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Nuclear Instruments and Methods in Physics Research A 567 (2006) 486–488

www.elsevier.com/locate/nima

High energy neutrino emission from young pulsars

G.F. Burgioa,�,1, B. Linkb

aINFN Sezione di Catania, Via S. Sofia 64, I-95123 Catania, ItalybDepartment of Physics, Montana State University, Bozeman, Montana 59717, USA

Available online 27 June 2006

Abstract

We propose that young (taget105 yr), rapidly rotating pulsars can accelerate ions to energies of �1PeV near the surface of a neutron

star. Protons undergo resonant excitation with surface X-rays and produce a beam of m neutrinos with energies of several tens of TeV

which could be detectable by current technology. Detection of these neutrinos would further our understanding of high-energy processes

that take place in the stellar magnetosphere.

r 2006 Elsevier B.V. All rights reserved.

PACS: 97.60.Gb; 94.30.�d; 95.85.Ry

Keywords: Neutrinos; Stars:neutron; Pulsars:general; Magnetic fields

Our current knowledge of the Universe is based onobservations in the electromagnetic spectrum. A new wayto probe the high-energy Universe is through the detectionof high-energy (\10GeV) neutrinos, to which the Uni-verse is almost completely transparent. Several projects areunderway to develop large-scale neutrino detectors underwater or ice; AMANDA-II and Baikal are running, whileIceCube [1], ANTARES, NEMO, and NESTOR [2] areunder construction.

Astrophysical neutrinos are expected to arise in manyenvironments in which neutrinos are produced by thedecay of pions created through hadronic interactions ðppÞ

or photomeson production (pg). Neutrinos escape from thesource and travel unimpeded to Earth, thus bringinginformation directly from the acceleration site. Neutrinosmay be produced by cosmic accelerators, like those insupernova remnants [3], active galactic nuclei [4], micro-quasars [5] and gamma-ray bursts [6,7].

Recently, we proposed [8] that young (taget105 yr) andrapidly rotating neutron stars could be intense neutrinosources. If the stellar magnetic moment has a componentantiparallel to the spin axis (half of neutron stars), ions willbe accelerated off the surface. If energies of �1PeV per

e front matter r 2006 Elsevier B.V. All rights reserved.

ma.2006.05.182

ing author.

ess: Fiorella.burgio@ct.infn.it (G.F. Burgio).

y G.F. Burgio.

proton are attained, pions will be produced throughphotomeson production as the protons scatter with surfaceX-rays, producing a beam of m neutrinos with energiesabove �10TeV. Detection of such neutrinos would be afascinating discovery in its own right, and would providean invaluable probe of the physical conditions that prevailin the magnetosphere of a neutron star.For photomeson production to occur, ions must be

accelerated to very high energies close to the stellar surface.How large might the accelerating potential be? Goldreichand Julian developed the first model of a quasi-staticmagnetosphere [9]. By assuming a dipolar configurationwith magnetic axis parallel to the rotation axis, theyshowed that the potential drop across the field lines of apulsar with angular velocity O ¼ 2p=P (where P is theperiod) from the magnetic pole to the last field line thatopens to infinity is of magnitude

DF ¼O2BR3

2c2’ 6:6� 1018B12R3

6P�2ms V. (1)

Here B ¼ 1012B12G is the strength of the dipole componentof the field at the magnetic poles, R ¼ 106R6 cm the stellarradius and Pms is the spin period in milliseconds. Inequilibrium (not realized in a pulsar), a corotatingmagnetosphere would exist in the regions above the starin which magnetic field lines close; the charge density

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Table 1

Estimated m fluxes at Earth

Source dkpc Pms B12 T0:1 keV f b dN=dAdt

Crab 2 33 3.8 p1.7 0.14 1200

Vela 0.29 89 3.4 0.6 0.04 800

We took f d Z�1 ¼ 1 so these rates are upper limits. The event number

dN=dAdt is given in units of km�2 yr�1.

4.5 5.0 5.5 6.0 6.5

log εν (GeV)

10−16

10−15

10−14

10−13

10−12

dφν/

dεν

(GeV

−1 m

−2 s

−1)

Crab

Fig. 1. The neutrino spectrum is displayed for the Crab pulsar, in the

cases of linear (solid line) and quadratic proton acceleration (dashed line).

G.F. Burgio, B. Link / Nuclear Instruments and Methods in Physics Research A 567 (2006) 486–488 487

would be rq ’ eZn0 ’ B=Pc (cgs), where n0 is the Gold-reich–Julian number density of ions. Deviation fromcorotation will lead to charge-depleted gaps somewhereabove the stellar surface, through which charges will beaccelerated to relativistic energies [10,11]. Suppose thatcharge depletion occurs near the stellar surface, with acharacteristic density f dn0, where f do1 is an unknowndepletion factor. If the neutron star is young, its surfacewill emit in soft X-rays, and the protons in acceleratednuclei will scatter with this radiation field. If the protonsare sufficiently energetic, they will exceed the threshold forphotomeson production through the Dþ resonance. The Dþ

quickly decays to a pþ, and muon neutrinos are producedthrough the following channel:

pg! Dþ ! npþ ! nnmmþ ! nnmeþnen̄m. (2)

The proton energy threshold �p for Dþ production is givenby

�p�gX0:3GeV2f g; f g � ð1� cos yÞ�1 (3)

where �g is the photon energy and y is the incidence anglebetween the proton and the photon in the lab frame.Young neutron stars typically have temperatures ofT1 ’ 0:1 keV, and photon energies �g ¼ 2:8kT1ð1þ zgÞ

�0:4 keV, where zg ’ 0:4 is the gravitational red-shift andT1 is the surface temperature measured at infinity. Theproton threshold energy for the D resonance is then�p;th ’ T�10:1 keVf g PeV, where T0:1 keV � ðkT1=0:1 keVÞ.Therefore, if the potential along field lines is only �1% ofthe full potential DF across field lines in the equilibriummagnetosphere, protons can reach the D resonance thresh-old. Assuming that a potential of order DF is available foracceleration along field lines, a necessary condition for theD resonance to be reached is

B12P�2msT0:1 keVX3� 10�4. (4)

Many nearby pulsars satisfy this condition, and so arepotential sources of m neutrinos. The best candidates areyoung neutron stars, which are usually rapidly spinningand hot.

In the photomeson production process of Eq. (2), themuon neutrinos receive 5% of the energy of the proton.Typical proton energies required to reach resonance are�1PeV, so the expected m neutrino energies will be�50TeV. The conversion probability for a proton is smallðt1%Þ; only a small number of protons are excited to theD resonance and the pulsar emission mechanism isessentially unaffected. Moreover, since the acceleratedprotons are far more energetic than the radiation fieldwith which they interact, any pions produced through the Dresonance, and hence, any muon neutrinos, will be movingin nearly the same direction as the proton was when it wasconverted. The radio and neutrino beams will be approxi-mately coincident, so that some radio pulsars might also bedetected as neutrino sources.

Large-area neutrino detectors use the Earth as a mediumfor conversion of a muon neutrino to a muon, which then

produces Cherenkov light in the detector. For a moderateor strong acceleration gap (f dt0:5), we estimate the muonevent rate to be (in units of km�2 yr�1)

dN

dAdt’ 105Z�1f bf dB12P�1msd

�2kpcT

20:1 keV (5)

where Z is the ion charge, f b is the pulsar duty cycle anddkpc is the source distance (in kpc). In Ref. [8], we gaveupper limits of the neutrino flux at Earth for several youngand close neutron stars; we find the most intense potentialsources to be the Crab pulsar (northern sky) and Velapulsar (southern sky). The muon event rate (Eq. (5))calculated for these sources is reported in Table 1; theneutrino energy flux for the Crab is displayed in Fig. 1.The solid (dashed) line shows the spectrum assuming thatthe proton energy increases linearly (quadratically) withheight above the stellar surface. Both curves show a well-defined lower energy threshold, corresponding to the Dresonance becoming kinematically allowed. At higherenergies, the spectrum drops approximately as E�2, asthe phase space for conversion becomes restricted. At somemaximum energy, the spectrum is suddenly truncated byeither kinematics (solid curve) or the termination of theproton acceleration as limited by the magnitude of theacceleration gap (not shown, since this cut-off cannot be

ARTICLE IN PRESSG.F. Burgio, B. Link / Nuclear Instruments and Methods in Physics Research A 567 (2006) 486–488488

predicted). The details of these calculations will bepresented in a forthcoming paper [12].

Results of about 807 d of data from AMANDA-II arenow available [13]. AMANDA-II has detected 10 events(over a background of 5.4) from the direction of the Crabpulsar, with energies higher than 10GeV. This result,though intriguing, is not statistically significant; IceCubewill be able to confirm or refute this result. As far as thesouthern sky is concerned, a neutrino signal from Velamight be detectable by ANTARES (expected to go intooperation during 2006) with as little as several weeks ofintegration time even for a modest depletion f d (otherpromising sources are given in Ref. [8]). While it would bemore exciting to see neutrinos from pulsars, the accumula-tion of null results would be interesting as well; it wouldprobably mean that the D resonance is not attained in theneutron star magnetosphere, thus providing a bound onthe accelerating potential.

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