The kHz QPOs as a probe of the X-ray color–color diagram and accretion-disk structure for the atoll source 4U 1728-34

Abstract

We have taken the kHz QPOs as a tool to probe the correlation between the tracks of X-ray color–color diagram (CCD) and magnetosphere-disk positions for the atoll source 4U 1728-34, based on the assumptions that the upper kHz QPO is ascribed to the Keplerian orbital motion and the neutron star (NS) magnetosphere is defined by the dipole magnetic field. We find that from the island to the banana state, the inner accretion disk gradually approaches the NS surface with the radius decreasing from r ∼ 33.0 km to ∼15.9 km, corresponding to the magnetic field from B(r) ∼ 4.8 × 106 G to ∼4.3 × 107 G. In addition, we note the characteristics of some particular radii of magnetosphere-disk r are: firstly, the whole atoll shape of the CCD links the disk radius range of ∼15.9–33.0 km, which is just located inside the corotation radius of 4U 1728-34 rco (∼34.4 km), implying that the CCD shape is involved in the NS spin-up state. Secondly, the island and banana states of CCD correspond to the two particular boundaries: (I)near the corotation radius at r ∼ 27.2–33.0 km, where the source lies in the island state; (II)near the NS surface at r ∼ 15.9–22.3 km, where the source lies in both the island and banana states. Thirdly, the vertex of the atoll shape in CCD, where the radiation transition from the hard to soft photons occurs, is found to be near the NS surface at r ∼ 16.4 km. The above results suggest that both the magnetic field and accretion environment are related to the CCD structure of atoll track, where the corotation radius and NS hard surface play the significant roles in the radiation distribution of atoll source.