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Magnetic Field Upper Limits for Jet Formation. M. Kaufman Bernadó 1,* & M. Massi 1 1 Max Planck Institut für Radioastronomie, Bonn, Germany * Humboldt Research Fellow. September 2007 - Dublin. Magnetic Field Upper Limits for Jet Formation. Necessary initial condition:

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September 2007 - Dublin

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Magnetic Field Upper Limits

for Jet Formation

M. Kaufman Bernadó1,* & M. Massi1

1Max Planck Institut für Radioastronomie, Bonn, Germany

*Humboldt Research Fellow

September 2007 - Dublin

Magnetic Field Upper Limits

for Jet Formation

Necessary initial condition:

alow magnetic fieldat the NS surface or at the last stable orbit of the accretion disk.

Aim: to quantify this important parameter and therefore give an upper limit for the magnetic field strength for which an ejection could happen in a NS or BH XRB system, as well as to predict the corresponding behaviour for Active Galactic Nuclei using standard scaling.

When will an accreting NS become a microquasar and when, on the other hand, an X-ray pulsar?

When will a BH XRB system be able to evolve into a microquasar phase?

Initial Condition

for Jet Formation:

twisted B

Magnetic Lines

are compressed

Cycle A

PB < Pp



PB vs Pp


PB > Pp


The formation of a jet is based on

a competition process between

the magnetic field pressure, PB, and the plasma pressure, Pp.

Summarised in a flowchart.

Because of the increasing compression of the magnetic field lines, the magnetic pressure will grow and may become larger than the gas pressure on the surface of the accretion disk, where the density is lower.

Then, the magnetic field becomes “active”, i.e. dynamically dominant, PB > Pp,and the plasma has to follow the twisted magnetic field lines, creating two spinning-plasma flows.

The strength of the large-scale poloidal field must be low enough that the Pp dominates PB (Blandford 1976).

Only under that condition, PB < Pp, the differentially rotating disk is able to bend the magnetic field lines in a magnetic spiral (Meier et al. 2001).

Numerical simulations show that the launch of a jet involves a weak large-scale poloidal magnetic field anchored in rapidly rotating disks or compact objects (Meier et al. 2001).


PB > Pp







two spinning

plasma flows


no JET

is formed


is formed




Neutron Star:

X-ray Pulsar

Cycle B

new compression

of the

magnetic lines





stored magnetic

energy released






The generation of jets and their presence in XRBs is coupled to the evolution of a cycle that can be observed in the X-ray states of this kind of systems.

We therefore complement the jet formation flowchart showing the parallelism between the presence of a jet and the different X-ray states.

RA / R* = 1

NS Surface Radius

RA / RLSO = 1

The Basic Condition

BH Last Stable Orbit

Magnetic Field Upper Limit

PB < Pp


The distance at which the magnetic and plasma pressure balance each other.

Alfvén Radius

for NS XRBs,

Using observed values of B and

Classical X-ray Pulsars

ms X-ray Pulsars

Atoll Sources

Z sources

Z sources

Atoll Sources

ms X-ray Pulsars

108.2 G

107.7 G


Theses theoretical values are in complete agreement with the up to now existing observational data:

Upper Limit for B

The association of a classical X-ray pulsar (B ~ 1012 G) with jets is excluded even if they accrete at the Eddington critical rate.

Millisecond X-ray pulsar could switch to a microquasar phase during maximum accretion rate.

In fact, in the millisecond source SAX J1808.4-3658 (which shows hints for a radio jet) the upper limit of the magnetic field strength was found to be a few times 107 G (Gilfanov et al. 1998).

The magnetic field strength has been determined in a Z-source, with jets, Scorpius X-1, using magnetoacoustic oscillations in kHz QPO reaching values of 107-8 G (Titarchuk et al. 2001)

Classical X-ray pulsar: in agreement with the systematic search of radio emission in this kind of sources with so far negative result (Fender et al. 1997; Fender & Hendry 2000; Migliari & Fender 2006)

Schwarzschild Stellar Mass BH

Kerr Stellar Mass BH

Schwarzschild and Kerr Supermassive BHs

Upper Limit for B

with Eddington mass accretion rate

Stellar-Mass BHSchw

Stellar-Mass BHKerr

Supermassive BH

1.35 x 108 G

5 x 108 G

105.9 G

Note: in the specific case of a supermassive Schwarzschild BH of 108 we get B < 104.3 G.

For a BH of the same mass Blandford & Payne (1982) established B < 104 G at 10rg.

Scaling our value, which is relative to LSO=6rg, to 10rg we get B < 104 G in complete agreement with the results of Blandford & Payne (1982).

The analysis of the basic condition for jet formation presented here has as well some important implications.


(A&A, in press)

Some Atoll sources have been detected in radio (Fender & Hendry 2000; Rupen et al. 2005) and recently evidence for a JET has been found in some of them (Migliari et al. 2006, Russell et al. 2007).

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