High Energy Neutrino Emission from Black-Hole...

High Energy Neutrino Emission from Black-Hole

Micro-Quasars

Theocharis S. Kosmas

Theoretical Physics Section, University of Ioannina, Greece

Theocharis S. Kosmas (Ioannina University) High Energy Neutrino Emission from Black-Hole Micro-Quasars 1 / 26

Overview of the Talk

Introduction

A typical X-ray binary systemp-p collisions in hadronic jets of MQs

High Energy γ-ray and ν-emission from MQ Jets

Semi-analytical ApproachExplicit solution of Transport Equation

Dynamical Simulations with PLUTO RMHD-code

Summary and Conclusions


A typical X-ray binary (Micro-quasar) system

The most common cases of X-ray binary stars comprise a compact star(usually a black hole or a neutron star), and the donor star, a normal starstill evolving.The spectral extent of such a system can be very broad. The classical BHcandidate (BHC) XRB, Cyg X-1, is a well-detected source from the radioband to high energy γ-rays and neutrino emission.

A generally accepted structure of a typical X-ray binary system.Theocharis S. Kosmas (Ioannina University) High Energy Neutrino Emission from Black-Hole Micro-Quasars 3 / 26

Mechanisms of mass Loss of a Star

During their evolution one of the stars may lose mass through four basicmechanisms:

One of the stars may eject mass in the form of a stellar wind

Eruptive or equatorial loss from rapidly spinning (of the compact object)

X-ray emission of the compact object can irradiate the outer layers of thecompanion star causing or increasing the mass transfer rate

Over the course of their stellar evolution, one of the two stars in a binarysystem may increase its radius or the binary separation may shrink to thepoint where the gravitational pull of the compact object gradually removesthe outer layers of its envelope


Geometry of a High Mass (BH) Microquasar

Jet Parameters

ξ ≈ 1− 1.5o: Jet’shalf-opening angle

θ ≈ 30o :Viewing angle

Due to the rotation of the binary system, gas flowing through point-L1 will

have relatively high angular momentum. Too large to directly accrete onto

the compact object

M. Reynoso and G. Romero, A&A 493, 1-11 (2009)


Hadronic Jets of MQ: p-p Collisions

Plasma is ejected from the accretion’s disc center, due tomagneto-centrifugal force (direction perpendicular to disc).

In the interior of the jet, bulk flow particles (protons) are mostly thermal(move ’slowly’, following the jet stream). Through first order Fermi process,a small portion of protons are accelerated (non-thermal protons). p-pcollisions of non-thermal protons on thermal ones create secondary particles(charged π±, K±, µ± etc.).

The pions produce neutrinos according to the reactions:

π+→ µ+ + νµ, π+

→ e++ νe

π−→ µ− + ν̄µ, π−

→ e−+ ν̄e

µ+→ e+ + νe + ν̄µ

µ−→ e− + ν̄e + νµ

Left boxes: prompt neutrinos. Right box: Delayed neutrinos. It is notpossible to distinguish those experimentally (terrestrial experiments,FermiLab, J-PARC, etc. may separate them).


Description of Neutrino Produced from MQ jets

The description of the energy spectrum and composition of theprimary particles.

The definition of the target material with which the primary particlesinteract

The modelling of the properties of particle production in hadronicinteractions (energy distributions).

The description of the properties of the medium where theinteractions occur, to determine the relevant mechanisms for energyloss.

The (well-known) properties of weak decays

Because of the limited statistics and angular resolution, the observationsof astrophysical neutrinos will necessarily integrate over the entire volumeof the source (in most cases they appear as point-like) and average overtime variations. Describing this situation, requires the averaging overdifferent source regions and conditions


The Scheme followed by the Calculations

First, the rate of production of the secondary particle of type α,Qα(Eα), can be calculated though the convolution procedure

The energy distribution of the particle α at decay, in general, differsfrom the distribution at production

The neutrinos created in the direct decay of particle α are calculated

The muon production rate can be calculated with an analogousexpression (by substituting the appropriate decay distributions)

Finally we sum over weakly decaying particles (π±,K±, etc.(neglecting much smaller contributions coming from heavier particles)

The last step is to compute the neutrinos generated by muon decaydelayed neutrinos

The neutrino flux is obtained by summing over all possible sources


Neutrino Production

For example, it holds that (Lipari et al, 2007):

dnp→π(E ;Ep)

dE=

1

Ep

F (pp)π

(

E

Ep

)

where F(pp)π denotes the energy density of the produced pions as a

function of ratio x = E/Ep , with E = Eπ.Neutrinos produced (directly from the decay of a particle α are describedby the relation

Qα→να(Eν) =

∫

∞

Eν

Qdec.α (Eα)

dnα→να(Eν ;Eα)

dEν

dEα

The energy distribution of muons before their decay is given by

Qdec.

µ±

h

(E ) =

∫

∞

E

Qµ±

h(Ei )

dPµdec (E ;Ei )

dEdEi


Phenomenological descrition

By using simulation codes (SIBIL, QGSJET, QCD purturbation theorycodes), and then fitting, (Kelner, et al.) , 2006) obtained semi-analyticalexpressions, for the interaction cross section and the pionenergy-distribution (per pp-collision), etc.

Qppπ (E ) = ngasc

∫ 1

E

E (max)

Np

(

E

x

)

F (pp)π σinel

pp

(

E

x

)

dx

x

where x = EEp

with dE(p) = −1x2Edx .


Neutrino production from muon decay

The neutrinos obtained from muon-decay are

Qµ±

h→να

(Eν) =

∫

∞

Eν

Qdec.

µ±

h

(Eµ)dnµ±

h→να

(Eν ;Eµ)

dEν

dEµ

The energy distribution of muons before decaying may be written as

Qdec.

µ±

h

(E ) =

∫

∞

E

Qµ±

h(Ei )

dPµdec (E ;Ei )

dEdEi


Total Neutrino emissivity

The total neutrino emissivity is calculated by adding up contributionscoming from the decay of secondary particles (pions, kaons etc.) andfrom muon decay.

Qemiss(Eν) =

α∑

α→ν

Qα→να(Eν)


Transport Equation

We start from a pion distribution Nπ(Ep) which satisfies the equation:

∂Nπ

∂t−∇(Dπ∇Nπ) +

∂(bπNπ)

∂E+

Nπ

T= Q(E , r, t)

∇(Dπ∇Nπ) : Describes the spatialdiffusion of pions.

∂(bπNπ)∂E

: Describes the energyvariation of Nπ due to accelerationand collision of protons.

bπ(E , z) = −E · (t−1sync + t−1

adb + t−1πp )

Q(E , r, t) : Intensity of theπ± source.

Nπ

T: Catastrophic collision

or exit of the energy band.

By solving numerically this equation, we compute the pion distribution Nπ(Ep)

which produces the neutrino beam of our interest.


Explicit Solution of the Transport ODE

By neglecting the spatial diffusion and time dependence inside the jet, thetransport equation takes the simple form:

∂(bπNπ)

∂E+

Nπ

T= Q(E , r)

Neutrino emissivity is subsequently obtained through the (numerical) integration:

Qν =

∫ Emax

E

dEπt−1π,dec(Eπ)Nπ(Ep , z) ·

Θ(1− rπ − x)

Ep(1− rπ)

where:

t−1π,dec = (2.6 · 10−8

· γπ)−1

(s−1), rπ = (mµ

mπ)2, x =

Eµ

Ep

M. Reynoso and G. Romero, A&A 493, 1-11 (2009)


Dynamical simulations in MQs. Jet density evolution

Modern Relativistic Magneto-Hydro-Dynamical (RMHD) hydrocodeused for the dynamic calculation (PLUTO).

High Energy γ-ray and ν-emission calculated from the model jet.

When model-results match observations, initial conditions of modelare then considered to approximate the actual ones at the source.

Initial results already compared to actual observations and detectoroutput.


Important model parameters

These parameter values (in c.g.s.) are fitted to SS 433 MQ data.Smponias, Kosmas, Advances in High Energy Physics 921757, (2015)


Role of magnetic fields in the propagation of MQ jets

We simulate ”RMHD” jet’s flow, for different magnetic fields valuesand derive 2-D and 3-D visualisations.

We may investigate the moderation of the MF on the emission ofhigh energy neutrinos and γ-rays, produced from the collisions.

MF components:

Toroidal component, (Bφ)

Poloidal component, (Bp)(opposite conversion thanfusion)


Jet formation/confinement

Accretion disk rotation (alternatively, GR frame dragging) causes rotation ofthe matter.

The acceleration of the jet is supported by an accretion disk threaded by aperpendicular magnetic field.

The magnetic field lines are stretched by the material (fixed on the lines)ending up surrounding them.

At relativistic jets, the direction of the outgoing flux injection is determined

by the angular momentum axis of the accretion disk (also by the spin of the

central object).


Processes Inside the Relativistic Jet

Before decaying, π± and µ± may interact, losing energy through various processes:

Synchrotron Radiation: Charged particles of mass m and energy E = γmc2 emitsynchrotron radiation at a rate:

t−1sync =

4

3

(me

m

)3 σTB2γ

8πmec

Proton-Pion Collisions: A portion of the pions collide with thermal protons at a rate:

t−1πp (E , z) ≈

n(z)cσ(innel)πp (E)

2

where

σ(innel)πp (E) ≈ (34.3 + 1.88L + 0.25L2) ·

(

1−

(Eth

Ep

)4)2· 10−27cm2

L = lnEp

1000GeV,Eth = 1.2GeV

Adiabatic Cooling:Since the jet is expanding with velocity ub , the adiabatic cooling rate is:

t−1adb

=2

3

ub

z


The logarithm of the Temperature T

Two-dimensional slicefrom athree-dimensionalsimulation, depictingthe logarithm of theTemperature T (unitsof 1013K.

The maximumtemperature is 1011K

The minimum is 108K(the actual minimum isnear zero).


The temperature T for the light jet case

The lighter jetadvances moreslowly,creating a richercocoon and aprotrusion effect justbefore the jet head.

The equatorial regionis also active now,albeit closer to the jetbase, and it persistslonger due to theslower jet expansion.

Smponias, Kosmas, Mon. Not. R. Astron. Soc. 412, 13201330 (2011)


The logarithm of the temperature T for the light jet case

A logarithmic plot of aslice of the density atmodel time 464, inunits of proton cm−3,with the sameorientation as thetemperature slices.

We can see the samepattern at theequatorial region as inthe previous images.

The domain lengthalong the jet is 1016

cm.


The model system of a heavy jet

A three-dimensionalview of the modelsystem of a heavy jetat model time 464(around 464 hr),depicting the modeloctant in 3D space,showing thetemperature in codeunits of 1013K.

The domain lengthalong the jet is 10 16cm. The length unitsalong thebounding-box axes are1014 cm.

Smponias, Kosmas, Mon. Not. R. Astron. Soc. (2014)


Summary and Conclusions

We study (i) High energy neutrinos and (ii) High energy γ -rays, produced(interior of the hadronic jets) through decays of secondary particles: chargedparticles (π±, K±, µ±, etc.) and neutral particles (π0, η, etc.), respectively,originating from p-p collision (thermal protons on non-thermal ones) inrelativistic black hole MQs.

We focus on the neutrino emissivity from MQ hadronic jets by employingPLUTO hydro code.

This computational tool has provided:(i) realistic modelling of radio and gamma-ray emission, and(ii) efficient estimation of neutrino emission events originating from MQ jets.

For the observation of such neutrino fluxes, current terrestrial detectors (e.g.IceCube (at South Pole) and KM3NeT (at Mediterranean sea) are inoperation.


Collaborators:

University of Ioannina, Greece: T. Smponias, D.K. Papoulias

Univ. of Ioannina (Dept. of Mathematics): M. Xenos

NCSR Democritos, Greece: G. Stavropoulos, D. Balasi (KM3NeTExperiment)

Univ. of Erlangen-Nureberg, Germany: Group of Alexander Kappes(IceCube Experiment)

Univ. of Manchester, U.K.: O.T. Kosmas


Thank you

for your attention


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