1 The Fundamental Plane Relationship of Astrophysical Black Holes Ran Wang Supervisor: Xuebing Wu Peking University Ran Wang Supervisor: Xuebing Wu Peking University

2 TopicsTopics Introduction – the black hole fundamental plane (FP) The sample –Selection –Properties Results – the FP relation and correlation tests Discussion Summary

3 IntroductionIntroduction Dominant energy producing mechanism in black hole systems – accretion. For observation, strong X-ray emission and sometimes accompanied by a relativistic jet. Such kind of systems exist at different scales from black hole X-ray binaries (XRBs) to active galactic nuclei (AGNs).

4 Analogy between Stellar-mass BH and Supermassive BH systems: Common physics: BH, accretion disk, jet,...

5 Introduction – the black hole FP The non-linear relationship between X-ray emission, core radio emission, and black hole mass, also called black hole fundamental plane (FP), was discovered and studied ( eg. Merloni et al. 2003; Heinz & Sunyaev et al. 2003; Falcke et al ). Merloni et al. (2003) studied a sample of XRBs and AGNs and fitted a FP relation among 5GHz radio luminosity (L R ), X-ray 2-10keV luminosity (L x ), and black hole mass (M BH ).

6 Introduction – the black hole FP Merloni et al. (2003)

7 IntroductionIntroduction The reliability of the FP in Merloni et al. (2003) was challenged. – Non-uniform sample – Distance – distance effect: (Bregman 2005; Merloni et al. 2006) – Have L X /L EDD in a large range – to 1 – Various methods in the black hole mass estimation. We test the black hole FP relationship with a uniform broad-line AGN sample in this work

8 The sample A RASS-SDSS-FIRST cross identified sample based on the X-ray-emitting SDSS AGN catalog in Anderson et al. (2003) –964 broad permitted line AGNs (FWHM > 1000km s -1 ) that have X-ray data from RASS. –132 sources are detected by the FIRST survey at 1.4GHz and a 3σ sensitivity of 0.45mJy ( White et al ). –We use Hβ λ4861Å and Mg II λ2798Å lines to determine the BH mass, thus excluded sources with low SNR optical spectra. – We also excluded 4 sources that have only C IV lines (z>2) in the SDSS spectra to reduce the scatter in BH mass estimation. –Finally, 115 sources are selected and divided into radio loud (76) and radio quiet (39) subsamples.

9 Black hole mass estimates Virial law (Kaspi et al. 2000) R-L Hβ relation (Wu et al. 2004) McLure -Jarvis (2002) relation

10 The sample The advantage of this sample –X-ray: keV from ROSAT All-Sky Survey (RASS). –Optical spectra from the SDSS survey. –Radio: 1.4GHz from the FIRST survey. –X-ray to Eddington luminosity ratios distribute from to 1. –Redshift: 0<z<2 –Minimize the scatters introduced by observations and calculations.

11 Results – Correlation tests We test the intrinsic correlation between M BH, and L X /L r. –The partial Kendall τtest indicates the BH mass is correlated to the X- ray and radio luminosities (P null < 0.05). –But this correlation disappears in the radio quiet sub-sample when scaling the luminosities with Eddington luminosity (P null ~0.6). Distance effect in L r -L X correlation. –The partial Kendall τtest suggests the L X -L r correlation still exists when excluding the effect introduced by distance. –We can also see the correlation in a flux plot.

12 ResultsResults

13 Discussion – the black hole FP Theoretically, the FP relationship reflect the common physics of a disc-jet system around the central black hole. The slopes of the FP should be different with different X-ray emission mechanism ( Yuan & Cui 2005 ): – Dominated by accretion flow – Dominated by jet Jet emission may dominate the X-ray when the accretion rate drop to certain critical value and give a slope > 1 (Heinz 2004). Yuan & Cui 2005

14 Heinz (2004, MNRAS) Scaling relations for scale-invariant cooled jets (both Lr & Lx are from jets): For canonical synchrotron spectrum of p=2,α r =0.5,α x =1 Consistent with our results for radio-loud AGNs! lg lg F - r- r -x-x

15 DiscussionDiscussion Beaming effect is most likely to be responsible for the steeper slope in radio loud sources. –Doppler beaming can increase the jet intrinsic power by a factor of δ 2+α. –The differences between observed radio luminosity and that derived from the radio quiet FP relation increase with radio loudness. –Thus the observed radio-loud FP is unreliable unless the beaming effect can be removed. –The difficulty is that the beaming factor is hard to measure directly.

16DiscussionDiscussion Radio-quiet FP: – We compared our radio-quiet FP relationship with different physical models. Accretion disc models listed in Merloni et al. (2003) The multicolor thermal emission from the inner part of a standard thin disk. Radiation cooling jet. – Our result can be marginally matched when: The X-ray luminosity has a nonlinear dependence on accretion rate with a power-law index ~2 – the radiatively inefficient accretion flow. – However, our sample have higher X-ray to Eddington luminosity ratios than that expected from the radiatively inefficient accretion flow models. – The soft X-ray emission in AGNs is complex and may be contributed by different mechanisms.

17 SummarySummary We studied the black hole FP relationship with a uniform sample of broad line AGN. Our found the FP relationship have a weak dependence on the black hole mass. The FP relationships are different for radio loud and radio quiet AGNs. The FP relationship for radio loud AGNs is likely to be affected by the Doppler beaming. The radio-quiet FP relationship is possibly consistent with the theoretical prediction from the accretion-flow-dominated X-ray model. More theoretical and observational studies are needed.

18 The end Thanks Thanks

19 ResultsResults On the log L r -log L X plot, We do not see the clear trend that tracks of different mass bins are parallel to each other. We can not see this trend on the logL r /L Edd -log L X /L Edd plot either.

20 However, when we plotted the sources in different radio loudness bins, we see the parallel tracks. The X-ray and radio luminosities are correlated in each radio loudness bin ResultsResults

21 DiscussionDiscussion The black hole FP relationships –We obtained different FP relationships from that in Merloni et al. (2003) –We use keV X-ray emission instead of 2- 10keV. –We use 1.4GHz rest frame radio luminosity instead of 5GHz. –These differences will only change the constant term if the emission can be described as power laws with a typical spectral index in each band for all sources. –Otherwise, the slope items may be affected.