Figure 4.5: Total density profile power-law slopes versus lookback time for the spheroidals from the Mag-neticum Box4 uhr simulation, with total masses above Mtot>1×1011Mshown as black histograms at each time-bin. The evolution of the density slope for the CETGs is shown as red open diamonds connected by a red line. The observations are shown as colored symbols: Yellow stars show the observations for the Coma Cluster ETGs from Thomas et al. (2007) at z ≈ 0.02. All other observations are from strong lensing: SLACS lenses (blue open stars, Auger et al., 2010), SL2S lenses (magenta open diamonds: Ruffet al. 2011; and lilac filled diamonds: Sonnenfeld et al. 2013b), and LSD lenses (green filled stars, Treu&Koopmans, 2004).
4.4.1 Slope Evolution with Redshift
Sonnenfeld et al. (2013b) showed that the power-law slopes of the radial density profiles inferred from observations of strong lensing ETGs are flatter at higher redshifts than at low redshifts, and in a subsequent paper, Sonnenfeld et al. (2014) argued that this indicates that merger events at low redshifts must contain a significant amount of cold gas to steepen the slope. While the idea of the gas as the main reason for the existence of slopes which are steeper than isothermal is in agreement with our approach from theory and simulations, the interpretation is not. Fig. 4.5 clearly shows the problem: While both our simulated samples of spheroidals clearly show that at higher redshifts the total density slopesγtotwere steeper than at lower redshifts (CETGs shown as red line, METGs are
4.4. CONSPIRACY EVOLUTION WITH REDSHIFT 99
Figure 4.6: Left panel: Total velocity dispersion slopeβtotversus the total density slopeγtotfor METGs at different redshifts shown as blue circles, with colors as indicated in the legend marking the different redshifts.
The black dashed line marks the solution for an isotropic sphere (or a sphere with constant anisotropy), while the red line shows the fit to the values found for the cosmological simulations studied in Chap. 3 (Remus et al., 2013).Right panel: The total velocity dispersion slope versus lookback time, shown as histogram for each time bin.
shown as black histograms for the slopes within each redshift bin of the simulation), the observations, which are shown as colored symbols, show the opposite behaviour.
While the total density slopes found for the CETGs at high redshifts are all much steeper than the observed ones, the METG sample actually includes galaxies with total density slopes as flat as the observed ones even at high redshifts. This is mostly due to the fact that the METG sample is selected from a full cosmological box, and thus also includes massive evolved galaxies even as high asz = 2 which are the progenitors of the most massive galaxies atz = 0. Additionally, we see a clear offset between the distribution of the METGs and the CETGs, with the CETGs having generally steeper slopes than the average METGs. Nevertheless, even if the actual values for the mean total density slopes at each redshift bin for the CETGs are smaller than for the METGs, the general evolution trends are the same. In addition, the evolution trends found for the METGs are similar to those found in Johansson et al. (2012) for their set of re-simulations, which include more physics than our CETGs as well.
While there are spheroidals in the METG sample which show similarly flat slopes than the obser-vations at high redshifts, those are still the outliers. Therefore, there are three possible explanations for this discrepancy: First, it might be possible that, at high redshifts, the most massive galaxies have a higher probability to be a lens galaxy, and thus the observational sample is biased towards massive, more evolved systems. Second, there might be a major problem in our simulations and the underlying theoretical framework. Third, there could be an issue with the calculation of the total density slopes
from observations.
One way to actually test this issue is to test other correlations known to depend on the mass accretion history. The left panel of Fig. 4.6 shows the dark-halo–spheroid conspiracy for the METGs as it was shown for the CETGs in Chap. 3 (Remus et al., 2013), and in Remus et al. (2015b) for a subset of the METGs: the slopesβtotof the power-law fits to the total velocity dispersion versus the slopesγtotof the power-law fits to the total density distributions. We find the same results for both our simulations, and we also clearly see that, whileγtotflattens with decreasing redshift,βtotstays nearly the same, aroundβtot≈0. This is also shown in the right panel of Fig. 4.6, where the evolution ofβtot with redshift is shown for the METGs as histogram.
Thus, we also find the dark-halo–conspiracy for our METG sample of spheroidal galaxies, that is the total density slopes evolve towards the isothermal case ofγtot = 2, while the total velocity dispersion is flat out to large radii at all redshifts, independent of the total density slope. Only at very high redshifts ofz >2, the total velocity dispersion profiles steepen slightly. Nevertheless, the origin of this behaviour is still unclear, especially the origin of the constantly flat total velocity dispersion profiles, and remains to be solved in the future.
4.4.2 Correlating Galaxy Properties with the Total Density Slope
As suggested above, since the central dark matter fractions fDM(R1/2) correlate with the in-situ frac-tions fin-situ of the spheroidals (Fig. 4.4), and the in-situ fractions show a correlation with the total density slopeγtot(Fig. 3.10), it is self-evident that there should also exist a correlation between the central dark matter fractions and total density slopeγtot. The upper left panel of Fig. 4.7 showsγtot versus fDM(R1/2), for the METGs (blue circles) and the CETGs (red circles), including all galaxies which are analyzed in this work, independent of their redshift. The latter is done to enhance the num-ber statistics to see the overall trends, independent of redshift. We find a clear correlation between both quantities for both samples of spheroidals, that is spheroidals with a flatter slope have larger central dark matter fractions, however, the correlations have very different slopes. While the CETGs show a steep, nearly linear increase inγtotwith increasing fDM(R1/2), the METGs show a strong in-crease in γtot for small changes in fDM(R1/2) at low central dark matter fractions, and a flattening of the correlation above fDM(R1/2) ≈ 20%, where the slopes only change slightly, and are on aver-age already close to isothermal. A comparison to observations from strong lensing (SLACS sample, Barnab`e et al. 2011) reveals a very good agreement with the correlation found for the METGs, while their match with the CETGs is rather poor. On the contrary, the Coma Cluster ETGs, which show a much larger scatter than both the observations from Barnab`e et al. (2011) and our simulated sam-ples, again show deviations from both simulations for a subset of the observed galaxies, which had extremely high masses but low central dark matter fractions. For the other Coma Cluster galaxies, the result is not as clear as for the strong lensing sample, however, the overall agreement with the METG spheroidal sample is better than for the CETGs.
Another interesting quantity to compare to is the stellar mass density:
Σ∗= M∗
2πr2eff, (4.2)
following Sonnenfeld et al. (2013b), which is basically a measurement of the concentration of the stellar component. The smallerΣ∗, the less concentrated a galaxy. Sonnenfeld et al. (2013b) report for their observations, that ETGs with more concentrated stellar components have steeper total density
4.4. CONSPIRACY EVOLUTION WITH REDSHIFT 101
Figure 4.7:Correlations between central dark matter fractions fDM(R1/2), total density slopesγtotand stellar mass densityΣ∗. METGs without cold gas disks are shown as filled blue circles, METGs with cold gas disks as open blue circles, and CETGs as red filled circles. Here, all spheroidals at z=0, z=0.5, z=1and z=2 are included in all panels to better see the overall relation between the three parameters. For comparison, observations are included if available, namely Coma Cluster ETGs (yellow stars Thomas et al., 2007), SLACS lens ETGs (blue open stars: Auger et al. 2010; and green open stars: Barnab`e et al. 2011), SL2S lens ETGs (magenta open diamonds: Ruffet al. 2011; and lilac filled diamonds: Sonnenfeld et al. 2013b), and LSD lenses (green filled stars, Treu&Koopmans, 2004). Upper left panel: Total density slopesγtot versus central dark matter fractions fDM(R1/2). Upper right panel: Total density slopesγtotversus stellar mass densityΣ∗. Lower left panel: Stellar mass densityΣ∗versus central dark matter fractions fDM(R1/2).
profiles and thus the estimated power-law slopes are steeper, which was also found before by Auger et al. (2010). This is well in agreement with our conclusions from simulations, however, since obser-vations have shown spheroidals to be more compact than their present-day counterparts, this would implicate that the slopes at higher redshifts should also be steeper.
We calculated the stellar mass density for our simulated halos, using the stellar half-mass radius instead of the effective radius in Eq. 4.2. There is a clear correlation between the stellar mass density and the total density slope (see upper right panel of Fig. 4.7), which is the same for both our simulation samples and for the observations, albeit the scatter in the observed total density slopesγtotis larger than the scatter found in the simulations at a given stellar mass density. The METGs again match the observations successfully, while most of the CETGs are much more concentrated than the METGs and the observations. This is most likely again due to the missing AGN feedback in the CETG simulations.
For completeness, we plot in the lower left panel of Fig. 4.7 the stellar mass densityΣ∗versus the central dark matter fraction fDM(R1/2). As expected, there is a clear tendency for spheroidals with larger fDM(R1/2) to be less compact, and while this is supported by both simulations, METGs and CETGs, there is a clear offset between the actual values of both simulations. In this case, the simulations and observations do not match too well, albeit the match again is much worse for the CETGs than for the METGs.
Fig. 4.8 shows the relations between the total density slopesγtotand the stellar mass densitiesΣ∗
(left columns) and central dark matter fractions fDM(R1/2) (right columns), at four different redshifts z = 0, 0.5, 1 and 2 from top to bottom. There is a clear evolution trend found for the simulations, namely that the central dark matter fractions increase with redshift, while the stellar central concen-tration is decreasing. These evolution trends are seen in both simulation samples, and support our idea that, after aboutz=2, the evolution of spheroidals is dominated by merger events, which enhance the central dark matter fractions, lead to stronger growth in size than in mass, and evolve the total density slope towards an isothermal solution through dynamical friction and violent relaxation.