small dark matter halos has been suggested, for example, by Peebles & Dicke (1968); Peebles (1984);
Rosenblatt et al. (1988); Padoan et al. (1997a), assuming that they lose all their dark matter during the accretion into their present-day host galaxies. An internal formation scenario within their host galaxies has been proposed by Fall & Rees (1985), with the GCs being formed in fragments of the protogalactic clouds due to the compression of the cold gas induced by the hot gas components. A third mechanism was introduced by Ashman & Zepf (1992), where the formation of the GCs is induced by shocks during merging events of massive structures. GCs (mostly) contain multiple stellar populations (see, for example, the review by Gratton et al. (2012) and references therein). To account for these multiple stellar populations, Trenti et al. (2015) recently suggested another formation scenario, where GCs are formed in high-redshift mergers of atomic cooling halos.
Their formation usually occurred at very high redshifts (about 10 Gyr ago) with only a small fraction of GCs younger than 5 to 6 Gyr (Brodie & Strader, 2006). Additionally, the number of GCs detected in a galaxy is known to correlate with the mass of its central black hole (Burkert &
Tremaine, 2010), and this correlation is tighter than the well-known black-hole–σrelation. There is strong observational evidence from recent studies of the colors of GCs that there actually exist two distinct populations of GCs (red and blue, see for example Peng et al. (2006) and Richtler et al. (2015), and Blom et al. (2012b,a) for NGC 4365 which even exhibits hints of a third population of GCs). A bimodality is also found in the metallicity (e.g., Zinn, 1985, for the Milky-Way GCs), with indications that the red GCs (RGCs) might have higher metallicities than the blue GCs (BGCs) (see Usher et al., 2012).
The RGCs have been shown to trace the light of the central stellar component, similarly to the PNe (Peng et al. 2004b; Schuberth et al. 2010; Pota et al. 2013; however, Coccato et al. (2013) find indications that PNe and RGCs might actually trace different stellar populations), while the BGCs show a different behaviour (e.g., Forbes et al., 1997; Schuberth et al., 2010). This led to the assumption that RGCs might have formed in-situ in the main galaxy, while the BGCs have been accreted onto the halo in violent merging events with other galaxies (Cˆot´e et al. 1998; Schuberth et al. 2010). Thus, it has been proposed by Forbes et al. (2012) who compared the X-ray halos with the surface density of BGCs and found a good agreement, that the BGCs could be effectively tracing the dark matter component of galaxies (see also Forte et al. 2005; Brodie & Strader 2006). However, the question remains whether BGCs really can be used to trace the dark matter properties of galaxies or not.
Deason et al. (2012) used PNe and GCs from the literature detected in 15 nearby early-type galax-ies to probe their dark matter halos, without splitting the GCs into two populations. They fitted single power-lawsρ ∝ rγ to the radial density profiles of those galaxies in the radius range from 2Reff to Rmax (the largest radius at which a tracer has been detected). Whenever three dimensional densi-ties had been provided for the density, they used those densidensi-ties for their fits, while they increased the power-law index by 1 whenever only two-dimensional surface densities had been provided. For all galaxies, they used the density and velocity profiles constructed from the tracers to calculate the potentials and the dark matter fractions of the galaxies within five effective radii (5Reff).
We use those dark matter fractions and density slopes to compare the observations with our sim-ulations, with the aim of understanding whether the tracers really provide information about the dark matter densities of early-type galaxies. To broaden the analysis in order to understand if the BGCs might be tracing the dark matter component, we also included NGC 5846 in our analysis, whose dark matter fraction at 5Reff is given by Napolitano et al. (2014). We used the number-density profiles for BGCs and RGCs from that work to perform single-power-law fits to both profiles, as well as S´ersic fits. The result is shown in the right panel of Fig. 6.6, with the data for the BGCs shown as blue
6.3. WHAT DO THE DIFFERENT KINDS OF TRACERS TRACE? 143
Figure 6.6:Number density profiles of the RGC (red diamonds) and BGC populations (blue diamonds) of the elliptical galaxies NGC 4365 (left panel) and NGC 5846 (right panel). Power law fits to the profiles in a radius regime of2Reffto the maximum radius at which there are still GCs detected (gray shaded areas) are shown as dashed lines, S´ersic fits to the whole profiles are shown as dash-dotted lines. The solid black line marks the effective radius. Data points are taken from Pota et al. (2013) for NGC 4365 and from Napolitano et al. (2014) for NGC 5846.
diamonds and the data for the RGCs shown as red diamonds. The dashed lines are the power-law fits between 2ReffandRmax(shaded gray areas), while the dotted lines show the S´ersic fits (colors red and blue for RGCs and BGCs respectively).
In addition, we also included three galaxies in the analysis where the dark matter fractions within 5Reff are given by Deason et al. (2012) and took the number-density profiles for BGCs and RGCs from Pota et al. (2013). As for NGC 5846 we performed single-power-law fits to both the RGC and BGC number density profiles as well as S´ersic fits, with the results shown in Fig. 6.7 for NGC 821 (left panel), NGC 1407 (middle panel) and NGC 3377 (right panel). However, NGC 821 only has 61 tracers which is a very low number to perform the fits, and we clearly see that the behaviour of RGCs to BGCs differs from the other two cases, i.e., the RGCs become dominant in the outskirts. NGC 3377 has 126 GCs as tracers, which would generally be enough for a good analysis, however, since the tracers are split into two populations the profiles found for this galaxy could also be suffering from low-number statistics. NGC 1407 has a total number of 369 GCs, and the fits are clearly the best. Nevertheless, we also see that a power-law is not a very good fit to both the RGC and the BGC profiles for this galaxy, as both profiles are strongly curved and much better represented by a S´ersic fit.
The left panel of Fig. 6.6 shows the same fits but for NGC 4365, with the data taken from Pota et al. (2013) as well. Here, both the power-law fits and the S´ersic fits are a very good approximation to the radial profile between 2Reff andRmax. Unfortunately, we could not find dark matter fractions within 5Reff for this galaxy in the literature, and thus we cannot include NGC 4365 in the following
Figure 6.7: Same as Fig. 6.6 but for NGC 821 (left panel), NGC 1407 (middle panel) and NGC 3377 (right panel). Data points are taken from Pota et al. (2013).
analysis, although it would be a very interesting candidate since this galaxy exhibits strong indications of having even a third GC component, as mentioned above.
In order to obtain approximations to the slopes of the three-dimensional number densities from our fits to the two-dimensional number densities, we followed Deason et al. (2012) and incremented the power-law exponents by 1. Fig. 6.8 shows the resulting density slopes for the 15 galaxies from Deason et al. (2012) (green circles for PNe, cyan circles for GCs), the galaxy from Napolitano et al.
(2014) (NGC 5846, red (RGC) and blue (BGC) filled diamonds) and the three galaxies with density slopes estimated from data taken from Pota et al. (2013) (red and blue bow-tie, stars and hourglass for NGC 821, NGC 1407 and NGC 3377, respectively) versus the dark matter fraction fDMwithin 5Reff in all three panels.
To address our question which parts of the galaxies are represented by the different tracer popu-lations, we included the density slopes calculated between 2R1/2and 5R1/2for the spheroidals from the Magneticum simulation Box4 uhr (see Sec. 2.4) with total masses larger thanMtot =5×1011M
as small grey circles (dark grey for spheroidals without any cold gas, light grey for spheroidals with small cold gas disks) in all panels of Fig. 6.8. In the left panel, we show the density slopesγtot ob-tained from single power-law fits to the total combined stellar and dark matter density profiles (see Chap. 3 for more details on the total density profiles), in the middle panel we show the density slopes γ∗from single power-law fits to the stellar component of the spheroidals (in this region we basically fit the stellar halo component, see Chap. 5 for more details), and in the right panel we show the density slopesγDMfor the dark matter alone. As can be seen from this figure, the range of observed dark mat-ter fractions within 5Reff agrees well with the dark matter fractions of the Magneticum spheroidals within 5R1/2, however, the power-law slopes of the density from the observations do not agree at all with the total power-law slopesγtotor the dark matter power-law slopesγDM. Both the total (around γtot ≈ −2) and the dark matter slopes (aroundγDM ≈ −1.7) are much too large in comparison to the observed values, independent of the tracers used for estimating the observed profiles.
However, the observed density slopes are all in excellent agreement with the density slopes found for the stellar (halo) component for the Magneticum spheroidals, as can be clearly seen in the middle panel of Fig. 6.8. Thus, we conclude that all tracers do actually trace the densities of the stellar components of the galaxies. Nevertheless, the observations clearly show a difference between the density slopes estimated for the different types of tracer, which can best be seen in the case of NGC
6.3. WHAT DO THE DIFFERENT KINDS OF TRACERS TRACE? 145
Figure 6.8: Density slopes from power-law fits to the density profiles between 2R1/2 and 5R1/2 for the spheroidals from the Magneticum simulation Box4 uhr, shown as small grey circles (dark grey for spheroidals without any cold gas, light grey for spheroidals with small cold gas disks). Left panel: density slopesγtot ob-tained from single power-law fits to the total combined stellar and dark matter density profiles.Middle panel:
density slopesγ∗from single power-law fits to the stellar component.Right panel: density slopesγDMfor the dark matter. In all three panels, the density slopes from power-law fits to the tracer densities from observations in the radius range2Reff and Rmaxversus the dark matter fractions fDMwithin5Reffare shown as well, for the 15 galaxies from Deason et al. (2012) (green circles for PNe, cyan circles for GCs), the galaxy from Napolitano et al. (2014) (NGC 5846, red (RGC) and blue (BGC) filled diamonds) and the three galaxies with density slopes estimated from data taken from Pota et al. (2013) (red and blue bow-tie, stars and hourglass for NGC 821, NGC 1407 and NGC 3377, respectively). We used the dark matter fractions from a Chabrier IMF for the values from Deason et al. (2012). Filled circles mark the values from Deason et al. (2012) for the galaxies included also in the sample of Pota et al. (2013), while open circles with crosses or pluses mark galaxies where there have been GCs and PNe used separately to estimate densities and dark matter fractions within the work by Deason et al.
(2012). For NGC 5846, Deason et al. (2012) provided a measurement from PNe independent of the RGC and BGC measurements from Napolitano et al. (2014), and the value from Deason et al. (2012) is shown as filled green diamond.
5846 where we have three density slopes for all three different tracers: γPNe = −3.1 from Deason et al. (2012), andγRGCs = −3.28 andγBGCs = −2.52 from our fits to the data from Napolitano et al.
(2014) for RGCs and BGCs, respectively. The slopes for the PNe and the RGCs are very similar, supporting the idea that RGCs and PNe might actually both trace the main stellar component of their host galaxies. The slope obtained for the BGCs, however, is much flatter. This is true for NGC 3377 and NGC 1407 as well, even if the fits for NGC 1407 give much steeper slopes than for the other galaxies since the density profiles are curved so much (middle panel of Fig. 6.7). Only NGC 821 shows an opposite behaviour, but this might be due to the low numbers of the GCs found in this galaxy. We conclude that a more detailed analysis of the simulations, including metallicities and decompositions of the different galaxy components is needed to give a final answer to the question what the different kinds of tracers actually trace, but we also find clear evidence that none of the tracers actually trace the density profiles of either the dark matter or the total density profile.
On a last note to this section, we tested the dependence of the density slopes found for the obser-vations on the largest radius at which a tracer is observed, and whether there is a correlation between
Figure 6.9: Left panel: Observed density slopesγobs versus the maximum radius of the fit in units of the effective radius, Rmax/Reff, for the same galaxies as in Fig. 6.8 (PNe from Deason et al. (2012), NGC 5846 from Napolitano et al. (2014), and Rmax/Reff andγobsfrom our analysis of the data presented in Pota et al. (2013) for NGC 821, NGC 3377 and NGC 1407). Colors and symbols also as in Fig. 6.8. Middle panel: Stellar mass of the same observed galaxies versus Rmax/Reff. Right panel: Histograms for the slopes of the fits to the total density profiles (upper panel) and the slopes of the fits to the stellar density profiles (lower panel) of the Magneticum spheroidals, fitted at different radius ranges of2R1/2to5R1/2 (red lines),2R1/2to9R1/2 (green line),2R1/2to20R1/2(blue line) and0.3R1/2to4R1/2(yellow dashed line).
this largest radiusRmax and the stellar mass of the galaxy. The results are shown in the left and the middle panel of Fig. 6.9, respectively, with the colors and symbols of the observations as in Fig. 6.8.
For the PNe we see a slight dependence of the observed density slopeγobs on the maximum radius of the fit in units of the effective radius,Rmax/Reff, with the slopes being slightly smaller for larger Rmax/Reff (see left panel of Fig. 6.9). However, this could also be an effect of galaxies with smaller stellar masses having slightly steeper slopes, as already discussed in Deason et al. (2012), since we also findRmax/Reff to be generally larger for galaxies of less stellar mass. We do not see a similar behaviour for the GCs, neither red nor blue, in fact neither the slope nor the stellar mass seem to correlate withRmax/Reff. This could be an effect of the different nature of GCs and PNe; however, if the red GCs really follow the same stellar component as the PNe there should be a similar behaviour and only the blue GCs should behave differently. This is supported by Kartha et al. (2014) who find a correlation between the spatial extent of GCs and the stellar mass of the host galaxy for a sample of 40 galaxies, including spirals, ellipticals and lenticulars. For the lenticulars and the ellipticals they also find that the spatial extent of the GC systems is proportional to the effective radius, which agrees with the mass-size relation seen for ETGs at present day (e.g., Shen et al., 2003, and Chap. 4). With the currently available data sets a conclusive interpretation of this problem is not possible and thus further studies are needed.
Nevertheless, from our simulations we find that the stellar slopes calculated for our spheroidals from the Magneticum simulation actually do depend slightly on the radius range in which the fit is performed, as demonstrated in the lower right panel of Fig. 6.9. The blue histogram shows the stellar slopes for our spheroidals fitted from 2R1/2to 20R1/2, while the red histogram shows the distribution