May 2008 - Ljubljana

May 2008 - Ljubljana

Magnetic Field Upper Limits

for Jet Formation

in X-ray binaries & AGNs

M. Kaufman Bernadó1,* & M. Massi1

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

INDEX

1. Introduction

2. Jet formation cycle A and B – Basic condition

3. Neutron Star X-ray Binaries

4. Black Hole X-ray Binaries and Supermassive Black Holes

5. Implications

6. Summary

1. Introduction

INDEX




5. Implicactions

6. Summary

1. Introduction

X-ray Binary System

Companion Star:

MASS DONOR Low- or High-Mass

Compact Object:

ACCRETORNeutron Star or Black Hole

Accretion Disk:

X-ray emissionMicroquasar

X-ray BinarySystem

Microquasars are defined as the XRB systems where either high-resolution radio interferometric techniques have shown the presence of collimated jets or a flat/inverted radio spectrum has been observed (indirect evidence of an expanding continuous jet).

The nature of the compact object, NS or BH, is still uncertain for several microquasars.

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 of a BH.

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?

1. Introduction

INDEX




5. Implications

6. Summary

2. Jet formation cycle A and BBasic condition

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

The strong magnetic field cannot be twisted and is dynamically dominant: the plasma is forced to move along the magnetic field lines and converges onto the magnetic poles of the neutron star. There, it releases its energy, creating two X-ray emitting caps (Psaltis 2004).

JET FORMATION PB < Pp

Magnetic Field Upper Limit

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

The Basic Condition RA / R* = 1

NS Surface Radius

BH Last Stable Orbit

RA / RLSO = 1

1. Introduction

INDEX



4. Black Hole X-ray Binary and Supermassive Black Holes

5. Implications

6. Summary


Using observed values of B and M

for NS XRBs,

Classical X-ray Pulsarsms X-ray PulsarsAtoll-sourcesZ-sources

Classical X-ray Pulsars:

- called “slow” accretion-powered pulsars, period ~ 1s or more.

- HMXB (five LMXB)

Millisecond (ms) X-ray Pulsars:

- rapidly spinning

- few detected / all LMXB

Atoll and Z - Sources:

- LMXBs divided in these two types depending on their timing

and spectral properties

- Z-type have larger mass accretion rates than Atoll-type

The intersection between the function, RA/R*, and the basic condition plane, RA/R*=1, indicates the combination of the magnetic field and the mass accretion rate values for which plasma pressure and magnetic field pressure balance each other at the surface of the star.

This ensures that the initial condition for jet formation, PB < Pp

is fulfilled over the whole accretion disk.

We see that Atoll-sources are indeed potential sources for generating

jets and in fact they have not only been detected in radio (Fender &

Hendry 2000; Rupen et al. 2005) but more recently evidence of jets in

these sources has been found (Migliari et al. 2006 and Russell et al.

2007).

For their average B~108 G, the basic condition would only be fulfilled

for a mass accretion rate , , whereas the maximum

observed accretion rate is nearly one order of magnitude lower,

.

In fact, in the millisecond source SAX J1808.4-3658, which shows hints for

a radio jet, during bright states, peak values of

were measured and 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, from 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).

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

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:

Instead, if

1. Introduction

INDEX




5. Implications

6. Summary

4. Black Hole X-ray Binaries&

Supermassive Black Holes

Upper Limit for B with Eddington mass accretion rate

Stellar-Mass BHSchw

Stellar-Mass BHKerr

1.35 x 108 G

5 x 108 Gwith

BHSchw

BHKerr

Kerr Stellar Mass BHSchwarzschild Stellar Mass BH

Straightforward dependency of the magnetic field strength with the mass of the BH allowing us to establish its upper limit for the jet formation in the case of supermassive BHs as well:

Upper Limit for B with Eddington mass accretion rate

Supermassive BHSchw

Supermassive BHKerr

105.4 G

105.9 G

Schwarzschild and Kerr Supermassive BHs

SBHSchw

SBHKerr

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

Scaling our value, which is relative to RLSO=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.

1. Introduction

INDEX




5. Implications

6. Summary

5. Implications

The analysis of the basic condition for jet formation has two interesting possible implications:

Nature of the compact object in XRB systems

ms X-ray pulsars spin distribution

The nature of the compact object in XRB systems& the magnetic field decay

Measurements of surface magnetic field strengths by cyclotron resonance effects were carried out in a dozen of X-ray classical pulsars show that B is tightly concentrated over:

(1 - 4) x 1012 G (Makishima et al. 1999)

To achieve the basic conditions for forming a jet the field must decay to

B=107-8 G


Analysis of pulsars data have indicated that B decays 4 orders of magnitude by Ohmic dissipation in a timescale longer than 109 yr

(Konar & Bhattacharya 2001).

In this case then, the only possible accretor would be a Black Hole.

Therefore this kind of magnetic field decay process excludes the possibility of a NS-HMXB evolving into a microquasar phase since this decay is longer than the lifetime of the high-mass companion star, 107 yr for .

Circinus X-1 is an XRB with a type I X-ray bursts NS. It has a confirmed jet, so it is a microquasar.

Faster decays of the magnetic field can occur with the high-accretion-induced crust screening process.

(Zhang 1998)


It is so young that its orbit has not yet had time to become circular circularization time ~ 105 yr.

(Ransom et al. 2005)

It has already reached B to fulfill the basic condition for jet formation.

In fact, Romani (1995) has deduced a characteristic timescale for the initial field decay by screeing in the range of

104 yr < t < 106 yr.

A decay in the B due only to Ohmic dissipation implies the presence of a BH as the compact object in a microquasar-HMXB because of the long timescales of this process.

Only in the case of high-accretion-induced crust screening process the timescales can be as short as t ~ 105 yr and the issue of the nature of the compact object remains open.


ms X-ray pulsars spin distribution

Due to the possibility of jets in millisecond X-ray pulsars,

then the jet might be the suitable agent of angular momentum sink, as in the bipolar outflows from young stellar objects.

The transport rate of angular momentum by the jet can be two thirds or more of the estimated rate transported through the relevant portion of the disk. (Woitas et al. 2005)

One of the major open issues concerning millisecond X-ray pulsars is the absence of sub-millisecond X-ray pulsars. The spin distribution sharply cuts off well before the strict upper limit on the NSs spin rate that is given by the centrifugal breakup limit (0.3 ms depending on the NS equation of state).

The physics setting that limit is unclear. (Chakrabarty 2005)

1. Introduction

INDEX




5. Implications

6. Summary

6. Summary

The association of a classical X-ray pulsar - B ~ 1012 G - with jets is excluded.

Z sources

Atoll Sources

108.2 G

107.7 G

Magnetic Field Upper Limits

for Jet Formation

107.5G, and max. ms X-ray Pulsars

Stellar-Mass BHSchw

Stellar-Mass BHKerr

1.35 x 108 G5 x 108 G

Supermassive BHSchw

Supermassive BHKerr

105.4 G

105.9 G

Implications

Compact object nature vs. B decay

ms X-ray pulsars spin distribution vs. presence of jets

Documents

May 2008 - Ljubljana