September 2007 - Dublin

Magnetic Field Upper Limits

for Jet Formation

M. Kaufman Bernadó1,* & M. Massi1

1Max Planck Institut für Radioastronomie, Bonn, Germany*Humboldt Research Fellow

Magnetic Field Upper Limits for Jet Formation

Necessary initial condition:a low magnetic field at 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?

PB > Pp

PB vs Pp

Initial Conditionfor Jet Formation:

twisted B

Magnetic Linesare compressed

PB

AMPLIFIED

START

PB < Pp

increaseM

Cycle A

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.

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).

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).

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 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.

YES

BH: HIGH/SOFT-------------

NS: BS / FB

BH: LOW/HARD------------ NS: IS / HB

new compressionof the

magnetic lines

reconnection

BH: VERY HIGH----------- NS: NB

stored magneticenergy released

untwistedB

no JETis formed

two spinning plasma flows

a JETis formed

QUIESCENT

NO BTwisted?

Neutron Star:X-ray Pulsar

increaseM

increaseM

PB > Pp

Cycle B

START

JET FORMATION PB < Pp

Magnetic Field Upper Limit

Alfvén Radius

The Basic Condition

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

BH Last Stable Orbit

RA / RLSO = 1

RA / R* = 1

NS Surface Radius

Using observed values of B and M

for NS XRBs,

Classical X-ray Pulsarsms X-ray PulsarsAtoll SourcesZ sources

Upper Limit for B

Z sources

Atoll Sources

ms X-ray Pulsars

108.2 G

107.7 G

107.5G

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

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

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)

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).

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

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).

Note: in the specific case of a supermassive Schwarzschild BH of

108 we get B < 104.3 G.

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

astro-ph/0709.4287(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).