DIFFERENT X-RAY SPECTRAL EVOLUTION FOR BLACK HOLE X-RAY BINARIES IN DUAL TRACKS OF RADIO–X-RAY CORRELATION

Most Galactic black hole (BH) X-ray binaries (XRBs) are transient sources that are detected in X-rays during bright, several-month-long outbursts with typical recurrence periods of many years. During an outburst, the XRB shows different spectral states associated with a q-like pattern in an X-ray hardness–intensity diagram (HID). At the beginning and end of the outburst, XRBs are normally observed in low/hard (LH) states, of which the emission is dominated by a power-law component extending to ∼100 keV with a photon index of 1.5 ≲ Γ ≲ 2. XRBs will stay in the high/soft (HS) states at high luminosities, where the X-ray spectrum is characterized by a strong thermal blackbody emission and a weak power-law component with Γ ≳ 2. Some XRBs also shows a steep power-law state with Γ ≳ 2.4, which differs from the HS state in that the power-law component, rather than the disk component, is dominant (Zdziarski 2000; McClintock & Remillard 2006; Done 2007; Fender & Belloni 2012; Zhang 2013 for recent reviews).

Different spectral states in XRBs are believed to be triggered by different accretion and/or jet processes. There is little doubt that a cold, optically thick, geometrically thin standard accretion disk (SSD; Shakura & Sunyaev 1973) captures the basic physical properties of XRBs in the HS state. Soft X-ray bumps as observed in the HS state can be naturally explained by the multi-temperature blackbody emission of the SSD. The accretion mode for the low/hard (LH) states of XRBs is still a matter of debate. The prevalent accretion model is a hot, optically thin, geometrically thick advection-dominated accretion flow (ADAF; also called a radiatively inefficient accretion flow, RIAF) which has been developed for BH accreting at a low-mass accretion rate (e.g., Narayan & Yi 1994, 1995; Abramowicz et al. 1995; see Ho 2008; Kato et al. 2008; Narayan & McClintock 2008 and Yuan & Narayan 2014 for recent reviews). The low-density, two-temperature plasma mainly radiates in X-rays, which can well reproduce the observed spectra of XRBs in the LH state. We note that there is also some evidence that challenges the pure ADAF model for the LH state of XRBs. The broad Fe K emission line (e.g., Miller et al. 2006; Reis et al. 2008; Tomsick et al. 2008) and/or analysis of disk continuum (e.g., Miller et al. 2006; Reis et al. 2010) suggest that SSD may extend to the innermost stable circular orbit in some bright hard states of XRBs. For XRBs in a steep power-law state, the accretion process is very unclear, which may be partly caused by the unknown physical mechanism for disk transition (e.g., McClintock & Remillard 2006).

Numerous studies in the past have shown that the hard X-ray photon index, Γ, is correlated with the Eddington ratio for both XRBs and active galactic nuclei (AGNs). Wu & Gu (2008) performed a detailed spectral study for six XRBs in the decay of an outburst and found that Γ anti-correlates with L_X/L_Edd (L_Edd is Eddington luminosity) when L_X/L_Edd is less than a critical value, while they become positively correlated when L_X/L_Edd is higher than this critical value. This phenomena also exist in AGNs, where Γ and Eddington ratios are positively correlated in bright AGNs (e.g., quasars and bright Seyferts; Wang et al. 2004; Shemmer et al. 2006; Zhou & Zhao 2010; Trichas et al. 2013), while the anti-correlations are found in a sample of low-luminosity AGNs (e.g., Gu & Cao 2009; Constantin et al. 2009; Younes et al. 2011). For a single AGN, the positive correlation of X-ray photon index and luminosity was also found in several bright sources (e.g., Lamer et al. 2003; Sobolewska & Papadakis 2009), while the anti-correlation was found in low-luminosity sources (e.g., NGC 7213; Emmanoulopoulos et al. 2012). The negative and positive correlations between the Γ and Eddington ratios can be regulated by ADAF and SSD/corona, respectively, as proposed by Wu & Gu (2008). The detailed model calculations on the ADAF and disk/corona support this scenario (e.g., Cao 2009; You et al. 2012; Qiao & Liu 2013). From the X-ray spectral evolution, the LH state can be separated into the bright hard state and the dim hard state, of which the XRBs stay in the positive and anti-correlation of Γ − L_X/L_Edd, respectively (Wu & Gu 2008). A small cold disk may exist in some bright hard states of XRBs due to the condensation of hot accretion flow when the accretion rate is larger than ∼0.01 Eddington rate, while the inner cold SSD will completely transit to ADAF at a lower accretion rate due to the possible evaporation (Liu et al. 2007, 2011).

There is a strong connection between radio and X-ray emission in the LH state of XRBs. The quasi-simultaneous radio and X-ray fluxes of more than 10 XRBs roughly follow a universal non-linear correlation of $F_{\rm R}\propto F_{\rm X}^{b}$ (b ∼ 0.5–0.7) as initially found in the LH-state GX 339–4 and V404 Cyg (Hannikainen et al. 1998; Corbel et al. 2003; Gallo et al. 2003), which seems to be maintained down to the quiescent state (Gallo et al. 2006). Wu et al. (2013) found that the radio–X-ray relation for a sample of AGNs with BH masses of 10^{8 ± 0.4} M_☉ is roughly similar to that of LH-state XRBs, where an AGN sample with similar BH mass can be used to simulate the behavior of a single BH XRB in a statistical manner. The quantitative comparison of XRBs and AGNs has made a major step forward in the last 10 years with the discovery of a fundamental plane for BH activity in place of BH mass, radio luminosity and X-ray luminosity (e.g., Merloni et al. 2003; Falcke et al. 2004; Wang et al. 2006; Körding et al. 2006; Li et al. 2008; Yuan et al. 2009; Gültekin et al. 2009; Plotkin et al. 2012). The radio spectrum of XRBs in the LH state is usually flat or even inverted with the spectral index α ≳ 0 (F_ν∝ν^α, F_ν is the radio flux at a certain frequency ν), which is often taken as evidence for the presence of jets (Fender 2001). The X-ray emission of XRBs is normally thought to originate in the accretion flows (e.g., ADAF, Yuan & Cui 2005; Narayan & McClintock 2008). Therefore, the tight correlation of radio and X-ray emission suggests that the jet may be coupled with accretion flow. The physical reasons for the jet formation are still unclear, which possibly include a spinning BH (e.g., Blandford & Znajek 1977; Lei et al. 2005; Tchekhovskoy et al. 2011; Li & Cao 2012; Narayan & McClintock 2012), a large-scale magnetic field (e.g., Cao 2011), and/or accretion mode (e.g., Meier 2001), etc. The physical reason why the quenched jet is in the HS state of XRBs is also still unclear, which may be caused by the decrease of the corona due to stronger cooling when the SSD is present if the jet is coupled with the hot plasma (ADAF/corona, Wu et al. 2013).

However, Xue & Cui (2007) found that the radio–X-ray correlation in XRBs might not be as universal as previously thought. In the following years, increasingly more XRBs were found to lie well outside the scatter of the former universal radio–X-ray correlation (e.g., XTE J1650−500, Corbel et al. 2004; XTE J1720-318, Brocksopp et al. 2005; Swift 1753.5−0127, Cadolle Bel et al. 2007; Soleri et al. 2010; IGR J17497-2821, Rodriguez et al. 2007; H1743−322, Jonker et al. 2010; Coriat et al. 2011; XTE J1752−223, Ratti et al. 2012). These "outliers" roughly form a much steeper "outlier" track with a correlation slope of b ∼ 1.4, as initially found in H1743−322 (Coriat et al. 2011). The physical reason for the dual tracks of radio–X-ray correlation is still unclear. Assuming the jet launching and radiation behave identically in both tracks, Coriat et al. (2011) speculated that the universal track and "outlier" track may be regulated by radiatively inefficient and radiatively efficient accretion flows, respectively, based on the several simple scalings of accretion and jet.

As addressed above, the hard X-ray spectral evolution can shed light on the accretion modes (e.g., ADAF, disk/corona, etc.). In this work, we aim to investigate whether or not the dual tracks of radio–X-ray correlation are regulated by radiatively inefficient and radiatively efficient accretion flows through exploring their hard X-ray spectral evolution. We present the observation and X-ray data reduction in Section 2. The results are shown in Section 3, which are concluded and discussed in Section 4.

We consider a sample of BH XRBs in the LH state that have multiple, quasi-simultaneous (e.g., within a day) radio and X-ray observations. In order to explore the X-ray spectral evolution for each XRB, we exclude the sources with only one or several observations. The radio flux densities are obtained directly from the literature, while the X-ray data is selected from the RXTE database according to the time of radio observation and analyzed by us. From these criteria, we select four XRBs (GX 339–4, H 1743–322, Swift J1753.50127, and XTE J1752–223). We describe the radio and X-ray data for these sources in more detail as follows.

2.1. Radio Data

For GX 339–4, we select the radio flux densities at 8.6 or 9.0 GHz from Corbel et al. (2013, Table 1), which were observed by the Australia Telescope Compact Array (ATCA) during several outbursts from 1997 to 2012. The 8.5 GHz radio data of H1743–322 are selected from Coriat et al. (2011, and references therein), which were regularly observed by ACTA and the Very Large Array (VLA) for several outbursts from 2003 to 2010. For Swift J1753.5–0127, Soleri et al. (2010) presented radio observations with VLA, the Westerbork Synthesis Radio Telescope (WRST), and MERLIN at 1.7–8.5 GHz during an outburst from 2005 to 2009. The radio fluxes of three data points observed at 1.7 GHz by MERLIN and four observed by VLA at 4.8 GHz are converted to fluxes at 8.5 GHz assuming a typical radio spectral index of α = −0.12 for LH state of XRBs (F_ν∝ν^−α; e.g., Corbel et al. 2013). For XTE J1752−223, we use the radio flux densities at 9.0 GHz that observed by ATCA during an outburst from 2009 to 2010 (Brocksopp et al. 2013). We list all the radio data in Tables 1–4. In the following analysis, we simply assume that the radio flux densities at 8.4–9.0 GHz are more or less similar based on the flat spectrum as observed in most LH-state XRBs, which will not affect our results.

Table 1. Summary of Data for GX 339–4

Date	Obs. Id	FR	FX	Γ	$\chi _{\nu }^2$(dof)	Modela
		(8.6 or 9.0 GHz)	(3–9 keV)
		(mJy)	(10−11 erg s−1 cm−2)
1997 Feb 3	20181-01-01-01	9.10 ± 0.10	$96.70_{-0.30}^{+0.30}$	$1.47_{-0.03}^{+0.02}$	0.86(65)	diskbb+gau+pow
1997 Feb 10	20181-01-02-00	8.20 ± 0.20	$84.26_{-0.24}^{+0.24}$	$1.45_{-0.02}^{+0.02}$	1.03(65)	diskbb+gau+pow
1997 Feb 17	20181-01-03-00	8.70 ± 0.20	$80.68_{-0.23}^{+0.23}$	$1.51_{-0.02}^{+0.02}$	0.90(65)	diskbb+gau+pow
1999 Mar 3	40108-01-04-00	5.74 ± 0.06	$43.32_{-0.16}^{+0.16}$	$1.59_{-0.03}^{+0.03}$	1.31(66)	diskbb+gau+pow
1999 Apr 22	40108-02-02-00	3.20 ± 0.06	$20.44_{-0.08}^{+0.09}$	$1.60_{-0.01}^{+0.01}$	1.27(61)	gau+pow
1999 May 14	40108-02-03-00	1.44 ± 0.06	$6.60_{-0.06}^{+0.06}$	$1.65_{-0.02}^{+0.02}$	0.89(63)	pow
1999 Jun 25	40105-02-02-00	0.24 ± 0.05	$0.44_{-0.07}^{+0.07}$	$1.83_{-0.25}^{+0.26}$	0.49(63)	pow
1999 Jul 7	40108-03-01-00	0.12 ± 0.04	$0.15_{-0.03}^{+0.03}$	$2.18_{-0.20}^{+0.21}$	0.50(63)	pow
1999 Aug 17	40108-03-03-00	0.27 ± 0.07	$0.20_{-0.04}^{+0.04}$	$2.14_{-0.19}^{+0.20}$	0.58(63)	pow
2002 Apr 3	70109-01-02-00	5.95 ± 0.15	$139.76_{-0.42}^{+0.42}$	$1.38_{-0.02}^{+0.02}$	0.90(59)	diskbb+gau+pow
2002 Apr 7	70109-01-01-00	8.27 ± 0.07	$293.89_{-1.09}^{+1.09}$	$1.48_{-0.03}^{+0.02}$	1.02(59)	diskbb+gau+pow
2003 May 25	80102-04-07-00	0.77 ± 0.06	$1.82_{-0.13}^{+0.13}$	$1.67_{-0.15}^{+0.15}$	0.61(64)	pow
2004 Feb 13	80102-04-57-01	1.13 ± 0.08	$7.44_{-0.23}^{+0.23}$	$1.62_{-0.07}^{+0.07}$	0.72(64)	pow
2004 Feb 24	80102-04-58-01	1.84 ± 0.20	$24.74_{-0.29}^{+0.29}$	$1.52_{-0.02}^{+0.02}$	0.77(64)	pow
2004 Mar 16	90118-01-05-00	4.88 ± 0.06	$90.21_{-0.41}^{+0.41}$	$1.42_{-0.05}^{+0.03}$	0.97(60)	diskbb+gau+pow
2004 Mar 17	90118-01-06-00	4.84 ± 0.11	$95.23_{-0.48}^{+0.50}$	$1.34_{-0.06}^{+0.05}$	0.66(60)	diskbb+gau+pow
2004 Mar 18	90118-01-07-00	4.98 ± 0.11	$98.89_{-0.32}^{+0.32}$	$1.40_{-0.03}^{+0.02}$	1.14(60)	diskbb+gau+pow
2004 Mar 19	80132-01-15-00	5.20 ± 0.10	$100.62_{-0.38}^{+0.38}$	$1.36_{-0.04}^{+0.04}$	0.85(60)	diskbb+gau+pow
2005 Apr 24	90704-01-13-01	4.23 ± 0.08	$27.65_{-0.27}^{+0.27}$	$1.63_{-0.02}^{+0.02}$	0.98(64)	pow
2005 Apr 28	91095-08-06-00	3.46 ± 0.13	$18.47_{-0.11}^{+0.11}$	$1.61_{-0.01}^{+0.01}$	0.99(62)	gau+pow
2005 Apr 29	91095-08-07-00	3.32 ± 0.10	$16.49_{-0.10}^{+0.10}$	$1.61_{-0.01}^{+0.01}$	0.96(62)	gau+pow
2005 Apr 30	91095-08-08-00	2.94 ± 0.07	$15.63_{-0.10}^{+0.10}$	$1.61_{-0.01}^{+0.01}$	1.17(64)	pow
2005 May 2	90165-01-01-02	1.92 ± 0.14	$12.57_{-0.16}^{+0.16}$	$1.61_{-0.03}^{+0.03}$	1.07(64)	pow
2005 May 4	91105-04-18-00	1.99 ± 0.10	$12.46_{-0.32}^{+0.32}$	$1.63_{-0.06}^{+0.06}$	0.80(64)	pow
2005 May 6	90704-01-14-00	1.69 ± 0.12	$10.64_{-0.18}^{+0.18}$	$1.63_{-0.04}^{+0.04}$	0.60(64)	pow
2005 May 12	90704-01-14-02	1.00 ± 0.18	$7.26_{-0.17}^{+0.17}$	$1.65_{-0.05}^{+0.05}$	1.00(64)	pow
2007 Jun 6	92704-03-25-00	2.63 ± 0.18	$15.28_{-0.18}^{+0.18}$	$1.63_{-0.03}^{+0.03}$	1.04(64)	pow
2007 Jun 11	92704-03-29-00	2.01 ± 0.15	$12.98_{-0.13}^{+0.13}$	$1.63_{-0.02}^{+0.02}$	1.31(64)	pow
2007 Jun 25	92704-03-38-00	1.69 ± 0.05	$12.51_{-0.15}^{+0.15}$	$1.61_{-0.03}^{+0.03}$	1.03(64)	pow
2007 Jun 29	92704-03-42-00	2.00 ± 0.20	$13.28_{-0.18}^{+0.18}$	$1.57_{-0.03}^{+0.03}$	0.92(64)	pow
2007 Jul 4	92704-03-44-01	2.10 ± 0.20	$17.46_{-0.25}^{+0.25}$	$1.59_{-0.03}^{+0.03}$	0.79(64)	pow
2007 Jul 13	92704-03-47-00	2.66 ± 0.05	$24.82_{-0.34}^{+0.34}$	$1.57_{-0.03}^{+0.03}$	0.68(64)	pow
2007 Aug 23	93409-01-05-03	2.95 ± 0.07	$35.63_{-0.25}^{+0.25}$	$1.40_{-0.10}^{+0.08}$	0.95(60)	diskbb+gau+pow
2007 Dec 27	93409-01-20-00	0.48 ± 0.07	$1.84_{-0.13}^{+0.13}$	$1.77_{-0.15}^{+0.16}$	0.61(64)	pow
2008 Jun 26	93076-08-01-00	1.16 ± 0.10	$7.08_{-0.10}^{+0.10}$	$1.59_{-0.03}^{+0.03}$	0.97(64)	pow
2008 Jul 5	93076-08-03-00	1.24 ± 0.07	$8.68_{-0.15}^{+0.15}$	$1.62_{-0.04}^{+0.04}$	0.70(64)	pow
2008 Jul 16	93076-08-05-05	1.51 ± 0.06	$11.58_{-0.23}^{+0.23}$	$1.56_{-0.04}^{+0.04}$	0.93(64)	pow
2008 Aug 18	93108-01-01-02	1.18 ± 0.10	$9.72_{-0.16}^{+0.16}$	$1.57_{-0.04}^{+0.04}$	0.67(64)	pow
2008 Oct 10	93702-04-03-00	0.73 ± 0.10	$1.65_{-0.08}^{+0.08}$	$1.72_{-0.10}^{+0.10}$	0.49(64)	pow
2010 Jan 21	95409-01-02-02	5.05 ± 0.05	$59.93_{-0.29}^{+0.29}$	$1.33_{-0.05}^{+0.05}$	0.58(60)	diskbb+gau+pow
2010 Feb 12	95409-01-06-00	5.90 ± 0.10	$82.83_{-0.37}^{+0.37}$	$1.32_{-0.05}^{+0.04}$	0.56(60)	diskbb+gau+pow
2010 Mar 2	95409-01-08-02	7.30 ± 0.10	$134.94_{-0.57}^{+0.60}$	$1.39_{-0.04}^{+0.03}$	1.12(60)	diskbb+gau+pow
2010 Mar 4	95409-01-08-03	7.30 ± 0.10	$145.24_{-0.51}^{+0.51}$	$1.39_{-0.03}^{+0.02}$	0.81(60)	diskbb+gau+pow
2010 Mar 6	95409-01-09-06	9.60 ± 0.05	$163.27_{-0.74}^{+0.74}$	$1.35_{-0.05}^{+0.05}$	0.88(60)	diskbb+gau+pow
2010 Mar 7	95409-01-09-01	8.05 ± 0.10	$164.11_{-0.86}^{+0.86}$	$1.43_{-0.04}^{+0.04}$	0.86(60)	diskbb+gau+pow
2010 Mar 14	95409-01-10-02	11.32 ± 0.10	$199.22_{-0.91}^{+0.91}$	$1.46_{-0.03}^{+0.03}$	0.81(60)	diskbb+gau+pow
2010 Mar 16	95409-01-10-04	12.04 ± 0.10	$218.29_{-0.69}^{+0.70}$	$1.48_{-0.02}^{+0.02}$	0.79(60)	diskbb+gau+pow
2010 Mar 20	95409-01-11-01	15.45 ± 0.06	$268.48_{-1.14}^{+1.15}$	$1.47_{-0.04}^{+0.03}$	0.69(60)	diskbb+gau+pow
2010 Mar 22	95409-01-11-02	15.45 ± 0.06	$291.93_{-1.38}^{+1.38}$	$1.53_{-0.03}^{+0.03}$	0.80(60)	diskbb+gau+pow
2010 Mar 24	95409-01-11-03	18.59 ± 0.05	$329.61_{-1.37}^{+1.38}$	$1.52_{-0.03}^{+0.03}$	1.00(60)	diskbb+gau+pow
2010 Mar 26	95409-01-12-00	21.88 ± 0.10	$352.09_{-1.19}^{+1.20}$	$1.53_{-0.03}^{+0.02}$	0.89(60)	diskbb+gau+pow
2010 Mar 30	95409-01-12-02	21.88 ± 0.10	$405.22_{-1.48}^{+1.51}$	$1.58_{-0.02}^{+0.02}$	1.36(60)	diskbb+gau+pow
2010 Mar 31	95409-01-12-04	25.94 ± 0.05	$414.09_{-1.40}^{+1.41}$	$1.62_{-0.02}^{+0.02}$	0.90(60)	diskbb+gau+pow
2010 Apr 3	95409-01-13-00	21.11 ± 0.15	$442.55_{-1.38}^{+1.40}$	$1.61_{-0.02}^{+0.02}$	1.14(60)	diskbb+gau+pow
2010 Apr 5	95409-01-13-02	24.69 ± 0.05	$467.72_{-1.45}^{+1.46}$	$1.63_{-0.02}^{+0.02}$	1.23(60)	diskbb+gau+pow
2010 Apr 6	95409-01-13-05	23.90 ± 0.06	$491.54_{-1.91}^{+1.92}$	$1.63_{-0.03}^{+0.02}$	1.02(60)	diskbb+gau+pow
2011 Feb 12	96409-01-07-03	4.17 ± 0.05	$29.68_{-0.31}^{+0.31}$	$1.76_{-0.02}^{+0.02}$	1.04(64)	pow
2011 Feb 14	96409-01-07-01	4.17 ± 0.05	$25.68_{-0.27}^{+0.27}$	$1.71_{-0.02}^{+0.02}$	1.23(64)	pow
2011 Feb 15	96409-01-07-02	3.87 ± 0.05	$34.65_{-0.30}^{+0.30}$	$1.84_{-0.02}^{+0.02}$	1.27(64)	pow
2011 Feb 17	96409-01-07-04	3.98 ± 0.10	$20.19_{-0.24}^{+0.24}$	$1.64_{-0.03}^{+0.03}$	0.63(64)	pow
2011 Feb 19	96409-01-08-00	3.98 ± 0.10	$16.14_{-0.21}^{+0.21}$	$1.70_{-0.03}^{+0.03}$	0.95(64)	pow
2011 Feb 21	96409-01-08-02	3.84 ± 0.05	$12.16_{-0.27}^{+0.27}$	$1.69_{-0.05}^{+0.05}$	0.80(64)	pow
2011 Feb 24	96409-01-08-03	2.95 ± 0.05	$9.72_{-0.23}^{+0.23}$	$1.70_{-0.05}^{+0.06}$	1.00(64)	pow
2011 Feb 28	96409-01-09-01	2.42 ± 0.08	$7.20_{-0.25}^{+0.25}$	$1.68_{-0.08}^{+0.08}$	0.45(64)	pow
2011 Mar 2	96409-01-09-02	1.64 ± 0.05	$6.55_{-0.21}^{+0.21}$	$1.70_{-0.07}^{+0.07}$	0.64(64)	pow
2011 Mar 6	96409-01-10-01	1.26 ± 0.10	$5.11_{-0.28}^{+0.28}$	$1.83_{-0.13}^{+0.13}$	0.62(64)	pow
2011 Mar 8	96409-01-10-02	1.26 ± 0.10	$4.69_{-0.14}^{+0.14}$	$1.78_{-0.07}^{+0.07}$	0.67(64)	pow
2011 Mar 10	96409-01-10-03	1.38 ± 0.08	$4.47_{-0.14}^{+0.14}$	$1.71_{-0.07}^{+0.07}$	0.52(64)	pow
2011 Mar 19	96409-01-12-01	0.74 ± 0.04	$2.38_{-0.12}^{+0.12}$	$1.88_{-0.11}^{+0.12}$	0.64(64)	pow

Note. ^aAn absorption model, phabs, was used in all fittings.

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Table 2. Summary of Data for H 1743-322

Date	Obs. Id	FR	FX	Γ	ΓH	χ2	Modela
		(8.5 GHz)	(3–9 keV)
		(mJy)	(10−11 erg s−1 cm−2)
2003 Apr 1	80138-01-02-00	6.45 ± 0.12	$253_{-0.42}^{+0.41}$	$1.56_{-0.01}^{+0.01}$	$2.19_{-0.01}^{+0.01}$	1.70(88)	diskbb+gau+bknpow
2003 Apr 4	80138-01-03-00	21.81 ± 0.13	$626_{-0.63}^{+0.63}$	$2.27_{-0.01}^{+0.01}$	$2.89_{-0.02}^{+0.02}$	1.08(88)	diskbb+gau+bknpow
2003 Apr 6	80138-01-04-00	19.43 ± 0.16	$545_{-0.55}^{+0.55}$	$2.23_{-0.04}^{+0.04}$	$3.0_{-0.02}^{+0.02}$	0.93(87)	diskbb+gau+bknpow
2003 Nov 5	80137-01-32-00	0.22 ± 0.05	$12.09_{-0.12}^{+0.11}$	⋅⋅⋅	$1.95_{-0.02}^{+0.02}$	0.96(88)	gau+pow
2004 Nov 1	90115-01-05-03	0.31 ± 0.06	$2.59_{-0.13}^{+0.13}$	⋅⋅⋅	$2.16_{-0.05}^{+0.05}$	0.83(88)	gau+pow
2008 Jan 29	93427-01-03-03	0.44 ± 0.09	$70.35_{-0.25}^{+0.25}$	⋅⋅⋅	$2.05_{-0.06}^{+0.06}$	1.05(87)	diskbb+gau+pow
2008 Feb 2	93427-01-04-00	0.52 ± 0.07	$50.19_{-0.19}^{+0.19}$	⋅⋅⋅	$1.93_{-0.04}^{+0.04}$	0.81(87)	diskbb+gau+pow
2008 Feb 4	93427-01-04-02	0.48 ± 0.08	$36.85_{-0.16}^{+0.16}$	⋅⋅⋅	$1.94_{-0.01}^{+0.01}$	1.23(89)	gau+pow
2008 Feb 6	93427-01-04-03	0.45 ± 0.09	$30.79_{-0.14}^{+0.15}$	⋅⋅⋅	$1.93_{-0.01}^{+0.01}$	1.00(89)	gau+pow
2008 Feb 8	93427-01-05-00	0.56 ± 0.05	$25.94_{-0.18}^{+0.18}$	⋅⋅⋅	$1.91_{-0.02}^{+0.01}$	1.01(89)	gau+pow
2008 Feb 18	93427-01-06-02	0.23 ± 0.12	$3.82_{-0.18}^{+0.18}$	⋅⋅⋅	$2.03_{-0.05}^{+0.05}$	0.82(89)	gau+pow
2008 Feb 20	93427-01-06-03	0.21 ± 0.05	$2.72_{-0.11}^{+0.11}$	⋅⋅⋅	$2.14_{-0.04}^{+0.04}$	0.79(89)	gau+pow
2008 Feb 22	93427-01-07-00	0.23 ± 0.06	$1.87_{-0.14}^{+0.14}$	⋅⋅⋅	$2.13_{-0.05}^{+0.05}$	0.92(89)	gau+pow
2008 Feb 24	93427-01-07-02	0.31 ± 0.05	$1.41_{-0.26}^{+0.26}$	⋅⋅⋅	$2.30_{-0.13}^{+0.15}$	1.04(89)	gau+pow
2008 Oct 7	93427-01-09-01	1.74 ± 0.07	$116.60_{-0.36}^{+0.36}$	$1.50_{-0.04}^{+0.04}$	$2.40_{-0.19}^{+0.27}$	1.18(85)	diskbb+gau+bknpow
2008 Oct 8	93427-01-09-03	2.54 ± 0.08	$116.62_{-0.36}^{+0.36}$	$1.50_{-0.05}^{+0.04}$	$2.15_{-0.11}^{+0.13}$	0.72(85)	diskbb+gau+bknpow
2008 Oct 9	93427-01-09-02	2.43 ± 0.09	$120.42_{-0.47}^{+0.47}$	$1.34_{-0.10}^{+0.11}$	$1.91_{-0.06}^{+0.06}$	0.94(85)	diskbb+gau+bknpow
2008 Oct 11	93427-01-10-00	2.38 ± 0.11	$121.92_{-0.63}^{+0.63}$	$1.50_{-0.06}^{+0.11}$	$2.08_{-0.16}^{+0.23}$	1.16(85)	diskbb+gau+bknpow
2008 Nov 4	93427-01-13-06	0.94 ± 0.12	$68.22_{-0.29}^{+0.29}$	⋅⋅⋅	$1.92_{-0.01}^{+0.01}$	1.42(91)	pow
2008 Nov 9	93427-01-14-02	0.94 ± 0.08	$60.86_{-0.39}^{+0.39}$	⋅⋅⋅	$1.83_{-0.01}^{+0.01}$	1.38(91)	pow
2009 May 29	94413-01-02-00	2.24 ± 0.03	$153.29_{-0.56}^{+0.57}$	$1.51_{-0.06}^{+0.06}$	$2.16_{-0.09}^{+0.12}$	1.15(85)	diskbb+gau+bknpow
2009 May 30	94413-01-02-01	2.73 ± 0.10	$163.60_{-0.68}^{+0.68}$	$1.43_{-0.01}^{+0.05}$	$2.07_{-0.04}^{+0.05}$	1.29(85)	diskbb+gau+bknpow
2009 Jul 7	94413-01-07-01	0.59 ± 0.06	$51.56_{-0.36}^{+0.36}$	⋅⋅⋅	$2.07_{-0.02}^{+0.02}$	0.94(91)	pow
2009 Jul 9	94413-01-07-02	0.41 ± 0.07	$46.94_{-0.36}^{+0.36}$	⋅⋅⋅	$2.10_{-0.02}^{+0.02}$	1.27(91)	pow
2009 Jul 11	94413-01-08-02	0.34 ± 0.06	$38.85_{-0.41}^{+0.41}$	⋅⋅⋅	$2.02_{-0.02}^{+0.02}$	0.89(91)	pow
2009 Jul 13	94413-01-08-00	0.59 ± 0.07	$30.82_{-0.21}^{+0.21}$	⋅⋅⋅	$1.97_{-0.01}^{+0.01}$	1.09(89)	gau+pow
2009 Jul 19	94413-01-09-00	0.63 ± 0.05	$13.95_{-0.22}^{+0.22}$	⋅⋅⋅	$1.87_{-0.03}^{+0.03}$	1.02(89)	gau+pow
2009 Aug 6	94413-01-11-02	0.19 ± 0.05	$0.65_{-0.15}^{+0.15}$	⋅⋅⋅	$2.25_{-0.08}^{+0.08}$	0.88(89)	gau+pow

Note. ^aAn absorption model, phabs, was used in all fittings.

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Table 3. Summary of Data for Swift J1753.5-0127

Date	Obs. Id	FR	FX	Γ	ΓH	χ2	Modela
		(8.4 GHz)	(3–9 keV)
		(mJy)	($10^{-11}\ \rm erg\rm \ s^{-1}\ cm^{-2}$)
2005 Jul 4	91094-01-01-01	0.68 ± 0.20	$300.44_{-0.68}^{+0.67}$	$1.69_{-0.02}^{+0.02}$	$2.22_{-0.09}^{+0.11}$	1.15(84)	diskbb+gau+bknpow
2005 Jul 6	91423-01-01-04	0.74 ± 0.20	$342.78_{-0.74}^{+0.75}$	$1.71_{-0.02}^{+0.02}$	$2.07_{-0.06}^{+0.08}$	1.12(84)	diskbb+gau+bknpow
2005 Jul 7	91423-01-01-00	0.68 ± 0.68	$315.09_{-0.82}^{+0.83}$	$1.64_{-0.01}^{+0.01}$	$1.96_{-0.03}^{+0.04}$	1.15(84)	diskbb+gau+bknpow
2005 Jul 8	91094-01-02-01	1.96 ± 0.04	$327.10_{-0.74}^{+0.75}$	$1.66_{-0.02}^{+0.02}$	$1.96_{-0.05}^{+0.07}$	1.03(84)	diskbb+gau+bknpow
2005 Jul 10	91094-01-02-02	1.14 ± 0.12	$318.24_{-0.70}^{+0.70}$	$1.63_{-0.02}^{+0.02}$	$1.99_{-0.05}^{+0.06}$	0.86(84)	diskbb+gau+bknpow
2005 Jul 19	91423-01-03-04	2.42 ± 0.05	$234.77_{-0.56}^{+0.56}$	$1.59_{-0.02}^{+0.02}$	$2.01_{-0.09}^{+0.13}$	0.95(84)	diskbb+gau+bknpow
2005 Jul 26	91423-01-04-04	1.81 ± 0.09	$186.15_{-0.47}^{+0.47}$	$1.56_{-0.02}^{+0.02}$	$2.24_{-0.16}^{+0.19}$	1.13(85)	diskbb+gau+bknpow
2005 Aug 3	91423-01-05-02	0.47 ± 0.10	$141.72_{-0.39}^{+0.39}$	$1.55_{-0.02}^{+0.02}$	$1.83_{-0.09}^{+0.15}$	1.01(85)	diskbb+gau+bknpow
2005 Aug 7	91423-01-06-01	0.57 ± 0.07	$118.55_{-0.36}^{+0.36}$	⋅⋅⋅	$1.60_{-0.01}^{+0.01}$	1.22(91)	pow
2005 Aug 11	91423-01-06-03	0.68 ± 0.01	$109.05_{-0.34}^{+0.33}$	⋅⋅⋅	$1.61_{-0.01}^{+0.01}$	1.61(91)	pow
2005 Oct 22	91423-01-17-00	0.28 ± 0.06	$37.03_{-0.22}^{+0.22}$	⋅⋅⋅	$1.60_{-0.01}^{+0.01}$	1.17(91)	pow
2005 Nov 19	91423-01-21-00	0.40 ± 0.09	$30.40_{-0.22}^{+0.22}$	⋅⋅⋅	$1.60_{-0.02}^{+0.02}$	0.78(91)	pow
2006 Mar 11	92404-01-02-00	0.08 ± 0.07	$25.33_{-0.22}^{+0.22}$	⋅⋅⋅	$1.65_{-0.02}^{+0.02}$	0.90(91)	pow
2007 Jul 1	93105-01-08-00	0.30 ± 0.05	$45.52_{-0.20}^{+0.20}$	⋅⋅⋅	$1.60_{-0.01}^{+0.01}$	1.09(91)	pow
2007 Jul 8	93105-01-09-00	0.30 ± 0.05	$45.89_{-0.20}^{+0.20}$	⋅⋅⋅	$1.61_{-0.01}^{+0.01}$	0.82(91)	pow
2007 Jul 15	93105-01-10-00	0.30 ± 0.05	$46.01_{-0.20}^{+0.20}$	⋅⋅⋅	$1.59_{-0.01}^{+0.01}$	1.03(91)	pow
2007 Jul 22	93105-01-11-00	0.08 ± 0.08	$44.70_{-0.26}^{+0.25}$	⋅⋅⋅	$1.60_{-0.01}^{+0.01}$	0.83(91)	pow
2009 Jun 9	93105-02-33-00	0.50 ± 0.02	$50.95_{-0.22}^{+0.21}$	⋅⋅⋅	$1.62_{-0.01}^{+0.01}$	1.09(91)	pow

Note. ^aAn absorption model, phabs, was used in all fittings.

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Table 4. Summary of Data for XTE J1752-223

Date	Obs. Id	FR	FX	Γ	ΓH	χ2	Modela
		(8.4 GHz)	(3–9 keV)
		(mJy)	($10^{-11}\ \rm erg\ \rm s^{-1}\ cm^{-2}$)
2009 Oct 30	94331-01-02-01	2.42 ± 0.05	$231.08_{-0.68}^{+0.68}$	$1.38_{-0.02}^{+0.01}$	0.91(60)	diskbb+gau+pow
2009 Nov 1	94331-01-02-05	1.99 ± 0.08	$231.37_{-0.69}^{+0.69}$	$1.37_{-0.02}^{+0.02}$	0.61(60)	diskbb+gau+pow
2009 Nov 5	94331-01-02-17	2.05 ± 0.07	$232.15_{-0.86}^{+0.87}$	$1.38_{-0.02}^{+0.02}$	0.93(60)	diskbb+gau+pow
2009 Nov 8	94331-01-03-05	2.10 ± 0.10	$228.82_{-0.70}^{+0.71}$	$1.39_{-0.02}^{+0.02}$	0.86(60)	diskbb+gau+pow
2010 Apr 13	95360-01-12-03	0.90 ± 0.05	$54.57_{-0.41}^{+0.41}$	$1.77_{-0.02}^{+0.02}$	1.25(64)	pow
2010 Apr 15	95360-01-12-04	0.90 ± 0.05	$52.05_{-0.49}^{+0.49}$	$1.78_{-0.02}^{+0.02}$	1.23(64)	pow
2010 Apr 17	95702-01-01-01	0.83 ± 0.06	$48.92_{-0.39}^{+0.39}$	$1.78_{-0.02}^{+0.02}$	1.23(64)	pow
2010 Apr 27	95702-01-02-04	1.07 ± 0.04	$33.59_{-0.32}^{+0.32}$	$1.75_{-0.02}^{+0.02}$	0.84(64)	pow
2010 Apr 28	95702-01-02-05	1.20 ± 0.03	$31.88_{-0.31}^{+0.31}$	$1.77_{-0.02}^{+0.02}$	1.08(64)	pow
2010 Apr 29	95702-01-02-06	1.13 ± 0.04	$30.95_{-0.41}^{+0.41}$	$1.74_{-0.03}^{+0.03}$	1.06(64)	pow
2010 May 17	95702-01-05-03	0.28 ± 0.04	$9.59_{-0.19}^{+0.19}$	$1.77_{-0.05}^{+0.05}$	0.83(64)	pow
2010 May 18	95702-01-05-04	0.19 ± 0.04	$9.26_{-0.24}^{+0.24}$	$1.78_{-0.06}^{+0.06}$	0.84(64)	pow
2010 Jun 3	95702-01-07-03	0.18 ± 0.03	$12.78_{-0.28}^{+0.28}$	$1.72_{-0.05}^{+0.05}$	0.82(64)	pow
2010 Jun 11	95702-01-09-00	0.15 ± 0.06	$15.81_{-0.31}^{+0.31}$	$1.71_{-0.04}^{+0.04}$	0.77(64)	pow

Note. ^aAn absorption model, phabs, was used in all fittings.

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2.2. X-Ray Spectral Analysis

We present relations between hard X-ray photon index, Γ, and 3–9 keV X-ray flux, F_3-9 keV, for four sources in the top panels of Figures 1–4, respectively, where the photon index in the harder band is adopted if it is fitted with a broken power-law model. For GX 339–4 and H 1743–322 (Figures 1 and 2), it can be clearly found that Γ is anti-correlated to F_3-9 keV (open circles) when F_3-9 keV is lower than a critical value, F_{X, crit}, while these two quantities become positively correlated (solid circles) when F_3-9 keV ≳ F_{X, crit}. The positive correlation of Γ − F_3-9 keV is evident in Swift J1753.5–0127 as a whole, even though the correlation becomes flat or slightly anti-correlated when the X-ray flux is lower than a critical value (see the top panel of Figure 3). For XTE J1752–223, there are some trends in both negative and positive correlations of Γ − F_3-9 keV with the exception of four data points that evidently deviate from both negative and positive correlations (see the top panel of Figure 4). We fit the relation of Γ − log F_3-9 keV with a piecewise linear regression (two segments) for each source (top panels in Figures 1–4). Four data points of XTE J1752–223 (with the highest X-ray fluxes) are excluded in the fitting which evidently deviate from both negative and positive correlations. We list the critical flux (or break point) and its 1 σ error for the transition of different X-ray spectral evolutions for each XRB in Table 5, where F_{X, crit} ≃ 1.3 × 10⁻⁹ erg s⁻¹ cm⁻² for GX 339–4 is several times higher than that of other two XRBs (≃ 2.5 × 10⁻¹⁰ erg s⁻¹ cm⁻², H 1743–322 and XTE J1752–223). In the fitting of Swift J1753.5–0127, only upper limit of critical flux is derived (F_{X, crit} ≲ 2.5 × 10⁻¹⁰ erg s⁻¹ cm⁻²), which may be caused by the data points in anti-correlation are not evident or too few.

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Table 5. Summary of the Radio–X-Ray Fits

Source	Fcrit, Xa	k1b	b1	k2c	b2
GX 339–4	$1.3^{+0.7}_{-0.5}\times 10^{-9}$	6.39 ± 0.30	0.61 ± 0.03	10.93 ± 2.39	1.14 ± 0.27
H1743–322	$2.5^{+0.6}_{-0.5}\times 10^{-10}$	1.91 ± 1.04	0.24 ± 0.10	12.83 ± 1.29	1.40 ± 0.14
Swift J1753.5–0127	≲ 2.5 × 10−10	⋅⋅⋅	⋅⋅⋅	9.55 ± 1.23	1.10 ± 0.13
XTE J1752–223	$1.6\times ^{+0.2}_{-0.3}10^{-10}$	⋅⋅⋅	⋅⋅⋅	12.83 ± 1.39	1.39 ± 0.19

Notes. ^aThe critical flux for the anti- and positive correlations of Γ − F_3-9 keV, and 1 − σ errors are also included. ^{b, c}The best fits for the data points with anti- and positive correlations of Γ − F_3-9 keV with a function of $F_{\rm R}=kF_{\rm X}^b$, respectively.

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We find that the radio–X-ray correlation also seems to change with the change of the Γ − F_3-9 keV correlation (see particularly Figures 1 and 2). Therefore, we divide the data of each source into one (Swift J1753.5–0127) or two groups (GX 339–4 and H 1743–322) according to the critical X-ray fluxes as defined by the Γ − F_3-9 keV correlation. Then we fit the radio–X-ray correlations for each source with a power-law form of $F_{\rm R}=kF_{\rm X}^b$ for the data points with F_3-9 keV lower or higher than F_{X, crit}, respectively. In the fittings, the typical flux variations (within one day) σ_R = 0.1 dex in the radio band and σ_X = 0.15 dex in the X-ray band (e.g., Coriat et al. 2011; Corbel et al. 2013) are assumed to be their flux uncertainties instead of using the observational flux errors. We list the fitting results in Table 5, where b₁ and b₂ represent the correlation slopes for the data points with F_3-9 keV ≲ F_{X, crit} and F_3-9 keV ≳ F_{X, crit}, respectively. We find that the correlation slopes b₁ = 0.61 ± 0.03 for GX 339–4 and b₁ = 0.24 ± 0.10 for H 1743–322, which are much smaller than the second correlation slopes of b₂ ∼ 1.1–1.4. For Swift J1753.5–0127, only the solid points with positive Γ − F_3-9 keV correlation are fitted (solid line in the bottom panel of Figure 3), and b₂ = 1.10 ± 0.16. Due to insufficient data, the radio–X-ray correlation for XTE J1752–223 is not fitted with our data. Instead, we select the quasi-simultaneous radio/X-ray data points from Brocksopp et al. (2013) where the X-ray data are reduced from several different X-ray satellites (e.g., Swift, MAXI and/or RXTE). By excluding the data points with F_3-9 keV ≲ F_{X, crit}, we fit the radio–X-ray correlation for 17 data points and find b₂ = 1.39 ± 0.19 (dashed line in the bottom panel of Figure 4), where the critical X-ray flux is derived from the X-ray spectral evolution in our work (top panel of Figure 4).

For comparison, we present the correlations of Γ − F_X and F_R − F_X for four XRBs in Figure 5. The data points of GX 339–4 with anti-correlation of Γ − F_X remain in the former universal track (open squares, bottom panel). All solid points with positive Γ − F_X correlation as defined in the top panel of Figure 5, roughly form the "outlier" track, even each source seems to follow its own trend (see the bottom panel). Some data points with anti-correlation of Γ − F_X (open circles and triangles) remain in the transition track.

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In this work, we analyze the X-ray data from RXTE for a sample of four XRBs with multiple, quasi-simultaneous radio and X-ray observations, and these sources either remain in the universal track or in the "outlier" track as reported in previous works. We find that the radio–X-ray correlation is tightly correlated to the X-ray spectral evolution. The data points with positive Γ − F_3-9 keV correlation normally stay in the steeper "outlier" track, while the data points with anti-correlation of Γ − F_3-9 keV either stay in a shallower universal track or stay in a roughly flat transition track. Both Γ − F_3-9 keV correlation and radio–X-ray correlation are changed at similar critical X-ray flux, which support that the different tracks of radio–X-ray correlation should be regulated by different accretion processes if the X-ray emission originate from accretion flows.

The negative and positive correlations between Γ and F_3-9 keV, occurring below and above a critical flux, F_{X, crit}, may be indicative for some "switch" in the radiation mechanism at a certain critical accretion rate. We note that the harder X-ray spectral indices for 17 data points that are fitted with a broken power-law are used to investigate X-ray spectral evolution, which will not affect our main conclusions because both spectral indices are positively correlated with the X-ray fluxes (see Table 3). Adopting a typical BH mass of 10 M_☉ (Russell et al. 2013 and references therein) and a distance of 8 kpc (Corbel et al. 2013 and references therein) for these XRBs, we find that the critical Eddington ratio for the transition of negative and positive Γ − F_3-9 keV correlation is L_bol/L_Edd ∼ 1% for H 1743–322, Swift J1753.5–0127 and XTE J1752–223, and is ∼10% for GX 339–4, where the bolometric luminosity, L_bol, is estimated from the power-law emission at 0.1–200 keV with the fitted X-ray photon index and flux. The critical Eddington ratio around several percent is roughly consistent with the theoretical prediction for the transition of ADAF and disk/corona (e.g., Narayan et al. 1998). In the ADAF model, the optical depth will increase with increasing accretion rate, increasing the Compton y-parameter, thereby leading to a harder X-ray spectrum, where the electron temperature remains roughly unchanged with the varying of the accretion rate. In the disk-corona model, the optical depth of the corona will decrease when the accretion rate increases due to stronger cooling, which leads to a smaller y-parameter and a softer X-ray spectrum. The detailed calculations of the ADAF and disk-corona models predict the negative and positive correlations of the photon index and Eddington ratio as observed in XRBs (e.g., Cao 2009; Qiao & Liu 2013). Therefore, the different accretion modes may be the physical reason for the change of the X-ray spectral evolution. It should be noted that different values of the viscosity parameter α will lead to different critical accretion rates for the disk transition (e.g., Liu & Taam 2009). For a larger α, the critical accretion rate for the disk transition will also be large, which may explain why GX 339-4 has a higher critical flux for the X-ray spectral evolution than the other three XRBs. For XTE J1752-223, there are four data points that evidently deviate from the X-ray spectral evolution of other points (see the top panel of Figure 4), which may be caused by the clearly different properties of the accretion flow (e.g., magnetic field and or viscosity, etc.) compared that in other data points. The broadband data and more careful analysis are wished to further investigate their accretion properties, which will be our future work.

The radio–X-ray correlation for the outliers of XRBs have been explored in several XRBs, where the correlation slopes are ∼1.1–1.7 for a certain XRB (Soleri et al. 2010; Rushton et al. 2010; Coriat et al. 2011; Brocksopp et al. 2013). Gallo et al. (2012) re-explored the radio–X-ray correlation for the "outliers" as a whole, and found that the correlation slope is ∼0.98, where the shallower relation may be caused by the data points in the "transition" track are also included in their fitting. From the X-ray spectral evolution, the "outliers" can well separated into two tracks: the "outlier" track with only positive correlation of Γ − F_3-9 keV and the "transition" track with the anti-correlation of Γ − F_3-9 keV. Excluding the data points in the transition track, the radio–X-ray correlation of the "outlier" track will become steeper, which is why our correlation slopes are larger than those reported in former works. It is interesting to note that the bright hard state of GX 339–4 with a positive correlation of Γ − F_3-9 keV also shows a much steeper radio–X-ray correlation (∼1.1) than the universal one. Therefore, all these data points may also belong to the "outlier" track, including the source that was divided into the universal track in former works (Coriat et al. 2011; Corbel et al. 2013). The correlation slopes are different for different "outliers" of XRBs, which may be caused by the different properties of accreting matter (e.g., the magnetic field, etc.). Due to the different trends of radio–X-ray correlation in each XRB, we do not fit the XRBs in the "outlier" track as a whole in the F_R − F_X relation. The luminosity–luminosity relation and/or Eddington-scaled luminosity–luminosity relation for a sample of XRBs may be more intrinsic, and, however, the distances and BH masses are still very uncertain for these several XRBs.

Coriat et al. (2011) proposed that different radio–X-ray correlations are possibly regulated by different accretion processes, which is supported by our results on the hard X-ray spectral evolution. For a classical jet, the jet power, P_jet, is a fraction of the accretion power and $P_{\rm jet}\propto \dot{M}$ (e.g., Falcke & Biermann 1995; Heinz & Sunyeav 2003). In the optically thick jet, the radio emission and jet power follow a scaling of $L_{\rm R}\propto P_{\rm jet}^{\sim 1.4}$ (e.g., Heinz & Sunyeav 2003; Coriat et al. 2011). The radiatively inefficient ADAF is expected to produce X-ray emission with $L_{\rm X}\propto \dot{M}^{q}$ and q ∼ 2.0 (e.g., Merloni et al. 2003; Yuan & Cui 2005; Wu & Cao 2006). Therefore, the ADAF model can not only explain the anti-correlation of Γ − F_3-9 keV (e.g., Qiao & Liu 2013), but it can also reproduce the observed universal correlation of $L_{\rm R}\propto L_{\rm X}^{\sim 0.7}$. For a magnetically heated corona above and below SSD, q ≃ 1 for a gas-pressure-dominated SSD, while q < 1 for a radiation-pressure-dominated SSD (e.g., Merloni & Fabian 2002). We expect $L_{\rm R}\propto L_{\rm X}^{\sim 1.4}$, which is supported by the detailed calculations based on the jet formation from the disk-corona system (Huang et al. 2014). Therefore, the disk-corona model can explain both the steeper radio–X-ray correlation and the positive Γ − F_3-9 keV relation simultaneously. From our results, the dual tracks of the radio–X-ray correlation are most likely regulated by different accretion processes. The "radio-quiet outliers" compared those sources in the universal track are caused by "X-ray-loud" due to the increasing of the radiative efficiency as a change of accretion mode. The transition track may be regulated by a transition state of accretion flow. The radiative efficiency will increase very fast at a critical accretion rate (e.g., from low radiative efficiency of ADAF to high radiative efficiency of disk-corona). If this is the case, we expect that the X-ray luminosity will increase much faster than the radio luminosity if the accretion rate approaches the critical rate for disk transition, which can roughly explain the flat transition track. However, the physical reason for the disk transition is still unclear, and the possible models include truncated SSD-ADAF (e.g., Lu et al. 2004), clumpy-ADAF (e.g., Wang et al. 2012), magnetically dominated accretion flow (e.g., Oda et al. 2012), and luminous hot accretion flow (e.g., Yuan 2001; Xie & Yuan 2012), etc. These transitional disks are more or less ADAF-like, so the anti-correlated Γ − F_3-9 keV will be also expected, and the detailed spectral calculation is beyond of this work.

We thank Xinwu Cao and the members of the HUST astrophysics group for many useful discussions and comments. This work is supported by the NSFC (grants 11303010, 11103003, and 11133005) and the New Century Excellent Talents in University (NCET-13-0238).