Research Article High Energy Neutrino Emission from ...High Energy Neutrino Emission from...

Research ArticleHigh Energy Neutrino Emission from AstrophysicalJets in the Galaxy

T Smponias1 and O T Kosmas2

1Division of Theoretical Physics University of Ioannina GR-45110 Ioannina Greece2Chair of Applied Dynamics University of Erlangen-Nuremberg Haberstrasse 1 D-91058 Erlangen Germany

Correspondence should be addressed to T Smponias tsmponiashushmailcom

Received 11 July 2014 Revised 22 October 2014 Accepted 3 November 2014

Academic Editor Athanasios Hatzikoutelis

Copyright copy 2015 T Smponias and O T Kosmas This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited The publication of this article was funded by SCOAP3

We address simulated neutrino emission originated from astrophysical jets of compact objects within the Galaxy These neutrinosare of high energies (119864] of the order up to a few TeV) and for their observation specialized instruments are in operation bothon Earth and in orbit Furthermore some next generation telescopes and detector facilities are in the process of design andconstructionThe jet flow simulations are performed using themodern PLUTOhydrocode in its relativistic magnetohydrodynamicversion One of the main ingredients of the present work is the presence of a toroidal magnetic field that confines the jet flow andfurthermore greatly affects the distribution of the high energy neutrinos

1 Introduction

In recent years a remarkable development of neutrino andgamma-ray astronomy took place New telescopes and detec-tor facilities were designed and implemented such as theCTA Cerenkov gamma-ray array [1] Fermi orbital telescope[2] or the IceCube neutrino detector [3] The IceCube neu-trino observatory located at the South Pole detects neutrinosin a wide energy range far exceeding the energies of man-made accelerator beams IceCube features a large detectorvolume increasing the possibility to detect neutrinos fromindividual astrophysical sources

Potential sites for gamma-ray and neutrino productionfrom jets include galactic sources of X-ray binaries (XRB) [4ndash6] as well as extragalactic sources [7] such as active galacticnuclei (AGN) ([8]) The above categories may be extendedto include a wide range of different phenomena such assupernova remnants [9 10] and other possible sources ofhigh energy particlesThese systems may produce 120574-rays andhigh energy neutrinos from interactions (collisions) of highenergy protons with thermal ones In general a large detectorvolume is needed since neutrinos are so weakly interactingwith matter

At the same time 120574-ray emission can also be observedfrom such sources by ground and satellite based gamma-ray telescopes (eg Fermi CTA)When studying accelerationprocesses of those sources it is often useful to compare theneutrino and 120574-ray fluxes emanating from them

XRB are binary stellar systems comprising a mainsequence star and a compact object emitting in the X-rayband often also called microquasars [4 11] in relation to thetheir cousins of galactic scale quasars They have relativisticjets that include acceleration sites allowing particles to reachenergies up to TeV [12] There the cooling of TeV electronsis very strong due to the high density of the radiationimplying a hadronicmechanism for the gamma-ray emissionSimultaneous neutrino emission is then possible as well[5 6]

In this work we aim to simulate the neutrino flux generat-ed from amodel microquasar X-ray binary system assuminga hadronic jet and hadron-related acceleration processes(nonthermal proton acceleration and interactions of highenergy protons) Towards this purpose a power law withan exponential cutoff spectrum is used [5 13] This is anextension of our previous calculations of 120574-ray emission froma simulated relativistic hydrodynamical jet [14]

Hindawi Publishing CorporationAdvances in High Energy PhysicsVolume 2015 Article ID 921757 7 pageshttpdxdoiorg1011552015921757

2 Advances in High Energy Physics

Table 1 Values of various physical andmodel parameters pertaining to the 120574-ray emission from the jet for the simulation run obtained withthe linear method and the Hancock integrator

Parameter CommentsCell size (times1010 cm) 025 PLUTOrsquos computational cell120588jet (cm

minus3) 10 times 1011 Initial jet matter density

120588sw (cmminus3) 10 times 1012 Stellar wind density

120588adw (cmminus3) 10 times 1012 Accretion disk wind density

119905maxrun (s) 15 times 10

3 Model execution timeInterpolation method LinearIntegrator MUSCL-HancockEOS Ideal Equation of stateBinSep (cm) 40 times 10

12 Binary star separation119872BH119872sun 3ndash10 Mass range of collapsed star119872star119872sun 10ndash30 Mass range of main Seq star120573 = V

0

119888 026 Initial jet speed119871119901

119896

2 times 1036 Jet kinetic luminosity

119902rel 10minus4 Fast proton energy fraction

119902] 01 Neutrino energy fraction (from fast protons)120572 minus2 Fast proton power law index119864max119901

(GeV) 106 Cutoff energy of the fast proton distribution

Grid resolution 120 times 200 times 120 PLUTO grid resolution (119909119910119911)

Neutrinos are mainly produced through pion and muondecay with the pions coming from inelastic 119901119901-scatteringsamong nonthermal protons and thermal ones within the jetPion decay by-products include amuon and amuon neutrinoas 120587plusmn rarr 120583

plusmn

+ ]120583

(]120583

) The muons can afterwards decay againinto an electron or a positron and the associated neutrinoAnother pion decay channel leads to two gamma-ray photons[6 13 15]

119901119901 997888rarr 1199011199011205870

+ 119865

119901119901 997888rarr 119901119899120587+

+ 119865

(1)

(119898119901

= 167 times 10minus24 g and 119898

120587

= 238 times 10minus25 g) 119865 comprises

1205870 and 120587

+

120587minus pairs Subsequently pion decay leads to muons

120574-rays and neutrino productionIn the present work we concentrate on simulations of

neutrino emission from relativistic galactic astrophysical jetsThese neutrinos have very high energy (of the order of TeV)and specialized instruments are in operation in order todetect them both on Earth and in space Furthermore somenext generation instruments are in the process of design andconstruction The jet flow simulations are performed usingthe modern PLUTO hydrocode in its relativistic magneto-hydrodynamic version [16] We assume the existence of atoroidalmagnetic field that confines the jet flow (in the regionof the compact object) [17] affecting the production of thehigh energy neutrinos [6]

2 Description of the Method

The jet is modelled using the relativistic magnetohydrody-namic (RMHD) version of the PLUTO hydrocode [16] ThePLUTO RMHD module is employed in order to simulate

the jet flow The Generalized Lagrange Multiplier (GLM)correction method is used enforcing magnetic divergencesuppression through hyperbolic divergence cleaning whilethe MUSCL-Hancock scheme is employed as the integratorA toroidal magnetic field is used that helps constrain the jetto an extent depending on the field strength In this paper weexplore the existence of a strong magnetic field that keeps theemitted neutrino flux highly concentrated [17]

The toroidal magnetic field setup employed leads to arather pronounced jet confinement due to Lorentz forcesacting on the jetmatter towards the jet axisThe stellar wind isset to decrease away from the companion star as 11199032 while acorona of 11199102 119910 being the jet axis direction is setup near thecompact object similar to [14] The most important modelparameters are shown in Table 1 The IDL suite and the VisItvisualization suite are then employed in order to present theresults of the simulations in a graphical manner

The boundary conditions are outflow at the top and at thesides of the computational domain (ldquoboxrdquo) and reflective atthe bottom where the jet base is located The jet emanatesfrom the middle of the bottom plane (119909-119911 plane) movingupwards that is along the modelrsquos 119910-axis

3 Radiative Transfer and Imaging

The line-of-sight (LOS) code of [18] is used to produce artifi-cial neutrino ldquoimagesrdquo of the jet-corona system The particleldquoemissionrdquo is calculated separately from each computationalcell under the twin assumptions that the particle distribu-tionrsquos dominant cooling time is smaller than the hydrocodersquostime step and also that the mean free path between collisionsis smaller than the hydrocode computational cell dimensionsThen each cell can be treated individually from a radiative

Advances in High Energy Physics 3

point of view and its neutrino emission contribution ata given energy level is added to its corresponding LOSNaturally no absorption is relevant for neutrinos in suchsystems

The emission calculation is performed in Mathematicamainly following the analysis of [5 6] Furthermore forconverting the neutrino emission from the jet reference frameto our rest frame the calculational procedure can be forexample that of [19] or that of [20] and we have respectively

119899 (119864Ω)

=119860

4120587

Γminus120572+1

119864minus120572

(1 minus 120573 cos(120579)radic1 minus 119898211988841198642)minus120572

[sin2(120579) + Γ2 (cos(120579) minus (120573radic1 minus 119898211988841198642))2

]

12

119899 (119864Ω)

=119860

4120587

Γminus120572minus1

119864minus120572

(1 minus 120573 cos(120579)radic1 minus 119898211988841198642)minus120572minus1


]

12

(2)

whereΩ is the line-of-sight solid angle Γ denotes the jet beamLorentz factor (for thermal slow protons) and 120573 = 119906119888 theknown ratio

The difference between the above expressions lies in thepowers of the two factors of the denominators on their lastfraction In the present work we have chosen to apply theexpression of [19]

The nonthermal proton distribution suffers synchrotronand adiabatic losses affecting the balance in the transportbetween protons and pions Following the formalism of [513] we may then obtain the neutrino emissivity

119865] (119909 119864119901) =2

120582int

120582

0

119865120587

(119864]

119909 119864119901

)119889119909

119909 (3)

where 119909 = 119864120587

119864119901

120582 = 0427 and the 119865120587

(for piondistribution) reads

119865120587

= int

119864119901

119864120587

119865(inj)120587

(1198641015840

) 119905minus1

119901119901

1003816100381610038161003816119887120587 (119864120587)1003816100381610038161003816

exp[1

119887119911

119864120587

+1

119887119911

1198641015840+

120572119911

1198872119911

log(119864120587

1198641015840)

+119886119911

1198872119911

log(119887119911

+ 120572119911

1198641015840

119887119911

+ 120572119911

119864120587

)]1198891198641015840

(4)

The function 119865(inj)120587

is given in [13] and 120572119911

119887119911

are given in [5]We note the dependency of 119887

119911

on themagnetic field 119861 amongothers

On the other hand adopting the approach of [6] also [15]we have the following line of calculations for the neutrinoemission that was actually used in the current work Forthe readers convenience we give here a brief presentation ofthe formalism of [6] (for more details see [6] and referencestherein)

Starting with the pion injection function we have

119876(119901119901)

120587

(119864 119911)

= 119899 (119911) 119888 int

1

119896

119889119909

119909119873119901

(119864

119909 119911) 119865(119901119901)

120587

(119909119864

119909) 120590(inel)119901119901

(119864

119909)

(5)

where 119896 = 119864119864(max)119901

and

119865(119901119901)

120587

(119909119864

119909)

= 4120572119861120587

119909120572minus1

(1 minus 119909120572

1 + 119903119909120572(1 minus 119909120572))

4

times (1

1 minus 119909120572+

119903 (1 minus 2119909120572

)

1 + 119903119909120572 (1 minus 119909120572))(1 minus

119898120587

1198882

119909119864119901

)

12

(6)

is the pion distribution per proton-proton interaction 119909 =

119864119864119901

119861120587

= 1198861015840

+025 1198861015840 = 367+083119871+00751198712 119903 = 26radic1198861015840

and 120572 = 098radic1198861015840 (see [6 13])The pion energy distribution is provided as the solution

of a transport equation

119873120587

(119864 119911)

=1

1003816100381610038161003816119887120587 (119864)1003816100381610038161003816

int

119864

(max)

119864

1198891198641015840

119876(1198641015840

119911) exp [minus120591120587

] (119864 1198641015840

)

(7)

where

120591120587

(1198641015840

119864) = int

119864

119864

1015840

11988911986410158401015840

119905minus1

120587

(119864 119911)

1003816100381610038161003816119887120587 (11986410158401015840)

1003816100381610038161003816

(8)

Finally for the emissivity of neutrinos emanating fromdirect pion decays (prompt neutrinos) we have [6 15]

119876120587rarr ] (119864 119911)

= int

119864max

119864

119889119864120587

119905minus1

120587dec (119864120587)119873120587 (119864120587 119911)Θ (1 minus 119903

120587

minus 119909)

119864120587

(1 minus 119903120587

)

(9)

where 119909 = 119864119864119901119894

and 119905120587dec is the pion decay time scale

The neutrino emissivity can then be integrated over 3Dcell volume (voxel volume) and divided by the surface ofa sphere whose radius is the distance to Earth The resultis a synthetic ldquoneutrino emission observationrdquo of the binarysystem By repeating the process for many energies we canthen obtain a SEDplot In order to simplify the computationsthe hydrodynamic quantities will first be obtained as anaverage over the whole of the jet and then used to calculatethe point emission from the jet system at a given energy (seebelow)

4 Results and Discussion

41 PLUTO Hydrodynamic Modeling The jet is confinedin a rather pronounced way by the toroidal magnetic field


560 570 580 590 600 610 630620

640

630

620

610

600

590

580

570

560

Contour3403306327222382204217011361102168063403

Max 3743Min 0000Vector

3743

2807

1872

9358

0000

Max 3743Min 0000

x-axis

Figure 1 A 2-dimensional plot (jet cross-section depicting a slicecut parallel to the 119909119911-plane) of the strongest components of thejet magnetic field in PLUTO simulation units We can see thatthe toroidal component (ringwise) constitutes a significant partof the field while other magnetic lines form part of the poloidalcomponent especially near the jet axis

component (Figure 1) as opposed to the null RHD case in[14] (Figures 2 and 3) The various emission sites are thenconcentrated along the jet axis This effect is even morepronounced because of local turbulence occurring naturallyin the jet flow The jet head advances through the surround-ing stellar and corona winds but its sideways expansionis limited The magnetic field contributes to the emissionmechanism so increased emission is expected from the innerflow funnel of the jet structure The strong confinement is aresult of adoption of a relatively intense field configurationallowing the beam to remain focused late into the simulationtherefore emission is expected to be present at late stages ofthe numerical experiment

The LOS code can create a synthetic image and we thenadd up all of its pixelrsquos intensities for total neutrino intensityfrom the system always at a given energy By repeating theprocess formanydifferent energies we can obtain the spectralemission distribution of the model system Using some kindof normalization in relation to an external factor such as anenergy estimate for the total energy emitted from the systemin neutrinos we could then adopt actual units and directlycompare to past and planned observations

Nevertheless we omit the LOS step and simply add upthe intensities of neutrino emission from all volume cellsof the system The reasons are twofold On the one handno absorption occurs for neutrinos therefore no need existsfor a full solution of the equation of radiative transferOn the other hand current and near-future observationsdetect stellar neutrino sources as strictly point ones so nospatial resolution whatsoever exists for them Combining theabove two arguments we arrive at the conclusion that merelyadding up emissions from all cells of the system provides

0

0

2040

6080

100120

0

50

100

150

Y

X

Z

1000

119

141

0168

0020

Max 682Min 208(minus06)

Figure 2 A plot of the magnetic field magnitude roughly half wayinto the simulation We can see the jet self-confinement due tomagnetic forces resulting in a narrow beam

an accurate model neutrino emission from a point sourcesystem all the while the system is being modelled internallyas a fully dynamical relativistic magnetohydrodynamical jet(RMHD jet) In Figure 1 a snapshot of the 3-dimensionaljet magnetic field configuration can be seen as the jet headadvances through the middle of the computational domainThe two main components of the field can be determinedand the presence of the toroidal component contributes tothe jet confinement through the Lorentz force towards the jetaxis There is a strong dependence of the neutrino emissionon the magnetic field since the synchrotron energy lossmechanismrsquos time scale strongly depends on the value of thefield 119861

In Figure 2 we can see the magnetic field magnituderoughly halfway into the simulation runThe jet remains wellconfined because of the magnetic force towards the jet axisacting due to the toroidal field component This mechanismintensifies the possible neutrino emission as it allows themagnetizedmatter to stay dense and also the field contributesto raise the emission levels (equation (4))

Figure 3 shows the jet density at themiddle of the simula-tion where the jet is well confined and relatively little mixinghas occurred between the jet matter and the surroundingwinds The sideways flow is still of secondary importanceand therefore less emission is expected from the sides of thejet This is opposed to the purely hydrodynamical jet case(eg [14]) where the jet expands much more and mixes withthe ambient medium allowing for more dynamical effectsto occur over a larger volume at the jet sides On the otherhand the magnetized jet here demonstrates a denser innerflow that stays focused and does not dissipate into the windsmaintaining stronger emission throughout the simulation


0

0

2040

6080

100120

0

50

100

150

Y

X

Z

Max 842(+10)Min 272(+05)

100(+09)

447(+08)

200(+08)

894(+07)

400(+07)

150

Figure 3 A plot of the jet density roughly halfway into thesimulation We can see the jet beam advancing along a narrowpath through the ambient medium kept together by the magnetictoroidal field component This confined jet is then a suitable site forincreased high energy 120574-ray and neutrino emissionproduction dueto maintaining extreme conditions along the jet length

42 Neutrino Emission Simulations In this work we simulatethe neutrino emission from the SS433microquasar system byextending the models of [5 14] which refer to the emissionof 120574-rays from these jets The differences between the twotypes of emission necessitate the employment of additionaltechniques Towards this aim we have used the following

(i) the formalism of [5 6] which consider the cascadeof particles in microquasar jets that lead to theproduction of neutrinos

(ii) the computationally demanding numerical integra-tion techniques used to reproduce the cascade ofparticles at individual hydrocode grid cells based onthe works of [6 13]

Due to the relatively limited availability of computingtime the grid resolution of the hydrocode data was reducedto a more manageable size Nevertheless we still obtain abetter resolution than that currently available from neutrinoldquoobservationsrdquo of microquasar systems where only pointsources are detected

We should mention that in studying the dependenceof neutrino intensity originating from our model systemthe PLUTO code produces jets whose dynamics directlyaffect the shape of the curve in the high energy tail (wellabove 100GeV) More specifically the fact that the innerjet has a higher proportion of faster protons and pionsrelative to the outer jet causes the neutrino emissivity thereto begin dropping abruptly at higher energies compared tothe behavior shown by the results of [6] A more detailed

10minus3

10minus8

10minus13

10minus18

102

104

106

I(E

) (

au)

E (GeV)

Figure 4 Unnormalized neutrino intensity 119868](119864]) on Earth asa function of the neutrino energy 119864] per energy interval Thisneutrino intensity is coming out of the jet simulations in thepresence of the strong toroidalmagnetic field that appreciably affectsthe emission

analysis including muonic neutrino emissions and higherhydrodynamical grid resolution is currently performed andwill appear in future work

Figure 4 shows the unnormalized neutrino intensity onEarth 119868](119864]) per energy interval coming out of the jetsimulations For simplicity only promptly generated neu-trinos from pion decay have been considered in this figure(delayed neutrinos [15] are to be included in future work)We concentrate on emissions produced not long after thebeginning of the jet ejection event (consequently our modelemission here mainly comes from the inner part of thejet)

As a first approximation the original hydrocode resultsof grid size 120 times 200 times 120 have been regridded into amuch smaller resolution of 3 times 5 times 3 Then following [6] theneutrino emission from119901119901 interactionswas obtainedWe cansee a general agreement with [6] It should be stressed thatthe difference between the behaviour of 119868

119899

119906(119864119899

119906) in the highenergy tail illustrated in Figure 4 and that of [6] is mainlyattributed to the strong magnetic confinement assumed inour present work as compared to that used in [6]

In order to facilitate comparison with observations theneutrino spectral intensity resulting from the jet is quantifiedusing an energetic argument At first we assume that theenergy fraction carried by the nonthermal (fast) protondistribution is of the order of 10minus4 [5] while the neutrinoenergy fraction of the fast protons carried away from thesystem is roughly of the order of 10 [21] In total neutrinosare considered to carry away from the system around 10

minus5

of the total kinetic luminosity of the bulk flow proton


stream The latterrsquos kinetic luminosity is calculated from thesimulation initial conditions to be around 2 times 10

36 ergsecIn order to constrain the luminosity 119868](119864]) we then

calculate the area under the curve in Figure 4 equal to 10minus4

(arbitrary units) times105 GeV = 10 (arbitrary units) timesGeV Thismay represent the power emitted therefore we equate thisarea to 2times10

31 ergsec or 1034 GeVsec which is the neutrinofraction of the jet kinetic luminosity This fixes the arbitraryunit to be equal to 10

33

(GeV s)minus1 The intensity curve ofFigure 4 flattens at around 10

minus4 which is therefore found tobe 10

29

(GeV s)minus1 This value is lower than that of [5] by 1-2 orders of magnitude at lower energies but is higher by asimilar amount at higher energiesThe reason is that our jet isstrongly confined by the toroidal magnetic field componentwhich means that a higher energetic proton population ismaintained later on This is shown before the emissioncalculation binning and averaging process Furthermore thisspectral emission distribution appears flatter at first andthen drops rapidly This favors emission at higher neutrinoenergies

Detectability by current and upcoming arrays is conse-quently relativelyworse than that in [5] (for the SS433 systemrsquosdistance) which is taken to be marginal already This impliesthat a more energetic jet is needed to provide higher neutrinoflux perhaps a jet of 100 times higher bulk mass flow rateOn the other hand a more turbulent jet with more shockacceleration sites for nonthermal protons may lead to a 119902relof 10 times higher that is 0001 This raises the expectedflux by a corresponding factor of 10 as well We concludethat the model jet may under favorable conditions fallwithin the detection limits of modern detectors discussed inSection 1

5 Summary and Conclusions

The neutrino production from a relativistic magnetohydro-dynamic model jet was studied using a hadronic modelfor proton-proton interactions leading to pion decay Highenergy neutrinos are assumed to be produced in galactic XRBthat include a stellar mass compact object The companion(donor) star is a main sequence one at an earlier stage ofits evolution The binary system in general emits in manydifferent wavelengths from radio and IR to high energygamma-rays and neutrinos The primary engine driving thejets and their emissions is the gravitational attraction ofmatter into the compact object Adiabatic and synchrotronlosses were assumed and a steady-state radiative conditionwas employed at a given hydrocode time step (the radiativeprocess is presumed to occur faster than the cell contentschange dynamically)

The toroidal magnetic field configuration of the systemconfines the jet and creates an environment that favors highenergy emission of 120574-rays and production of TeV neutrinosin the jet A first attempt to model the energetic neutrinoproduction in the system is expected to yield a directconnection between the jet dynamics and the energy spectraof the particles Further work may accommodate additionaleffects such as the full use of hydrocode data into the radiative

transfer calculations and the consideration of the relativisticnature of the imaged jet system

Finally for the numerical solution of the partial differen-tial equations (PDEs) arising from the problem furthermoreaccurate numerical schemes can be also considered like theones of [22]

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

One of the authors (T Smponias) wishes to thank Professor TS Kosmas for stimulating and useful discussions and the gridnode personnel of the University of Ioannina for technicalassistance T Smponias also thanks D Papoulias for technicalassistance with Mathematica

References

[1] M Actis G Agnetta F Aharonian et al ldquoDesign concepts forthe Cherenkov Telescope Array CTA an advanced facility forground-based high-energy gamma-ray astronomyrdquo Experimen-tal Astronomy vol 32 pp 193ndash316 2011

[2] A A Abdo M Ackermann M Axelsson et al ldquoModulatedhigh-energy gamma-ray emission from themicroquasar cygnusX-3rdquo Science vol 326 no 5959 pp 1512ndash1516 2009

[3] F Halzen G M Fuller and X Shi ldquoObserving the birth ofsupermassive black holes with the IceCube neutrino detectorrdquoPhysical Review Letters vol 81 p 5722 1998

[4] I F Mirabel and L F Rodrguez ldquoSources of relativistic jets inthe galaxyrdquo Annual Review of Astronomy and Astrophysics vol37 pp 409ndash443 1999

[5] M M Reynoso G E Romero and H R Christiansen ldquoPro-duction of gamma rays and neutrinos in the dark jets of themicroquasar SS433rdquoMonthly Notices of the Royal AstronomicalSociety vol 387 no 4 pp 1745ndash1754 2008

[6] M M Reynoso and G E Romero ldquoMagnetic field effects onneutrino production in microquasarsrdquo Astronomy amp Astro-physics vol 493 no 1 pp 1ndash11 2009

[7] E Waxman ldquoViewpoint the beginning of extra-galactic neu-trino astronomyrdquo Physics vol 7 p 88 2014

[8] F W Stecker ldquoPeV neutrinos observed by IceCube from coresof active galactic nucleirdquo Physical Review D vol 88 Article ID047301 2013

[9] R Mou ldquoUltra high energy neutrinos from supernova rem-nantsrdquo Journal of Physics G Nuclear and Particle Physics vol25 no 1 pp 129ndash134 1999

[10] F Vissani and F L Villante ldquoCosmic rays and neutrinos fromsupernova remnants (or the time when HESS met Ginzburgand Syrovatskii)rdquo Nuclear Instruments and Methods in PhysicsResearch Section A Accelerators Spectrometers Detectors andAssociated Equipment vol 588 no 1-2 pp 123ndash129 2008

[11] I F Mirabel ldquoVery energetic 120574-rays from microquasars andbinary pulsarsrdquo Science vol 312 no 5781 pp 1759ndash1760 2006

[12] F Aharonian A G Akhperjanian K-M Aye et al ldquoDiscoveryof very high energy gamma rays associated with an X-raybinaryrdquo Science vol 309 no 5735 pp 746ndash749 2005


[13] S R Kelner F A Aharonian andVV Bugayov ldquoEnergy spectraof gamma rays electrons and neutrinos produced at proton-proton interactions in the very high energy regimerdquo PhysicalReview D vol 74 no 3 Article ID 034018 16 pages 2006

[14] T Smponias and T S Kosmas ldquoDynamical and radiativesimulations of 120574-ray jets in microquasarsrdquo Monthly Notices ofthe Royal Astronomical Society vol 438 no 2 pp 1014ndash10262014

[15] P Lipari M Lusignoli and DMeloni ldquoFlavor composition andenergy spectrum of astrophysical neutrinosrdquo Physical ReviewDvol 75 Article ID 123005 2007

[16] A Mignone G Bodo S Massaglia et al ldquoPLUTO a numericalcode for computational astrophysicsrdquoTheAstrophysical JournalSupplement Series vol 170 no 1 pp 228ndash242 2007

[17] D A Clarke M L Norman and J O Burns ldquoNumericalsimulations of a magnetically confined jetrdquo The AstrophysicalJournal Letters vol 311 pp L63ndashL67 1986

[18] T Smponias and T S Kosmas ldquoModelling the equatorialemission in a microquasarrdquo Monthly Notices of the RoyalAstronomical Society vol 412 no 2 pp 1320ndash1330 2011

[19] D Purmohammad and J Samimi ldquoOn the hadronic beammodel of TeV 120574-ray flares from blazarsrdquo Astronomy and Astro-physics vol 371 no 1 pp 61ndash67 2001

[20] D F Torres and A Reimer ldquoHadronic beammodels for quasarsand microquasarsrdquo Astronomy amp Astrophysics vol 528 p L22011

[21] A Levinson and E Waxman ldquoProbing microquasars with TeVneutrinosrdquo Physical Review Letters vol 87 Article ID 1711012001

[22] O T Kosmas and D Papadopoulos ldquoMultisymplectic structureof numerical methods derived using nonstandard finite differ-ence schemesrdquo Journal of Physics Conference Series vol 490Article ID 012123 2013

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Table 1 Values of various physical andmodel parameters pertaining to the 120574-ray emission from the jet for the simulation run obtained withthe linear method and the Hancock integrator

Parameter CommentsCell size (times1010 cm) 025 PLUTOrsquos computational cell120588jet (cm

minus3) 10 times 1011 Initial jet matter density

120588sw (cmminus3) 10 times 1012 Stellar wind density

120588adw (cmminus3) 10 times 1012 Accretion disk wind density

119905maxrun (s) 15 times 10

3 Model execution timeInterpolation method LinearIntegrator MUSCL-HancockEOS Ideal Equation of stateBinSep (cm) 40 times 10

12 Binary star separation119872BH119872sun 3ndash10 Mass range of collapsed star119872star119872sun 10ndash30 Mass range of main Seq star120573 = V

0

119888 026 Initial jet speed119871119901

119896

2 times 1036 Jet kinetic luminosity

119902rel 10minus4 Fast proton energy fraction

119902] 01 Neutrino energy fraction (from fast protons)120572 minus2 Fast proton power law index119864max119901

(GeV) 106 Cutoff energy of the fast proton distribution

Grid resolution 120 times 200 times 120 PLUTO grid resolution (119909119910119911)

Neutrinos are mainly produced through pion and muondecay with the pions coming from inelastic 119901119901-scatteringsamong nonthermal protons and thermal ones within the jetPion decay by-products include amuon and amuon neutrinoas 120587plusmn rarr 120583

plusmn

+ ]120583

(]120583

) The muons can afterwards decay againinto an electron or a positron and the associated neutrinoAnother pion decay channel leads to two gamma-ray photons[6 13 15]

119901119901 997888rarr 1199011199011205870

+ 119865

119901119901 997888rarr 119901119899120587+

+ 119865

(1)

(119898119901

= 167 times 10minus24 g and 119898

120587

= 238 times 10minus25 g) 119865 comprises

1205870 and 120587

+

120587minus pairs Subsequently pion decay leads to muons

120574-rays and neutrino productionIn the present work we concentrate on simulations of

neutrino emission from relativistic galactic astrophysical jetsThese neutrinos have very high energy (of the order of TeV)and specialized instruments are in operation in order todetect them both on Earth and in space Furthermore somenext generation instruments are in the process of design andconstruction The jet flow simulations are performed usingthe modern PLUTO hydrocode in its relativistic magneto-hydrodynamic version [16] We assume the existence of atoroidalmagnetic field that confines the jet flow (in the regionof the compact object) [17] affecting the production of thehigh energy neutrinos [6]

2 Description of the Method

The jet is modelled using the relativistic magnetohydrody-namic (RMHD) version of the PLUTO hydrocode [16] ThePLUTO RMHD module is employed in order to simulate

the jet flow The Generalized Lagrange Multiplier (GLM)correction method is used enforcing magnetic divergencesuppression through hyperbolic divergence cleaning whilethe MUSCL-Hancock scheme is employed as the integratorA toroidal magnetic field is used that helps constrain the jetto an extent depending on the field strength In this paper weexplore the existence of a strong magnetic field that keeps theemitted neutrino flux highly concentrated [17]

The toroidal magnetic field setup employed leads to arather pronounced jet confinement due to Lorentz forcesacting on the jetmatter towards the jet axisThe stellar wind isset to decrease away from the companion star as 11199032 while acorona of 11199102 119910 being the jet axis direction is setup near thecompact object similar to [14] The most important modelparameters are shown in Table 1 The IDL suite and the VisItvisualization suite are then employed in order to present theresults of the simulations in a graphical manner

The boundary conditions are outflow at the top and at thesides of the computational domain (ldquoboxrdquo) and reflective atthe bottom where the jet base is located The jet emanatesfrom the middle of the bottom plane (119909-119911 plane) movingupwards that is along the modelrsquos 119910-axis

3 Radiative Transfer and Imaging

The line-of-sight (LOS) code of [18] is used to produce artifi-cial neutrino ldquoimagesrdquo of the jet-corona system The particleldquoemissionrdquo is calculated separately from each computationalcell under the twin assumptions that the particle distribu-tionrsquos dominant cooling time is smaller than the hydrocodersquostime step and also that the mean free path between collisionsis smaller than the hydrocode computational cell dimensionsThen each cell can be treated individually from a radiative




119899 (119864Ω)

=119860

4120587

Γminus120572+1

119864minus120572



]

12

119899 (119864Ω)

=119860

4120587

Γminus120572minus1

119864minus120572



]

12

(2)




119865] (119909 119864119901) =2

120582int

120582

0

119865120587

(119864]

119909 119864119901

)119889119909

119909 (3)

where 119909 = 119864120587

119864119901

120582 = 0427 and the 119865120587


119865120587

= int

119864119901

119864120587

119865(inj)120587

(1198641015840

) 119905minus1

119901119901

1003816100381610038161003816119887120587 (119864120587)1003816100381610038161003816

exp[1

119887119911

119864120587

+1

119887119911

1198641015840+

120572119911

1198872119911

log(119864120587

1198641015840)

+119886119911

1198872119911

log(119887119911

+ 120572119911

1198641015840

119887119911

+ 120572119911

119864120587

)]1198891198641015840

(4)


is given in [13] and 120572119911

119887119911


119911




119876(119901119901)

120587

(119864 119911)

= 119899 (119911) 119888 int

1

119896

119889119909

119909119873119901

(119864

119909 119911) 119865(119901119901)

120587

(119909119864

119909) 120590(inel)119901119901

(119864

119909)

(5)

where 119896 = 119864119864(max)119901

and

119865(119901119901)

120587

(119909119864

119909)

= 4120572119861120587

119909120572minus1

(1 minus 119909120572

1 + 119903119909120572(1 minus 119909120572))

4

times (1

1 minus 119909120572+

119903 (1 minus 2119909120572

)

1 + 119903119909120572 (1 minus 119909120572))(1 minus

119898120587

1198882

119909119864119901

)

12

(6)


119864119864119901

119861120587

= 1198861015840

+025 1198861015840 = 367+083119871+00751198712 119903 = 26radic1198861015840



119873120587

(119864 119911)

=1

1003816100381610038161003816119887120587 (119864)1003816100381610038161003816

int

119864

(max)

119864

1198891198641015840

119876(1198641015840

119911) exp [minus120591120587

] (119864 1198641015840

)

(7)

where

120591120587

(1198641015840

119864) = int

119864

119864

1015840

11988911986410158401015840

119905minus1

120587

(119864 119911)

1003816100381610038161003816119887120587 (11986410158401015840)

1003816100381610038161003816

(8)


119876120587rarr ] (119864 119911)

= int

119864max

119864

119889119864120587

119905minus1

120587dec (119864120587)119873120587 (119864120587 119911)Θ (1 minus 119903

120587

minus 119909)

119864120587

(1 minus 119903120587

)

(9)

where 119909 = 119864119864119901119894






560 570 580 590 600 610 630620

640

630

620

610

600

590

580

570

560

Contour3403306327222382204217011361102168063403


3743

2807

1872

9358

0000

Max 3743Min 0000

x-axis





0

0

2040

6080

100120

0

50

100

150

Y

X

Z

1000

119

141

0168

0020







0

0

2040

6080

100120

0

50

100

150

Y

X

Z

Max 842(+10)Min 272(+05)

100(+09)

447(+08)

200(+08)

894(+07)

400(+07)

150







10minus3

10minus8

10minus13

10minus18

102

104

106

I(E

) (

au)

E (GeV)





119899

119906(119864119899



minus5








33



29










Acknowledgments


References





























FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics






119899 (119864Ω)

=119860

4120587

Γminus120572+1

119864minus120572



]

12

119899 (119864Ω)

=119860

4120587

Γminus120572minus1

119864minus120572



]

12

(2)




119865] (119909 119864119901) =2

120582int

120582

0

119865120587

(119864]

119909 119864119901

)119889119909

119909 (3)

where 119909 = 119864120587

119864119901

120582 = 0427 and the 119865120587


119865120587

= int

119864119901

119864120587

119865(inj)120587

(1198641015840

) 119905minus1

119901119901

1003816100381610038161003816119887120587 (119864120587)1003816100381610038161003816

exp[1

119887119911

119864120587

+1

119887119911

1198641015840+

120572119911

1198872119911

log(119864120587

1198641015840)

+119886119911

1198872119911

log(119887119911

+ 120572119911

1198641015840

119887119911

+ 120572119911

119864120587

)]1198891198641015840

(4)


is given in [13] and 120572119911

119887119911


119911




119876(119901119901)

120587

(119864 119911)

= 119899 (119911) 119888 int

1

119896

119889119909

119909119873119901

(119864

119909 119911) 119865(119901119901)

120587

(119909119864

119909) 120590(inel)119901119901

(119864

119909)

(5)

where 119896 = 119864119864(max)119901

and

119865(119901119901)

120587

(119909119864

119909)

= 4120572119861120587

119909120572minus1

(1 minus 119909120572

1 + 119903119909120572(1 minus 119909120572))

4

times (1

1 minus 119909120572+

119903 (1 minus 2119909120572

)

1 + 119903119909120572 (1 minus 119909120572))(1 minus

119898120587

1198882

119909119864119901

)

12

(6)


119864119864119901

119861120587

= 1198861015840

+025 1198861015840 = 367+083119871+00751198712 119903 = 26radic1198861015840



119873120587

(119864 119911)

=1

1003816100381610038161003816119887120587 (119864)1003816100381610038161003816

int

119864

(max)

119864

1198891198641015840

119876(1198641015840

119911) exp [minus120591120587

] (119864 1198641015840

)

(7)

where

120591120587

(1198641015840

119864) = int

119864

119864

1015840

11988911986410158401015840

119905minus1

120587

(119864 119911)

1003816100381610038161003816119887120587 (11986410158401015840)

1003816100381610038161003816

(8)


119876120587rarr ] (119864 119911)

= int

119864max

119864

119889119864120587

119905minus1

120587dec (119864120587)119873120587 (119864120587 119911)Θ (1 minus 119903

120587

minus 119909)

119864120587

(1 minus 119903120587

)

(9)

where 119909 = 119864119864119901119894






560 570 580 590 600 610 630620

640

630

620

610

600

590

580

570

560

Contour3403306327222382204217011361102168063403


3743

2807

1872

9358

0000

Max 3743Min 0000

x-axis





0

0

2040

6080

100120

0

50

100

150

Y

X

Z

1000

119

141

0168

0020







0

0

2040

6080

100120

0

50

100

150

Y

X

Z

Max 842(+10)Min 272(+05)

100(+09)

447(+08)

200(+08)

894(+07)

400(+07)

150







10minus3

10minus8

10minus13

10minus18

102

104

106

I(E

) (

au)

E (GeV)





119899

119906(119864119899



minus5








33



29










Acknowledgments


References





























FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




560 570 580 590 600 610 630620

640

630

620

610

600

590

580

570

560

Contour3403306327222382204217011361102168063403


3743

2807

1872

9358

0000

Max 3743Min 0000

x-axis





0

0

2040

6080

100120

0

50

100

150

Y

X

Z

1000

119

141

0168

0020







0

0

2040

6080

100120

0

50

100

150

Y

X

Z

Max 842(+10)Min 272(+05)

100(+09)

447(+08)

200(+08)

894(+07)

400(+07)

150







10minus3

10minus8

10minus13

10minus18

102

104

106

I(E

) (

au)

E (GeV)





119899

119906(119864119899



minus5








33



29










Acknowledgments


References





























FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




0

0

2040

6080

100120

0

50

100

150

Y

X

Z

Max 842(+10)Min 272(+05)

100(+09)

447(+08)

200(+08)

894(+07)

400(+07)

150







10minus3

10minus8

10minus13

10minus18

102

104

106

I(E

) (

au)

E (GeV)





119899

119906(119864119899



minus5








33



29










Acknowledgments


References





























FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics









33



29










Acknowledgments


References





























FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics



















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics



Research Article High Energy Neutrino Emission from ...High Energy Neutrino Emission from...

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Transcript of Research Article High Energy Neutrino Emission from ...High Energy Neutrino Emission from...