The Fundamental Plane Relationship of Astrophysical Black Holes

1
The Fundamental Plane Relationship of
Astrophysical Black Holes

• Ran Wang
• Supervisor Xuebing Wu
• Peking University

2
Topics

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

3
Introduction

• 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).

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Analogy between Stellar-mass BH and Supermassive
BH systems

• Common physics BH, accretion disk, jet, ...

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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. 2004).
• Merloni et al. (2003) studied a sample of XRBs
  and AGNs and fitted a FP relation among 5GHz
  radio luminosity (LR), X-ray 2-10keV luminosity
  (Lx), and black hole mass (MBH).

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

• 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 LX/LEDD in a large range 10-6 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

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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 gt 1000km s-1)
  that have 0.1-2.4 X-ray data from RASS.
• 132 sources are detected by the FIRST survey at
  1.4GHz and a 3s sensitivity of 0.45mJy (White et
  al. 1997).
• We use Hß ?4861Å and Mg II ?2798Å 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 (zgt2) 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 .

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Black hole mass estimates

• Virial law (Kaspi et al. 2000)
• R-LHßrelation (Wu et al. 2004)
• McLure -Jarvis (2002) relation

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The sample

• The advantage of this sample
• X-ray 0.1-2.4keV 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 10-3.5 to 1.
• Redshift 0ltzlt2
• Minimize the scatters introduced by observations
  and calculations.

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Results Correlation tests

• We test the intrinsic correlation between MBH,
  and LX/Lr.
• The partial Kendall ttest indicates the BH mass
  is correlated to the X-ray and radio luminosities
  (Pnull lt 0.05).
• But this correlation disappears in the radio
  quiet sub-sample when scaling the luminosities
  with Eddington luminosity (Pnull0.6).
• Distance effect in Lr-LX correlation.
• The partial Kendall ttest suggests the LX-Lr
  correlation still exists when excluding the
  effect introduced by distance.
• We can also see the correlation in a flux plot.

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Results
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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 gt 1 (Heinz 2004).

Yuan Cui 2005
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Heinz (2004, MNRAS) Scaling relations for
scale-invariant cooled jets (both Lr Lx are
from jets)
lg F?
-? r
-?x
lg ?
For canonical synchrotron spectrum of
p2,ar0.5,ax1
Consistent with our results for radio-loud AGNs!
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Discussion

• 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 d2a.
• 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.

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Discussion

• 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.

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Summary

• 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.

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• The end
• Thanks

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Results

• On the log Lr-log LX 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 logLr /LEdd -log
  LX/LEdd plot either.

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Results

• 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

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Discussion

• The black hole FP relationships
• We obtained different FP relationships from that
  in Merloni et al. (2003)
• We use 0.1-2.4keV 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.