The SubEddington Boundary part 3:

Looking at Steinhardt and Elvis and comparing Fig 3 from S&E-I and Fig 2 from S&E-II

I noticed that something is wrong! They represented the same redshift bin but their data is very different! The more I read their papers the less I can trust their work! I stop even trying to answer their points. It is just wasting time.

Fig 3 from S&E-I 0.2 < z < 0.4 x-axis data are spanned from 7 to 9.2 y-axis data are spanned from 44.8 to 46 saturation limit is 47.2 detection limit is 44.9	Fig 2 from S&E-II 0.2 < z < 0.4 x-axis data are spand from 8.2 to 9.8 y-axis data are spand from 46.3 to 47.5 saturation limit is 48 detection limit is 46.3

The SubEddington Boundary part 2:

S&E uses 0.4 < z < 0.6 to show that the SEB exist. here is two plots comparing Shen 2008 (DR5) and Shen 2010 (DR7) for the same redshift range and same range but using new calibration from equation 11 of Wang et al. (2009).

Conclusion: going from DR5 to DR7 using Shen et al. results partially closes the gap between data and Eddington-ratio=1.

comparing Fig 1 to Fig 2 shows that SEB goes away partially.

comparing Fig 1 to Fig 3 (and Fig 2 to Fig 4) shows that the new calibration along with a bigger sample may resolve the SEB problem.

 

                      Fig 1: Shen 2008 old calibration

                Fig 2: Shen 2010 old calibratoion

If we use the new calibration from Wang et al. (2009) since this is in the Hbeta range, then we have:

                     Fig 3: Shen 2008, New Calibration following Wang et al. (2009)

                       Fig 4: Shen 2010, New calibration following

                             same equation (11 )in Wang et al. (2009)

I can use this 4 plots instead of Fig 1a and b in SEB paper. Advantages: we can see clearly the evolution of the SEB as we go from DR5 to DR7 and from old calibration (Shen et al. 2008) to new calibration (Wang et al. 2009) and cross-evolution too.

(a) to (b) shows how DR7 closes the gap partially

(a) to (c) or similarly (b) to (d) show how new calibration make the non-zero slop a unity slope and close it then partially.

 

same plot as above but without contours.

 

  I can use either of the above plots instead of Fig 1 of our SEB paper.

The SubEddington Boundary part 1:

It seems that the present of the SEB is mostly due using FWHM instead of sigma when using single epoch spectra.

1) According to Peterson et al. (2004), Fig 3, when we use rms spectra then FWHM and sigma_{line} are equally valid and good enough to satisfy a virial relationship in the form where FWHM is linearly represents the virial velocity. Yet using single epoch spectrum is more like mean spectrum. Fig 4 of Peterson et al. (2004) shows that FWHM relationship, if it is considered as a virial relationship, might be represented in a nonlinear form of relationship between FWHM and virial velocity.

                                           Fig 3 of Peterson et al. (2004)

 

                                       Fig 4 of Peterson et al. (2004)

2) lets say we have the virial relation exist for both, mean and rms of the FWHM (by the way that's what Shen et al. (2008) work is based on) so we have:

$MBH_{mean}  \propto  \tau_{mean} \times FWHM_{mean}^{2}$\\
$MBH_{rms}    \propto   \tau_{rms}   \times FWHM_{rms}^{2}$\\

However, from Fig 3 and Fig 4 (comparing the lower plots for FWHM using rms and mean)  of Peterson et al. (2004) we approximately have (this is my key point):

$\tau_{rms} < \tau_{mean}    for any given FWHM when FWHM > 3000 km/s$\\
$\tau_{rms} > \tau_{mean}    for any given FWHM when FWHM < 3000 km/s$\\

(Indeed and by a little exaggeration, I can say that $\tau_{mean}$ is just a constant with some scatter! just cut out the two or three data points in far left of the plot 4-lower panel.)

2-2) Now, for a given FWHM (in which $FWHM_{mean}=FWHM_{rms}$) we have:

$\frac{MBH_{mean}}{\tau_{mean}} = \frac{MBH_{rms}}{\tau_{rms}}$\\

which can be re-written as:

$\frac{MBH_{mean}}{MBH_{rms}} = \frac{\tau_{mean}}{\tau_{rms}}$\\

Now, from (2-1) we had relations between $\tau_{mean}$ and $\tau_{rms}$ for two cases of FWHM above or bellow the 3000 km/s. lets apply them on (2-2) equation and we have:

$MBH_{mean} > MBH_{rms}$      for a given FWHM $>$ 3000 km/s\\
$MBH_{mean} < MBH_{rms}$      for a given FWHM $<$ 3000 km/s\\

which means, any calibration to virial relationship for FWHM will overestimates the BH masses for the highest mass (approximately when FWHM $>$ 3000 km/s) with respect to the true BH mass (based on rms spectra) and it underestimates the mass when FWHM is smaller than 3000 km/s.

-----------

Here is the plot comparing Shen 2008 and R&H 2011 masses versus FWHM.

The pivot point here is about logFWHM=3.65 which is almost 4400 km/s (and not 3000 km/s).

DR7 mass estimates and anomalies: Part 5

Here is the new run on a single object asked by Pat.

name=124437.49+050029.8    

MJD=52426, Plate=847, Fiber=395    

z=1.2457

I am speechless. this is a perfect fit :))))

DR7 mass estimates and anomalies: Part 4

Here is a plot of the LogMBH vs redshift to she the anomalies:

the plots of reduced-chi2 bin of the same plot show a better distribution:

so panel (a) to (f) and also panel (i) shows some anomalies present.

There are not anomalies after these bins.

DR7 mass estimates and anomalies: Part 3

Objects in panel (d) in previous post (part 2)

top-panel: red is the DR7 original spectra, black is the PCA reconstructed spectra, green dotted lines show the normalization windows. all in rest frame.

bottom panel: balck is the PCA reconstruct used. red is the power-law, blue is th epesudo-continuum. red dotted lines show the normalization windows. all in rest frame.

Here I have multiplied the amplitude of the Pseudo-continuum by 1.02 to get the curve in magenta color. It seems that %2 increase in amplitude can resolve the problem but why?

 

DR7 mass estimates and anomalies: Part 2

Here is a multi-plot of the Shen 2010 mass versus R&H 2011 mass for redshift bins

This data set has 71527 objects. apparently some objects in panel (d) and (i) in redshift range between 1.2 < z < 1.37  and z > 2.03 which have problem in R&H 2011 mass estimates.

 

Their mass-luminosity plot show no SEB however, BH masses in panel (i) with z > 2.03 are not reliable either. (I don't know yet why panel (i) masses are so scattered!)

DR7 mass estimates and anomalies:

DR7 mass is estimated the same way as DR3. However, there are some anomalies in DR7. The Shen et al. 2010 versus R&H 2011 mass-mass plot shows an island on the side of the plot. This island shows very massive BHs estimates in R&H 2011. Such massive estimates could either due very broad MgII or very luminous objects or it could be only an error due mis-measurement in sigma_line.

I have tested some of the most massive objects in this island. As we have expected, the pseudo-continuum is not estimated correctly in these objects and so as a direct results the sigma is much larger than true value. Here are some examples:

So these objects must be re-analyzed before reporting their masses or they can be cut from the list for now.

I have also compared the FWHM from Shen et al 2010 and sigma_line from R&H DR7. The anomaly is due measurements of sigma_line and not the luminosity. As you have guessed, the pseudo-continuum is a moderately low.

Diagnostic plots, re-plotted with vertical lines:

here is the zoomed plots after subtracting the FeII template and continuum. the dotted-red vertical lines are the approximate boundaries we use to calculate the sigma. of course I didn't recorded the information about these boundaries. I kept it for CIV technique but not the MgII. This approximately based on what I assumed in measurements.

============ Notation:

panel top-left: cyan is the raw-spectrum, black is the reconstructed spectrum. both pseudo-continuum subtracted

panel top-right: black is the spectrum after PCA, red is the FeII+continuum, green is the continuum.

panel top (the big one): spectrum after PCA

panel low-right: same as top-right panel but before PCA

panel low (the big one): spectrum before PCA

=========================

vari=0.79, MBH_ab=1.01E9

vari=0.72, MBH_ab=1.47E9

for this case, if the line doesn't cross the zero we eventually stop when the profile is approximately horizontal in average.

vari=0.72, MBH_ab=1.7E9

===========

this is the case when after and before PCA gives very close masses.

vari=0.06, MBH_ab=9.21E8

Comparing spectra and fitting before and after PCA applied:

notation in all plots:

single plot: black is the raw spectrum, red is the PCA reconstructed spectrum, M_ab is the mass of the BH after PCA, vari is the relative mass ratio = (M[ab]  -  M[bb]) / M[ab]. these single panels show how PCA reconstructed spectra fit the raw spectra.

double plot: the upper panel is after PCA, lower panel is before PCA applied. red is the pesudo-continuum, green is the continuum and black is the spectrum. these plots show how well the mass estimates is in both case before or after PCA applied however in calculating the parameter "vari" I assume that PCA mass is accurate.

1)  vari = 0.79 means raw mass is about 21% of the PCA-mass

below is the same as above but zoom in around 2800 Angstrom.

2) vari = 0.72 means the raw mass is about 28% of the PCA-mass.

same as above but zoomed in

 

3) vari = 0.78 means the raw mass is 22% of the PCA-mass

same as above but zoomed in

  

=============================

4) a good example for object which PCA doesn't improve the mass estimates. vari = 0.06 means the raw mass is about 94% of the PCA-mass

same as above but zoomed in

Spiky spectra vs PCA reconstructed:

here is some examples of the spiky spectra with very low BH mass estimates in which we reconstruct the spectra and then we have a normal range BH mass. here the relative difference between after and before PCA applied BH mass is more than 70%.

eta=(M_BH(ab)-M_BH(bb))/M_BH(ab) > 0.7  assuming that M_BH(ab) is correct.

there are cases where eta is larger than 0.85 or 0.9 but the row data has significant problem (missing data around 2800 Angs or absolute noise)

black curve is the row data

red curve is the reconstructed spectra

the variable "vari" in the left panel is the relative differences between masses.

 

 

and these are samples for the case when there is very low differences between before of after PCA applied: the relative differences between BH mass are smaller than 10%

Catalogue paper step 2:

I wanted to understand a little more about differences between Shen et al. 2008 and Shen et al. 2010 results. Here is a plot showing mass-mass contour plots for redshift bins of 0.5 for all 3 emission lines.

well, there is something more to consider before interpreting these plots and that is the distribution of objects on redshift.

this means, there are more objects between 0.5 < z < 2. but that should not change the mass difference distributions.  So the mass-mass plots may be interpreted in two ways:

1)  assume that the new FWHM (2010) is more accurate, so that means, CIV is less sensitive to number of Gaussian fit.  (since new and old measurements are very close). so multiple Gaussian fit is only working for some of the lines.

2)  not assuming that, then high luminosity in high redshift bins is dominant in mass estimation. thus the calibration-factors for luminosity is determining the mass not the FWHM measurement. that means they need to check the calibration-factor. as you mentioned this somewhere, using 0.6 or 0.5 then matters here and indeed is very significant.

these can be added to Catalogue paper section 8.1.

using only MgII range for redshifts then we have:

it looks like semi-random distribution around a mean value for BH mass. this mean value increases from 8.5 in first redshift bin to 9.5 in the last redshift bin. its like the mean of their mass measurement has not changed by changing technique but the error has changed.!!!!

TODO: I need to plot the FWHM(2010) vs FWHM(2008) to see differences too.

Catalogue paper Step 1:

126 duplicated objects are out now.

the catalogue list has 27602 lines now with a flag for completness at the end (created by Pat).

The caption for Fig 4 is rewritten. it is more clear now.

I have compared the Shen et al. 2010 with Shen et al. 2008. The question is, should I add this into the Catalogue paper or not?

for example here is the FWHMs:

the FWHMs plot is very scattered. good news, some of the objects previously (in 2008) have not the mass estimates, they have has estimates for them in 2010. However, some high redshift objects, in CIV plot, had estimates in 2008 but have zero FWHM estimates in 2010, which is surprising.

but in general, the 2010 FWHMs are lower than 2008 estimates. that explains why in the mass-mass plot there is a trend towards the lower estimates for BH masses. The Lbol vs Lbol shows some scatter but it is moderately symmetrical, possibly due random noise.

so the question is, does it worth anything to show this mass-mass plot.