A toy model for HFQPOs in XRBs

Ye Yong-Chun (叶永春 ), Wang Ding-Xiong(汪定雄 )

Department of Physics, Huazhong University of Science and Technology,

Wuhan, 430074, China

Content

Background

Description of model

Discussion

Background

HFQPOs in XRBs

Quasi-periodic oscillations in X-ray binaries have become a very active research field since the launch of the Rossi X-Ray Timing Explorer (RXTE; Bradt, Rothschild & Swank 1993). A key feature in these sources is that some of high frequency quasi-periodic oscillations (HFQPOs) appear in pairs. Five black hole (BH) X-ray binaries exhibit transient HFQPOs. Thereinto, three sources have pairs occurring,

Some models

GRO J1655-40 (450, 300Hz; Strohmayer 2001a; Remillard et al 1999)GRS 1915+105 (168, 113Hz; McClintock & Remillard 2003) XTE J1550-564 (276, 184, 92Hz; Miller 2001; Homan et al 2001; Remill

ard et al 2002a; Remillard et al 2002b).

Strohmayer (2001a; 2001b) : The azimuthal and radial coor

dinate frequencies ;Wagoner et al. (2001) : Discoseismic oscillations in a relativi

stic accretion disc ;Abramowicz & Kluzniak (2001) : Resonance between or

bital and epicyclic motion of accreting matter.

Model

The puzzling 3:2:1 ratio

Description of model

Configuration of magnetic field (non-axisymmetric)

Three processes are involved:

The magnetic coupling (MC) processThe Blandford-Znajek (BZ) processThe Disc accretion (DA) process

Figure 1. The poloidal magnetic field configuration including the screw instability in the MC process (SIMC)

Astrophysical Load

Black Hole Accretion Disc

rms

rSIMC

LMC

MC

BZ

rBZ

BZHotspot

SIMCHotspotHotspot

2,p p

H HB B f

1 , 0 ,

1, 2 ,f

2 02

1

1

f

Figure 2. Azimuthal profile of the non-axisymmetric magnetic field on the BH horizon

Non-axisymmetric

2 1p TSIMC MC d dr L B B

is the critical radius constrained by SIMC, which is determined by SIMCr

The formation of hotspot

Considering the BZ power transferred through two adjacent magnetic surfaces between and on the horizon, and the mapping relation between and the cylindrical radius in the BZ process:

d x

2 3

* 2

2 1 sin( , , )

2 1 sinBZ

a k kdPa k

d q

2sin /(1 ) xd q xe dx

2 2 2* 0 0 0( , , ) ( / )QPO ms MC DAF a n r F r F F F F F

A hotspot is produced by the energy transferred from the BH to the disc

at the place where attains its maximum(Nowak 1998; Wang 2003)QPOF

2

1

DMC D D

dF E L E L H d

d

4 MCrH T r

3

0 2

1 sin4 1

2 1 sin

L

MCMC

dT T a q

q

Astrophysical Load

Black Hole Accretion Disc

rms

rSIMC

LMC

MC

BZ

rBZ

BZHotspot

SIMCHotspotHotspot

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

0.0015

0.002

0.0025

0.003

0.0035

0.004

FO

PQ

The QPO frequencies

Considering that the two hotspots are frozen at the disc, we have the QPO frequencies by substituting and

into the Keplerian angular velocity as follow

max

3 2 3 1* 0 max( , ) / 2 ( )MC

QPO D msa n a

SIMC max

3 2 3 1* 0( , ) / 2 ( )

SIMC

SIMCQPO D SIMC msa n a

The QPO frequency corresponding to SIBZ is determined by the angular velocity of the magnetic field lines F Hk

** 0 2

*

( , )2(1 1 )

BZQPO

kaa k

a

1 40 3.23 10BHm Hz

Discussion

The observations and our results

Figure 3. The observations of XTE J1550-564 (Remillard 2002b)

Table 1. The 3:2:1 ratio of HFQPOs produced by our model

The explanation for the X-ray QPOs

It is believed that a disc is probably surrounded by a high-temperature corona analogous to the solar corona (Liang & Price 1977; Haardt 1

991; Zhang et al 2000). Very recently, some authors argued that the coronal heating in some stars including the Sun is probably related to dissipation of currents, and very strong X-ray emissions arise from variation of magnetic fields (Galsgaard & Parnell 2004; Peter et al. 2004). Analogously, if the corona exists above the disc in our model, we expect that it might be heated by the induced currents due to SIMC and SIBZ. Therefore a very strong X-ray emission would be produced to form X-ray Hotspot

The astrophysics surrounding

Figure 4. The observations of XTE J1550-564 (Miller 2001:longer

marks denote observation in which a HFQPO is found)

Abramowicz, M. A., & Kluzniak, W., 2001, A&A, 374, L19Bradt, H. V., Rothschild, R. E., & Swank, J. H., 1993, A&AS, 97, 355Galsgaard K., & Parnell C., Procedings of SOHO 15 Coronal Heating, ESA publication, astr

o-ph/0409562Haardt F., & Maraschi L., 1991, ApJ, 380, L51Homan J. et al., 2001, ApJS, 132, 377Liang E. P. T., Price R. H., 1977, ApJ, 218, 247McClintock J. E., & Remillard, R. A., 2003, in “Compact Stellar X-ray Sources,” eds. W. H.

G. Lewin & M. van der Klis, (Cambridge U. Press), in press; astro-ph/0306213Miller J. M. et al., 2001, ApJ, 563, 928Nowak, M. A., Lehr, D. E., 1998, in Theory of Black Hole Accretion Disks, ed. M. A. Abramowicz, G. Bjornsson, & J. E. Pringle, (Cambridge: Cambridge Univ. Pr

ess), p.233, preprint (astro-ph/9812004)

Reference

Peter H., Gudiksen B., & Nordlund A., Procedings of SOHO 15 Coronal Heating, ESA publication, astro-ph/0409504

Remillard, R. A., et al., 1999, ApJ, 522, 397Remillard R. A. et al., 2002a, ApJ, 564, 962Remillard R. A. et al., 2002b, ApJ, 580, 1030Strohmayer, T. E., 2001a, ApJ, 552, L49Strohmayer, T. E., 2001b, ApJ, 554, L169Wagoner, R. V., Silbergleit, A. S., & Ortega-Rodriguez, M. 2001, ApJ, 559, L25Wang D.-X., Lei W.-H., and Ma R.-Y. 2003, Mon. Not. R. Astron. Soc. 342, 851

Reference (continue)

Thank you!