harding et al. 2002,
The Multicomponent Nature of the Vela Pulsar Nonthermal X-Ray SpectrumApJ (576) 376.[12] L. Kuiper and W. Hermsen
The soft γ -ray pulsar population: a high-energy overview , MNRAS (449) 3827.[13] G.C.K. Leung et al.
Fermi-LAT Detection of Pulsed Gamma-Rays above 50 GeV from the Vela Pulsar , ApJ (797) 13.[14] S. Mangano, on behalf of the CTA Consortium,
Cherenkov Telescope Array Status Report , Very HighEnergy Phenomena in the Universe, Rencontres de Moriond [ astro-ph.HE 1705.07805 ].[15] A. Manzali, A. De Luca, and P. A. Caraveo, Phase-resolved Spectroscopy of the Vela Pulsar withXMM-Newton , ApJ (669) 578.[16] I. Mochol and J. Pétri
Very high energy emission as a probe of relativistic magnetic reconnection inpulsar winds , MNRAS (449) 51.[17] R.W. Romani
Gamma-Ray Pulsars: Radiation Processes in the Outer Magnetosphere , ApJ (470) 469.[18] R.W. Romani, O. Kargaltsev and G.G. Pavlov,
The Vela Pulsar in the Ultraviolet , ApJ (627) 383.[19] Yu.A. Shibanov,A.B. Koptsevich, J. Sollerman, P. Lundqvist,
The Vela pulsar in the near-infrared , A&A (406) 645.[20] J. Takata, C. W. Ng, K.S. Cheng,
Probing gamma-ray emissions of Fermi-LAT pulsars with anon-stationary outer gap model , MNRAS (455) 4249.(455) 4249.