CARACTERIZACIÓN DE LAS FRUTILLAS EN SU ESTADO DE COMERCIALIZACIÓN

Not in all seven galaxies do we observe a change inMBH when we include DM.MBH in two

galaxies, NGC 1374 and NGC 1550 seems unaffected by DM inclusion while in NGC 1407 it is virtually unchanged (the nominal change is well within the 1σ errors). Out of seven, there are only two galaxies whose black hole masses change significantly outside their 1σ

errors, i.e. NGC 3091 and NGC 7619. No galaxy shows a decrease in MBH due to DM.

On average, there is an increase of MBH by a factor of 2.1, which is similar to the

increase found in MBH in M87 (Gebhardt & Thomas, 2009). On the other hand, these

results are not in agreement with the finding of Schulze & Gebhardt (2011), who perform a similar analysis on their sample galaxies. They find an average increase of only 20 percent due to DM inclusion. The effect of DM analysed from their sample is, however, effectively negligible because the change in MBH are well within the measurement errors.

Gebhardt et al. (2011) suggest two strategies for deriving an accurate MBH. It is either

by getting Υ right in the first place or by having high resolution data that covers the central region of the galaxy. Both strategies have been tested on M87 (Gebhardt & Thomas (2009) for the first one and Gebhardt et al. (2011) for the second). Below we address how these two strategies apply to our sample galaxies.

All galaxies see a nominal change in Υ, i.e. it systematically decreases from models with- out DM to models with DM. We show how the change in Υ is related to the change inMBH

in the left panel of Fig. 4.6. We include M87 (Gebhardt & Thomas, 2009; Gebhardt et al., 2011), NGC 6086 (McConnell et al., 2011a) and NGC 4649 (Shen & Gebhardt, 2010) in the plot to complete the sample of black holes in massive galaxies that have been studied for the DM effect. At a first glance, there is only a weak statistical correlation (if at all) between the two quantities, which could mean that the change in MBH is not predomi-

nantly influenced by the change in Υ. This is however not the end of the story. For the two galaxies where MBH changes outside the formal error bars, we find that we can recover

the ’correct’ MBH (MBH,DM) from the models without DM when we consider only the Υ

obtained from the run with DM (ΥDM). In the case of NGC 3091, models without DM

where Υ is 4.1 give the minimum χ2 _{at M}

BH = 3.3×109M⊙. For models of NGC 7619

with Υ = 2.9, MBH,DM is exactly recovered without having DM in the model.

Although the change of Υ is not directly related to the change in MBH, this finding

confirms that having a correct Υ is one important aspect of measuring an accurate MBH.

Based on our results in Section 4.5.1, it is clear that including the DM is necessary to derive unbiased Υ. When DM is not included, Υ obtained with less extended kinematic data is more reliable although this does not completely remove the bias. It is however not clear, in advance of the modelling, where to spatially truncate the kinematic data. Re is

not necessarily a good criterion. In the case of NGC 1407 and NGC 4472, the data go out to only a fraction of Re (around 0.5 and 0.25 Re respectively) but still contribute to an

appreciable change of Υ, while in NGC 1550 the Υ is not biased although the data extend out to Re (Table 4.5).

To address the second strategy, we show the plot of spatial resolution vs the change of MBH in the right panel of Fig. 4.6. Dres is the diameter of the resolution element,

4 .7 T h e C h a n g e o f M BH Du e to DM 7 1

Figure 4.6: Left panel: the ratio ofMBH against the change of Υ. Note the different numerator and denominator in both ratios. Right panel: the ratio of MBH vs the achieved spatial resolution. Dinf is the diameter of the sphere of influence of the black hole, calculated based on MBH obtained from the modelling without DM, with central σ from HyperLeda. Dres is the diameter of the resolution element (see text). We include three galaxies outside our sample for comparison purposes (NGC 4649, NGC 6086 and M87). There are two datapoints for M87 in the right panel, corresponding to the two measurements by Gebhardt and Thomas (marked as ’M87’) and Gebhardt et al. (marked as ’M87(NIFS)’).

72 4. The Effect of Dark Matter Halo on the Black Hole Mass

being the aperture size, seeing, the PSF FWHM or the model bin size. For our galaxies,

Dres represents PSF FWHM (last column in Table 4.2), except for NGC 1407 where we

use the average size of the model bins inside the SINFONI FOV, i.e. 0.24 arcsec (larger than the PSF FWHM of 0.19 arcsec). The diameter of the sphere of influence (Dinf) is

calculated using MBH without dark matter. We do not use MBH derived with the dark

matter because when DM is included, Υ is constrained to the right value and in that case it is no longer clear if the spatial resolution is still the dominant factor in recovering the correctMBH, or if it plays a role at all. The velocity dispersion values from HyperLeda (σ0

in Table 4.1) were used to derive Dinf. We have checked that for the seven galaxies in our

sample, the velocity dispersions from spatially-averaged SINFONI spectra are similar to these and using SINFONIσ does not change the appearance of the plot. We again include NGC 4649, NGC 6086 and M87 as in the left panel.

The plot shows a very clear trend. It confirms the importance of good data resolution for

MBH measurements, in the context of DM influence. When Dinf is not or only marginally

resolved (less than a factor of 5), there is a larger risk of getting the wrong MBH. The

change of MBH becomes negligible when the resolution element is smaller than Dinf by a

factor of at least _∼10. Between 5 and 10, MBH is wrong by ∼30 percent, but still on the

safe side given that this number is similar to a typical MBH measurement error. Based on

this plot, one can, to some degree, assess individual galaxies to see whether it is necessary to have DM present in models without first having to go through the time-consuming modelling with DM.

By comparing both plots in Fig. 4.6, it appears that the aspect of resolution gives a more straightforward implication. As long as the sphere of influence is well sampled by the data, a biased Υ is no longer a problem in recovering the correctMBHbecause Υ andMBH are no

longer degenerate to each other and thus, including DM is not a necessity. The example for this would be NGC 1407 and NGC 4472. When the data resolution is not sufficiently high, it is important to have an unbiased Υ to derive an accurate MBH, as in the case of

NGC 3091 and NGC 7619. However, it is not easy to derive an unbiased Υ when DM is not included and it is difficult to infer a bias inMBH from a bias in Υ. One can perhaps rely on

ΥSSP as a measure of the true Υ, independent of DM. For NGC 1407 and NGC 7619, the

Kroupa-based ΥSSPagrees with dynamical Υ when DM is included (Section 4.6). However,

up to now the IMF in massive early-type galaxies is still a controversial issue and ΥSSP is

uncertain to about a factor of two (Conroy & van Dokkum 2011; Cappellari et al. 2006; Thomas et al. 2011; Napolitano et al. 2010). Checks on a much larger sample of galaxies would be necessary to justify the use of ΥSSP as a surrogate.